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Detecting and imaging time-lapse conductivity changes using electromagnetic methods Devriese, Sarah G. R. 2016

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Detecting and imaging time-lapse conductivity changesusing electromagnetic methodsbySarah G. R. DevrieseB. Sc., Colorado School of Mines, 2010A THESIS SUBMITTED IN PARTIAL FULFILLMENTOF THE REQUIREMENTS FOR THE DEGREE OFDoctor of PhilosophyinTHE FACULTY OF GRADUATE AND POSTDOCTORALSTUDIES(Geophysics)The University of British Columbia(Vancouver)December 2016c© Sarah G. R. Devriese, 2016AbstractSteam-assisted gravity drainage (SAGD) is an in situ recovery process used to ex-tract bitumen from the Athabasca oil sands in Northern Alberta, Canada. Thesteam heats the oil, allowing it to be pumped to the surface. The success of thistechnique depends on being able to propagate steam throughout the reservoir but ir-regular growth may occur due to the heterogeneity of the reservoir. This affects theamount of oil that is produced and illustrates the need to monitor steam chambergrowth.The steam affects the electrical conductivity of the reservoir, thus creating aphysical property contrast. This thesis investigates how electromagnetic methodscan be used to monitor the time-lapse conductivity changes due to SAGD pro-cesses.A simple but illustrative survey design procedure was developed to examine avariety of field surveys that include surface and borehole transmitters operating inthe frequency or time domain. Compared to standard DC resistivity surveys, theability to resolve the steam chamber is significantly enhanced using EM. Notably,the feasibility study showed that the steam can be recovered using a low-cost large-loop surface transmitter and borehole measurements, despite the shielding effectsof the overlying conductive cap rock. When applied to an example based on a fieldsite, this survey recovered the synthetic steam chambers and discerned an area oflimited growth that resulted from a blockage in the reservoir.At a different field site, the reservoir is too deep to use surface methods butsteam growth was monitored using crosswell DC resistivity. The sensitivity matrixshows that these electric crosswell surveys do not contain enough information toimage the entire reservoir between the wells. By extending to multi-frequency elec-iitromagnetic methods using the same survey design, the sensitivity to the reservoirincreased and allowed for recovery of the steam chambers.Electromagnetic methods also provide valuable information about the back-ground conductivity of the layers above the reservoir, including structures suchas paleo-channels and the conductive cap rock. By using airborne, surface-based,and downhole surveys, I show that the Athabasca oil sands can be explored andmonitored using electromagnetic methods.iiiPrefaceIn this thesis, I present the original research I completed at the Geophysical Inver-sion Facility (GIF) in the Department of Earth, Ocean and Atmospheric Sciences atthe University of British Columbia (UBC), Vancouver, Canada. This research hasbeen published in peer-reviewed and non-peer-reviewed journals and as expandedconference proceedings.The first portion of Chapter 2 presents a longer version of the survey designapproach published in an extended abstract for presentation at the Society of Ex-ploration Geophysicists (SEG) Annual Meeting (Devriese and Oldenburg, 2014).The survey design approach first came up in discussions with Dr. Douglas Olden-burg. I performed the theoretical derivations, did the numerical experiments, andwrote the extended abstract. Dr. Oldenburg guided the research and provided com-ments on the abstract. Later portions of Chapter 2 were published in an abstractand presented at the Geoconvention (Devriese et al., 2014), a paper in Recorderby the Canadian Society of Exploration Geophysicists (Devriese and Oldenburg,2015a), and in the peer-reviewed journal Geophysics (Devriese and Oldenburg,2016b). The work was done by me, with guidance from Dr. Oldenburg. I wrotethe published material and Dr. Oldenburg edited and commented on the pieces.Portions of Chapter 3 were published in an SEG extended abstract (Devrieseand Oldenburg, 2015b) and in the peer-reviewed paper inGeophysics (Devriese andOldenburg, 2016b). This research and writing was done by me, with commentingand editing from Dr. Oldenburg.The first part of Chapter 4 was published as an SEG extended abstract (Devrieseand Oldenburg, 2016a) and will be submitted for journal publication. I proposedand completed the research and writing while Dr. Oldenburg provided commentsivon the writing.The research in Chapter 5 was published as an SEG extended abstract (Devrieseand Oldenburg, 2016c). A report on this research will be submitted to ImperialOil at the end of 2016 and submitted for journal publication. The research wasmotivated by a field data set from Imperial Oil and initial questions from theirgeoscientists. The research and writing was completed by me, with comments andsuggestions from Dr. Oldenburg.The manuscript for this thesis was prepared by me with advice from Dr. Old-enburg on its organization. Dr. Oldenburg aided me by providing feedback andproof-reading the manuscript.vTable of ContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ivTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiiAcknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxvDedication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxvii1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 Steam-assisted gravity drainage . . . . . . . . . . . . . . . . . . 31.2 Understanding conductivity changes in SAGD processes . . . . . 51.3 Research questions . . . . . . . . . . . . . . . . . . . . . . . . . 71.4 Electromagnetic methods . . . . . . . . . . . . . . . . . . . . . . 81.4.1 Controlled source EM surveys . . . . . . . . . . . . . . . 101.4.2 Numerical modelling of EM data . . . . . . . . . . . . . 121.5 Empirical resistivity formulations . . . . . . . . . . . . . . . . . 151.6 Thesis outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162 Feasibility of electromagnetic methods to detect and image SAGDsteam chambers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18vi2.1 Survey configurations . . . . . . . . . . . . . . . . . . . . . . . . 192.2 Dipole moment-based survey design . . . . . . . . . . . . . . . . 212.2.1 Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . 222.2.2 Application using an example . . . . . . . . . . . . . . . 242.2.3 DC versus multi-frequency . . . . . . . . . . . . . . . . . 282.2.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . 282.3 Feasibility study of EM methods . . . . . . . . . . . . . . . . . . 302.3.1 Galvanic sources . . . . . . . . . . . . . . . . . . . . . . 312.3.2 Multi-frequency galvanic sources . . . . . . . . . . . . . 342.3.3 Inductive sources . . . . . . . . . . . . . . . . . . . . . . 352.3.4 Large surface loop transmitter: Time-domain . . . . . . . 392.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 393 Three-dimensional electromagnetic inversion of growth-impeded SAGDsteam chambers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 413.1 Site background . . . . . . . . . . . . . . . . . . . . . . . . . . . 413.2 1D model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 443.3 Modelling steam chambers . . . . . . . . . . . . . . . . . . . . . 443.4 Steam chamber imaging using surface loop transmitters . . . . . . 463.4.1 Example with non-perturbed chambers . . . . . . . . . . 483.4.2 Example with a perturbed chamber . . . . . . . . . . . . 533.5 Cascading time-lapse inversion for growing steam chambers . . . 553.6 Improving the recovered model using a-priori information . . . . 573.6.1 Adding additional data . . . . . . . . . . . . . . . . . . . 573.6.2 Apply distance weighting . . . . . . . . . . . . . . . . . 593.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 634 Application of sensitivity analysis in DC resistivity monitoring ofSAGD steam chambers . . . . . . . . . . . . . . . . . . . . . . . . . 654.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 654.2 Geology and surveys . . . . . . . . . . . . . . . . . . . . . . . . 674.3 Estimation of the sensitivity . . . . . . . . . . . . . . . . . . . . 704.3.1 Comparison of sensitivity estimators . . . . . . . . . . . . 72vii4.3.2 Effect of survey design on sensitivity . . . . . . . . . . . 764.3.3 Effect of conductivity model on sensitivity . . . . . . . . 794.3.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . 794.4 Sensitivity analysis . . . . . . . . . . . . . . . . . . . . . . . . . 804.4.1 Impact due to location changes . . . . . . . . . . . . . . . 824.4.2 Impact due to size changes . . . . . . . . . . . . . . . . . 844.4.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . 854.5 Validation with 3D inversion . . . . . . . . . . . . . . . . . . . . 854.6 Imaging with electromagnetics . . . . . . . . . . . . . . . . . . . 904.7 Steam growth over time . . . . . . . . . . . . . . . . . . . . . . . 954.8 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 964.9 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 985 From exploring to reclamation: using EM methods at SAGD sites inthe Athabasca oil sands . . . . . . . . . . . . . . . . . . . . . . . . . 995.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 995.2 Stage I . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1025.3 Stage II . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1035.3.1 Airborne TEM data . . . . . . . . . . . . . . . . . . . . . 1045.3.2 1D inversion of synthetic data . . . . . . . . . . . . . . . 1055.3.3 Regional pseudo-3D inversions of field data . . . . . . . . 1105.3.4 Local pseudo-3D inversion of field data . . . . . . . . . . 1175.3.5 Local 3D inversion of field data . . . . . . . . . . . . . . 1175.3.6 Modelling the McMurray . . . . . . . . . . . . . . . . . . 1195.4 Stage III . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1205.5 Stage IV . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1235.6 Stage V . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1235.7 Stage VI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1245.8 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1256 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1266.1 Feasibility of electromagnetics . . . . . . . . . . . . . . . . . . . 1276.2 Recovery using large surface transmitters and borehole receivers . 128viii6.3 Improving recovered models by analyzing survey design . . . . . 1296.4 Heavy oil exploration and monitoring using EM . . . . . . . . . . 1296.5 Future research . . . . . . . . . . . . . . . . . . . . . . . . . . . 130Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132ixList of TablesTable 2.1 When inverting data, uncertainties are assigned as a percentageof the data plus a noise floor. Noise floors are assigned either asa value based on instrument sensitivities, of which representa-tive minimum values are given, or a value such that a percentageof the data fall below the noise floor. . . . . . . . . . . . . . . 20Table 2.2 General thicknesses and resistivity values for the lithology unitswithin the Athabasca oil sands (Bauman, 2005; Zhdanov et al.,2013). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21Table 2.3 For each survey, the RD and AD are calculated for each datatype (e.g., the imaginary component of Ez) at each receiver lo-cation using Equations 2.20 and 2.21. These are then used tocalculate a median value for each data type. Lastly, the me-dian values are subsequently averaged to get a global RD or ADfor the voltage, electric field, or magnetic field. For the time-domain, the median RD and AD for the magnetic flux densityare provided for the early, middle, and late time channels (TC). 33Table 3.1 For each survey, the median RD and AD are calculated for thez-component of the electric field. These metrics show that theeastern transmitter is more sensitive to the steam chambers andthe nonsteamed blockage. . . . . . . . . . . . . . . . . . . . . 49xTable 4.1 The four surveys (Figure 4.2) used at the Leismer Demonstra-tion Area are ranked based on the sensitivity. Surveys 2 and 4receive the same ranking due to a very similar sensitivity. Thetable shows that as the number of data increases, the sensitivityincreases. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82Table 4.2 The relative difference (Equation 2.20) for the four surveys (Fig-ure 4.2) using Models 1 and 2 at Time 3 (Figure 4.4). . . . . . 87xiList of FiguresFigure 1.1 Wells pads in plan view. The white lines represent the subsur-face horizontal wells. Figure courtesy of Suncor. . . . . . . . 4Figure 1.2 A conceptual diagram of the SAGD process. Steam is injectedinto the top horizontal well, producing a balloon-shaped steamchamber. The steam heats and liquefies the bitumen oil. Theoil is collected and pumped to the surface by the bottom well.Figure courtesy of Suncor. . . . . . . . . . . . . . . . . . . . 4Figure 1.3 (a) A theoretical balloon-shaped SAGD steam chamber and (b)a more realistic, irregular chamber. The steam chamber canbe affected by heterogeneity within the reservoir, causing anirregular shape. Modified from Peacock (2010). . . . . . . . . 5Figure 1.4 (a) Galvanic sources use current electrodes, which can be placedin the same borehole, different boreholes, at the surface, or inany combination of those locations. (b) Inductive sources con-sist of current loops on the surface or small coils in boreholes.Current I is injected into the subsurface in (a) while a time-varying current in (b) generates a primary magnetic field. . . . 11Figure 1.5 Comparison between frequency-domain (top) and time-domain(bottom) waveforms, where t is time and A is amplitude. Infrequency domain, the waveform is sinusoidal over time. Fortime domain, the waveform is divided into on-time (amplitude= A) or off-time (amplitude is zero). Typically, measurementsare taken during the off-time portion. . . . . . . . . . . . . . 11xiiFigure 1.6 In EM methods, both electric (E) and magnetic (B) fields canbe measured, either in a borehole (shown) or at the surface.Electric fields are measured using potential electrodes whilemagnetometers measure B and small coils inside the boreholesmeasure dB/dt. The electric field and potential difference arerelated by the separation distance (L) of the potential elec-trodes. Each field has 3 components. . . . . . . . . . . . . . . 12Figure 2.1 (a) A synthetic steam chamber with a pyramidal shape reflectsthe irregular growth that can occur in SAGD. The chamber hasa resistivity of 10 Ωm and is hosted in a 400 Ωm background.(b) A cap rock with thickness of 50 m and a resistivity of 17Ω m is added above the steam chamber. There is a 10 m gapbetween the top of the steam chamber and the bottom of thecap rock. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25Figure 2.2 A portion of the possible transmitters, after applying a distancerestriction. The blue dots show the electrode positions in theobservation wells and the red lines connect the two currentelectrodes. Continuing this throughout the pad gives roughly170,000 transmitters. . . . . . . . . . . . . . . . . . . . . . . 25Figure 2.3 (a) The roughly 170,000 dipole moments plotted on a unitsphere. The moments cover nearly every direction. The coloursindicate the magnitude of the moments, with a larger momentindicating greater excitation of the anomalous body. (b) Theunit sphere divided into 24 equal areas. The blue lines outlineeach region and the red dots show their centre. . . . . . . . . 27Figure 2.4 The 24 selected transmitters. The lines connect the two currentelectrodes and their colour references their number from 1 to24 (for ease of visibility). It is clear that the sphere is excitedin many directions. . . . . . . . . . . . . . . . . . . . . . . . 27Figure 2.5 Skin depth is a function of resistivity and frequency (Equation2.1, meaning that each frequency samples a different area. . . 28xiiiFigure 2.6 As frequency increases, the amplitude and phase of the currentdensity changes. This means that more and different informa-tion is provided by each transmitter. (a) Current density in thex-direction (left) and y-direction (right) is plotted as as phase(y-axis) vs frequency (x-axis) while colour indicates the am-plitude. (b) Alternatively, the current density can be plotted asreal and imaginary vectors for both the x-component (left) andthe y-component (right). . . . . . . . . . . . . . . . . . . . . 29Figure 2.7 Seismic time-delay attribute data from multiple SAGD wellpads were translated into steam chamber height. A small sub-set, represented by the rectangle, is used to generate the syn-thetic irregular steam chamber. . . . . . . . . . . . . . . . . . 32Figure 2.8 (a) Two traditional crosswell surveys straddle the area of in-terest. The survey has 98 current electrode pairs and 40 volt-age measurements per current electrode pair. (b) This galvanicsurvey was designed to excite the anomaly in three dimensions.The survey has 24 current electrode pairs and 124 receivers percurrent electrode pair. Electrode locations are shown as blackstars. The lines connect the current electrodes. In (c), blackdots show the locations of the magnetic dipole sources whilegray dots indicate the receiver locations. In (d) and (e), blacklines indicate the transmitter loop. Receivers are indicated us-ing black dots. In each figure, the location of the irregularsteam chamber is shown using a gray sphere. . . . . . . . . . 36Figure 2.9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37xivFigure 3.1 (a) Map showing properties and their respective companies.The Aspen property, owned by Imperial Oil, is located roughly45 NE of Fort McMurray and 25 km SE of Fort McKay innortheastern Alberta. Figure courtesy of Imperial Oil. (b)The eight wells used in this paper are indicated by large dotswhile other wells are shown as small dots. The map shows theboundary of the Aspen Property, boundaries for Townships 93and 94 in Range 7, and the sections within those townships. . 42Figure 3.2 (a) For each of the 8 wells, the top of each lithologic unit waspicked. (b) The elevations of the picks were averaged to geta single stratigraphic column of the different units. (c) Theresistivity logs from the eight wells are plotted with the averageresistivity for each lithology unit. . . . . . . . . . . . . . . . 43Figure 3.3 (a) Cross-section of the 3D temperature distribution within thereservoir for three synthetic steam chambers. (b) Cross-sectionof the 3D resistivity model based on resistivity log data and theWaxman-Smits equation. . . . . . . . . . . . . . . . . . . . . 46Figure 3.4 (a) True model showing three steam chambers. (b) True modelshowing three chambers where the center chamber is impededdue to a blockage. Each panel shows a depth slice 215 m belowthe surface and a cross-section of the reservoir at a northingof 250 m. In plan view, white dots denote borehole locationsand the white line indicates the location of the cross-section.The borehole locations in the cross-section are indicated usingwhite dots. . . . . . . . . . . . . . . . . . . . . . . . . . . . 47Figure 3.5 Two surface transmitters, each 1 km by 1 km, at the surface areused individually and simultaneously to recover three SAGDsteam chambers. For each survey, the z-component of the elec-tric field is measured at receivers in boreholes (dots) that sur-round the three horizontal wells (black lines). Each boreholehas 33 receivers, spaced every 20 m. Receivers are spaced ev-ery 5 m in the bitumen reservoir. . . . . . . . . . . . . . . . . 48xvFigure 3.6 The top and bottom rows show the secondary currents for theeastern and northern transmitters, respectively. Panels (a) and(d) show the secondary currents between the background 1Dmodel and the unperturbed model with 3 steam chambers (Fig-ure 3.4a). Panels (b) and (e) show the currents between thebackground 1D model and the perturbed model (Figure 3.4b).Panels (c) and (f) show the secondary currents in the blockageusing the perturbed and unperturbed 3D models. . . . . . . . 50Figure 3.7 (a) True model showing three regular SAGD steam chambers.Recovered models using Ez data and αy = 10 from (b) the east-ern transmitter, (c) the northern transmitter, and (d) both trans-mitters. Each panel shows a depth slice 215 m below the sur-face and a cross-section of the reservoir at a northing of 250m. In plan view, white dots denote borehole locations and thewhite line indicates the location of the cross-section. The bore-hole locations in the cross-section are indicated using white dots. 51Figure 3.8 (a) True model showing three steam chambers where the cen-tre chamber is impeded due to a blockage. Recovered modelsusing Ez data and αy = 10 from (b) the eastern transmitter,(c) the northern transmitter, and (d) both transmitters. Eachpanel shows a depth slice 215 m below the surface and a cross-section of the reservoir at a northing of 250 m. In plan view,white dots denote borehole locations and the white line indi-cates the location of the cross-section. The borehole locationsin the cross-section are indicated using white dots. . . . . . . 54xviFigure 3.9 True models at three time-steps: (a) early time where the cham-bers are 20 m high and 11 m at their widest, (b) middle timewhere the chambers are 35 m high and 20 m at their widest,and (c) late time where the chambers are 50 m high and 28 mat their widest. In (c), steam has penetrated through the block-age and grown to a height of 20 m and width of 11 m. Eachpanel shows a depth slice 215 m below the surface and a cross-section of the reservoir at a northing of 250 m. In plan view,white dots denote borehole locations and the white line indi-cates the location of the cross-section. The borehole locationsin the cross-section are indicated using white dots. . . . . . . 57Figure 3.10 Results from cascading time-lapse inversion. 1 . . . . . . . . 58Figure 3.11 (a) True model showing three steam chambers where the cen-tre chamber is impeded due to a blockage. Recovered modelsusing E and H data and αy = 10 from (b) the eastern transmit-ter, (c) the northern transmitter, and (d) both transmitters. Eachpanel shows a depth slice 215 m below the surface and a cross-section of the reservoir at a northing of 250 m. In plan view,white dots denote borehole locations and the white line indi-cates the location of the cross-section. The borehole locationsin the cross-section are indicated using white dots. . . . . . . 60Figure 3.12 Distance weights are used to force resistivity changes awayfrom the borehole locations. The panel shows a depth slice215 m below the surface and a cross-section of the reservoir ata northing of 250 m. . . . . . . . . . . . . . . . . . . . . . . 61Figure 3.13 (a) True model. Recovered models are shown from invert-ing all electric and magnetic data using αy = 10 and distanceweights for (b) the eastern, (c) the northern, and (d) both trans-mitters. Each panel shows a depth slice 215 m below the sur-face and a cross-section of the reservoir at a northing of 250m. In plan view, white dots denote borehole locations and thewhite line indicates the location of the cross-section. The bore-hole locations in the cross-section are indicated using white dots. 62xviiFigure 4.1 Cross section at a northing of 0 m through the 3D resistivitymodel for the Leismer Demonstration Area. Two observationwells are located at 0 and -150 m in the easting direction. Thewells contain electrodes (black dots). The horizontal injectorand producer well pairs (black circles) are at -230 m, -130 m,-30 m, and 70 m. in the easting direction. . . . . . . . . . . . 68Figure 4.2 Four DC resistivity surveys were collected daily at the LeismerDemonstration Area to monitor steam chamber growth. Blackdots indicate electrode locations. Grey lines connect transmit-ter electrodes for crosswell transmitters. Surveys 1, 3, and 4also have along-well transmitters (not shown). . . . . . . . . . 69Figure 4.3 Four steam chambers are added to the background geology(Figure 4.1). The steam chambers grow over time in the east-ing and vertical directions. The chamber sizes are: Time 1 - 5m by 5 m, Time 2 - 10 m by 10 m, Time 3 - 20 m by 15 m,and Time 4 - 30 m by 25 m. The chambers extend 280 m inthe northing direction, centred at a northing of 0 m. Black dotsindicate the electrodes in the two vertical wells. . . . . . . . . 70Figure 4.4 This chapter investigates two scenarios. Model 1 reflects thesteam growth observed by Tøndel et al. (2014). Model 2 showsthe inner right steam chamber moved towards the centre of thereservoir between the two vertical wells. Black dots indicatethe electrodes in the two vertical wells. . . . . . . . . . . . . 71Figure 4.5 (a) A crosswell survey with a single transmitter: current elec-trodes at (-50, 0) and (150, 0). (b) A two-dimensional resistiv-ity model with a 10 Ωm anomaly in a 400 Ωm background. . . 73Figure 4.6 The diagonal of JT J can be approximated in several ways: (a)the exact solution, (b) the average sensitivity (Equation 4.2),(c) Hutchinson’s approach using 5 iterations, (d) Hutchinson’sapproach using m iterations, (e) probing method using 5 iter-ations, (f) probing method using m iterations. The number ofcells in the mesh is m= 4004. . . . . . . . . . . . . . . . . . 74xviiiFigure 4.7 Crosswell surveys with (a) a single transmitter with currentelectrodes at (-50, 0) and (150, 0), (b) a single transmitter withcurrent electrodes at (-50, 0) and (150, -240), (c) the previoustwo transmitters combined, and (d) 49 transmitters in a typicalsurvey design. . . . . . . . . . . . . . . . . . . . . . . . . . . 77Figure 4.8 The probing method using 5 iterations approximates the sen-sitivity for the four surveys shown in Figure 4.7. Because thesensitivity decays outside of the region between the boreholes,only the region of interest is plotted. . . . . . . . . . . . . . . 77Figure 4.9 Recovered models from inverting the voltage data from thefour surveys in Figure 4.7. . . . . . . . . . . . . . . . . . . . 78Figure 4.10 The sensitivity approximation using the probing method with5 iterations for a 400 Ωm halfspace and the four surveys inFigure 4.7. Because the sensitivity decays outside of the regionbetween the boreholes, only the region of interest is plotted. . 80Figure 4.11 Plan-view sections (z = 215 m) of the sensitivity calculatedusing the probing method with 5 iterations for the four surveys(Figure 4.2). In each case, sensitivity decreases away from thelocations of the vertical observation wells but the magnitudevaries. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81Figure 4.12 A profile of the approximate sensitivity along the easting di-rection (z= 215 m and y= 0 m) for the 4 surveys (Figure 4.2).Black vertical lines indicate the locations of the steam cham-bers in Models 1 and 2 (Figure 4.4). . . . . . . . . . . . . . . 81Figure 4.13 The sensitivity is approximated using models that include aconductive steam chamber at different easting locations. Toprow: Plan-view sections through the sensitivity. Bottom row:the difference between the sensitivity in the top row and thebackground sensitivity. . . . . . . . . . . . . . . . . . . . . . 83Figure 4.14 Plan-view sections (z = 215 m) of the sensitivity using Sur-vey 4 (Figure 4.2d) for Models 1 and 2 (Figure 4.4) calculatedusing the probing method with 5 iterations. . . . . . . . . . . 84xixFigure 4.15 Plan-view sections (z= 215 m) of the sensitivity using Survey4 (Figure 4.2d) for the time-lapse models (Figure 4.3) calcu-lated using the probing method with 5 iterations. . . . . . . . 86Figure 4.16 Each panel shows the recovered models at a y = 0 m for thefour different surveys for Model 1 (Figure 4.4a). Only thereservoir portion is shown as only these cells were allowed tochange resistivity in the inversion. Colour scale indicates thechange in Ωm from the initial model. . . . . . . . . . . . . . 87Figure 4.17 Each panel (y= 0 m) shows the recovered models for the fourdifferent surveys using Model 2 (Figure 4.4b). Only the reser-voir portion is shown as only these cells were allowed to changeresistivity in the inversion. Colour scale indicates the changein Ωm from the initial model. . . . . . . . . . . . . . . . . . 89Figure 4.18 The real and imaginary parts of Ez is plotted for a single trans-mitter (with current electrodes at (-150, 0, 126) and (-150, 0,299)) at five frequencies. The real part remains relatively un-changed compared to the imaginary part, which generally in-creases as frequency increases. Solid and dashed lines indicatepositive and negative data, respectively. . . . . . . . . . . . . 91Figure 4.19 Using a single transmitter (with current electrodes at (-150,0, 126) and (-150, 0, 299)) and a receiver at (0, 0, 215), theapproximate sensitivity is calculated for the real and imaginaryparts of Ez at five frequencies using Model 1 (Figure 4.4a). Theplots show a plan-view section at an elevation of 215 m. Asfrequency increases, the sensitivity from the real part remainsrelatively unchanged while the sensitivity from the imaginarypart increases up to 1000 Hz and has decreased at 10000 Hz. . 92Figure 4.20 The models are subtracted from the background model to showthe difference: the true difference is compared to the differencemodels using EM data from Survey 4 at (a) 1 Hz, (b) 10 Hz, (c)100 Hz, (d) 1000 Hz, and (e) 10000 Hz. Colour scale indicatesthe change in Ωm from the background model. . . . . . . . . 93xxFigure 4.21 The models are subtracted from the background model to showthe difference: the true difference for Model 1 is comparedto the difference models using multi-frequency EM data fromSurvey 4. Colour scale indicates the change in Ωm from theinitial model. . . . . . . . . . . . . . . . . . . . . . . . . . . 94Figure 4.22 The recovered models are subtracted from the background modelto show the difference: the true difference for Model 2 is com-pared to the difference models using multi-frequency EM datafrom Survey 4. Colour scale indicates the change in Ωm fromthe background model. . . . . . . . . . . . . . . . . . . . . . 95Figure 4.23 Left column: the difference (from the background model) inModel 1 at four time steps. Middle column: recovered modelsusing DC resistivity. Right column: recovered model usingmulti-frequency EM. Colour scale indicates the change in Ωmfrom the initial model. . . . . . . . . . . . . . . . . . . . . . 96Figure 4.24 Left column: The difference (from the background model) inModel 2 at four time steps. Middle column: recovered modelsusing DC resistivity. Right column: recovered models usingmulti-frequency EM. Colour scale indicates the change in Ωmfrom the initial model. . . . . . . . . . . . . . . . . . . . . . 97Figure 5.1 A six-stage timeline outlines the development of SAGD sitesin the Athabasca oil sands (left). EM methods can supplementinformation at each stage (right) ranging from regional surveysto time-lapse monitoring. EIA = environmental impact assess-ment, AER = Alberta Energy Regulator. . . . . . . . . . . . . 100Figure 5.2 Map showing properties in the Athabasca oil sands and theirrespective companies. The Aspen property, owned by ImperialOil, is located roughly 45 NE of Fort McMurray and 25 kmSE of Fort McKay in northeastern Alberta. Figure courtesy ofImperial Oil. . . . . . . . . . . . . . . . . . . . . . . . . . . 101Figure 5.3 Resistivity logging data from 8 wells at the Aspen property areused to create a simple 1D resistivity model. . . . . . . . . . . 102xxiFigure 5.4 The VTEM survey contained 86 flight lines and 12 tie lines,providing 428,340 data locations over a 100 km2 survey area inthe Athabasca oil sands. The blue line indicates the boundaryof the Aspen property. . . . . . . . . . . . . . . . . . . . . . 104Figure 5.5 The VTEM waveform is shown in blue. Black dots indicatethe 44 time channels. The inset shows a closer look at the timechannels on a logarithmic scale from 10−5 to 10−3 seconds. . 105Figure 5.6 (a) A 1D model generated from borehole resistivity logs inthe Aspen region. The top two layers represent the Quater-nary and Grand Rapids Formation with a resistivity of about25 Ωm. The conductor of approximately 10 Ωm representsthe Clearwater Formation, with the Wabiskaw Member belowit. The resistive unit starting at approximately 200 m in depthand at 500 Ωm is the McMurray Formation. Below the Mc-Murray lies the Devonion limestone. (b) A randomly-chosendecay curve (blue) from the VTEM data set is compared to theforward modelled data (orange) using the synthetic 1D model(Figure 5.6a). The two decay curves are fairly similar to eachother, suggesting that the 1D synthetic model is a decent rep-resentation of the resistivity structures at the Aspen property. . 106Figure 5.7 Inversion of the forward modelled data (Figure 5.6b) using aninitial and reference model of (a) 25 Ωm, (b) 100 Ωm, and (c)500 Ωm. Below the conductive layer, the model pushes to-wards the reference model, providing an estimate of the depthof investigation. In each panel, (a) compares the observed(blue) and predicted (orange) data, (b) shows the normalizeddata misfit for each time channel, (c) compares the recoveredmodel (black), the true model (blue), and the initial/referencemodel (orange). . . . . . . . . . . . . . . . . . . . . . . . . . 107xxiiFigure 5.8 Inversion of the forward modelled data (Figure 5.6b) using an(a) L2 norm and (b) L1 norm for φm. In (c), an L1 norm is usedand αz is reduced from 1 to 0.1. In each panel, (a) comparesthe observed (blue) and predicted (orange) data, (b) shows thenormalized data misfit for each time channel, (c) compares therecovered model (black), the true model (blue), and the ini-tial/reference model (orange). . . . . . . . . . . . . . . . . . 109Figure 5.9 Inversion of the field data located near 4 boreholes with resis-tivity logging data. In each panel, (a) compares the observed(blue) and predicted (orange) data, (b) shows the normalizeddata misfit for each time channel, (c) compares the recoveredmodel (black), the true model (blue), and the initial/referencemodel (orange). . . . . . . . . . . . . . . . . . . . . . . . . . 111Figure 5.10 The downsampled VTEM data set contains 5,772 data loca-tions. The blue line indicates the boundary of the Aspen property.112Figure 5.11 The figure shows a planview section from the interpolated 3Dmodel at an elevation of 465 m. The model shows a channel-like resistive unit in the centre, with more conductive regionsto the northwest and southeast. Solid line shows location offocus for SAGD; dashed line shows location of cross-sectionsin Figure 5.12. . . . . . . . . . . . . . . . . . . . . . . . . . 113Figure 5.12 The figure shows cross-sections at a northing of 12.6, 8.4, and3 km. The figures are vertically exaggerated to show variationsin the conductivity with depth. Solid black lines indicate thetops of the Grand Rapids, Clearwater, and McMurray Forma-tion determined from the recovered model. . . . . . . . . . . 114Figure 5.13 Comparison between the top of the McMurray Formation from(a) borehole core logging and seismic data and (b) the recov-ered model from inversion. Panel (a) is courtesy of ImperialOil (Imperial Oil Resources Ventures Limited, 2013). . . . . . 115xxiiiFigure 5.14 Comparison of (left) plan-view and (right) cross sections for(a) the coarse pseudo-3D, (b) the fine pseudo-3D, and (c) the3D recovered models. The left-hand figures are at an elevationof 465 m. The right-hand figures, at a northing of 8.4 km, arevertically exaggerated to show variations in the conductivitywith depth. . . . . . . . . . . . . . . . . . . . . . . . . . . . 116Figure 5.15 Using the pseudo-3D recovered model, data were forward mod-elled in 3D (blue line) and compared to observed field data(black circles). The mismatch between the soundings in (a)suggests that the data contain 3D effects that cannot be ex-plained by the pseudo-3D model while (b) shows that in someareas, the pseudo-3D model appears valid. . . . . . . . . . . . 118Figure 5.16 3D model from inverting the VTEM airborne data in three di-mensions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119Figure 5.17 A semi-synthetic McMurray Formation and Devonian base-ment are added to the 3D recovered model in Figure 5.16 usingthe well log data (Figure 5.3). . . . . . . . . . . . . . . . . . 120Figure 5.18 A surface EM survey, using a 1 km by 1 km loop and 3-component E and B receivers, is used to recover informationabout the reservoir after the airborne EM survey. . . . . . . . 121Figure 5.19 Inversion of E and B data from a surface EM survey (Figure5.18) recovers the McMurray Formation. . . . . . . . . . . . 121Figure 5.20 An EM survey using two transmitters (each 1 km by 1 kmloops) at the surface. Receivers are placed in boreholes (blackdots) and measure Ez. The survey is used to monitor steamchamber growth over time. . . . . . . . . . . . . . . . . . . . 122Figure 5.21 Synthetic steam chambers are added to the background modelin Figure 5.17, generating a realistic model which is used todetect and image chamber growth using EM. . . . . . . . . . 123Figure 5.22 Plan-view slices (z = 320 m) for (a) the true model and (b)the recovered model, showing three irregularly-shaped SAGDsteam chambers. . . . . . . . . . . . . . . . . . . . . . . . . 125xxivAcknowledgmentsMy utmost gratitude goes to my advisor, Dr. Douglas Oldenburg, for taking meon as his student and providing the ideal atmosphere to grow, both intellectuallyand emotionally. You instill a desire to never stop learning and living life to thefullest. Thank you for the exceptional learning opportunities and research projectsat UBC-GIF. And, I am indebted to you for your tireless efforts liaising with UBCand industry for the data in this thesis.My experience at UBC would not be the same if it wasn’t for my labmates atUBC-GIF. Thank you for proof-reading my written work, listening to me whenI came into your offices, and discussing anything and everything while grabbinglunch or coffee. It’s been a pleasure working with all of you; you’ve taught me somuch.My thanks extend to UBC-GIF, the Society of Exploration Geophysicists, Im-perial Oil, the Canadian Exploration Geophysical Society, the Department of Earth,Ocean, and Atmospheric Sciences at UBC, and the University of British Columbiafor scholarships and funding received over the last six years. As well, I’d like tothank the people at Suncor, Imperial Oil, Geotech, and Statoil for the valuable dis-cussions on SAGD and field data. My thanks goes out to Roman Shekhtman foraltering codes and providing new utilities so I could complete the research for thisthesis.I don’t think this thesis would have ever been completed if it were not for thesupport of my family. An enormous thank you to my parents for pushing me, al-ways believing in me, and sacrificing so much so I could continue studying. I’mso happy you were always just a phone call away. Throughout the last ten yearsat Mines and UBC, I have to thank my sister for being a constant source of comicxxvrelief, whether it be with little notes or pictures of her cat, and later on, for answer-ing my questions on life after grad school. You are wise beyond your years. I missyou all.Most of all, my gratitude is unmatched for my husband Ryan. Thank you foradopting me into your circle of friends when I was new to Canada and becomingmy best friend. Thank you for standing next to me each and every day and believingin me every time I doubt myself. I love you so much.xxviDedicationTo my family.Every time I see an adult on a bicycle I no longer despair for the future of thehuman race.- H. G. WellsxxviiChapter 1IntroductionSteam, the simple result from boiling water in a tea kettle, has increasingly beenused for earth applications in both the environmental sector and the oil and gasindustry. The most prevalent use of steam is to extract heavy oil and oil sands fromreservoirs. Cyclic steam simulation (CSS), also known as “huff and puff”, uses avertical well to inject steam into a formation. Following a “soaking” period wherethe oil is heated, the same well is used to produce the oil (Thomas, 2008). Thismethod has been successfully used in Venezuela, China, California, and Canada’sCold Lake oil sands (Alvarez and Han, 2013). The more common method nowused in Canada’s oil sands is steam-assisted gravity drainage (SAGD), which usesa horizontal well to steam-flood a reservoir (Butler, 1994). The heated oil flowsdownwards and is collected and pumped to the surface by a second, lower horizon-tal well.Since the development of steam for oil recovery, it has also become a success-ful method for the remediation of environmental problems. Davis (1998) providesan extensive overview of how steam has been used to remove volatiles and contam-inants from soils and aquifers. Schmidt et al. (2002) describe how the use of steamto remove contaminants from the subsurface can cause it to move in undesired di-rections and a possible solution for this problem. Nilsson et al. (2011) study howsteam injection can be used to remove jet fuel from heterogeneous soils.However, neither application of steam injection is a simple process and it is im-portant to monitor steam-flooding over time for several reasons. Proper monitoring1techniques provide information about where steam is propagating and secondly,whether it is removing all the contaminant or producing the maximum amount ofoil. Fortunately, steam injection generally causes a change in the electrical resis-tivity (Butler and Knight, 1998), meaning that electric and electromagnetic (EM)methods can be used.In addition, monitoring fluids using these methods is a well-established con-cept. Asch and Morrison (1989) used borehole and surface electrodes to monitora nuclear waste repository. Giese et al. (2009) utilized electrical resistivity tomog-raphy (ERT) to monitor CO2 storage in a saline aquifer. ERT was also used byOldenborger et al. (2007) to monitor fluid injections and by Daily et al. (1992),Daily et al. (1995), and LaBrecque et al. (1996) to monitor subsurface water flow.Ramirez et al. (1995) describe the use of ERT to monitor steam injection at a sitecontaminated with gasoline, indicating that changes in resistivity were caused byincreased temperatures from the steam.Ramirez et al. (1993) used ERT to monitor steam injection, detecting an in-crease in conductivity and identifying the layer to which the steam was confined.Crosswell electromagnetics was used to monitor steam growth at an oil field in theSan Joaquin Valley, California, and demonstrated the ability to monitor changes insmaller time increments than crosswell seismic (Marion et al., 2011). Wilt (1994)and Wilt et al. (1996) described the use of crosswell EM to monitor steaming ef-forts in oil sands at Lost Hills, California and indicated an increase in conductivitydue to steaming. Wilt et al. (1997) suggested that crosswell EM monitoring ofsteam flooding may even be possible in the presence of steel-cased wells.For SAGD, Engelmark (2007) proposed using time-domain EM using galvanicsources and receivers in a straight line to monitor the chambers in two dimensions.Tøndel et al. (2012) described a permanent ERT system in conjunction with verticalseismic profiling to monitor steam-flooding in the Athabasca oil sands. In theirproject, two horizontal production wells and accompanying steam chambers liebetween the two vertical observation wells. The results of the monitoring projectshowed a 85% decrease in resistivity over a two-year time period (Tøndel et al.,2014).Electromagnetic (EM) methods have great potential to image SAGD chambersbut the methodologies have not been rigorously tested (Engelmark, 2010). Previous2studies limited the surveys to the surface, two dimensions, and/or the DC resistivitymethod. SAGD steam chambers are three-dimensional structures that may growirregularly in any direction, and thus ought to be characterized in 3D to study theirbehaviour and effects on the reservoir.This motivates the research in this thesis to analyze the feasibility of usingelectromagnetic methods to monitor time-lapse conductivity changes due to steam-flooding and specifically focus on steam chamber growth due to SAGD in theAthabasca oil sands.1.1 Steam-assisted gravity drainageIt is reported that the Athabasca oil sands contain 1.6 trillion barrels of bitumenoil with 175 billion barrels of reserves actually recoverable (Humphries, 2008).If close enough to the surface, the sands are mined. However, 90% of the oilsands are too deep and require in-situ methods (Mossop, 1980). In-situ recoveryprocesses can be non-thermal or thermal, including electrical heating, combustion,steam injection, and CO2 flooding (Alvarado and Manrique, 2010; Hammershaimbet al., 1983). Steam-assisted gravity drainage (SAGD) is a steam injection processpredominantly used in the Athabasca oil sands to extract bitumen that is too deepfor mining methods.In SAGD, two horizontal wells are drilled along the bottom of the bitumenreservoir. The well pairs are separated about 5 m vertically and extend approxi-mately a kilometer (Dembicki, 2001). The pairs are about 100 m apart within eachpad (Figure 1.1). Steam is injected into the top well and produces a steam chamber(i.e., a zone saturated with steam) that grows upwards and outwards. At the edge ofthe chamber, the steam condenses and the surrounding oil is heated through ther-mal conduction. The condensed steam and the heated, less viscous oil are collectedby the underlying production well (Figure 1.2). The heated bitumen and condensedsteam mixture flows downward or along the side of the steam chamber. As the oildrains, the chamber expands further into the bitumen reservoir (Butler, 1994).SAGD was first tested in the late 1980’s and has been used in industry for over10 years (Etris et al., 2012; Jimenez, 2008). The technique enables production ofa resource that is too deep to mine and too viscous for conventional technologies3Figure 1.1: Wells pads in plan view. The white lines represent the subsurfacehorizontal wells. Figure courtesy of Suncor.Figure 1.2: A conceptual diagram of the SAGD process. Steam is injectedinto the top horizontal well, producing a balloon-shaped steam chamber.The steam heats and liquefies the bitumen oil. The oil is collected andpumped to the surface by the bottom well. Figure courtesy of Suncor.(Hein and Cotterill, 2006). A detailed account of SAGD development history isgiven by Al-Bahlani and Babadagli (2009).The success of this technique is dependent upon steam propagation throughoutthe bitumen reservoir. Unfortunately, complexities in the earth conspire so that thesteam does not always propagate as desired (Charles et al., 2013; Strobl et al., 2013;Zhang et al., 2005). Instead of the idealized balloon shape, the steam chambermay develop irregularly in shape due to these heterogeneities (Figure 1.3). Chenet al. (2008) numerically demonstrate how irregular SAGD steam chambers candevelop. These complexities exemplify the importance of monitoring the growthof the steam chambers. Successful monitoring can aid in optimizing production4(a) (b)Figure 1.3: (a) A theoretical balloon-shaped SAGD steam chamber and (b) amore realistic, irregular chamber. The steam chamber can be affected byheterogeneity within the reservoir, causing an irregular shape. Modifiedfrom Peacock (2010).efforts by decreasing the steam-to-oil ratio (i.e., the amount of water needed toproduce a unit of oil), reducing missed pay, and decreasing the environmental foot-print (Singhai and Card, 1988).Currently, monitoring procedures rely heavily on seismic imaging methods(Forgues et al., 2006; Nakayama et al., 2010; Wolf, 2010; Wolf et al., 2008; Zhanget al., 2005). While successful in many cases, 4D seismic data may be limited incharacterizing changes due to low sensitivity in the petro-elastic parameters fromchanges in fluid content, saturation, and porosity. It can also be expensive to col-lect and time-consuming to process (Engelmark, 2007). Thus, there is considerablemotivation to find more cost-effective monitoring techniques, such as electromag-netic methods.1.2 Understanding conductivity changes in SAGDprocessesIn order to monitor steam chamber growth with EM methods, it is important tounderstand how steaming affects the electrical conductivity of an oil-bearing reser-5voir. All materials of the Earth have an intrinsic, measurable conductivity. Electri-cal conductivity can be measured or calculated empirically based on measurementsof secondary physical properties. The simplest empirical equation is Archie’s law,which depends purely on conductivity of the fluid in the pores, porosity, and thesaturation exponent (Glover, 2010). Other secondary physical properties that in-fluence conductivity are temperature, clay content, permeability, tortuosity, wetta-bility, and pressure (Keller, 1988; Martinez et al., 2012; Middleton and Wilcock,1994). The higher the number of secondary physical properties that are accountedfor, the more complex the empirical geologic model becomes. Glover (2010)provided an overview of the most common expressions, starting with Archie’slaw. One particular interesting variation of Archie’s law is the Waxman-Smitsmodel, which is idealized for oil-bearing shaly-sand formations (Waxman andSmits, 1968; Waxman and Thomas, 1974).Many papers have been published on the effect of steam on conductivity invarious media. Butler and Knight (1995) discussed how steam decreases the con-ductivity of clean water-saturated sands. They showed that heat affects the sandbefore the steam-front arrival, causing the conductivity to increase. However, asthe steam replaced the pore fluid, the conductivity decreased with decreasing salin-ity. Ultimately, it was the steam quality, or the vapour-to-liquid ratio, that had thegreatest effect on how much the conductivity changes (i.e., higher-quality steampromotes more dramatic changes in conductivity). In subsequent work, Butler andKnight (1998) showed that the presence of clay in sands caused conductivity toincrease during steaming. However, if the steam front moved faster than the steamliquid, a distilled water bank formed and the steam zone remained resistive, re-gardless of the presence of clays. These experiments show that the conductivity isaffected by the lithology, the steam quality and salinity, the steam front speed, andthe amount of clay present (Butler, 1995).Furthermore, in Southern California, Ranganayaki et al. (1992) showed that asa heavy oil reservoir was steamed, both the conductivity and temperature increased.The relationship between temperature and conductivity is supported by Archie’slaw, the Waxman-Smits model, and other empirical formulations. Newmark andWilt (1992) used a modified version of the Waxman-Smits model to explain theirlogging data before and after steaming. The logs showed an increase in conductiv-6ity due to steaming, which the authors attributed to the increasing temperature andpresence of clays.Mansure et al. (1993) described how steam-flooding changed well-log data.The data were collected at oil fields in Kern River and Elk Hills in California.Mansure et al. (1993) compared the field data to predicted results from three empir-ical formulas: Archie’s law, the Waxman-Smits model, and the dual-water model.Steam-flooding at Kern River decreased the resistivity from approximately 28 to11 Ωm. Archie’s law poorly characterized the field data, largely because it did notaccount for the effect of clay. Both the Waxman-Smits model and the dual-watermodel provided better approximations. At Elk Hills, steam-flooding decreased theresistivity from 10 to 5 Ωm. The higher salinity values at Elk Hills explained thelarger conductivity values compared to Kern River.These studies demonstrate that the change in conductivity due to steam flood-ing is heavily dependent on reservoir parameters, and that these parameters cangreatly increase the mathematical complexity of conductivity models. In heavyoil reservoirs, however, steaming has generally been shown to increase the reser-voir conductivity. Therefore, this thesis adopts the hypothesis that SAGD steam-flooding causes an increase in conductivity but the methodologies that were devel-oped are generic and can apply to any steam-flooding scenario.1.3 Research questionsThe literature indicates that electromagnetic methods are a viable option to monitorconductivity changes due to steam-flooding. However, the use of EM has not beenrigorously investigated for monitoring SAGD in the Athabasca oil sands, whichmotivates the research in this thesis. Thus, the main question is:Can EM be used to monitor SAGD steam growth?To answer this, many factors need to be considered that prompt the following spe-cific questions:1. What survey designs allow detection of the steam chambers and how canthey be recovered using inversion?72. How does the background geology affect survey design and the feasibility ofusing EM?3. Can the resistivity of the background models and steam chambers be relatedback to geology? How is this information useful for SAGD operations?The research conducted to answer these questions includes practical considerationsto better understand how EM can be useful during SAGD. The work can thus helpshape future SAGD monitoring and exploration surveys and provide valuable in-formation about production over time. In addition, the research can be appliedto monitoring steam floods for other purposes, such as when using cyclic steamsimulation or for environmental remediation.Given these questions, the remainder of this chapter introduces the concepts tocarry out the research, starting with Maxwell’s equations and the type of surveysthat can be conducted. Throughout this thesis, I numerically forward model EMdata and invert the data for a recovered resistivity model of the earth. The perti-nent equations are described below. Finally, before outlining the thesis chapters, Iprovide a summary of empirical formulations for resistivity.1.4 Electromagnetic methodsTo address the research questions, this thesis focuses on electromagnetic methods,which are geophysical exploration tools to find contrasts in electrical resistivity.The underlying equations are Maxwell’s, which, for source-free regions, are writ-ten in the frequency domain as:∇×E+ iωµH = 0, (1.1)∇×H− iωεE−σE = 0, (1.2)In these equations, E is the electric field, H is the magnetic field, and σ , µ , andε are the electric conductivity, magnetic permeability, and dielectric permittivity,respectively. Maxwell’s equations can be rewritten as Helmholtz equations (Wardand Hohmann, 1988):∇2E+ k2E = 0, (1.3)8∇2H+ k2H = 0, (1.4)where k =√µεω2− iµσω is the wave number. For typical physical propertiesfound within the earth and frequencies lower than 105 Hz, µσω >> µεω2, mean-ing that the displacement current D = εE is much smaller than the conduction cur-rent J = σE. Therefore, the displacement current is neglected and the equationsare rewritten, now including a source-term Je, as following:∇×E+ iωµH = 0, (1.5)∇×H−σE = Je, (1.6)By applying a Fourier transform, these expressions can be rewritten in the timedomain as∇× e+ ∂ (µh)∂ t= 0, (1.7)∇×h−σe = je. (1.8)where e, h, j are the Fourier transforms of the frequency-domain fields. In thefrequency domain, the fields and fluxes are related by the constitutive relationsJ = σE and and B = µH, where the electrical conductivity σ relates the currentdensity J and the electric field. The magnetic permeability µ relates the magneticfield to the magnetic flux density B. For the work here, it is assumed that there areno highly magnetic materials present and the magnetic permeability is constant,so µ = µ0, where µ0 is the permeability of free space. The electric resistivityis ρ = 1/σ : Both terms are used throughout this thesis. The frequency-domainexpressions use the angular frequency ω = 2pi f ( f is the frequency in Hz). Finally,it is important to note that Gauss’s law for magnetics states that ∇ ·B= 0, meaningthat no magnetic monopoles exist.In the electrostatic case, the angular frequency ω is zero, reducing Equation 1.5and allowing the electric field to be expressed as the gradient of a scalar potentialV :E =−∇V. (1.9)I substitute Equation 1.9 into Equation 1.6 and take the divergence, which elim-inates the magnetic field component, and obtain the following expression for the9DC resistivity problem:∇ ·σ∇V = ∇ ·Je. (1.10)For detailed discussions on the theory for both DC resistivity and electromagnetics,the reader is referred to Ward and Hohmann (1988), Nabighian and Macnae (1991),Reynolds (1998), Telford et al. (1990), and West and Macnae (1991).1.4.1 Controlled source EM surveysA typical EM experiment consists of a transmitter that carries a time-varying cur-rent. The resulting time-varying magnetic field induces currents in the earth. Thosecurrents produce electromagnetic fields that can be measured by a receiver. Thesource can either be galvanic or inductive. For galvanic sources, the transmitterconsists of two current electrodes, which can be in a borehole or at the surface(Figure 1.4a). Alternatively, inductive sources consist of wire loops that are un-grounded (Figure 1.4b). Surface loop transmitters can have sides ranging frommeters to hundreds of meters, while borehole coils are small. The current in thetransmitter can be constant, which gives rise to the DC resistivity survey for gal-vanic sources. Alternatively, the current can be sinusoidal, as in frequency domain,or consist of a waveform, as in time domain, that has both “on-time” and “off-time”segments. The frequency-domain and time-domain waveforms are illustrated inFigure 1.5.Possible measurements can be voltages, as in DC resistivity, and/or three com-ponents of the magnetic field. The electric field is measured with a voltmeter at-tached to two electrodes; the magnetic field can be measured with a magnetometer;and the time-derivative of the magnetic field can be measured with a coil. The fieldsmay be measured at the surface or along a borehole, as shown in Figure 1.6.To summarize, there are multiple variations and survey arrangements for ap-plied EM. Each application has competitive advantages and disadvantages withrespect to geophysical parameters, geological context, acquisition efficiency, andresolution. It is therefore important to investigate each type of EM survey design,in order to identify which will sufficiently detect the target while remaining practi-cal and cost-effective.10(a) Galvanic sources (b) Inductive sourcesFigure 1.4: (a) Galvanic sources use current electrodes, which can be placedin the same borehole, different boreholes, at the surface, or in any com-bination of those locations. (b) Inductive sources consist of currentloops on the surface or small coils in boreholes. Current I is injectedinto the subsurface in (a) while a time-varying current in (b) generatesa primary magnetic field.Figure 1.5: Comparison between frequency-domain (top) and time-domain(bottom) waveforms, where t is time and A is amplitude. In frequencydomain, the waveform is sinusoidal over time. For time domain, thewaveform is divided into on-time (amplitude = A) or off-time (ampli-tude is zero). Typically, measurements are taken during the off-timeportion.11Figure 1.6: In EM methods, both electric (E) and magnetic (B) fields can bemeasured, either in a borehole (shown) or at the surface. Electric fieldsare measured using potential electrodes while magnetometers measureB and small coils inside the boreholes measure dB/dt. The electric fieldand potential difference are related by the separation distance (L) of thepotential electrodes. Each field has 3 components.1.4.2 Numerical modelling of EM dataThis thesis utilizes forward modelling and inversion of three-dimensional electro-magnetic methods. The inverse problem is posed as an optimization problem thatincorporates Tikhonov regularization Tikhonov and Arsenin (1977). To solve theproblem numerically, Maxwell’s equations, shown in the time domain in Equations1.7 and 1.8 and in the frequency domain in Equations 1.5 and 1.6, are discretized.The earth is represented as a set of prismatic cells, each of which has a constantconductivity (Haber et al., 2004). Letting F denote the Maxwell operator, theforward problem is written asF [m] = d, (1.11)where the model m contains the conductivity values of the cells. The data d consistof E, H, and/or ∂B/∂ t, in frequency or in time, in the three spatial directions (x, y,and z). The data are inverted by minimizing the objective function φ(m):φ(m) = φd+βφm(m), (1.12)where φd is the misfit between the observed data dobs and the predicted dataF [m]:φd = ||Wd(F [m]−dobs)||22. (1.13)12The matrix Wd contains the reciprocal uncertainty values assigned to each datum.The goal is to find a model that fits the data to within the uncertainty but alsohas certain features, i.e., similarity to a reference model mre f , minimal structure,particular geologic features, and/or a priori information. This is included using amodel objective function φm(m):φm(m) = αs||Ws(m−mre f )||22+3∑i=1αi||Wim||22, (1.14)where the first term controls how close the model is to the reference model and thelast term dictates smoothness in the three spatial directions (x, y, z) denoted by i =1, 2, 3. The α values regulate the relative importance of each term, whereas theW matrices can incorporate additional weighting and a priori information. Specif-ically, Wi include derivative operators that act on the model. In addition, thesematrices provide the flexibility to only allow certain cells to change value. WhileEquation 1.14 provides a smoother overall model, including the reference modelmre f in the smoothness terms allows changes in the model to be smooth whilepreserving certain characteristics:φm(m) = αs||Ws(m−mre f )||22+3∑i=1αi||Wi(m−mre f )||22. (1.15)A trade-off parameter β balances the data misfit and the model objective func-tion. As β approaches zero, the objective function consists only of the data misfit,possibly resulting in high-structured models that are not geologically feasible. Atthe other end of the spectrum, β approaches infinity, which emphasizes the modelobjective function, providing a smooth and small model that fits the data poorly.The forward problem here is nonlinear, and thus, in order to minimize theobjective function in Equation 1.12, it is first written as a Taylor series where δmis a small perturbation in the model:φ(m+δm) = φ(m)+(∇φ(m))Tδm+12(δm)T (∇∇φ(m))δm+ ... (1.16)13To find the minimum, the derivative of the above function is set to zero:∂φ(m+δm)∂m= 0. (1.17)This then results in the following expression:(∇∇φ(m))δm =−∇φ(m), (1.18)where∇∇φ(m) is the Hessian and∇φ(m) is the gradient. The gradient of Equation1.18 is:∇φ(m) = JTW Td Wd(F [m]−dobs)+βW TmWm(m−mre f ). (1.19)The sensitivity matrix J is defined as:J =∂F [m]∂m. (1.20)The Hessian is the gradient of the gradient and is expressed as:H = ∇∇φ(m) = (∇JT )W Td Wd(F [m]−dobs)+ JTW Td WdJ+βW TmWm. (1.21)However, the Hessian is often approximated as:H ≈ JTW Td WdJ+βW TmWm (1.22)because the first term in Equation 1.21 is difficult to compute and has only a smallinfluence on the entire expression (Oldenburg and Li, 2005).The final equation to solve for δm then becomes:(JTW Td WdJ+βWTmWm)δm = JTW Td Wd(dobs−F [m])−βW TmWm(m−mre f ),(1.23)which is called the Gauss-Newton equation. Standard Gauss-Newton methodolo-gies are used to solve the inverse problem (Nocedal and Wright, 2006; Oldenburgand Li, 2005). Several inversion codes are used in this thesis. Oldenburg and Li(1994) describe the 2D inversion of DC resistivity, whereas the 3D algorithm is14presented in Haber et al. (2012). Frequency-domain data can be inverted on eithera 3D tensor or ocTree mesh (Haber et al., 2004), whereas the time-domain data canbe inverted using the algorithm described in Oldenburg et al. (2013).1.5 Empirical resistivity formulationsThe forward modelling and inversion of EM data require a resistivity model thatrepresents the studied region. In lieu of an existing model, resistivity can be es-timated reasonably well using empirical formulations that use reservoir-specificparameters. The most well-known is Archie’s law, which is an empirical formula-tion for the resistivity of clean sands. A modified version of Archie’s law is givenas (Knight and Endres, 2005):1ρ= σ =φmsnσwγ, (1.24)where ρ is the resistivity, σ is the conductivity, φ is the porosity, m is the cementa-tion exponent, s is the water saturation, n is the saturation exponent, σw is the waterconductivity, and γ is the tortuosity. Note that resistivity is inversely proportionalto conductivity.However, Archie’s law does not adequately represent the conductivity changesdue to steaming in oil-rich sands (Mansure et al., 1993). Formulations such asthe Waxman-Smits equation and the dual-water model are superior because theyincorporate the behavior of clays and the bound-water interactions, respectively.Given the available data, the Waxman-Smits equation is used in later chapters tomodel the conductivity changes due to SAGD in the Athabasca oil sands. TheWaxman-Smits equation (Mansure et al., 1993; Waxman and Smits, 1968; Waxmanand Thomas, 1974) is written as following:σ =sn(σw+ BQvs)F∗, (1.25)where B is the specific counter-ion conductance, Qv is the cation exchange capac-ity, and F∗ is the shaley-sand formation factor. The water conductivity σw(T ) =c/(T +21.5) is dependent on temperature T , where c= σw0(T0 +21.5). The spe-15cific counter-ion conductance B can be further written as (Mansure et al., 1993)B= 3.83(0.04T )(1−0.83exp(−0.5σw|T=25)). (1.26)Additionally, the cation exchange capacity is written here as (Juha´sz, 1979)Qv =VclCδφ, (1.27)where Vcl is the percentage of clay, C is the cation exchange coefficient, and δis the density of the clay minerals. The Waxman-Smits expression can be used toestimate conductivity changes due to steaming in conjunction with previous studiespresented in the literature.It is noted that steam-flooding a reservoir is inherently complex and the aboveempirical relationships will only provide first-order approximations of the changein resistivity. Other parameters, such as changes in wettability and formation factor,will affect the resistivity change as well (Mansure et al., 1993; Martinez et al.,2012) but extend beyond the scope of this thesis.1.6 Thesis outlineGiven the background material in this introduction, Chapter 2 describes a surveydesign approach that can quickly and efficiently generate electric and electromag-netic surveys to excite subsurface bodies in three dimensions. This approach isused to test the feasibility of several types of transmitter and receiver combinationsfor a small synthetic SAGD example. The feasibility is determined based on bothdetecting the anomaly and the capability to image it using 3D inversion.Chapter 3 applies a specific survey design to an example with multiple SAGDsteam chambers, which was based on a field site in the Athabasca oil sands. Theresearch focuses on building models from a-priori information, modelling the con-ductivity change based on reservoir parameters, and recovering growth-impededsteam chambers over time.Chapter 4 investigates the efficacy of currently in-practice crosswell electricalsurveys without the need to resort to full inversions. Shortcomings in the electricalsurveys are addressed by expanding to multi-frequency EM methods using the ex-16isting infrastructure and acquisition tools and are validated using three-dimensionalinversion.Chapter 5 proposes how to use electromagnetic methods at six critical stagesduring exploration, development, and production at a SAGD site. The chapteruses airborne electromagnetic data to recover the background geologic setting ofa specific field site, including details about paleo-channels and cap rock thickness.The result is combined with other EM surveys to generate a complete backgroundmodel, in which steam chambers can be placed. The research from earlier chaptersis then utilized to achieve a detailed strategy to detect and monitor steam chambergrowth in the Athabasca oil sands using EM methods.Conclusions of the research are presented in Chapter 6, including remarksabout the importance of this work to the heavy oil industry, further improvements,and future work.17Chapter 2Feasibility of electromagneticmethods to detect and imageSAGD steam chambersIn this chapter, I investigate the use of electric and electromagnetic methods tomonitor the growth of steam-assisted gravity drainage (SAGD) steam chambers.SAGD has proven to be a successful method for extracting bitumen from theAthabasca oil sands in Alberta, Canada. However, complexity and heterogene-ity within the reservoir can impede steam chamber growth, limiting oil recovery,and increasing production cost. Using seismic data collected over an existingSAGD project, a synthetic steam chamber is generated and modelled as a con-ductive body within the bitumen-rich McMurray Formation. Simulated data fromstandard crosswell electrical surveys, when inverted in 3D, show existence of thechamber but lack the resolution necessary to determine the shape and size. Byexpanding to electromagnetic surveys, the ability to recover and resolve the steamchamber is significantly enhanced. A simplified survey design procedure is usedto design a variety of field surveys that include surface and borehole transmittersoperating in the frequency or time domain. Each survey is inverted in 3D and theresults are compared. The effectiveness of the surveys show that EM methodologyis worthy of future investigation and field deployment for characterizing SAGDsteam chambers.182.1 Survey configurationsThere are multiple variations and survey arrangements for EM methods. Galvanicsources use grounded current electrodes, which can be at the surface or in bore-holes. Inductive sources consist of wire loops that are ungrounded. Transmitterloops at the surface can have sides ranging from meters to hundreds of meters,while coils can be used as borehole transmitters (Wilt et al., 1995).The transmitter currents can be sinusoidal, and this leads to a frequency-domainsurvey. Each frequency samples the earth differently in accordance with its skindepth. The skin depth d (in m) is the distance that a plane wave propagates in ahomogeneous background before attenuating by a factor of 1/e:d ≈ 500√ρ/ f , (2.1)where ρ (in Ωm) is the background resistivity and f (in Hz) is the frequency. Thederivation for the skin depth expression is given by Ward and Hohmann (1988) andshows that each frequency is sensitive to earth structure at different distances froma transmitter. Data from a frequency-domain EM survey are complex numberswritten as an amplitude and phase or as in-phase and quadrature. DC resistivityis a special case of frequency-domain EM that uses a single frequency, f = 0, andgalvanic sources. The regions of illumination are governed purely by geometry andthe electrical conductivity.Time-domain EM experiments are carried out by using a different waveform,such as a step-off current, and data are generally measured in the “off-time”. Thetime-varying magnetic field produced by the step-off current diffuses into the earthaccording tor ≈ 1260√tρ, (2.2)where r (in m) is the diffusion distance and t (in s) is the time after transmittershut-off. Data are real numbers measured at multiple logarithmically spaced timechannels (TC). Frequency- and time-domain data are related through Fourier trans-forms and the general concept that data at high frequencies and early TC samplethe earth closer to the transmitter, whereas low frequency and late time data samplethe earth farther from the transmitter.19Data type Instrument sensitiv-ityV 1 × 10−6 VE 1 × 10−12 V/mB 2 × 10−5 nT∂B∂ t 1 × 10−11 V/m2Table 2.1: When inverting data, uncertainties are assigned as a percentage ofthe data plus a noise floor. Noise floors are assigned either as a valuebased on instrument sensitivities, of which representative minimum val-ues are given, or a value such that a percentage of the data fall below thenoise floor.Receivers can measure a variety of EM fields. The magnetic flux B and itstime-derivative ∂B/∂ t are measured with a magnetometer and a coil, respectively.Depending on the system, noise floors for ∂B/∂ t can range from 10−9 to 10−11V/m2 for a transmitter with a moment of 1 Am2. A SQUID sensor provides thehighest precision for a B-field sensor: approximately 20 femtotesla or 2 × 10−5nT. Electric field sensors are grounded or capacitive electrodes, which measurea potential difference. When the distance between the two sensors is small, thepotential difference is divided by the the distance between the two sensors to yieldan estimate of the electric field E. Otherwise, the potential difference itself is usedas a datum. This is the case for DC resistivity surveys. Capacitive sensors have low-noise thresholds and can measure fields as small as 10−11 V/m with dipole lengthsof 20-40 m (Hibbs et al., 2014). Table 2.1 summarizes the noise thresholds. Fieldsmay be measured at the surface or in a borehole. The magnitude of the measuredfields can be boosted by increasing the transmitter moment, either by increasingthe amount of current, the area of the loop, and/or by the number of turns in theloop. Receiver effective areas can also be increased by adding extra turns of wirein the receiver.All EM methods are sensitive to electrical conductivity, but the choice of whichsurvey to use depends upon the sought geophysical parameters, geological context,acquisition efficiency, desired resolution, and cost. Survey design is thus compli-cated. One can always get better images by using more transmitters, having more20Geologic unit Formation name Thickness (m) Resistivity (Ωm)Overburden Quaternary 0-200 100’sCap rock Grand Rapids &Clearwater0-30 2-30Oil sands McMurray 50-100 100-1000Limestone Devonian - 1-1000Table 2.2: General thicknesses and resistivity values for the lithology unitswithin the Athabasca oil sands (Bauman, 2005; Zhdanov et al., 2013).data, and putting sources and receivers closer to the target. To make some prac-tical progress with investigating realistic and cost effective surveys, the followingapproach is taken. Transmitters and receivers locations are restricted to be on thesurface or in boreholes that are likely to exist because they are required for othermeasurements. Even with these restrictions, there are numerous geometries andcombinations that can be used. A selection of these are used to simulate the dataand invert in three dimensions. The efficacy of the survey is evaluated by the de-tail that is observed in the inverted model. In carrying out the inversions, care istaken to ensure that any floor value for assigned uncertainty is at least as large asthe noise floors provided in Table 2.1. It is well-known that the inverse problemis nonunique and that the model recovered from an inversion depends upon thedetails of the inversion algorithm itself. Important details of the inversion method-ology are therefore provided in Chapter 1. All inversions carried out in this chapterfollow the same methodology although different numerical codes are implemented.2.2 Dipole moment-based survey designTwo criteria must be satisfied in order for a survey to provide useful data: (a) theEM fields from a transmitter must have sufficient strength and orientation to couplewith the sought body and generate significant anomalous currents; and (b) receiversmust be close enough and have the correct orientation to detect the anomalousEM fields in the presence of various types of noise. Both of these items can beaddressed, at least to first order, by working with a simplified resistivity model andapproximating the excitation using galvanic and magnetic dipoles.212.2.1 TheoryBeginning with Maxwell’s equations in the frequency domain (Equations 1.5 and1.6), an integral equation is derived for the electric field by following the work byHohmann (1975). The earth is considered to be a halfspace with conductivity σ1that contains a target with conductivity σ2. Ampere’s law is rewritten as:∇×H−σ1E−Ja = Je, (2.3)where the anomalous current density is defined as:Ja = (σ2−σ1)E, (2.4)which only exists inside the target. After taking the the curl of Faraday’s law, thecurl of the magnetic field is isolated on on the right-hand side:∇×∇×E =−iωµo∇×H−∇×Jm (2.5)−1iωµo(∇×∇×E+∇×Jm) = ∇×H. (2.6)Then, Equation 2.6 is substituted into Equation 2.3:−1iωµo(∇×∇×E+∇×Jm)−σ1E−Ja = Je, (2.7)and simplified:∇×∇×E− k2E =−iωµo(Ja+Je)−∇×Jm, (2.8)where k2 = −iωµoσ1 in the ground and k2 = ω2µoεo in the air. The electric fieldcan be expressed in terms of the primary (Ep) and the secondary (Es) field:E = Ep+Es. (2.9)Equation 2.8 is then split into two parts:∇×∇×Ep− k2Ep =−iωµoJe−∇×Jm, (2.10)22∇×∇×Es− k2Es =−iωµoJa. (2.11)The solution to Equation 2.10 is the electric field due to magnetic and electricsources in a halfspace. The solution for Equation 2.11 provides an integral equationusing a dyadic Green’s function G (r,r′) (Tai, 1994):Es(r) =∫vG (r,r′)Ja(r′)dv′. (2.12)The total electric field is then determined by adding the primary electric field backto Equation 2.12:E(r) = Ep(r)+∫vG (r,r′)Ja(r′)dv′, (2.13)In the case where σ2 is a constant, the expression becomes:E(r) = Ep(r)+(σ2−σ1)∫vG (r,r′)E(r′)dv′. (2.14)This expression shows the relationship between the total, primary, and secondaryelectric fields and how they relate to anomalous current density.For simple conductivity distributions, solutions for the electric field can be de-rived (semi-)analytically. For example, the primary electric field Ep in a halfspacedue to a galvanic transmitter with two current electrodes can be easily determinedusing the following analytic expression:Ep(r) =I2piσ1(rA− r|rA− r|3 −rB− r|rA− r|3), (2.15)where the current I = 1 A, and rA and rB are the locations of the two currentelectrodes. In the case of a conducting sphere in a halfspace, the total electric fieldinside the sphere is (Ward and Hohmann, 1988):E =σ2−σ1σ2+2σ1Ep. (2.16)The anomalous current density Ja, which only exists in the target, can be repre-sented by simple dipole moments that summarize the direction and magnitude ofthe current density. The galvanic dipole moment mg points in the same direction asthe currents while the inductive dipole moment mi depends upon the cross-product23of the anomalous currents with their positions:mg =∫vJa(r′)dv′ ≈K∑k=1Jak∆vk, (2.17)mi =12∫vr×Ja(r′)dv′ ≈ 12K∑k=1rk×Jak∆vk. (2.18)K is the number of cells that comprise the anomalous body, ∆vk is the volume ofeach cell, and r is the distance between the anomalous current vector location r′and the centroid location rc: r = r′−rc. The centroid of the anomalous currents isanalogous to the centre of mass of a body and its location is written as:rc =∫v r′|Ja(r′)|dv′∫v |Ja(r′)|dv′≈ ∑Kk=1 r′k|Jak |∆vk∑Kk=1 |Jak |∆vk. (2.19)A stronger dipole moment means the excitation in the anomalous body is greater:this yields larger secondary fields. Therefore, the strength of the dipole momentcan be used as a proxy for the level of excitation in the anomalous body due to agiven transmitter. It is ideal to excite the body from as many directions as possible,thus the azimuthal and elevation angles of the moments are also considered.2.2.2 Application using an exampleSelection of the transmitters is demonstrated with an example using galvanic bore-hole transmitters. A small irregular steam chamber is generated from a 4D seismictime-delay attribute map, which acts as a first-order represenation of steam thick-ness. The attribute map is translated into height (Figure 2.7), and a subset is used asthe steam chamber. The pyramid-shaped anomalous steam chamber (Figure 2.1a)vaires in thickness from 5 to 50 m. It extends 150 m in the easting direction and200 m in the northing direction and lies between 200 and 250 m below the surface.Based on published values of resistivity decreases (Mansure et al., 1993; Tøndelet al., 2014), a value of 10 Ωm is chosen for the steam chamber, which is hosted ina uniform 400 Ωm background. This conductivity model allows for understandingof the inherent challenges of survey design and detectability. Its simplicity alsopromotes fast turn-around times for forward modelling and inversion.24(a) (b)Figure 2.1: (a) A synthetic steam chamber with a pyramidal shape reflects theirregular growth that can occur in SAGD. The chamber has a resistivityof 10 Ωm and is hosted in a 400 Ωm background. (b) A cap rock withthickness of 50 m and a resistivity of 17 Ω m is added above the steamchamber. There is a 10 m gap between the top of the steam chamber andthe bottom of the cap rock.Figure 2.2: A portion of the possible transmitters, after applying a distancerestriction. The blue dots show the electrode positions in the observationwells and the red lines connect the two current electrodes. Continuingthis throughout the pad gives roughly 170,000 transmitters.25An important component of the geologic model is the Clearwater Formationthat acts as a cap to the oil-bearing McMurray Formation. This conductive layerchannels currents from grounded sources and acts as a shield to the sought steamchamber. The layer also acts as an attenuator for any surface inductive source.The Clearwater Formation is added to the initial chamber model. The layer has athickness of 50 m and a resistivity of 17 Ωm. The model in Figure 2.1b shows thecap rock overlying the irregular steam chamber.The steam in Figure 2.1a is approximated by a 25 m radius sphere and sur-rounded by 61 vertical observation wells, as might be used in industry (Zhanget al., 2007). The wells extend from the surface to 400 m in depth and are spreadout equally across a 1 km by 1.5 km area. Each well is populated with electrodes,spaced every 20 m in depth to provide sufficient data coverage. The total 1281electrodes generate 1.6 million galvanic transmitter combinations. A distance re-striction between the electrodes is imposed so they can be in separate but nearbywells, reducing the possible transmitters to approximately 170,000. A portion ofthem are shown in Figure 2.2. For each transmitter, the primary electrostatic fieldis analytically calculated for a halfspace of 400Ωm using Equation 2.15. Then, theanomalous current density for a 10 Ωm sphere is calculated by combining Equa-tions 2.16 and 2.4. Subsequently, the galvanic dipole moment is calculated usingEquation 2.17, where ∆v is the volume of the sphere. In the presence of an electro-static field, there is no inductive dipole moment.The approximately 170,000 galvanic moments are plotted on a unit sphere (Fig-ure 2.3a), which is then divided into n regions of equal area (Leopardi, 2006),where n is the number of desired transmitters; in this example, n= 24. From eachregion, the transmitter that generates the largest moment is chosen. The final trans-mitter thus have large dipole strengths and a good sampling of directions, allowingeach chosen transmitter to uniquely excite the anomalous body. Figure 2.4 showsthe distribution of the 24 selected transmitters. It is noted that the selected trans-mitters lie close to the anomalous body because large dipole moment magnitudeswere favoured. This supports the distance restriction imposed: a large distancebetween current electrodes would give a weak dipole moment and would not beselected using this approach anyway.26(a) (b)Figure 2.3: (a) The roughly 170,000 dipole moments plotted on a unit sphere.The moments cover nearly every direction. The colours indicate themagnitude of the moments, with a larger moment indicating greater ex-citation of the anomalous body. (b) The unit sphere divided into 24equal areas. The blue lines outline each region and the red dots showtheir centre.Figure 2.4: The 24 selected transmitters. The lines connect the two currentelectrodes and their colour references their number from 1 to 24 (forease of visibility). It is clear that the sphere is excited in many direc-tions.27Figure 2.5: Skin depth is a function of resistivity and frequency (Equation2.1, meaning that each frequency samples a different area.2.2.3 DC versus multi-frequencyThe previous example used the DC resistivity formulation, meaning that the fre-quency f is zero. More information can be obtained from the same survey config-uration if multiple frequencies are measured. This is illustrated in Figure 2.5 usingEquation 2.1. To quantify this, the electric field is forward modelled using a sin-gle transmitter at 7 discrete frequencies at the centre of the steam chamber (Figure2.1a) and the secondary current density is calculated. The results are plotted in Fig-ure 2.6 and show that as frequency changes, the secondary current density vectorchanges both in size and direction. This indicates that different frequencies providedifferent information about the subsurface, showcasing that more information canbe collected by moving to multi-frequency EM methods.2.2.4 SummaryThis survey design approach translates easily to time-domain EM or inductivesource EM with the use of numerical forward modelled anomalous currents. De-pending upon the transmitter geometry however, not all regions of the unit spherewill be sampled (i.e. as when using current loops at the surface) because the mo-ment directions are limited. In this example, excitation occurred in many direc-tions because borehole transmitters were used. To address the influence of the cap28(a)(b)Figure 2.6: As frequency increases, the amplitude and phase of the currentdensity changes. This means that more and different information is pro-vided by each transmitter. (a) Current density in the x-direction (left)and y-direction (right) is plotted as as phase (y-axis) vs frequency (x-axis) while colour indicates the amplitude. (b) Alternatively, the cur-rent density can be plotted as real and imaginary vectors for both thex-component (left) and the y-component (right).29rock, the analytically-calculated moments are compared to those calculated nu-merically for a model that includes the cap rock. To first order, the moments aresimilar. Using numerical modelling, the design method can easily be adapted forgeologically-complex models.The dipole-moment survey design approach is used to generate galvanic andinductive surveys to determine the feasibility of electric and EM methods in de-tecting and imaging the small, irregularly shaped steam chamber in the presence ofan overlying conductive cap rock , as shown in Figure 2.1b.2.3 Feasibility study of EM methodsThe feasibility study uses the small, irregular steam chamber generated from a 4Dseismic time-delay attribute map, which was translated into height (Figure 2.7).The resultant resistivity model, shown in Figure 2.1b, is discretized into cubic cellsand different transmitter and receivers are selected and input into the numericalforward modelling. The goal is to detect the existence and details of the steamchamber in the presence of the background geology. This requires two forwardmodellings: one with the chambers and one with just the background geology. Twometrics are defined that can be used to estimate the feasibility of an EM survey todetect the steam chamber: relative and absolute difference anomalies. The relativedifference (RD) addresses whether the secondary field (or the response due to thesteam chamber) is large enough compared with the total field:RD=∣∣∣∣FSFT∣∣∣∣∗100, (2.20)where FT is the total field (electric or magnetic) and FS is the secondary field:FS = FT −FP, where FP is the primary field associated with a conductivity modelthat does not contain the sought anomaly. The absolute difference (AD) addressesthe magnitude of the secondary field:AD= |FS|. (2.21)30It should be larger than the sensitivity of the receiver and larger than various sourcesof noise (e.g., EM noise and geologic noise). The absolute difference can be in-creased by changing some elements of the survey, such as increasing the magni-tude of the transmitter current. However, this will not affect the relative difference,which is dependent on the geology and the transmitter-target coupling.The synthetic irregular chamber is imaged using the following transmitters: (1)borehole galvanic sources, (2) borehole magnetic sources, and (3) large inductivesources at the surface. For each survey, data are forward modelled using a currentof 1 A in the transmitter and the median RD and AD are calculated for each datatype (e.g., the imaginary component of Ez). The average of these values for eachfield is then computed (e.g., the magnetic field), and these are shown in Table2.3. To each forward modelled set, 2% Gaussian noise is added. Uncertaintiesare assigned as a percentage of the data plus a noise floor. The noise floor canbe either (1) a value based on instrument sensitivity or (2) a value such that 10%of the data fall below the noise floor, depending on which is higher. This is donesuch that the noise floor is not unreasonably low and hopefully reflects what mightbe achievable in practice. Table 2.1 lists the instrument sensitivities used for thedifferent measurements. In each 3D inversion, the initial and reference model isthe true background model shown in Figure 2.1b, and for the 2D inversions, a 2Dsection through this model was used. The final misfit for each inversion was at, orclose to, the target misfit.2.3.1 Galvanic sourcesThe conductive cap rock is a major impediment to using grounded sources at thesurface. Numerical experiments showed that too much of the current is channeledinto the cap rock or attenuated as it attempts to propagate through. Therefore, onlysurveys with galvanic sources that are implemented in boreholes are considered.Based on current industry practice, I begin with DC resistivity, using a cross-well survey, which has been used to monitor SAGD steam chambers in two di-mensions (Tøndel et al., 2014). The design consists of a crosswell survey usingfour boreholes, spaced 200 and 300 m apart, that straddle the location of the steamchamber (Figure 2.8a). These locations would be typical for observation wells for310100020003000Northing (m)0 1000 2000 3000 4000Easting (m) 01020304050Steam height (m) Figure 2.7: Seismic time-delay attribute data from multiple SAGD well padswere translated into steam chamber height. A small subset, representedby the rectangle, is used to generate the synthetic irregular steam cham-ber.SAGD operations (e.g., Zhang et al., 2007). Electrodes are placed along the bore-hole every 20 m, for a total of 80 electrodes. This survey provides 98 transmitterswith 40 voltage measurements for each transmitter, for a total of 3920 measure-ments. The data in the 200 m spaced boreholes have a larger RD and AD thanthose in the 300 m spaced boreholes (“Crosswell 200” and “Crosswell 300” in Ta-ble 2.3). This indicates that the data are sensitive to the synthetic steam chamberbut it is noted that closer proximity to the target allows for greater detectability.Each crosswell data set is inverted separately using a 2D inversion algorithm(Oldenburg and Li, 1994). The final models are shown in Figure 2.9b. The modelshave substantial artifacts, especially for the survey where the boreholes are 300 mapart. For the example with a well spacing of 200 m, the anomaly is recovered, butthe resistivity is too high and the shape is not well defined. Given that the steamchamber has a 3D shape, it is difficult to fit a 2D model to these data. Therefore,the two data sets are inverted in three dimensions simultaneously (Haber et al.,2012). The recovered model shows a smooth, compact body with no artifacts (Fig-32DC resistivity surveysSurvey RD: V AD: VCrosswell 200 10.3 0.0054Crosswell 300 4.5 0.0049Crosswell 3D 13.3 0.0037Frequency-domain surveysSurvey RD: E, H AD: E, HGalvanic EM 19, 19 1.2x10−5, 4.0x10−6Borehole loops 47, 9 2.1x10−10, 8.6x10−11Surface loop - surface RX 0.28, 0.19 9.6x10−8, 3.9x10−8Surface loop - borehole RX 38, 5 2.5x10−7, 1.0x10−7Time-domain surface loop survey - borehole RXSurvey RD: ∂B/∂ t(x,y,z) AD: ∂b/∂ t(x,y,z)TC 4 - 30 µs 0.21, 0.70, 0.63 1.2x10−9, 3.4x10−10, 5.6x10−10TC 60 - 600 µs 1.34, 7.21, 1.77 2.4x10−9, 8.2x10−10, 1.9x10−9TC 900 - 6000 µs 2.98, 10.11, 3.84 3.1x10−10, 9.7x10−11, 2.6x10−10Table 2.3: For each survey, the RD and AD are calculated for each data type(e.g., the imaginary component of Ez) at each receiver location usingEquations 2.20 and 2.21. These are then used to calculate a median valuefor each data type. Lastly, the median values are subsequently averagedto get a global RD or AD for the voltage, electric field, or magnetic field.For the time-domain, the median RD and AD for the magnetic flux den-sity are provided for the early, middle, and late time channels (TC).ure 2.9c). However, the steam chamber shape is poorly defined, and the resistivityis much higher than the true value.By designing a 3D survey, the same level of resolution can be achieved butwith fewer transmitters and data. The design approach uses anomalous secondarycurrents of a confined body to select transmitters that will excite the steam chamberin multiple directions and generate substantial secondary fields (Chapter 2.2). There-designed survey has 24 bi-pole transmitters, each using two electrodes, and 124borehole receivers per transmitter which are distributed in six boreholes (Figure2.8b). The electrodes are placed every 20 m down the hole, providing 2976 voltagemeasurements. This is 25% fewer data than the crosswell survey. While the ADvalues are lower for this survey compared to the crosswell survey, the RD values aresubstantially higher (“Crosswell 3D” in Table 2.3). The recovered model is shown33in Figure 2.9d. The resolution of the steam chamber is very similar to the exampleusing the crosswell survey although the resistivity is slightly lower. This shows thatby developing a more appropriate survey design that collects 3D information aboutthe target, similar results can be achieved using fewer data compared to industry-standard survey designs.The model in Figure 2.9d still does not provide enough information to confi-dently identify the anomaly as either a regular or irregular steam chamber. Partof the difficulty is that the inversions are allowing all cells in the 3D volume tovary. The result can be improved upon if the background is fixed and only thecells within the bitumen layer are allowed to change. The background model couldcome from a combination of geophysical surveys and well logs. It is noted that thesurvey design used here to find the steam is not an adequate survey from which toestimate the entire background model.For the following inversion, it is assumed that the background, including thelow-resistivity cap rock, is known. In the inversion, only the resistivity of cellswithin the 60 m thick bitumen layer is allowed to change. The recovered model(Figure 2.9e) has significantly improved, especially in the recovered resistivity,which now reaches a low of 10 Ωm. Nevertheless, the anomaly still cannot beconfidently interpreted as an irregular steam chamber. These examples show thatalthough the data are able to detect the steam chamber with DC sources, there isnot enough information to recover a model with the desired resolution. Therefore,I turn the investigation toward EM methods.2.3.2 Multi-frequency galvanic sourcesBy measuring data at multiple frequencies, more information can be obtained aboutthe subsurface using the same survey design as in the previous section. Seven fre-quencies were chosen, ranging from 1Hz to 10 kHz based on skin depth (Equation2.1) and analyzing the changes in amplitude and phase of the secondary currentsin a confined conductor. The survey geometry remains the same as in the DC re-sistivity experiment (Figure 2.8b) except that the transmitters now operate at sevenfrequencies. Modelling these data requires solving the full Maxwell’s equations,for which a finite volume technique was used (Haber et al., 2004). The data include34both electric and magnetic fields. The RD and AD metrics, shown in Table 2.3 as“Galvanic EM”, indicate that the steam chamber is detectable.The data are inverted in three dimensions with resistivity changes restricted tocells within the bitumen layer. The recovered model (Figure 2.9f) is far superior toany of the inversions that only use DC resistivity data. The irregularity of the steamchamber is imaged: It becomes progressively thinner towards the southwest, andthe depth to the top of the steam increases. Moreover, the chamber manifests itselfas a substantial conductor with resistivity values as low as 2 Ωm. This contrastswith the muted dynamic range of the resistivity recovered in Figures 2.9c and 2.9e.Overall, it is concluded that by using EM data at multiple frequencies and design-ing a 3D survey, important information about the steam chamber’s existence andlocation is obtained.2.3.3 Inductive sourcesTwo forms of inductive sources are of practical significance. The first is a boreholemagnetic source, which is made up of multiple turns of a current wire. The strengthof the source depends upon the area of the coil, the number of turns in the wire, andthe current. The magnetic moment of these sources can vary from 1,000 to 10,000Am2 (Wilt et al., 1995). The other source is a large loop that lies on the surface.Such a source is appealing because the logistics of deploying a surface transmitterare straightforward and anything done on the surface is generally less expensivethan downhole surveys. The drawback is that a surface transmitter is physicallydistant from the target, and hence, the primary field is attenuated by geometry,causing inductive losses before it has the opportunity to excite the target. In thecase of the Athabasca oil sands, which are only a few hundred meters deep, thisdeficit might be overcome.1Each panel shows a cross-section at easting = 50 m and a depth slice at elevation = -215 m, except(b) which shows easting = 50 m and northing = -950 m. (a) True model, (b) 2 2D recovered modelsusing the DC surveys in Figure 2.8a, (c) 3D recovered model using the combined DC survey inFigure 2.8a, and (d) 3D recovered model using the DC survey in Figure 2.8b. In (e)-(j), conductivitychanges are restricted to the bitumen layer between elevations of -200 and -260 m: (e) 3D recoveredmodel using the DC survey in Figure 2.8b, (f) 3D recovered model using the EM survey in Figure2.8b, (g) 3D recovered model using the survey in Figure 2.8c, (h) 3D recovered model using thesurvey in Figure 2.8d, (i) 3D recovered model using the frequency-domain survey in Figure 2.8e,and (j) 3D recovered model using the time-domain survey in Figure 2.8e.35(a) (b) (c)(d) (e)Figure 2.8: (a) Two traditional crosswell surveys straddle the area of inter-est. The survey has 98 current electrode pairs and 40 voltage measure-ments per current electrode pair. (b) This galvanic survey was designedto excite the anomaly in three dimensions. The survey has 24 currentelectrode pairs and 124 receivers per current electrode pair. Electrodelocations are shown as black stars. The lines connect the current elec-trodes. In (c), black dots show the locations of the magnetic dipolesources while gray dots indicate the receiver locations. In (d) and (e),black lines indicate the transmitter loop. Receivers are indicated usingblack dots. In each figure, the location of the irregular steam chamberis shown using a gray sphere.36−375−300−225−150−750Elevation (m)−1100−1000 −900 −800Northing (m) (i)1101 102Ωm−1100−1000−900−800Northing (m)−75 0 75 150Easting (m) (i)2−375−300−225−150−750Elevation (m)−1100−1000 −900 −800Northing (m) (j)1−1100−1000−900−800Northing (m)−75 0 75 150Easting (m) (j)2−375−300−225−150−750Elevation (m)−1100−1000 −900 −800Northing (m) (h)1−1100−1000−900−800Northing (m)−75 0 75 150Easting (m) (h)2−375−300−225−150−750Elevation (m)−1100−1000 −900 −800Northing (m) (g)1−1100−1000−900−800Northing (m)−75 0 75 150Easting (m) (g)2−375−300−225−150−750Elevation (m)−1100−1000 −900 −800Northing (m) (e)1−1100−1000−900−800Northing (m)−75 0 75 150Easting (m) (e)2−375−300−225−150−750Elevation (m)−1100−1000 −900 −800Northing (m) (f)1−1100−1000−900−800Northing (m)−75 0 75 150Easting (m) (f)2−375−300−225−150−750Elevation (m)−1100−1000 −900 −800Northing (m) (d)1−1100−1000−900−800Northing (m)−75 0 75 150Easting (m) (d)2−375−300−225−150−750Elevation (m)−1100−1000 −900 −800Northing (m) (c)1−1100−1000−900−800Northing (m)−75 0 75 150Easting (m) (c)2−375−300−225−150−750Elevation (m)−1100−1000 −900 −800Northing (m) (a)1−1100−1000−900−800Northing (m)−75 0 75 150Easting (m) (a)2−375−300−225−150−750Elevation (m)−1100−1000 −900 −800Northing (m) (b)1−375−300−225−150−750Elevation (m)−75 0 75 150Easting (m) (b)2Figure 2.9Results from feasibility study1.37Small borehole transmittersThe same six boreholes used in the previous example are employed here and thesurvey design approach is used to delineate locations for 29 vertical magneticdipole transmitters (Figure 2.8c). Electric and magnetic fields are forward mod-elled using the same seven frequencies as before and a magnetic dipole moment of1 Am2. The 125 receivers are distributed among the six boreholes in the same loca-tions as in the previous example. The RD values indicate that the steam chamber isdetectable, but the AD values are much lower than those seen in the galvanic exam-ples (“Borehole coils” in Table 2.3). These values are boosted by assuming a muchlarger dipole moment. The data are inverted in three dimensions, and the recoveredmodel is shown in Figure 2.9g. The model nicely recovers the essential shape andthe resistivity of the steam chamber to the same extent as the galvanic example.However, there are subtle differences, which are attributed to the different types oftransmitters.Large surface transmitter: Frequency domainAn ideal cost-effective survey would undoubtedly have both transmitters and re-ceiver combinations located at the surface. Again, multiple transmitter configura-tions are possible to explore, but one of the more likely candidates is a large-looptransmitter because this can provide a high magnetic moment. Here, a transmitterthat is 1 km by 1 km with a current of 1 A is chosen. Surface receivers are placedin a grid with 50 m spacing, for a total of 126 receivers (Figure 2.8d). Five com-ponents (Ex, Ey, Hx, Hy, and Hz) are forward modelled in the frequency domainusing the same seven frequencies used before, which range from 1 Hz to 10 kHz.The RD values, shown in Table 2.3 as “Surface loop - surface RX,” indicate thatthe survey is not very sensitive to the steam chamber. This was confirmed by in-verting the data: The recovered model (Figure 2.9h) is unable to recover the steamchamber.This result is significantly improved by using borehole receivers (Figure 2.8e).Receivers are placed at the same locations in the six boreholes as in previous ex-amples. Electric and magnetic fields are forward modelled at the same seven fre-quencies. The RD and AD values are much higher when using borehole receivers38(Table 2.3 as “Surface loop - borehole RX”), indicating that the steam chamber ismore likely to be detected.The 3D inversion shown in Figure 2.9i is able to nicely recover the steam cham-ber. In fact, this image is similar, but not identical, to the other EM inversions,where the shape and the resistivity of the irregular steam chamber are imaged.2.3.4 Large surface loop transmitter: Time-domainAs a compliment to the frequency-domain experiments considered thus far, the useof time-domain EM is also explored. A major difference between time-domain andfrequency-domain surveys is that time-domain responses are generally measuredafter the current in the transmitter has been shut off. This means that measurementsonly include the secondary response, whereas frequency-domain measurementsinclude both the primary and secondary responses.The survey using the surface transmitter and borehole receivers is repeated.The data correspond to the time-derivative of the magnetic field using a step-offwaveform (Oldenburg et al., 2013). Data are measured at 11 off-time time chan-nels which were chosen using Equation 2.2: 4, 6, 9, 30, 60, 90, 300, 600, 900, 3000,and 6000 µs. The RD values vary for different time channels, with low values forearly times and higher values at middle and late times (“Time-domain surface loopsurvey - borehole RX” in Table 2.3). The AD values are highest for the early timechannels. These metrics indicate that the steam chamber is being detected and thatthe measured time channels capture the majority of the response of the anomaly.The data are inverted in three dimensions, which yields the recovered model pre-sented in Figure 2.9j. The result is similar to the frequency-domain inversion withgood recovery of both the shape and resistivity of the irregular steam chamber.2.4 ConclusionThis chapter examined the feasibility of electric and electromagnetic methods us-ing an irregularly shaped steam chamber. Based on current industry practices, aDC resistivity survey was used first and showed that 3D inversions are essentialto reduce artifacts that can arise if data are inverted in two dimensions. Using asurvey with fewer data, but designed to detect a 3D object, allowed for somewhat39better information to be recovered than traditional crosswell surveys. Nonetheless,the recovered model still lacked resolution in both shape and resistivity amplitude.The major impact of the feasibility study was to illustrate the large benefit ofcarrying out multi-frequency or time-domain EM surveys. In all cases, the combi-nation of borehole receivers with an EM transmitter provided data that were highlysensitive to the steam chamber, and the inversions recovered models with supe-rior resolution in shape and better recovery of the resistivity amplitude. UsingEM methods, it became feasible to distinguish the steam chamber as growing ir-regularly. Of special significance was the result obtained from using a surfacetransmitter and borehole receivers. The receivers for this survey would be similarto those used in crosswell surveys, and can thus be installed permanently in thewells. The transmitter would be a large wire loop at the surface, which is generallyinexpensive to deploy. Because of the utility and cost effectiveness of this survey,it is applied to an example based on an existing field site in Chapter 3.40Chapter 3Three-dimensionalelectromagnetic inversion ofgrowth-impeded SAGD steamchambersThe feasibility results in Chapter 2 show that EM methods can be superior to ERTsurveys in recovery of SAGD steam chambers. It was also noted that costs can bedecreased by using surface methods but that borehole receivers are necessary tomeasure the secondary response. In the SAGD environment, not all receiver typesmay withstand the high heat, but it has been shown that electrodes can be used forlong periods of time (Tøndel et al., 2014). Therefore, in this chapter, a surface looptransmitter is used in conjunction with borehole electrode receivers that measureonly the vertical component of the electric field. This survey is used to image threeSAGD steam chambers in a layered medium that was constructed from well-logsand physical properties from an actual field site.3.1 Site backgroundThe Aspen property is owned by Imperial Oil and is the future site of several SAGDwell pads. The project area lies about 45 km northeast of Fort McMurray and 2541(a) (b)Figure 3.1: (a) Map showing properties and their respective companies. TheAspen property, owned by Imperial Oil, is located roughly 45 NE of FortMcMurray and 25 km SE of Fort McKay in northeastern Alberta. Fig-ure courtesy of Imperial Oil. (b) The eight wells used in this paper areindicated by large dots while other wells are shown as small dots. Themap shows the boundary of the Aspen Property, boundaries for Town-ships 93 and 94 in Range 7, and the sections within those townships.km southeast of Fort MacKay in northeastern Alberta, Canada (Figure 3.1a). Nu-merous vertical wells have been drilled on and around the Aspen property (Im-perial Oil Resources Ventures Limited, 2013). Since many of these are publiclyavailable, eight vertical wells that contain resistivity logging and lithology picksare used (Wynne et al., 1994). Figure 3.1b shows the location of these wells alongwith the other wells within the property.42Figure 3.2: (a) For each of the 8 wells, the top of each lithologic unit waspicked. (b) The elevations of the picks were averaged to get a singlestratigraphic column of the different units. (c) The resistivity logs fromthe eight wells are plotted with the average resistivity for each lithologyunit.433.2 1D modelThe resistivity logging data from the eight wells are first compiled and shown inFigure 3.1b. Horizons were added for the tops of the overlying Quaternary units,the Grand Rapids Formation, the Clearwater Formation (including the WabiskawMember), the McMurray Formation, and the underlying Devonian units (ImperialOil Resources Ventures Limited, 2013; Wynne et al., 1994). Figure 3.2 shows thelithology picks, stratigraphic column, and resistivity log data. For each lithologicunit, the resistivity logging data are averaged to generate a semisynthetic 1D resis-tivity model for the Aspen property. The 1D model is overlain on the resistivitylogging data in Figure 3.2c.At the Aspen property, the oil saturation is approximately 80% for the McMur-ray Formation with an average porosity of 33% (Imperial Oil Resources VenturesLimited, 2013). Density is reported as 2.65 g/cm3, the cementation exponent mas 1.8, and the saturation exponent n as 1.7. The background temperature at theAspen property is 7◦C. A tortuosity value of 1.63 was used (Bell et al., 2011).A clay volume of 1% and a cation exchange capacity of 0.25 meq/g for the Mc-Murray Formation are assumed while 60% and 0.4 meq/g, respectively, are usedfor the Wabiskaw Member (S. Charles, personal communication, 2012). Salinitieswere estimated as 2,460 and 530 ppm for the McMurray Formation and WabiskawMember (Imperial Oil Resources Ventures Limited, 2013). Applying these param-eters to the Waxman-Smits equation (Equations 1.25-1.27 in Chapter 1), a resis-tivity of 147 is calculated Ωm for the McMurray Formation and 46 Ωm for theWabiskaw Member. These values match with those from the resistivity well logs.3.3 Modelling steam chambersThe formulation by Reis (1992) and Reitz et al. (2015) to generate a series of steamchambers is adapted:Ws = tH√2/a, (3.1)whereWs is the half-width of the steam chamber, H is the vertical distance betweenthe top of the steam chamber and the producing well, a = 0.4 is a dimension-less temperature coefficient, and t = 0.25 is a dimensionless time since production44started. This example uses three chambers with a height of 35 m. Each chamber is400 m in length and is separated by 100 m at the base.For this investigation, salinity and saturation are kept constant over time. Thetemperature will radiate outwards from the steam chamber and thus alter the con-ductivity of the surrounding geology. Here, the temperature distribution describedby Reis (1992) is used and formulated as a function of radial distance d from thesteam chamber:T (d) = T0+(Ts−T0)e− aUdα , (3.2)where T0 is the initial reservoir temperature, Ts is the steam temperature, U is thesteam front velocity, and α is the temperature diffusivity. The constant a = 0.4 isthe same as in Equation 3.1. For this problem, the temperature diffusivity is 0.0507m2/day, the steam front velocity is 0.0417 m/day, and the steam temperature is200◦C. Figure 3.3a shows a cross-section of the temperature distribution throughthe three steam chambers.Given the initial resistivity values (Figure 3.2), the resultant resistivity due tothe change in temperature is calculated using the Waxman-Smits equation (Equa-tions 1.25-1.27 in Chapter 1). Instead of a constant initial temperature, the 3Dtemperature distribution calculated in Equation 3.2 is used. The calculated resis-tivity within the steam chambers is 16 Ωm, which then diffuses back to the back-ground value away from the chambers. A cross-section of the 3D resistivity modelis shown in Figure 3.3b while a plan-view section is shown in Figure 3.4a. Becauseheterogeneity can cause steam chambers to not grow properly, a blockage is addedto the middle steam chamber, impeding the steam growth. The blockage is 100m long and is surrounded by 50 m of steam to the south and 250 m of steam tothe north. Figure 3.4b shows the perturbed steam chamber resistivity model. Overtime, the SAGD steam chambers grow upwards and outwards. This is modelled byusing Equation 3.1, where the height H is now 50 m. Some growth (H = 20 m) isallowed in the location of the blockage. This model is shown in Figure 3.4c.45200300400500Elevation (m)0 100 200 300 400Easting (m) 101102°C(a)200300400500Elevation (m)0 100 200 300 400Easting (m) 104580115150Ωm(b)Figure 3.3: (a) Cross-section of the 3D temperature distribution within thereservoir for three synthetic steam chambers. (b) Cross-section of the3D resistivity model based on resistivity log data and the Waxman-Smitsequation.3.4 Steam chamber imaging using surface looptransmittersIn Chapter 2, it was shown that it is possible to excite a steam chamber with alarge surface loop carrying harmonic waveforms at different frequencies. Here,two surface transmitters are employed: one to the east of the chambers and theother to the north. Each transmitter is 1 × 1 km (Figure 3.5). Because of thegeometry, the EM fields couple differently with the steam chambers, and hence,the two surveys provide complementary information.The models in Figures 3.4a, 3.4b, and 3.4c are investigated for three scenarios:(1) using the eastern transmitter, (2) using the northern transmitter, and (3) usingboth transmitters. The receiver locations are restricted to observation wells thatwould be routinely drilled. Figure 3.5 shows the locations of the 22 wells in relationto the transmitters and steam chambers. Although in principle, all components ofthe electric and magnetic fields can be measured in the boreholes, here the dataare restricted to a single type: the vertical component of the electric field. Tøndelet al. (2014) discussed that due to the high temperature environment for SAGDprocesses, certain instruments fail over time but they were able to successfully useelectrodes in boreholes for multiple years. Therefore, only the vertical component460100200300400500600Northing (m)(a)250300350Elevation (m)0 100 200 300 400Easting (m) (b)0 100 200 300 400Easting (m) 1030507090110130150ΩmFigure 3.4: (a) True model showing three steam chambers. (b) True modelshowing three chambers where the center chamber is impeded due to ablockage. Each panel shows a depth slice 215 m below the surface and across-section of the reservoir at a northing of 250 m. In plan view, whitedots denote borehole locations and the white line indicates the locationof the cross-section. The borehole locations in the cross-section areindicated using white dots.of the electric field is used in the following examples. Receivers are spaced every20 m in the observation wells,, except in the bitumen reservoir where there arereceivers at every 5 m. Three frequencies (10, 50, and 100 Hz) were chosen basedon skin depth (Equation 2.1) and the average resistivity of the layers above theMcMurray Formation.For each model and each survey, the z-component of the electric field is for-ward modelled at each frequency and 2% Gaussian noise is added to the data. Un-certainties are assigned as a percentage of the data and a noise floor before the dataare inverted in three dimensions using the code described in Haber et al. (2012).47Figure 3.5: Two surface transmitters, each 1 km by 1 km, at the surfaceare used individually and simultaneously to recover three SAGD steamchambers. For each survey, the z-component of the electric field is mea-sured at receivers in boreholes (dots) that surround the three horizontalwells (black lines). Each borehole has 33 receivers, spaced every 20 m.Receivers are spaced every 5 m in the bitumen reservoir.For each inversion, the background 1D model was used as the initial and referencemodel. Resistivity changes are limited to the heavy oil reservoir between elevationsof 263 and 318 m. Because the steam is expected to decrease the resistivity, the re-sistivities in the recovered model were limited to be no higher than 147 Ωm, whichwas the assumed resistivity of the McMurray Formation. The model smoothness inthe direction of the horizontal well pairs, for which the orientation is well known,is increased by increasing αy in Equation 1.14. For each inversion, the followingparameters are used: αs = 1e-5, αx = αz = 1, and αy = 10.3.4.1 Example with non-perturbed chambersThe model shown in Figure 3.4a is considered first. For each transmitter, the RDand AD values are calculated using Equations 2.20 and 2.21 in Chapter 2. Table48Non-perturbed steam chambers - Compared to 1D modelSurvey RD ADEast TX 72 4.5x10−8North TX 45 2.4x10−8Perturbed steam chambersCompared to 1D model Compared to non-perturbed modelSurvey RD AD RD ADEast TX 76 4.8x10−8 8 6.1x10−9North TX 51 3.3x10−8 1.6 1.1x10−9Table 3.1: For each survey, the median RD and AD are calculated for thez-component of the electric field. These metrics show that the easterntransmitter is more sensitive to the steam chambers and the nonsteamedblockage.3.1 presents the median values. These metrics show that the steam chambers aremuch more detectable using the eastern transmitter compared with the northerntransmitter. This is attributed to different coupling between the transmitter andsteam chambers. When the primary electric field is parallel to the main axis of thesteam chambers (as when using the eastern transmitter), there are major currents inthe north-south direction. That is, there is good coupling with the steam chambers.For the northern transmitter, the primary electric fields are in the east-west directionand currents are forced through a succession of resistive and conductive regions.To quantify this, the secondary current density is calculated for these two sur-vey designs (as done in Chapter 2), where the anomalous conductivity consistsof the three steam chambers. For the eastern transmitter, the anomalous currentsare substantial and point predominantly in the northern direction; whereas for thenorthern transmitter, the currents point in the eastern direction. Figures 3.6a and3.6d show the secondary current density for the eastern and northern transmitter,indicating that the excitations from the two surveys are perpendicular and that theexcitation is greater closer to the respective transmitter. In addition, the currentdensity due to the eastern transmitter is larger than currents due to the northerntransmitter. This shows that the amount of excitation differs but that complemen-490100200300400500600Northing (m)                                                                                                                                 (a)                                                                                                                                     (b)                                                                                                                                                                                   (c)0100200300400500600Northing (m)0 100 200 300 400Easting (m)                                                                                                                                                                                       (d)0 100 200 300 400Easting (m)                                                                                                                                                                               (e)10−9 10−8 10−7 10−6A/m^20 100 200 300 400Easting (m)                                                                                                                                                                                                   (f)Figure 3.6: The top and bottom rows show the secondary currents for theeastern and northern transmitters, respectively. Panels (a) and (d) showthe secondary currents between the background 1D model and the un-perturbed model with 3 steam chambers (Figure 3.4a). Panels (b) and (e)show the currents between the background 1D model and the perturbedmodel (Figure 3.4b). Panels (c) and (f) show the secondary currents inthe blockage using the perturbed and unperturbed 3D models.tary information is being provided by the two transmitters. From this, it is expectedthat the eastern transmitter will provide a better inversion result than the northerntransmitter, whereas, a simultaneous inversion of both will yield the best result.These analyses are supported by the inversions of the data. Plan view and cross500100200300400500600Northing (m) (c)250300350Elevation (m)0 100 200 300 400Easting (m) 10 30 50 70 90 110 130 150Ωm (d)0 100 200 300 400Easting (m)  (b) 0100200300400500600Northing (m) (a)250300350Elevation (m) Figure 3.7: (a) True model showing three regular SAGD steam chambers.Recovered models using Ez data and αy = 10 from (b) the eastern trans-mitter, (c) the northern transmitter, and (d) both transmitters. Each panelshows a depth slice 215 m below the surface and a cross-section of thereservoir at a northing of 250 m. In plan view, white dots denote bore-hole locations and the white line indicates the location of the cross-section. The borehole locations in the cross-section are indicated usingwhite dots.51sections of the 3D recovered models for the eastern and northern transmitters areshown in Figures 3.7b and 3.7c. The first major observation is that the overall lo-cation of the steam chambers is well-imaged horizontally. More detailed scrutinyshows that the inversion model from the eastern transmitter suggests that there aretwo major north-south conductors. The eastern-most conductor is colocated withthe eastern steam chamber, but the other conductor is a blurred image of the centraland western chambers. Its maximum value lies midway between the two chambers,close to the observation wells. This blurring is a consequence of the transmitter be-ing on the eastern side. The primary currents from the transmitter are weakened onthe west side, compared with the east, because they are farther from the transmitterand some shielding arises from the eastern-most chamber. A second transmitter onthe west would help to overcome this difficulty. So too would a transmitter locatedat the northern or southern end of the steam zones. The northern transmitter is cho-sen as a second transmitter because it excites the steam chambers from a differentdirection. The northern transmitter generates a weaker conductivity anomaly, butis has better delineation of the three chambers. The conductivity highs, althoughsomewhat subtle, are colocated with the steam chambers. Figures 3.7b and 3.7cshow plan view and cross sections for recovered conductivity. Rather good hori-zontal resolution is observed, but there is little vertical resolution.A simultaneous inversion of data from both transmitters is shown in Figure3.7d. The image is considerably enhanced compared with either of the individ-ual inversions. The three chambers are now high-amplitude structures located intheir correct horizontal location. These inversion results show that excitation in thesteam chambers highly depends on the location of the transmitter and that anoma-lous currents and metrics about data differences can be used to predict the sensitiv-ity to the steam chambers before inversion. It is noted that these images were gen-erated with only minimal a-priori information, restricting the steam chambers to bepreferentially oriented in the north-south direction. Additional known information,such as fixing the conductivity around the observation wells or incorporation ofsensitivity weighting to push the recovered model away from the observation loca-tions, was not included. Doing so can provide results with enhanced resolution andis explored in a later section of this chapter, but the goal here is to generate a modelthat is controlled as much as possible by the EM data and relies only minimally52upon a priori information.3.4.2 Example with a perturbed chamberDuring SAGD processes, a steam chamber may not grow as expected due to reser-voir heterogeneity, which blocks the steam from penetrating through the reservoir.Thus, an example where the middle chamber has such a blockage is also consid-ered (Figure 3.4b). For each transmitter, median RD and AD values are calculatedto evaluate the potential effectiveness of the surveys. The results are tabulated inTable 3.1. The metrics are first compared using the earth containing the perturbedsteam chamber and the 1D background. Those results are comparable, but slightlylarger, than the metrics for the previous inversion where the steam chambers werecontinuous. The RD and AD are next evaluated assuming the background modelis the continuous steam chamber embedded in a 1D background, and the model ofinterest is the same conductivity model with a blockage. The metrics are consider-ably reduced but the values are large enough to infer that the two steam chambermodels, one with and one without the perturbation, should be distinguishable fromthe data. For both transmitters, the secondary current density is calculated for theblockage compared to the 1D background model (Figures 3.6b and 3.6e) and theunperturbed model (Figures 3.6c and 3.6f). This again indicates that the two trans-mitters provide complementary information about the subsurface.The data for the two transmitters are inverted individually, and the results areshown in Figures 3.8b and 3.8c. The blocked region is visible in both. The resultsfrom the eastern transmitter contain some of the features shown in Figure 3.7bcorresponding to an unblocked chamber. At the northern end, the high conductivityis mislocated over one of the observation wells; that is, it is between the two steamchambers. Nevertheless, the location and recovered conductivity of the blockedregion are very well recovered. The image from the northern transmitter displaysmany of the characteristics in Figure 3.7c, but it too clearly shows the blocked area.The results are further improved by simultaneously inverting data from bothsurveys. Figure 3.8d shows better resolution and recovered resistivity of the threesteam chambers with improved imaging of the blockage. Again, there is little ver-tical resolution, but the high conductivities fan out towards the top of the reservoir530100200300400500600Northing (m) (c)250300350Elevation (m)0 100 200 300 400Easting (m) 10 30 50 70 90 110 130 150Ωm (d)0 100 200 300 400Easting (m)  (b) 0100200300400500600Northing (m) (a)250300350Elevation (m) Figure 3.8: (a) True model showing three steam chambers where the centrechamber is impeded due to a blockage. Recovered models using Ez dataand αy = 10 from (b) the eastern transmitter, (c) the northern transmitter,and (d) both transmitters. Each panel shows a depth slice 215 m belowthe surface and a cross-section of the reservoir at a northing of 250 m.In plan view, white dots denote borehole locations and the white lineindicates the location of the cross-section. The borehole locations in thecross-section are indicated using white dots.54as they do in the true model.3.5 Cascading time-lapse inversion for growing steamchambersThe previous example recovered the steam chamber at a particular time during thesteaming process. As SAGD chambers grow over time, this section investigatesthe recovery of the conductivity changes as the model changes. Of interest is de-termining if the inversion can recover smaller steam chamber (i.e., at earlier times)and if the perturbation can be imaged at both earlier and later times. This providescritical information about the ability of EM to monitor relatively small changes involume in the steam chambers.Using Equation 3.1, two additional time-steps are generated: one before andone after the perturbed model shown in Figure 3.4b. The three time-steps are shownin Figure 3.9. At the earliest time, the chambers are 20 m in height and 11 m wideat the top. The blockage seen in the previous section exists at this time-step. Themiddle time-step is the same model used in the previous section and has chambersthat are 35 m high and 20 m wide at the top. The final time-step shows steamchambers that have grown to the top of the reservoir, are 50 m in height, and 28 mwide. In addition, some steam now penetrates through the blockage.The data are forward modelled in the same manner as before: using the easternand northern transmitter shown in Figure 3.5. Only the vertical component of theelectric field is used in the inversions. The same inversion parameters as beforeare used, including directional smoothing in the northing direction and limited cellchanges to the reservoir. However, instead of using the background geologic modelas the initial and reference model, cascading time-lapse inversion is now applied.In cascading time-lapse inversion, an initial inversion is used to recover a back-ground model. This model is then used as the initial and reference model in theinversion for the subsequent time-step. The benefit of this is that previously re-covered structures are retained and the computation time is reduced compared tostarting with a halfspace initial and reference model. Cascading inversion is re-55flected in the model objective function (Equation 1.15) and rewritten as following:φm(m) = αs||Ws(mt −mt−1)||22+3∑i=1αi||Wi(mt −mt−1)||22, (3.3)where mt and mt−1 are the recovered models for the current and previous time-steps, respectively.The recovered models from inverting the three time steps using cascaded time-lapse inversion when using the eastern, northern, and both transmitters togetherare shown in Figure 3.10. As expected from the previous inversions, the easterntransmitter allows for better recovery of the resistivity values for all three time-steps but the western two chambers appear as a larger conductor. Alternatively, therecovered models using the northern transmitter have higher recovered resistivityvalues but the three chambers are distinguishable. Using either transmitter, theblockage is imaged nicely. The best results use the combined eastern and northerntransmitter survey, as expected.The impact of this is two-fold. First, the results show that the survey is sen-sitive even to small steam chambers and thus allows the survey to be useful fromthe moment SAGD steaming starts. Secondly, the survey clearly detect relativelysmall changes in steam chamber growth, as shown by the recovery of the middlechamber at the late time-step. This experiment indicates that the combination ofsurface transmitters and borehole receivers can provide updates about steam cham-ber growth over time and that 3D inversion of the data can readily recover changesin the chambers.1Each panel shows a depth slice 215 m below the surface and a cross-section of the reservoirat a northing of 250 m. The top row shows the results from time-lapse inversion using the easttransmitter while the middle row shows the results using the northern transmitter. The bottom rowuses both transmitters and clearly shows better recovery of the 3 chambers than the first and secondrow. The true models are shown in Figure 3.9. White dots denote borehole locations and in planview, the white line indicates the location of the cross-section.560100200300400500600Northing (m)(a)250300350Elevation (m)0 100 200 300 400Easting (m) (b)0 100 200 300 400Easting (m) (c)0 100 200 300 400Easting (m) 1030507090110130150ΩmFigure 3.9: True models at three time-steps: (a) early time where the cham-bers are 20 m high and 11 m at their widest, (b) middle time wherethe chambers are 35 m high and 20 m at their widest, and (c) late timewhere the chambers are 50 m high and 28 m at their widest. In (c),steam has penetrated through the blockage and grown to a height of 20m and width of 11 m. Each panel shows a depth slice 215 m below thesurface and a cross-section of the reservoir at a northing of 250 m. Inplan view, white dots denote borehole locations and the white line in-dicates the location of the cross-section. The borehole locations in thecross-section are indicated using white dots.3.6 Improving the recovered model using a-prioriinformationIn the previous sections, only minimal a-priori information was used as the goalwas to generate models that are controlled as much as possible by the EM data.Additionally, the data only consisted of one component of the electric field. Fur-ther improvements are made by adding additional information, such as increasedamounts of data or incorporation of sensitivity weighting to push the recoveredmodel away from the observation locations.3.6.1 Adding additional dataIn the previous sections, only the vertical component of the electric field was in-verted. This provided nice results that delineated the three steam chambers and theblockage (Figure 3.8). By using all three components of both the electric and mag-570100200300400500600Northing (m)(a)250300350Elevation (m) (b) (c) 0100200300400500600Northing (m)(d)250300350Elevation (m) (e) (f) 0100200300400500600Northing (m)(g)250300350Elevation (m)0 100 200 300 400Easting (m) 10 30 50 70 90 110 130 150Ωm(h)0 100 200 300 400Easting (m) (i)0 100 200 300 400Easting (m) Figure 3.10: Results from cascading time-lapse inversion. 158netic field at the same locations, the chambers are better resolved. The inversionparameters are the same as used before and the inversion use the eastern, northern,and both transmitters. The results are shown in Figure 3.11. An immediate im-provement is seen for the eastern transmitter: compared to just using Ez, each ofthe three chambers can now be identified. Thus, the addition of more data compo-nents but only one transmitter (Figure 3.11b) provides better results than using twotransmitters with one data component (Figure 3.8d).Figure 3.11c shows the result using the northern transmitter, which has muchbetter defined edges at the south end of the chamber compared to Figure 3.8c. Inaddition, there is a much better distinction between the chambers. The combinedsurvey using both transmitters lends the best results (Figure 3.11d), exhibiting thelower resistivity values seen in Figure 3.11b and the well-defined chamber edgesin Figure 3.11c. A major improvement by using multiple components and fieldsis the horizontal separation, recovering three distinct chambers and less blurring atthe blockage. Vertical resolution remains relatively unchanged and will likely onlyimprove by adding additional receivers to the reservoir layer.However, collecting 3-component magnetic and electric fields may not be fea-sible long-term in the field. The high-temperature environment, especially at latertimes, can destroy equipment (Tøndel et al., 2014).3.6.2 Apply distance weightingGiven that the vertical observation wells also contain temperature sensors, SAGDoperators can know if and when the steam chamber has reached a particular well.In this example, it is assumed that it is known the chambers do not reach the verticalboreholes. To push resistivity changes in the inversion away from the vertical wells,distance weighting can be applied to the model objective function (Equation 1.15in Chapter 1). Distance weighting w is defined as following:w(r j) =1√v j(N∑i=1[∫∆v jdv(Ri j+R0)τ]2)1/4, (3.4)where v j is the volume of the jth cell, Ri j is the distance between a point in themesh and jth observation location (r j), R0 is a small constant such that the integral590100200300400500600Northing (m) (c)250300350Elevation (m)0 100 200 300 400Easting (m) 10 30 50 70 90 110 130 150Ωm (d)0 100 200 300 400Easting (m)  (b) 0100200300400500600Northing (m) (a)250300350Elevation (m) Figure 3.11: (a) True model showing three steam chambers where the centrechamber is impeded due to a blockage. Recovered models using E andH data and αy = 10 from (b) the eastern transmitter, (c) the northerntransmitter, and (d) both transmitters. Each panel shows a depth slice215 m below the surface and a cross-section of the reservoir at a nor-thing of 250 m. In plan view, white dots denote borehole locations andthe white line indicates the location of the cross-section. The boreholelocations in the cross-section are indicated using white dots.600100200300400500600Northing (m) 250300350Elevation (m)0 100 200 300 400Easting (m) 10−310−210−1100Figure 3.12: Distance weights are used to force resistivity changes away fromthe borehole locations. The panel shows a depth slice 215 m below thesurface and a cross-section of the reservoir at a northing of 250 m.remains well-behaved, τ is a constant that defines the rate of decay, and N is thenumber of observation locations.To calculate distance weights for the model shown in Figure 3.4a, the followingvalues were used in Equation 3.4: τ = 7 and R0 = 0.25. The resulting weights fileplaces a high weight at the location of the vertical observation wells and decays toa very small weight as distance from the well increases (Figure 3.12). The weightswere incorporated into the inversion using all electric and magnetic data (Figure3.13) for the eastern, northern, and both transmitters. The results are similar tothose obtained when the weighting was not included but the resistivity changes arefurther from the boreholes and the chambers exhibit sharper edges.While other values of τ and R0 were explored, this combination restricted theinversion from allowing resistivity changes directly at the borehole but changesclose to the borehole were still permitted. If τ is smaller, the recovered steamchambers snaked between the boreholes, which was deemed as not a realistic re-sult. Overall, the results using weights did not add significant improvements andbecause of uncertainty in steam chamber location, this type of a priori informationis not favoured.610100200300400500600Northing (m) (c)250300350Elevation (m)0 100 200 300 400Easting (m) 10 30 50 70 90 110 130 150Ωm (d)0 100 200 300 400Easting (m)  (b) 0100200300400500600Northing (m) (a)250300350Elevation (m) Figure 3.13: (a) True model. Recovered models are shown from invertingall electric and magnetic data using αy = 10 and distance weights for(b) the eastern, (c) the northern, and (d) both transmitters. Each panelshows a depth slice 215 m below the surface and a cross-section ofthe reservoir at a northing of 250 m. In plan view, white dots de-note borehole locations and the white line indicates the location of thecross-section. The borehole locations in the cross-section are indicatedusing white dots.623.7 ConclusionIn this chapter, I applied a survey using large surface loop transmitters and bore-hole receivers to a synthetic example based on a site in the Athabasca oil sands.The data were limited to the vertical component of the electric field, which can bemeasured by electrodes within observation wells. The benefit of this configura-tion is that the electrodes can withstand the high-temperature SAGD environment,and the loop transmitters are easily deployed at the surface. The use of two trans-mitter configurations were examined, which were chosen because they generatedorthogonal excitation within the reservoirs.Although each survey provided valuable information about the conductivity,models from an individual survey are prone to artifacts. It was shown that invert-ing data from two transmitters substantially reduces these artifacts and producesan enhanced resolution image. These transmitters provided perpendicular excita-tion of the target and it is noted that additional strategically placed transmitterscould further improve recovery of the chambers. For this study, the location andextent of the no-growth area were discernible using two transmitters. However, thevertical resolution of conductivity in the bitumen layer was fairly poor using thisconfiguration. Further development of the survey design could improve this.Furthermore, the availability of a priori information can greatly enhance thefinal result. In these examples, limiting resistivity changes to the reservoir andproviding directional smoothing based on the orientation of the horizontal wellshelped the inversion provide better images. This type of information would beavailable during SAGD operations and can therefore be easily incorporated wheninverting field data. One downside of these constraints is that the focus is on thereservoir layer and any other changes occurring (such as changes in the cap rock)will not be adequately imaged. Additional improvement can be obtained by work-ing with more detailed background models, constraining the conductivity of themodel around the observation locations, and adding in other a priori informationthat might be available. In the first examples shown, the amount of constraintsapplied to the inversion was limited to focus on the ability of the EM data to re-cover the steam chambers. Later examples showed how additional constraints andinformation can improve the inversion results to a certain extent.63Surveys as those used here can readily be used to monitor the SAGD steamchamber growth over time and at greater frequency than typical surface seismicsurveys. As EM methods are further researched to understand how they can be usedto monitor SAGD processes it will become important to consider the infrastructureat the surface and within the reservoir. The cased injector and producer wellswill generate an EM signal, and further research is required to understand theirimpact on detecting the steam chamber. Also, infrastructure noise will need to becontended with. Some of these issues can be handled through time-lapse inversiontechniques. Cascading time-lapse inversion was used here to invert multiple EMdata sets over time and characterize the steam chamber growth, providing severalinterpretations per year, and thus, better oversight of the SAGD process.Overall, the ability to permanently install transmitters and receivers means datacan be collected often and remotely. Combined with efficient inversion techniquesand a priori information, these EM methods allow for fast turn-around and practi-cally real-time results. This can greatly impact monitoring capabilities when com-bined with less-frequently collected seismic surveys for better management andplanning of SAGD production in the Athabasca oil sands.64Chapter 4Application of sensitivity analysisin DC resistivity monitoring ofSAGD steam chambersResearch and pilot programs have shown that steam chamber growth can be de-tected and monitored using electrical methods, due to a decrease in electrical re-sistivity from the steaming process. In this chapter, surveys currently in-practiceare analyzed using the sensitivity of the data to model perturbations. I show thatthese surveys have limited sensitivity to important regions of the reservoir, and thatsome steam chambers therefore cannot be recovered using inversion. The sensi-tivity analysis provides a computationally fast and inexpensive approximation ofwhat a full inversion can recover, making it ideal in survey design studies. Givena specific field site, sensitivity analysis is used to better understand survey designand improve model recovery using multi-frequency electromagnetic methods.4.1 IntroductionThis chapter focuses on a field site at the Leismer Demonstration Area, which islocated in the Athabasca oil sands in Alberta, Canada. The area is approximately100 km south of Fort McMurray and 120 km north of Lac La Biche. In one ofthe SAGD well pads, two vertical boreholes were drilled to monitor SAGD steam65chamber growth using crosswell seismic, vertical seismic profiling, and crosswellDC resistivity. The two vertical boreholes straddle two horizontal injector and pro-ducer pairs as shown in Figure 4.1. DC resistivity data were collected twice a dayusing multiple survey orientations for four years (Tøndel et al., 2014). The resultsindicated a 85% decrease in resistivity due to the growth of two steam chambersover a two-year period.Chapter 2 focused on survey designs based on simple resistivity models and an-alytic solutions to determine the feasibility of electrical and electromagnetic meth-ods to detect and image SAGD steam chambers. A well-designed survey is able toprovide detailed information about the region of interest such that the steam cham-bers can be recovered using inversion. Chapter 2 largely validated the differentsurveys by inverting the data and qualitatively evaluating how well the anomalywas recovered. However, three-dimensional inversions are computationally costlyand take time. It would be ideal to have an established idea of what an inversioncan recover prior to running it. This chapter, therefore, investigates the use of thesensitivity matrix as a proxy for determining model resolution from a given sur-vey design. The focus is on currently in-practice crosswell DC resistivity surveysused to monitor SAGD steam chambers. To validate the results, DC resistivity dataare inverted in three dimensions, indicating that the sensitivity analysis provides afast and computationally inexpensive method to judge a particular survey designwithout resorting to full inversions.Two scenarios are explored. The first mimics the resistivity changes publishedby Tøndel et al. (2014) and shows similar results. The second scenario uses asteam chamber in a shifted location and indicates the result of a lack of sensitivityto the entire region which can result in misinterpretation. To address the variabil-ity of sensitivity in the reservoir using crosswell DC resistivity, multi-frequencyelectromagnetics is investigated to adequately recover the steam chambers in bothscenarios. Finally, the DC resistivity and EM surveys are compared for a time-lapsescenario with growing steam chambers.664.2 Geology and surveysI first generate a synthetic time-lapse resistivity model using the geology and acqui-sition parameters at the Leismer Demonstration Area. A background layered earthmodel is created with six distinct layers, based on the model from Tøndel et al.(2014) (Figure 4.1). A Quaternary-aged glacial layer extends from the surface at650 m to approximately 340 m and is modelled using a resistivity of 20 Ωm. Be-low the Quaternary lies the shale-rich Clearwater Formation and acts as a cap rockfor the SAGD process. The Clearwater Formation is modelled as an 80 m thicklayer with a resistivity of 5 Ωm. The McMurray Formation, which is the main oilreservoir, lies below the cap rock and is comprised of multiple sections. The topand bottom sections, both modelled as 20 Ωm, are approximately 30 m thick. Themiddle section contains the growing steam chambers and has a thickness of 30 m.The resistivity of this section is substantially higher and is modelled as 200 Ωm.Below the McMurray, a Devonian limestone unit is modelled as 50 Ωm and startsat an elevation of 170 m.The same well configuration as in Tøndel et al. (2014) is used: two verticalobservation wells sit between the horizontal wells, as shown in Figure 4.1. Thetwo vertical wells are 150 m apart. The horizontal separation between each pair ofthe horizontal wells is 100 m while each horizontal well pair lies at an elevation ofapproximately 210 m.The observation wells reach the surface at an elevation of 650 m but the instru-mentation within the wells is restricted to elevations between 400 and 100 m. Theelectrodes are spaced every 13.5 m down each well, except in the middle McMur-ray Formation where they are placed every 7 m. The four surveys, shown in Figure4.2, consist of (1) 169 transmitters and 5,352 data, (2) 174 transmitters and 16,928data, (3) 125 transmitters and 8,640 data, and (4) 274 transmitters and 17,088 data.Transmitters are placed both across the two vertical wells and along the same ver-tical well in all surveys except Survey 2, which only has crosswell transmitters.Survey 4 is identical to Survey 2, except for the addition of 100 along-well trans-mitters. In addition, Survey 4 (the largest survey) has 54 and 82 transmitters incommon with Surveys 1 and 3, respectively. Receiver electrode pairs use the sameconfiguration as the transmitters and measure the potential difference.67100150200250300350400450500550600650Elevation (m)−200 −100 0 100Easting (m) 101102ΩmFigure 4.1: Cross section at a northing of 0 m through the 3D resistivitymodel for the Leismer Demonstration Area. Two observation wells arelocated at 0 and -150 m in the easting direction. The wells containelectrodes (black dots). The horizontal injector and producer well pairs(black circles) are at -230 m, -130 m, -30 m, and 70 m. in the eastingdirection.68Figure 4.2: Four DC resistivity surveys were collected daily at the LeismerDemonstration Area to monitor steam chamber growth. Black dots in-dicate electrode locations. Grey lines connect transmitter electrodes forcrosswell transmitters. Surveys 1, 3, and 4 also have along-well trans-mitters (not shown).Two scenarios are explored using the crosswell surveys. In the first scenario,four steam chambers are added to the middle McMurray Formation at the locationsof the horizontal well pairs and have a resistivity of 20 Ωm. The chambers growover time, starting from the horizontal well elevation of 205 m. This provides fivetime steps:• Time 0: No steam is present• Time 1: Chambers are 5 m by 5 m in the easting and vertical direction,respectively.• Time 2: Chambers are 10 m by 10 m.• Time 3: Chambers are 20 m by 15 m.• Time 4: Chambers are 30 m by 25 m.69150200250300Elevation (m)Time 1 Time 2150200250300Elevation (m)−200 −100 0 100Easting (m)Time 3−200 −100 0 100Easting (m)Time 4101102ΩmFigure 4.3: Four steam chambers are added to the background geology (Fig-ure 4.1). The steam chambers grow over time in the easting and verticaldirections. The chamber sizes are: Time 1 - 5 m by 5 m, Time 2 - 10m by 10 m, Time 3 - 20 m by 15 m, and Time 4 - 30 m by 25 m. Thechambers extend 280 m in the northing direction, centred at a northingof 0 m. Black dots indicate the electrodes in the two vertical wells.The modelled chambers have a length of 280 m in the northing direction, where thecentre is aligned with the vertical wells at a northing of 0 m. The four time-stepsare shown in Figure 4.3. In the second scenario, the inner right chamber is centredat an easting of -80 m, compared to -30 m in the first scenario. Figure 4.4 showsthe two scenarios for Time 3.4.3 Estimation of the sensitivityThe DC resistivity problem is nonlinear and the inverse problem is solved by min-imizing an objective function (Equation 1.12). The optimal solution to the inverseproblem is found when the derivative of the objective function is set to zero, givingrise to the sensitivity matrix J, as defined in Equation 1.20 and repeated here:J =∂F [m]∂m. (4.1)70150200250300Elevation (m)−200 −100 0 100Easting (m)Time 3 − Model 1−200 −100 0 100Easting (m)Time 3 − Model 2101102ΩmFigure 4.4: This chapter investigates two scenarios. Model 1 reflects thesteam growth observed by Tøndel et al. (2014). Model 2 shows theinner right steam chamber moved towards the centre of the reservoir be-tween the two vertical wells. Black dots indicate the electrodes in thetwo vertical wells.J is a n×m matrix, where n is the number of data and m is the number of modelparameters in the model m. The sensitivity matrix describes how the data changegiven a model perturbation. Accordingly, it directly relates the survey design to themodel. For small problems, J can be explicitly formed and the average sensitivityfor the jth cell, s j, is calculated as follows:s j =1nVjn∑i=1|Ji j|, (4.2)whereVJ is the volume of the cell. For the inversion of DC data, J is not necessarilyexplicitly formed to avoid storage of the large matrix. However, matrix-vectorproducts are easily formed using the sparse differential operators that make up Jvand JTw, where v and w are vectors.Fortunately, a measure of the average sensitivity can be determined by calcu-lating the diagonal of JT J, which is an m×m matrix. The magnitude of the entriesin JT J decay away from the diagonal, thus the diagonal itself contains the majorityof the sensitivity. The diagonal contains m number of values and can be plottedusing the mesh, thus providing information spatially that is easily interpretable.One solution to calculating the diagonal of JT J is to use a diagonal estimator71(Bekas et al., 2007):D≈[p∑k=1vk JT (Jvk)][p∑k=1vk vk], (4.3)where p is a user-defined number of iterations, and  and  indicate component-wise vector multiplication and division, respectively. This diagonal estimator usestwo matrix-vector products: Jvk (which returns a vector) and JT (Jvk), and thusappeals to the problem where the sensitivity is never fully formed. Hutchinson’strace estimator uses random vectors of -1 and 1 in Equation 4.3 (Hutchinson, 1990)but generally requires a large number of iterations to reach an adequate result.Computation time is decreased by using the probing method, which uses pseudo-random vectors. In the probing method, the pseudo-random vectors consist of 0and 1 and is best explained using an example. If the number of iterations p is setto 3, the pseudo-random vectors become:v1 = [1001001...]T ,v2 = [0100100...]T ,v3 = [0010010...]T . (4.4)Because these pseudo-random vectors act on the structure of the matrix JT J, wherethe diagonal has the largest magnitude, only a small number of iterations are re-quired to reach an adequate result. In addition, if p were set to the number of modelvalues m, then the matrix containing the v vectors becomes the identity matrix andthe diagonal of JT J is recovered exactly.4.3.1 Comparison of sensitivity estimatorsA two-dimensional problem is an ideal way to illustrate the different methods toestimate the diagonal of JT J. The problem is small enough that the full sensitiv-ity matrix J can be calculated and stored and thus the actual diagonal can be becompared to the estimators. The example uses a crosswell survey design with twovertical boreholes separated by 200 m, as shown in Figure 4.5a. A single trans-mitter is located at the surface and receivers are positioned along the two wells,72(a) (b)Figure 4.5: (a) A crosswell survey with a single transmitter: current elec-trodes at (-50, 0) and (150, 0). (b) A two-dimensional resistivity modelwith a 10 Ωm anomaly in a 400 Ωm background.providing 40 voltage measurements. This survey is not ideal for monitoring ananomaly at depth but is used here to investigate the different sensitivity approx-imation methods as well as understand the connections between the survey, theapproximate sensitivity, and the final recovered model from inversion. The modelconsists of a 400 Ωm background with a 10 Ωm anomaly (Figure 4.5b).Because the model is small (m = 4004 cells) and the number of data is small(n = 40 data), the sensitivity matrix is manageable and accessible. Thus, the exactdiagonal of JT J is calculated using the true resistivity model and is plotted in Fig-ure 4.6a. The diagonal of JT J shows high sensitivity at the current electrodes thatdecays away from these locations. The decay is symmetric about the current elec-trodes. In addition, the sensitivity is distorted around the location of the conductivebody.Given the true model and the forward modelled data, the average sensitivityis calculated using Equation 4.2 and shown in Figure 4.6b. The distribution ofthe average sensitivity compares well to the exact solution but has overall lowervalues. However, the same interpretation can be made: the sensitivity decreasesradially away from the current electrodes and there is minimal sensitivity to the73(a) (b)(c) (d)(e) (f)Figure 4.6: The diagonal of JT J can be approximated in several ways: (a) theexact solution, (b) the average sensitivity (Equation 4.2), (c) Hutchin-son’s approach using 5 iterations, (d) Hutchinson’s approach using miterations, (e) probing method using 5 iterations, (f) probing method us-ing m iterations. The number of cells in the mesh is m= 4004.74lower region between the vertical wells. The disadvantage of this approach is thatit requires the entire sensitivity matrix. This works for small problems, such as this2D example, but is not practical for DC resistivity data for models on 3D meshesor for EM data. This shows the appeal of the diagonal estimator (Equation 4.3).I first use Hutchinson’s approach, which uses random vectors of -1 and 1, toestimate the diagonal of JT J. As the number of iterations increases, a better ap-proximation to the exact diagonal is found. However, the computation time alsoincreases with the number of iterations so the focus here is on using a low numberof iterations to obtain an approximation of the sensitivity.Figures 4.6c and 4.6d show the sensitivity using 5 and m = 4004 iterations. Thesensitivity appears random and scattered due to the use of random vectors of -1 and1 in the diagonal estimator. This makes it slightly harder to interpret compared tothe average sensitivity and exact solution. However, the result with a low numberof iterations shows the general trends. As the number of iterations increases, thedistribution of sensitivity remains the same but the range of values approaches thatof the exact solution.The probing method, which uses pseudo-random vectors (Equation 4.4) in thediagonal estimator, also provides a good approximation using a small number ofiterations. Figure 4.6e shows the result using 5 iterations. Although the values areoverall higher, the sensitivity decays in the same manner as in the previous exam-ples: there is high sensitivity at the current electrodes which decays symmetricallyaway from those locations. Here also, it can be observed that the conductor distortsthe sensitivity in the middle of the region between the vertical wells. Overall, theapproximation is smoother than using Hutchinson’s approach.The probing method recovers the exact diagonal of JT J when using m numberof iterations, as shown in Figure 4.6f. Thus, for problems with a mesh that is smallenough, the probing method can provide the exact solution even if only matrix-vector products can be computed.In summary, each of the three methods provide good approximations to the ex-act solution of the diagonal of JT J. In each, the general trends are present, allowingfor first-order interpretation of the sensitivity distribution. For larger DC problemsand EM problems, the average sensitivity is not available. Hutchinson’s approachand the probing method provide alternatives that use matrix-vector products to esti-75mate the sensitivity. Because Hutchinson’s provides a more random final outcome,preference is given towards the probing method for visual interpretation.4.3.2 Effect of survey design on sensitivityBy definition, the sensitivity matrix describes how the data, which are controlledby the survey design, change due to model perturbation. Thus, by studying thediagonal of JT J, connections between the survey design and model recovery canbe made before inverting. The above 2D example is ideally suited to explore theseconnections as the forward modelling and inversions are relatively fast.Using the same electrode layout as in Figure 4.5a, four survey designs arecompared. The first and second survey each have a single transmitter, as shown inFigure 4.7a and 4.7b. The third survey is the combination of the first two (Figure4.7c) and the fourth survey is a typical crosswell survey that might be used inindustry (Figure 4.7d). The fourth survey contains 49 transmitters.The diagonal of the sensitivity is estimated using the probing method with 5iterations. The results are shown in Figures 4.8. The goal of these surveys is toilluminate the anomaly and be able to recover it using an inversion. Thus, theyshould have good sensitivity to the region where an anomaly is expected. Thesensitivity approximation shows that the first survey is the least sensitive to thisregion (Figure 4.8a), as would be expected from a transmitter with both currentelectrodes at the surface. In comparison, placing a current electrode at depth, as inthe second survey, generates a larger sensitivity to the region (Figure 4.8b).In the case where the location of an anomaly is not confidently known, thesetransmitters independently do not completely sample the region between the twovertical wells. Thus, the survey design is improved by using both transmitters,as in the third survey, where the sensitivity is approximately the summation ofestimated sensitivities from the individual transmitters (Figure 4.8c). In this case,higher sensitivity is maintained to the surface region as well as the lower region.For the fourth survey, the sensitivity is much higher to the region of interest andalmost blankets the region uniformly. This indicates that the survey provides thebest information about the region between the vertical wells. It is expected that thisuniform sensitivity will allow for better recovery of the anomaly during inversion.76(a) (b) (c) (d)Figure 4.7: Crosswell surveys with (a) a single transmitter with current elec-trodes at (-50, 0) and (150, 0), (b) a single transmitter with current elec-trodes at (-50, 0) and (150, -240), (c) the previous two transmitters com-bined, and (d) 49 transmitters in a typical survey design.(a) (b) (c) (d)Figure 4.8: The probing method using 5 iterations approximates the sensitiv-ity for the four surveys shown in Figure 4.7. Because the sensitivitydecays outside of the region between the boreholes, only the region ofinterest is plotted.77(a) (b) (c) (d)Figure 4.9: Recovered models from inverting the voltage data from the foursurveys in Figure 4.7.To validate these observations, the voltage data from each survey are invertedand the recovered models are shown in Figure 4.9. Using a single transmitter atthe surface does not recover the anomaly (Figure 4.9a), which is expected as thereis very limited sensitivity at depth. When using the second survey, which alsoonly has a single transmitter but in a different location, the sensitivity to the regioncontaining the anomaly was greater and the recovered model shows a much largerconductive anomaly in the correct location (Figure 4.9b). However, the conduc-tive region extends to the surface where sensitivity was low, indicating a lack ofinformation constraining the inversion.The result is immediately improved by combining the two surveys. The recov-ered model (Figure 4.9c) shows a conductive anomaly in the correct location withless smearing towards the surface. This result was anticipated by the sensitivity.The first survey provides information about the surface region while the secondsurvey contains information to recover the anomaly. By combining these surveys,the sensitivity increased across the region of interest and the resultant recoveredmodel is better constrained. It is then not unexpected that the fourth survey pro-vides the best recovered model (Figure 4.9d). The sensitivity was almost equalacross the region of interest and the inversion recovered the anomaly better than inthe previous three cases.784.3.3 Effect of conductivity model on sensitivitySo far in this example, I used the true resistivity model to calculate the approximatesensitivity and tie observations from the sensitivity to the survey design and theinversion results. However, in a field scenario, the true model is not available. Ingeneral though, a background model can be created that will represent the regionfairly well, especially for SAGD where background models can be built from otherdata, such as borehole logging (as done in Chapter 3).To study the impact of a different model on the sensitivity, I use the back-ground model and approximate the sensitivity with the probing method for each ofthe four surveys (Figure 4.7). In this case, the background is a halfspace. Figure4.10 shows the results for each survey. Comparison with the sensitivities using thetrue model (Figure 4.8) shows that the conductive anomaly distorts the sensitivitydistribution. The sensitivity below the conductor decreases while the location ofthe conductor shows a higher sensitivity. First-order observations, however, remainthe same. When using a single transmitter (Figure 4.10a and 4.10b), the sensitivityis highest near the transmitters and decays smoothly away from those locations.The combination of the two transmitters shows a more uniform spread of sensi-tivity (Figure 4.10c) while using all transmitters provides the greatest coverage.Thus, first-order observations can be made using just the background model but itis important to keep in mind that conductive (and resistive) anomalies will distortthe current distribution and thus affect the sensitivity.4.3.4 SummaryThis example is simple and the results are exactly what would be expected but itshows how sensitivity changes as the survey changes and confirms the observationsusing inversion. It also shows how the model affects the sensitivity and that con-ductors within the survey region will affect the current distribution. The exampleshows the importance of sensitivity to the entire survey region to adequately con-strain the inversion and recover a compact anomaly. These types of interpretationscan be extended to larger DC problems as well as to EM problems to better un-derstand what can and cannot be recovered from inversion before committing to atime-consuming inversion. This methodology will be used to better understand the79(a) (b) (c) (d)Figure 4.10: The sensitivity approximation using the probing method with5 iterations for a 400 Ωm halfspace and the four surveys in Figure4.7. Because the sensitivity decays outside of the region between theboreholes, only the region of interest is plotted.strengths and limitations of survey designs and is applied to the surveys used at theLeismer Demonstration Area in the remainder of this chapter.4.4 Sensitivity analysisGiven the above background on sensitivity approximation and the simple 2D ex-ample, the surveys and models based on the Leismer Demonstration Area are in-vestigated. The sensitivity is approximated using the probing method with fiveiterations for each of the 4 surveys shown in Figure 4.2 for the layered backgroundmodel shown in Figure 4.1. The results are plotted in Figure 4.11. The first obser-vation is that the sensitivity radially spreads around the vertical borehole locationsand decreases away from the boreholes. Secondly, the sensitivity varies for eachof the surveys. Most notable is the lack of sensitivity from Survey 1 (Figure 4.11a)to the region between the two boreholes compared to the other surveys. This ismore easily seen in Figure 4.12, which shows a profile of the approximate sensi-tivity along the easting direction at an elevation of 215 m and a northing of 0 m.Survey 1 clearly has the lowest sensitivity to the region between the boreholes. Italso decays the fastest from the borehole locations.Surveys 2 and 4 have the highest sensitivity to the region of interest while80−225 −150 −75 0 75Easting (m)(d) Survey 4−5.0−4.5−4.0−3.5−3.0−2.5log10−100−50050100Northing (m)−225 −150 −75 0 75Easting (m)(c) Survey 3(b) Survey 2−100−50050100Northing (m)(a) Survey 1Figure 4.11: Plan-view sections (z = 215 m) of the sensitivity calculated us-ing the probing method with 5 iterations for the four surveys (Figure4.2). In each case, sensitivity decreases away from the locations of thevertical observation wells but the magnitude varies.Figure 4.12: A profile of the approximate sensitivity along the easting direc-tion (z = 215 m and y = 0 m) for the 4 surveys (Figure 4.2). Blackvertical lines indicate the locations of the steam chambers in Models 1and 2 (Figure 4.4).81Survey # of TX # of data Sensitivity ranking1 169 5352 32 174 16928 13 125 8640 24 274 17088 1Table 4.1: The four surveys (Figure 4.2) used at the Leismer DemonstrationArea are ranked based on the sensitivity. Surveys 2 and 4 receive thesame ranking due to a very similar sensitivity. The table shows that asthe number of data increases, the sensitivity increases.Survey 3 falls in between. Table 4.1 ranks the surveys based on the approximatesensitivity to the region between the boreholes and compares the rankings withthe number of transmitters and data for each survey. Because the sensitivity forSurveys 2 and 4 are practically identical, they both receive the highest ranking(i.e., 1). The table shows that a higher number of data corresponds to increasedsensitivity, as is expected from the previous 2D example. However, the table showsthat a higher number of transmitters does not always equate to higher sensitivityto the region of interest. This reiterates the importance of survey design: not allsurveys are equal. Here, the approximate sensitivity provides a first-order idea ofwhat a particular survey is capable of detecting in a specific part of the model.For field applications, where the location of anomalies is unknown, using thebackground resistivity model is perhaps the best way to determine which surveys tocollect. In SAGD applications, because the location of the horizontal well pairs arewell-known, synthetic models can be generated to include conductive steam cham-bers and study their impact on the approximate sensitivity. This is broken downinto two steps. First, I study the impact of changes in the location of a steam cham-ber and then investigate how steam chamber size impacts the sensitivity. Furtheranalysis is focused on Survey 4 because of its high sensitivity to the reservoir.4.4.1 Impact due to location changesTo understand the impact of introducing a conductive steam chamber into the back-ground model on the sensitivity, I generate a series of models with a single steam82x = −80 m−5.0−4.5−4.0−3.5−3.0−2.5log10x = −130 mx = −170 m−1000100Northing (m) x = −230 m−1000100Northing (m)−150 0Easting (m)−150 0Easting (m)−150 0Easting (m)−150 0Easting (m)−0.2−0.10.00.10.2Figure 4.13: The sensitivity is approximated using models that include a con-ductive steam chamber at different easting locations. Top row: Plan-view sections through the sensitivity. Bottom row: the difference be-tween the sensitivity in the top row and the background sensitivity.chamber at Time 3. The chamber moves from -230 m to -80 m in the easting di-rection in 50 m increments. Only the left side of the model space is investigated asthe survey and model are fairly symmetric.For each model, the sensitivity is approximated using the probing method forSurvey 4. The results are plotted in the top row of Figure 4.13. The bottom rowshows the difference from the background sensitivity. Each panel shows how theconductive chamber distorts the sensitivity. This is due to the redistribution ofcurrent density in the region of the steam chamber. For each case, the sensitivitydecreases compared to the background at a northing of 0 m but the sensitivityalong the chamber (i.e., in the northing direction) increases. This indicates that thesensitivity is redistributed along the steam chamber. Thus, cells at a northing of 0m will influence the data less compared to when the background model was used,and cells to the north and south of y = 0 m will influence the data more. For steamchambers that are relatively far away from the two vertical wells, the data will beless impacted by changes in the conductivity in those locations. Thus, Survey 4loses sensitivity to a chamber as it moves away from the vertical boreholes, whichis expected.Given this understanding, the sensitivity is approximated for Models 1 and 2at Time 3 using Survey 4 and shown in Figure 4.14. For Model 1, the sensitivityspreads north and south along the two chambers and indicates that the survey is83−225 −150 −75 0 75Easting (m)(b) Time 3 − Model 2−5.0−4.5−4.0−3.5−3.0−2.5log10−100−50050100Northing (m)−225 −150 −75 0 75Easting (m)(a) Time 3 − Model 1Figure 4.14: Plan-view sections (z = 215 m) of the sensitivity using Survey4 (Figure 4.2d) for Models 1 and 2 (Figure 4.4) calculated using theprobing method with 5 iterations.sensitive to these regions. For Model 2, the same is observed for the inner leftchamber but the right chamber has a lower sensitivity. The inversion of the datafor Model 2 (Figure 4.4b) might therefore struggle to recover the inner right cham-ber. This first-order interpretation could have been obtained using sensitivity forthe background model, which also shows that sensitivity decreases away from thevertical wells.4.4.2 Impact due to size changesThe geology at the Leismer Demonstration Area can impact the migration of thesteam through the reservoir and therefore the location of the steam chamber. Inaddition, the chambers grow over time, which also affects the sensitivity of the sur-vey. To investigate the impact of chamber growth, the sensitivity is approximatedfor the four models in Figure 4.3 using Survey 4.Figure 4.15 shows plan-view slices through the sensitivity for each time-step.As the chambers grow, the sensitivity along the steam chamber increases with smalldecreases at y = 0, indicating the same redistribution as identified in the previoussection. This is observed for Times 1-3. At Time 4, the increased sensitivity doesnot reach as far north or south due to the increased width of the chamber in theeasting direction. Because of their increased size, there appears some sensitivity tothe outer two chambers as well at Time 4.The sensitivity to the chambers between the two vertical wells increases as the84chamber grow in size. The chamber on the left has a slightly higher sensitivityat each time step due to its closer proximity to a vertical borehole. While thechambers extend in the northing direction, the sensitivity decreases rapidly awayfrom a northing of 0 m. Therefore, any inversion using Survey 4 (or any of the foursurveys) will only provide two-dimensional information. As the chambers grow,the sensitivity to the outer chambers also changes but the sensitivity is relativelysmall compared to that of the inner chambers.These results indicate the even when the chamber is very small (i.e., 5 m by 5m in cross-section), Survey 4 is sensitive to changes at the earliest time-steps. Thedifferences in the sensitivity as time increases indicates that data collection andinversion over time should provide new information.4.4.3 SummaryIn summary, investigating the approximate sensitivity using the resistivity modelsthat contain the growing steam chambers sheds light on how well Survey 4 candetect the chambers. It is expected that as the chambers grow larger, it will be eas-ier to recover conductive anomalies through inversion but even the earliest timesshow an increase in sensitivity to the chambers. Additionally, the sensitivity pro-vides information about how location affects detectability. These observations areexpected to translate to recoverability on a first-order basis. As discussed in Chap-ter 2, the inversion may not always be able to recover anomalies adequately eventhough the data detect a measurable change. In contrast to Chapter 2 where thedetectability was represented as a single value for an entire data set, the sensitivityanalysis here shows which anomalies have greater detectability and what can beexpected to first-order in the recovered model from inversion.4.5 Validation with 3D inversionFor four surveys used at the Leismer Demonstration Area, the sensitivity was ap-proximated using the probing method for a background model based on Tøndelet al. (2014). Analysis of the sensitivity provided an understanding of how thesurveys illuminate the model and were ranked in Table 4.1. Using Survey 4, theanalysis provided insight into how sensitivity changes as the steam chambers grow85−225 −150 −75 0 75Easting (m)(e) Time 4−5.0−4.5−4.0−3.5−3.0−2.5log10−100−50050100Northing (m)−225 −150 −75 0 75Easting (m)(d) Time 3(c) Time 2−100−50050100Northing (m)(b) Time 1(a) Time 0Figure 4.15: Plan-view sections (z = 215 m) of the sensitivity using Survey4 (Figure 4.2d) for the time-lapse models (Figure 4.3) calculated usingthe probing method with 5 iterations.over time and as the chamber location varied. These observations provided a first-order idea of how detectable the steam chambers are and what can possibly berecovered using inversion. However, in order to fully compare the surveys and thedifferent models, full inversion of the data is required.To validate the observations from sensitivity analysis, I compare the recoveredmodels from inversions of DC resistivity data for the four different surveys (Figure4.2) using Model 1 at Time 3 (Figure 4.4a). The data are forward modelled in 3D(Haber et al., 2012) and 0.5% Gaussian noise is added to simulate real data. Sucha low value is used assuming that field data are collected repeatedly to improve86200225250Elevation (m) True Difference Time 3200225250Elevation (m) (a) Survey 1 (b) Survey 2200225250Elevation (m)−150 −100 −50 0Easting (m)(c) Survey 3−150 −100 −50 0Easting (m)(d) Survey 4−180−160−140−120−100−80−60−40−200ΩmFigure 4.16: Each panel shows the recovered models at a y= 0 m for the fourdifferent surveys for Model 1 (Figure 4.4a). Only the reservoir portionis shown as only these cells were allowed to change resistivity in theinversion. Colour scale indicates the change in Ωm from the initialmodel.Survey Time 3 - Model 1 Time 3 - Model 21 3.0% 2.3%2 2.7% 2.2%3 3.7% 3.2%4 3.2% 2.4%Table 4.2: The relative difference (Equation 2.20) for the four surveys (Figure4.2) using Models 1 and 2 at Time 3 (Figure 4.4).signal-to-noise ratios. Uncertainties for the DC resistivity data are assigned as0.5% percent of the data plus a noise floor of 30 mV. The layered backgroundmodel (Figure 4.1) was used for the initial and reference model. Additionally, onlythe resistivity of cells within the reservoir and between the boreholes were allowedto change. The inversion for each survey reaches target misfit and reproduces thedata. The recovered models are subtracted from the background model and thedifference is shown in Figure 4.16.Each of the four surveys recover the two inner inner steam chambers. While87differences exist between the models, the recovered steam chambers have approx-imately the same size and resistivity. Thus, each of the 4 surveys adequately re-covered the chambers. Overall, Surveys 3 and 4 provided the best results with adistinct separation between the two chambers, indicating the importance of usingboth along-well and large off-set crosswell transmitters.The fact that each of the surveys recovered the steam chambers adequatelyshows a limitation of only using the approximate sensitivity as a way to rank surveydesigns. The method allowed the sensitivities to be ranked compared to each other,but the information is only relative. The relative difference, which was used inChapter 2 and 3 using Equation 2.20, provides an estimate of whether the datadetect the anomalies. In conjunction with the visual image from the sensitivityanalysis, this provides a more complete picture of a survey’s capability to imagesteam chambers. The relative difference is calculated for each survey at Time 4relative to Time 1 and shown in Table 4.2. The values from each survey are verycomparable to each other and range between 2.7 and 3.7%. Compared to the addednoise of 0.5%, the relative difference shows that the data from the four surveysequally detect the two steam chambers. This supports the inversion results, whichrecover very similar information.Thus, the sensitivity provides a first-order image of what the sensitivity canrecover and the relative difference provides a reference for the values observed inthe sensitivity. The combination of the two metrics shows that the surveys generatea change in the data and that both chambers should be recoverable using inversion.In contrast, the sensitivity analysis for Model 2 at Time 3 (Figure 4.4b) showedvery low sensitivity to the inner right chamber, now located at -80 m, comparedto the location of the two chambers in Model 1, indicating that the surveys maynot detect the anomaly. Data are forward modelled and inverted for this scenarioin the same manner as before. The relative difference is calculated and shown inTable 4.2. The values are smaller compared to Model 1, which is expected as thesensitivity to the inner right chamber has decreased. The relative difference on itsown indicates a detectable change in the data, suggesting both chambers can be re-covered. However, the sensitivity aids this interpretation by warning that the innerright chamber has a low sensitivity. The combination of the sensitivity analysis andthe relative difference predicts that the right chamber may not be recovered using88200225250Elevation (m) True Difference Time 3b200225250Elevation (m) (a) Survey 1 (b) Survey 2200225250Elevation (m)−150 −100 −50 0Easting (m)(c) Survey 3−150 −100 −50 0Easting (m)(d) Survey 4−180−160−140−120−100−80−60−40−200ΩmFigure 4.17: Each panel (y = 0 m) shows the recovered models for the fourdifferent surveys using Model 2 (Figure 4.4b). Only the reservoir por-tion is shown as only these cells were allowed to change resistivity inthe inversion. Colour scale indicates the change in Ωm from the initialmodel.inversion.This is validated by inverting the data for Model 2. The recovered models,shown in Figure 4.17, show that none of the surveys are able to recover two distinctanomalies. The left chamber is well recovered in both size and amplitude. Forsome results, there is smearing from the left chamber towards the centre of thereservoir. However, for none of the four survey designs can the recovered modelsbe confidently interpreted as containing two steam chambers. This shows how thesensitivity analysis complements the relative difference: while the data do detect achange, the sensitivity provides a first-order visual of where that change occurs. Inthis case, the inversion does not have enough information to recover the inner rightchamber.The two scenarios reiterate what was interpreted from the sensitivity analysis.First, the DC resistivity surveys have a decaying sensitivity away from the verticalobservation wells, meaning that anomalies within the centre of the reservoir aredifficult to detect. This was shown in the inversion results: for Model 1 at Time893 (Figure 4.4a), the left and right chambers were approximately equally recoveredbut some smearing exists between the two anomalies when using Surveys 1 and 2.Surveys 3 and 4 recovered two distinct chambers with no smearing in between. ForModel 2 at Time 3 (Figure 4.4b), the inversions were unable to recover the rightchamber at all.This shows that while the DC resistivity surveys worked well for the monitor-ing situation in Tøndel et al. (2014), the surveys are not a universal monitoringtool. The sensitivity analysis indicated that the surveys have limited detectabilityto the inner right chamber in Model 2 and therefore act as a first-order confidencemap of what a survey and an inversion can provide. In order to improve monitor-ing of SAGD steam chambers, the sensitivity between the vertical wells needs toincrease. An obvious solution is to drill additional observation wells and populatethose with electrodes to collect more DC resistivity surveys but that is costly. Inthe next section, I explore a solution that utilizes the exact same survey orientationbut uses frequency-domain electromagnetic methods to increase sensitivity to thereservoir.4.6 Imaging with electromagneticsWhile DC resistivity uses a single frequency of 0 Hz, electromagnetic methodscan operate at multiple and higher frequencies. To minimize additional surveycosts and to better compare the results, the transmitters from Survey 4 are usedalong with receivers in the same locations measuring the vertical electric field.This slightly increases the number of data from 17,088 voltage measurements to17,536 measurements of the complex vertical electric field at each frequency. Fivefrequencies are investigated to understand how frequency impacts the ability torecover Models 1 and 2 for Time 3 (Figure 4.4): 1, 10, 100, 1000, and 10000 Hz.The data are forward modelled in three dimensions. To understand how fre-quency changes the vertical component of the electric field, data from a singletransmitter with current electrodes at (-150, 0, 126) and (-150, 0, 299) are plottedin Figure 4.18. The real part of Ez remains relatively unchanged as frequency in-creases. Only for the highest frequency are there significant changes in the data.The DC resistivity problem, which is here approximated by using 1 Hz, contains90Figure 4.18: The real and imaginary parts of Ez is plotted for a single trans-mitter (with current electrodes at (-150, 0, 126) and (-150, 0, 299))at five frequencies. The real part remains relatively unchanged com-pared to the imaginary part, which generally increases as frequencyincreases. Solid and dashed lines indicate positive and negative data,respectively.a very small imaginary part compared to the real, as is expected. The imaginarypart steadily increases as frequency increases, indicating the additional informationcoming from induction. Therefore, it is expected that multi-frequency electromag-netics will provide more information and allow for better recovery of Models 1 and2.A second method to visualize how EM data provide additional information isby calculating the approximate sensitivity. This is done using the probing methodto estimate the diagonal of JT J (Equation 4.3). The sensitivity is calculated foreach of the five frequencies using the same transmitter as for the data in Figure4.18 and a single receiver at (0, 0, 215). The results are shown in Figure 4.19. Thesensitivity calculated using the real part of Ez is relatively unchanged as frequencyincreases, until the very highest frequency. This mimics what was observed inthe data. Like the EM data, the sensitivity using the imaginary part increases asfrequency increases, indicating that higher frequencies will provide better recoveryof Model 1 using inversion. Notably, the sensitivity for the imaginary part of Ezat the highest frequency has decreased compared to 1000 Hz. This observationcorresponds with intuition built from skin depth (Equation 2.1): as frequencies91−50050Northing (m) 1 Hz − real 1 Hz − imag−50050Northing (m) 10 Hz − real 10 Hz − imag−50050Northing (m) 100 Hz − real 100 Hz − imag−50050Northing (m) 1 kHz − real 1 kHz − imag−50050Northing (m)−200 −100 0 100Easting (m)10 kHz − real−200 −100 0 100Easting (m)10 kHz − imag−7.0−6.5−6.0−5.5−5.0−4.5−4.0−3.5−3.0−2.5−2.0−1.5−1.0log10Figure 4.19: Using a single transmitter (with current electrodes at (-150, 0,126) and (-150, 0, 299)) and a receiver at (0, 0, 215), the approximatesensitivity is calculated for the real and imaginary parts of Ez at fivefrequencies using Model 1 (Figure 4.4a). The plots show a plan-viewsection at an elevation of 215 m. As frequency increases, the sensitivityfrom the real part remains relatively unchanged while the sensitivityfrom the imaginary part increases up to 1000 Hz and has decreased at10000 Hz.increase, skin depth decreases. In this case, skin depth has become smaller than thedistance between the vertical observation wells which likely caused the decrease insensitivity.The measured EM data, along with the approximate sensitivity, indicate thatthe information content for each frequency is different and therefore, the inversionwill recover different resistivity structures at each frequency. In addition, it can beexpected that as frequency increases, the recovered models will improve comparedto the DC resistivity (approximated using 1 Hz) result.92200225250Elevation (m) True Difference (a)200225250Elevation (m) (b) (c)200225250Elevation (m)−150 −100 −50 0Easting (m)(d)−150 −100 −50 0Easting (m)(e)−180−160−140−120−100−80−60−40−200ΩmFigure 4.20: The models are subtracted from the background model to showthe difference: the true difference is compared to the difference modelsusing EM data from Survey 4 at (a) 1 Hz, (b) 10 Hz, (c) 100 Hz, (d)1000 Hz, and (e) 10000 Hz. Colour scale indicates the change in Ωmfrom the background model.To validate these first-order observations, 0.5% Gaussian noise is added to theforward modelled Ez data for Model 1 at Time 3 (Figure 4.4a). Uncertainties areassigned as a percentage of the data plus a noise floor. The data are first invertedfor each frequency separately to investigate how the recovered model changes asfrequency increases. The results, shown in Figure 4.20, show that as frequencyincreases, the recovery of the two chambers improves, up to 1000 Hz. The cham-bers become more distinct with less smearing and the resistivity change becomesgreater. At 10000 Hz, the right chamber is slightly displaced. From the five fre-quencies presented, a frequency of 1000 Hz recovers the anomalies best. Thismatches with the observation made from the approximate sensitivity. The resultsalso show that the information from the increasing imaginary part of Ez improvesthe result compared to DC resistivity alone.As expected, the recovered model improves if the frequencies are inverted si-multaneously because the amount of information increases. Results in Chapter 2have previously shown that inversion of multi-frequency EM data provides better93200225250Elevation (m) True Difference (a)−180−120−600ΩmFigure 4.21: The models are subtracted from the background model to showthe difference: the true difference for Model 1 is compared to the dif-ference models using multi-frequency EM data from Survey 4. Colourscale indicates the change in Ωm from the initial model.results than DC resistivity alone and this idea is duplicated here. The data from thefive frequencies are inverted simultaneously and shown in Figure 4.21. The resultis the recovery of both steam chambers with equal resistivity. The chambers areclearly separated and the size reflects the true anomalies.Although the EM data for Model 1 contained information from multiple fre-quencies, the final recovered model is not a drastic improvement over the DC re-sistivity result in Figure 4.16d. In both cases, the two chambers were adequatelyrecovered and the additional computation time required to solve the EM problemdoes not provide a drastically superior model in this case. However, the DC resis-tivity result for Model 2 (Figure 4.17d) did not recover one of the steam chambersand therefore, the additional information from multi-frequency can provide a betterresult. This is shown in Figure 4.22.The use of multi-frequency electromagnetic data allowed for recovery of bothsteam chambers. The right chamber is not as well recovered as the left, indicatingthat this problem is more difficult compared to Model 1. In addition, the frequen-cies used here may not be the best but were used to show how the data and sensitiv-ity change as frequency changes and relate those changes to the inversion results.Considering these limitations, the EM result is still much improved compared tothe DC resistivity result, showing the value of multi-frequency EM.The multi-frequency EM approach allowed for recovery of Models 1 and 2while the DC resistivity alone only recovered Model 1 adequately. For monitor-ing SAGD steam growth, the EM approach provides the confidence that the entirereservoir between the vertical wells is illuminated and any anomalies withing re-gion should be recoverable.94200225250Elevation (m) True Difference (a)−180−120−600ΩmFigure 4.22: The recovered models are subtracted from the backgroundmodel to show the difference: the true difference for Model 2 is com-pared to the difference models using multi-frequency EM data fromSurvey 4. Colour scale indicates the change in Ωm from the back-ground model.4.7 Steam growth over timeThe above results show how the use of multiple frequencies impact model recov-ery. The EM survey has greater sensitivity to the reservoir region, resulting inbetter monitoring capability. In this final example, multi-frequency EM and DCresistivity data are forward modelled using the Survey 4 design for a time-lapseversion of Model 1 (Figure 4.3). Gaussian noise is added to the data in the samemanner as before and uncertainties assigned as a percentage of the data plus a noisefloor. Each time step is inverted using the background model (Figure 4.1) as theinitial and reference model. Changes to the model are restricted to the reservoironly.The time-lapse results are shown in Figure 4.23. Both the DC resistivity andEM surveys allow for recovery of the steam chambers at each time-step and themodels show distinct growth. The EM results recover the resistivity values andshape of the anomalies at the earliest times slightly better, but at later times, theresults are very similar to those from the DC resistivity inversion.In contrast, when this time-lapse example is repeated using Model 2, the DCresistivity does not recover the right chamber at any of the time steps while the EMadequately recovers both chambers at all but the earliest time step. (Figure 4.24).For the earliest time step, the influence of the two small chambers on the data isrelatively small, indicating the limitations of monitoring SAGD steam chambergrowth early on.Later time-steps still provide well-recovered models using EM, providing re-liable monitoring data to production engineers about the SAGD steaming process.95−150 −100 −50 0Easting (m)Time 4−180−160−140−120−100−80−60−40−200ΩmTime 3Time 2Time 1Time 1Time 2Time 3−150 −100 −50 0Easting (m)Time 4200225250E le va ti on  ( m) Time 1200225250E le va ti on  ( m) Time 2200225250E le va ti on  ( m) Time 3200225250E le va ti on  ( m)−150 −100 −50 0Easting (m)Time 4Figure 4.23: Left column: the difference (from the background model) inModel 1 at four time steps. Middle column: recovered models usingDC resistivity. Right column: recovered model using multi-frequencyEM. Colour scale indicates the change in Ωm from the initial model.As mentioned earlier, while DC resistivity works well for Model 1 and the fieldcase presented by Tøndel et al. (2014), EM provides the confidence that the en-tire region is imaged and the inversion will recover the steam chambers even if thesteam growth is irregular or in an unexpected location.4.8 DiscussionThe results show that multi-frequency EM methods have greater sensitivity to thereservoir region between two vertical observation wells compared to traditionalDC resistivity. While for specific cases, such as Statoil’s field case at the LeismerDemonstration Area (Tøndel et al., 2014), DC resistivity adequately recovers time-lapse growth of SAGD steam chambers, the sensitivity varied over the reservoirbetween the two vertical observation wells. The example using Model 2 showcasedthe limitations of the DC resistivity surveys used at Leismer. By extending the96−150 −100 −50 0Easting (m)Time 4−180−160−140−120−100−80−60−40−200ΩmTime 2Time 2Time 1Time 1Time 2Time 3−150 −100 −50 0Easting (m)Time 4200225250E le va ti on  ( m) Time 1200225250E le va ti on  ( m) Time 2200225250E le va ti on  ( m) Time 3200225250E le va ti on  ( m)−150 −100 −50 0Easting (m)Time 4Figure 4.24: Left column: The difference (from the background model) inModel 2 at four time steps. Middle column: recovered models usingDC resistivity. Right column: recovered models using multi-frequencyEM. Colour scale indicates the change in Ωm from the initial model.survey design to measure multiple frequencies, the inversion was able to recoverboth steam chambers for Model 1 and Model 2.To improve the monitoring of the chambers at the Leismer DemonstrationArea, more observation wells with electrodes are needed to image the outer twochambers as well as provide information about the chambers in three dimensions.This will greatly increase the amount of data collected, especially if surveys similarto the ones in this chapter are used. The computation cost to invert will dramaticallyincrease due to the increase in sources. Sensitivity analysis can be utilized to en-sure equal sensitivity to the entire region while decreasing the amount of transmit-ter, thereby reducing computation costs. In addition, the research in Chapters 2 and3 has shown that surface inductive transmitters, where there are only a few sources,can detect and image SAGD steam chambers. However, in this location, the depthto the reservoir is significantly deeper and modelling attempts using such a surveygeometry did not provide adequate results. The amount of conductive overburden97material limits the amount of currents induced in the reservoir. Borehole trans-mitters and receivers are likely the best option for this region of the Athabasca oilsands.Casing also presents a problem in this scenario. While currently not modelled,the cased horizontal wells and any cased observation wells should be included inthe numerical modelling as they are expected to have a large EM response. Mod-elling the casing is not trivial and goes beyond the scope of this thesis. For ob-servation wells that are steel-cased, it is expected that monitoring will work usinglower frequencies (i.e., up to 500 Hz) (Wilt et al., 1997).4.9 ConclusionIn this chapter, the approximate diagonal of the sensitivity matrix was calculatedand used to understand how well four currently-used surveys designs detect andimage SAGD steam chambers. The sensitivity analysis is computationally inex-pensive and fast compared to full inversion. It provides adequate information tojudge the strengths and weaknesses of a particular survey design and interpretationswere validated by inverting synthetic data. All four surveys recovered the cham-bers through 3D inversion for the first scenario, which was modelled after a fieldproblem (Tøndel et al., 2014). However, in a second example, the inversions failedto recover the right chamber due to the low sensitivity to the middle region of thereservoir when using DC resistivity. This motivated the use of multi-frequency EM.The EM data and approximate sensitivities showed that as frequency increases, theinformation within the data changes, allowing for successful recovery of the steamchambers in both examples.98Chapter 5From exploring to reclamation:using EM methods at SAGD sitesin the Athabasca oil sandsDeveloping a site that uses SAGD to extract heavy oil involves many stages: iden-tidying an exploration region, gaining approval for development, constructing thenecessary infrastructure, producing the heavy oil, and finally, reclamating the re-gion (Alberta Energy, 2016). Each of the six distinct stages are detailed in Figure5.1. Several types of data are collected and utilized throughout this timeframe, in-cluding core and resistivity logging, pre-development 3D seismic, temperature andpressure monitoring, and repeated seismic surveys. In this chapter, I show what ad-ditional information electromagnetic (EM) methods can provide, and further, howthey can play a role in SAGD.5.1 IntroductionEM methods are sensitive to electrical resistivity, which varies as geologic for-mations change. In addition, as the reservoir is steamed, the resistivity decreases(Mansure et al., 1993; Tøndel et al., 2014). EM data can be collected on the sur-face, in boreholes, or with airborne systems, providing many opportunties to addadditional information to each stage in Figure 5.1. Zhdanov et al. (2013) inverted99Figure 5.1: A six-stage timeline outlines the development of SAGD sites inthe Athabasca oil sands (left). EM methods can supplement informationat each stage (right) ranging from regional surveys to time-lapse moni-toring. EIA = environmental impact assessment, AER = Alberta EnergyRegulator.100Figure 5.2: Map showing properties in the Athabasca oil sands and their re-spective companies. The Aspen property, owned by Imperial Oil, islocated roughly 45 NE of Fort McMurray and 25 km SE of Fort McKayin northeastern Alberta. Figure courtesy of Imperial Oil.airborne EM data to recover the regional structure of the upper layers over a prop-erty in the Athabasca oil sands. Tøndel et al. (2014) used permanent crosswell DCresistivity surveys to monitor the growth of SAGD chambers over time in 2D andChapter 2 in this thesis studied the feasibility of surface and borehole EM methodsto recover a steam chamber in 3D. Chapters 3 and 4 further studied the applicationof EM surveys to monitor steam growth over time. Airborne, ground-based, andborehole electromagnetic surveys can be used together to characterize and under-stand an oil sands region. This chapter utilizes different EM surveys at each stageof the SAGD process and showcases them for a property currently under develop-ment in the Athabasca oil sands.The focus is on the Aspen property, which is owned by Imperial Oil, and is thefuture site of several SAGD well pads. The project area lies about 45 km northeastof Fort McMurray and 25 km southeast of Fort MacKay in northeastern Alberta,101250275300325350375400425450475500Elevation (m)1 2 3log10 Ωm  Quaternary: 60−100 m, 29 ΩmGrand Rapids Fm: 30−110 m, 24 ΩmClearwater Fm: 65−90 m,12 ΩmWabiskaw Mmb: 5 m, 46 ΩmDevonian: − m, 56 ΩmMcMurray Fm: 45−115 m,147 Ωm101 102ΩmFigure 5.3: Resistivity logging data from 8 wells at the Aspen property areused to create a simple 1D resistivity model.Canada. Figure 5.2 shows the Aspen property in relation to the two towns and theother properties in the area.5.2 Stage IThe first stage involves background research of the exploration region, includinganalysis of existing geologic and geophysical surveys, core, and well-log data.An initial, simple resistivity model was constructed in Chapter 3 using publicly-available data from eight wells, shown in Figure 5.3 (Wynne et al., 1994). Averagedvalues from the logs are assigned to each geologic formation. The geology at theAspen property contains the following flat-lying layers (Imperial Oil ResourcesVentures Limited, 2013):• The Quaternary consists of paleo-channels and glacial tills.• The Grand Rapids Formation is a transgressional layer consisting of shalesand sands, and can be incised by overlying Quaternary channels.102• The Clearwater Formation consists of shales and acts as a cap rock forSAGD operations. The Wabiskaw Member is a trangressional layer con-taining sands and shales at the bottom of the Clearwater.• The McMurray Formation is the main oil sands reservoir.• A Devonian limestone unit is separated from the McMurray Formation by anunconformity. Prairie Evaporites may exist along the unconformity, either assalt or salt dissolution (Broughton, 2013).Thicknesses and average resistivity values for each geologic unit are given in Fig-ure 5.3.5.3 Stage IIOnce a property is identified, mineral rights and well licenses are obtained andadditional geophysical data are collected, including seismic and well logging. Atthis stage, airborne electromagnetic data is an additional source of information thatcan be acquired, processed, and inverted relatively quickly. Airborne EM surveysprovide detailed structural information about the Quaternary, Grand Rapids, andClearwater Formations, and are significantly less expensive than seismic surveys.Of particular interest is extracting information about the Clearwater Forma-tion, such as its depth, thickness and integrity. The Clearwater is essential forSAGD operations as it acts as a cap rock for the steam. The resistivity of the Mc-Murray Formation can also provide information about the quality of the heavy oil,where a higher resistivity may indicate higher bitumen content compared to lowerresistivities (Cristall et al., 2004). A third region of interest to EM studies is theunconformity between the McMurray and Devonian units. Water samples withinthe Athabasca oil sands range in salinity due to salt dissolution, suggesting thereare pathways between the aquifers in the Devonian and the McMurray Formation(Cowie et al., 2015). This can significantly lower the resistivity of the McMurrayFormation, leading to incorrect interpretations of the bitumen content. Finally, re-sistivity variations in the Quaternary can provide information about channels andincisions, especially when well data may not be available near the surface (ImperialOil Resources Ventures Limited, 2013).103Easting (m)-2000 -1000 0 1000 2000 3000 4000 5000 6000 7000 8000Northing (m)-20000200040006000800010000120001400016000Figure 5.4: The VTEM survey contained 86 flight lines and 12 tie lines,providing 428,340 data locations over a 100 km2 survey area in theAthabasca oil sands. The blue line indicates the boundary of the As-pen property.To investigate these questions, this chapter inverts and interprets time-domaindata flown over the Aspen property.5.3.1 Airborne TEM dataThe data at the Aspen property are collected using an airborne electromagnetic sys-tem call Versatile Time-Domain Electromagnetic (VTEM) which uses a helicopter-towed transmitter and receiver loop. The data were collected in February 2014 anda total of 1,095 line-kilometers were flown. Flight lines were oriented north-southwith a spacing of 100 m for a total of 86 flight lines over a region that extends 8.7km in the easting direction and 11.7 km in the northing direction. Twelve tie linesspaced 1,000 m apart were flown in the east-west direction. Figure 5.4 shows the104Figure 5.5: The VTEM waveform is shown in blue. Black dots indicate the44 time channels. The inset shows a closer look at the time channels ona logarithmic scale from 10−5 to 10−3 seconds.flight lines in relation to the property boundary. The data set contains a total of428,340 data locations.For this data set, the data consist of the z-component of the time-derivative ofthe magnetic field (∂Bz/∂ t) and are measured at 44 off-time time channels. Figure5.5 shows the waveform and the different time channels ranging from 2e-5 to 9e-3seconds after transmitter shut-off.5.3.2 1D inversion of synthetic dataIn Chapter 3, I used borehole data to generate a synthetic 1D model to represent theresistivity structure at the Aspen property. The model is shown in Figure 5.6a andincludes the main units: Quaternary, Grand Rapids Formation, Clearwater Forma-tion, Wabiskaw Member, McMurray Formation, and Devonion limestone. Whilein most cases, it is prudent to use 3D forward modelling and inversion codes (asshown in Chapter 2), a one-dimensional model is fairly reasonable to recover theAthabasca oil sands background geology as the different formations are generallyflat-lying and the topography is relatively flat. Thus, the synthetic model providesa good starting point to forward model and invert airborne time-domain data and a1D code can be utilized.A random sounding location is chosen from the VTEM data set and the trans-105(a) (b)Figure 5.6: (a) A 1D model generated from borehole resistivity logs in theAspen region. The top two layers represent the Quaternary and GrandRapids Formation with a resistivity of about 25 Ωm. The conductorof approximately 10 Ωm represents the Clearwater Formation, with theWabiskaw Member below it. The resistive unit starting at approximately200 m in depth and at 500 Ωm is the McMurray Formation. Belowthe McMurray lies the Devonion limestone. (b) A randomly-chosendecay curve (blue) from the VTEM data set is compared to the forwardmodelled data (orange) using the synthetic 1D model (Figure 5.6a). Thetwo decay curves are fairly similar to each other, suggesting that the 1Dsynthetic model is a decent representation of the resistivity structures atthe Aspen property.mitter and receiver parameters are used to forward model data using the synthetic1D model. The forward modelled data are compared to the actual field data in Fig-ure 5.6b and shows that the data fitting is good. This suggests that the syntheticmodel is a good representative of the resistivity structure at Aspen.Gaussian noise of 1.5% is added to the forward modelled data and uncertaintiesare assigned as a percentage of the data and a noise floor. I used 1.5% and 1e-12V. The synthetic decay curve is inverted using L2 norms for both the data mis-fit (Equation 1.13) and the model objective function (Equation 1.14) using UBC-GIF’s EM1DTM code (Farquharson and Oldenburg, 1993). Values for αs and αz106(a) (b)(c)Figure 5.7: Inversion of the forward modelled data (Figure 5.6b) using aninitial and reference model of (a) 25 Ωm, (b) 100 Ωm, and (c) 500Ωm. Below the conductive layer, the model pushes towards the refer-ence model, providing an estimate of the depth of investigation. In eachpanel, (a) compares the observed (blue) and predicted (orange) data, (b)shows the normalized data misfit for each time channel, (c) comparesthe recovered model (black), the true model (blue), and the initial/refer-ence model (orange).107are set to 0.001 and 1, respectively. An initial and reference model of 25 Ωm wasused. The results are shown in Figure 5.7a. The predicted data fit the observed datavery well and the data misfit is randomly distributed. The model recovers the lay-ers up to a depth of approximately 175 m. Below 175 m, the data may have somesensitivity to the resistive McMurray Formation but this layer is not well-recoveredin the inversion. To better understand the sensitivity of the data to layers at depth,the inversion is repeated using an initial and reference model of 100 Ωm. The re-sults are shown in Figure 5.7b. The data are fitted just as well as in the previousinversion but the model slightly changes below 175 m. It is pushed closer to theinitial/reference model, suggesting limited sensitivity to layers below the Clearwa-ter Formation. This is further supported by a third inversion where the initial andreference model are set to 500 Ωm. The recovered model is shown in Figure 5.7c.These inversions suggest that good recovery of the Quaternary, Grand RapidsFormation, and Clearwater Formation can be expected. It may be possible to dis-cern the location of the top of the McMurray Formation but this will likely dependon the resistivity and thickness of the conductive Clearwater. These results also in-dicate that the synthetic model should not be used as an initial and reference modelas it may lead to falsely recovering the McMurray Formation and over-interpretingthe recovered model . For this reason, an initial and reference model of 25 Ωm isused in future inversions.Before inverting the field data, the synthetic decay curve is inverted using an L1norm for the model objective function (Equation 1.14) to recover blockier modelscompared to the L2 norm. As the layers within the Athabasca oil sands tend to bewell-defined, distinct units, using an L1 norm may allow for improved recoveredmodels. The result is shown in Figure 5.8b with the L2 results duplicated in Fig-ure 5.8a. The result is noticeably blockier, with better recovery of the ClearwaterFormation. To generate an even blockier result, the value of αz is decreased from 1to 0.1 to lessen smoothing on changes in the model. This result is shown in Figure5.8c. In all results, the observed data are reproduced well by the model and thenormalized data fitting misfit is random. By decreasing αz, the model is blockiercompared to using the L1 norm alone.The 1D inversions of the forward modelled data provide initial informationabout depth of investigation, the influence of inversion parameters, and what to ex-108(a) (b)(c)Figure 5.8: Inversion of the forward modelled data (Figure 5.6b) using an (a)L2 norm and (b) L1 norm for φm. In (c), an L1 norm is used and αz isreduced from 1 to 0.1. In each panel, (a) compares the observed (blue)and predicted (orange) data, (b) shows the normalized data misfit foreach time channel, (c) compares the recovered model (black), the truemodel (blue), and the initial/reference model (orange).109pect in the recovered model. These parameters can be carried over to the inversionof field data in 1D and using a pseudo-3D approach.1D inversion compared to boreholesDecay curves from the field data set are now individually inverted in 1D using theparameters determined earlier. It was observed that the data were very clean andcould be easily fit to uncertainties of 1.5% plus a noise floor of 1e-12 V. Here, aninitial and reference model of 25 Ωm was used. I focused on four decay curvesthat lie near well locations with resistivity logging data. The inversions used an L1norm in the regularization term and the predicted data fit the observed data well.For each of the four inversions, the observed and predicted data, the misfit, andthe recovered model are shown in Figures 5.9a-5.9d. The results show that therecovered model mimics the borehole resistivity log and brings out specific layers.Most notably is the large conductive layer between 100 m and 170 m belowthe surface. This conductor agrees with the expected depth of the Clearwater For-mation, or the shale cap rock that overlies the oil-laden McMurray Formation. TheMcMurray Formation itself is more resistive than the reference model, which is ex-pected, but does not read the same resistivity values as the borehole log. As seen inthe synthetic example, this is likely because the data lose sensitivity to the geologicstructures below the conductive cap rock.Above the Clearwater Formation, multiple structures are identified, which arelikely related to variances in the Quaternary glacial tills and the Grand RapidsFormation. There is significant disagreements between the recovered models andthe resistivity logs for these layers, which may be due to smaller 3D variances inthe geology and the fact that the decay curves may be up to 200 m away from theborehole. A 3D model from inverting more data would provide better informationabout the spatial extent of the resistivity structures of this region, compared to afew sparse locations.5.3.3 Regional pseudo-3D inversions of field dataTo obtain a pseudo-3D model, the VTEM data set is downsampled to 5,772 sound-ings (Figure 5.10), which are cooperatively inverted in 1D using lateral constraints110(a) (b)(c) (d)Figure 5.9: Inversion of the field data located near 4 boreholes with resistiv-ity logging data. In each panel, (a) compares the observed (blue) andpredicted (orange) data, (b) shows the normalized data misfit for eachtime channel, (c) compares the recovered model (black), the true model(blue), and the initial/reference model (orange).111Easting (m)-2000 -1000 0 1000 2000 3000 4000 5000 6000 7000 8000Northing (m)-20000200040006000800010000120001400016000Figure 5.10: The downsampled VTEM data set contains 5,772 data locations.The blue line indicates the boundary of the Aspen property.(Fournier et al., 2014). The 1D models are interpolated onto a 3D mesh to gener-ate a pseudo-3D model. The 3D model has cells that extend 200 m in the eastingand northing directions and 5 m in the vertical direction, allowing detailed infor-mation about the subsurface layers to be recovered. This method is appropriatefor this region as the 1D assumption holds fairly well, given the expected layeredgeology at the Aspen property. For each inversion iteration, the reference modelis updated to include the influence of nearby soundings. This gives a large-scaleregional resistivity model.The recovered model is interpreted using known geologic information aboutthe area. Figure 5.11 shows a plan-view section through the interpolated 3D modelat an elevation of 470 m (or roughly 30-90 m below the surface). The thin resistiveunit trending northeast-southwest is believed to be associated with a Quaternarypaleo-channel cutting into the underlying Grand Rapids Formation, which is con-11220004000600080001000012000Northing (m)2000 4000 6000 8000 10000Easting (m) 101102ΩmFigure 5.11: The figure shows a planview section from the interpolated 3Dmodel at an elevation of 465 m. The model shows a channel-like resis-tive unit in the centre, with more conductive regions to the northwestand southeast. Solid line shows location of focus for SAGD; dashedline shows location of cross-sections in Figure 5.12.sistent with geologic and seismic data that have been collected in the area (ImperialOil Resources Ventures Limited, 2013). In the northwestern and southeastern por-tions of the model, the shaley Grand Rapids Formation shows at lower elevation asa conductor. This plan-view image indicates the great spatial details and variationsin the geologic structures above the Clearwater Formation that can be obtainedusing EM data.Cross-sectional views of the 3D interpolated model are shown in Figure 5.12.The recovered model shows that the topography changes from approximately 500m to 560 m in elevation from west to east. Notably, the large conductor startingat an elevation of about 400 m does not follow the topography but instead is is113Figure 5.12: The figure shows cross-sections at a northing of 12.6, 8.4, and3 km. The figures are vertically exaggerated to show variations inthe conductivity with depth. Solid black lines indicate the tops of theGrand Rapids, Clearwater, and McMurray Formation determined fromthe recovered model.very flat with a thickness between 30 and 100 m. This conductor is interpretedas the Clearwater Formation and its uniform conductivity of 7 Ωm and relativelyuniform thickness is a first indicator that it may act well as a cap rock for SAGDoperations. Above the Clearwater Formation, there are several layers, including athin conductive unit at the surface. Below is a resistive unit that varies in thickness.It is at its thickest towards the west, with agrees with the end of the channel notedin Figure 5.11. Towards the east, this resistive unit thins out and more conductiveunits underlie it. These two units are associated with the Quaternary glacial tillsand the Grand Rapids Formation.Isosurfaces for the tops of the Grand Rapids, Clearwater, and McMurray For-mation were calculated by choosing transitional resistivity values. These bound-aries are shown in Figure 5.12. While it was originally thought that only minimal11420004000600080001000012000Northing (m)2000 4000 6000 8000 10000Easting (m) 2000 4000 6000 8000 10000Easting (m) 300310320330340350Elevation (m)Figure 5.13: Comparison between the top of the McMurray Formation from(a) borehole core logging and seismic data and (b) the recovered modelfrom inversion. Panel (a) is courtesy of Imperial Oil (Imperial OilResources Ventures Limited, 2013).information could be extracted about the McMurray Formation from the EM data,the calculated isosurface shows very similar structures and characteristics to thestructure map by Imperial Oil Resources Ventures Limited (2013), as shown inFigure 5.13. In addition, the elevations recovered from the model for the Mc-Murray Formation are very comparable to those from borehole core logging. Thissuggests that airborne EM can be a great exploration and first-hand interpretationtool for oil sands deposits in Alberta. The recovered model also shows that theMcMurray Formation is more resistive than the other layers but it is unlikely thatthe airborne EM system has enough sensitivity to detect the bottom of the forma-tion, the unconformity at the Devonian limestone, and any salts or salt dissolutionthat may be present. In addition, without more information, it would be difficultto interpret the thickness of the Wabiskaw Member, which is expected to be a 5 mtransitional layer between the Clearwater and McMurray Formations.The recovered layers and resistivity values in the interpolated 3D model aresimilar to those from an airborne time-domain survey using the AeroTEM system11580009000Northing (m)4000 5000 6000Easting (m) (c)80009000Northing (m) (b)80009000Northing (m) (a)300400500Elevation (m) (a)300400500Elevation (m) (b)300400500Elevation (m)4000 5000 6000Easting (m) (c)101102ΩmFigure 5.14: Comparison of (left) plan-view and (right) cross sections for (a)the coarse pseudo-3D, (b) the fine pseudo-3D, and (c) the 3D recoveredmodels. The left-hand figures are at an elevation of 465 m. The right-hand figures, at a northing of 8.4 km, are vertically exaggerated toshow variations in the conductivity with depth.116over a Husky property, directly north of the Aspen property (Figure 5.2) (Zhdanovet al., 2013). This indicates that by using the VTEM system and the pseudo-3Dinversion method, similar information can be extracted.5.3.4 Local pseudo-3D inversion of field dataThe goal is to use the airborne data to build a detailed background resistivity modelthat can be used when monitoring SAGD steam chamber growth using EM meth-ods. The pseudo-3D model shows many details but the mesh is coarse, comparedto the size of SAGD chambers (approximately 1 km long and separated by 100m at the base). Thus, the focus becomes a smaller region that is of interest forSAGD development (Imperial Oil Resources Ventures Limited, 2013) and increasethe data density used in the pseudo-3D inversion. The region is approximately 2.7by 2 km and lies roughly in the middle of the survey area. The mesh is now finer,using cells that are 30 m in the easting and northing directions. The pseudo-3Dinversion is repeated to invert 2,284 soundings and recover a detailed resistivitymodel of this smaller region. Figure 5.14 compares the fine pseudo-3D recoveredmodel with the portion of the coarse model in the same area at the same elevationof the coarse model shown in Figure 5.11. The finer mesh and greater data densityallowed for significantly more detail in the recovered model. This model can serveas an initial and background model in time-lapse inversion of SAGD chambers.5.3.5 Local 3D inversion of field dataAlthough providing a 3D model, the above results are based on 1D inversions,which would not account for 3D effects. If 3D structures are predominant inthis region, the pseudo-3D methodology may not accurately represent the geology.Therefore, it is important to test the pseudo-3D model against three-dimensionalelectromagnetic computations. To validate, data are forward modelled in 3D on anocTree mesh with the same base cell size and using the pseudo-3D model. Thesecalculated data are compared to the observed field data to understand how well thepseudo-3D model represents the region. The findings indicate that in some partsof the survey area, the calculated data fit the observed data well, meaning that thepseudo-3D model provides an accurate representation. However, in other regions,117Figure 5.15: Using the pseudo-3D recovered model, data were forward mod-elled in 3D (blue line) and compared to observed field data (black cir-cles). The mismatch between the soundings in (a) suggests that thedata contain 3D effects that cannot be explained by the pseudo-3Dmodel while (b) shows that in some areas, the pseudo-3D model ap-pears valid.the data fitting is not as nice, suggesting there are 3D structures that cannot be re-covered using the pseudo-3D methodology. Figure 5.15 compares the soundingsfor two different locations, showing how 3D effects may not be captured in thepseudo-3D model. The calculated data fit the observed data well through most ofthe middle and late time channels, with variations largely present only in the earlytime channels. This suggests that the 3D structures exist closer to the surface, andlikely in the Quaternary layer, whereas the Clearwater and McMurray Formationsare more one-dimensional. These conclusions are supported by what is knownabout the local geology.Considering these findings, it is worthwhile to invert the airborne data in 3D.The pseudo-3D model serves as an initial and reference model, providing a warmstart for the 3D inversion. A subset of 571 soundings are inverted in 3D usingparallelization and local meshes (Yang et al., 2014). Plan-view and cross sectionsof the recovered model are compared to the coarse and fine pseudo-3D models inFigure 5.14, showing small differences in the top layers. The Clearwater Formationremains relatively unchanged, as was expected. The 3D model is shown in Figure118Figure 5.16: 3D model from inverting the VTEM airborne data in three di-mensions.5.16.5.3.6 Modelling the McMurrayUsing the airborne EM data, a highly detailed background resistivity model wasrecovered. However, the data have limited sensitivity to the McMurray Formationand the inversion could recover neither the bottom of the reservoir nor provide anestimate of its resistivity. The core and logging data, shown in Figure 5.3, are usedto add a semi-synthetic reservoir to the recovered 3D model, shown in Figure 5.17.To recover the reservoir and underlying Devonian, a second survey is required.Surface-based loops can be larger than airborne loops, generating greater currentsin the subsurface. Receivers at the surface can measure 3-component electric andmagnetic fields to detect deeper layers and recover them using 3D inversion. Here,EM data are forward modelled using a survey consisting of a 1 km by 1 km surfaceloop with 627 receivers at 4 distinct frequencies: 10, 25, 40, and 70 Hz. Thesurvey geometry is shown in Figure 5.18. The receivers measure the two horizontalcomponents of the electric field and the three components of the magnetic field.Gaussian noise is added to the data and uncertainties are assigned as a percentage119Figure 5.17: A semi-synthetic McMurray Formation and Devonian basementare added to the 3D recovered model in Figure 5.16 using the well logdata (Figure 5.3).of the data plus a noise floor. The airborne result is used as the initial and referencemodel. The recovered model is shown in Figure 5.19. The reservoir is recoveredwhile preserving the information about the upper layers. On the downside, thetransition between the Clearwater and McMurray Formations is smoother in therecovered model compared to the true model. This shows a limitation of using theL2 norm in the EM inversion. A blockier model could be obtained by employingthe L1 norm in the model objective function (Equation 1.15).5.4 Stage IIIWhile waiting for approval from the Alberta Energy Regulator, SAGD scenariosare modelled to determine appropriate EM monitoring surveys. Synthetic cham-bers are added to the resistivity model (Figure 5.21), using the formulation by Reis(1992), which was previously used in synthetic SAGD studies by Reitz et al. (2015)and in Chapter 3. Chapter 2 investigates possible monitoring surveys, includingthose with inductive source transmitters, which use ungrounded wire loops. Loopsat the surface can have side ranging from 10 to 1,000 m or in boreholes, coils are120Figure 5.18: A surface EM survey, using a 1 km by 1 km loop and 3-component E and B receivers, is used to recover information aboutthe reservoir after the airborne EM survey.Figure 5.19: Inversion of E and B data from a surface EM survey (Figure5.18) recovers the McMurray Formation.121Figure 5.20: An EM survey using two transmitters (each 1 km by 1 km loops)at the surface. Receivers are placed in boreholes (black dots) and mea-sure Ez. The survey is used to monitor steam chamber growth overtime.used. Grounded current electrodes, such as those used in DC resistivity, can beused both at the surface or in boreholes at multiple frequencies or times to excitethe earth galvanically. SAGD modelling allows for winnowing of feasible surveydesigns and determining what types of EM instrumentation need to be installedduring the construction stage.Chapter 3 showed that a combination of large transmitter loops with boreholereceivers detect steam chambers at Aspen while limiting survey costs. The re-ceivers, using electrodes, measure only the vertical component of the electric field,which can withstand the high-heat environment and collect multi-year data (Tøndelet al., 2014). Existing observation wells are used to minimize additional drillingcosts. The use of two (or more) loops at the surface excite the chambers in or-thogonal directions, providing different information about the chambers. Such aconfiguration allows for better recovery of the chambers through inversion than a122Figure 5.21: Synthetic steam chambers are added to the background modelin Figure 5.17, generating a realistic model which is used to detect andimage chamber growth using EM.single transmitter alone. This survey configuration, shown in Figure 5.20, is usedin Stage V to detect and image the chambers shown in Figure 5.21.5.5 Stage IVInfrastructure is built during Stave IV, and included pipes, buildings, roads, andpower lines, which are all sources of noise and affect EM data. Once constructionfinished and the monitoring EM surveys are installed, collecting and inverting databefore SAGD commences allows for an updated background model to be used asthe initial model for chamber growth monitoring. Understanding how the infras-tructure impacts the EM and resistivity model can provide key information aboutreliability, repeatability, and noise levels within the data.5.6 Stage VDuring production, the permanently-installed EM surveys are used to monitorsteam chamber growth. Because of the installation constructed in Stage IV, data123can be collected periodically in the same location. While seismic surveys are col-lected every 1-2 years, EM can provide more frequent information about the cham-ber growth. As steam growth occurs relatively slow compared to EM data collec-tion, multiple data sets increase signal-to-noise ratio and provide better data uncer-tainty estimates. In addition, unlike borehole temperature and pressure monitoring,inversion of EM data readily provides a 3D image that can easily be interpreted.Semi-synthetic steam chambers were added to the background model (Figure5.21) and EM data were forward modelled using two loops on the surface andborehole receivers that measure the z-component of the electric field. Noise isadded to the data and uncertainties are assigned prior to inversion. A backgroundmodel built from airborne and ground-based EM surveys is used as the initial andreference model in the inversion. Changes to the resistivity are limited to the regionwithin the reservoir. The results, compared to the true model in Figure 5.22, showthat the chambers are well-recovered in size and shape, including areas where nosteam has penetrated and areas where the steam meanders. The data were invertedon 3 cluster nodes with 24 processors and produces a recovered model in 19 hours,indicating that the feasibility of EM to monitor steam growth is almost real-time.5.7 Stage VIOnce SAGD production stops, reclamation must return the site to its original state.An environmental assessment determines the impact of SAGD on the region. Here,EM methods aid in understanding how the area changed due to steaming the sub-surface. Airborne surveys delineate changes in channels and aquifers within theQuaternary and identify changes to the resistivity of the Clearwater Formationwhen compared with the airborne survey, and recovered resistivity model, col-lected in Stage II. This provides insight into the cap rock’s integrity over time andeffects of SAGD’s high temperature and pressure environment. Finally, ground-based and monitoring surveys show how the reservoir has changed, now that theoil has been removed from the sand matrix. These post-SAGD surveys can providegreater insight into the environmental effects of SAGD.1248900900091009200Northing (m) (a)8900900091009200Northing (m)4400 4600 4800Easting (m) (b)20406080100120140ΩmFigure 5.22: Plan-view slices (z = 320 m) for (a) the true model and (b)the recovered model, showing three irregularly-shaped SAGD steamchambers.5.8 ConclusionUsing the development timeline for a SAGD site, this chapter showed how elec-tromagnetic methods can be utilized at each stage to provide detailed informationabout the Athabasca oil sands geology, both at the regional and local scale, andhow to detect and image SAGD steam chambers. Inversions of airborne EM dataallow for detailed models to be recovered and monitoring surveys accurately re-cover steam chamber locations and extents while delineating blockages or areaswith no steam penetration. This chapter places previous chapter into context forSAGD development and production, providing a start-to-finish approach on how touse EM in the Athabasca oil sands.125Chapter 6ConclusionSteam-assisted gravity drainage remains the predominant in-situ extraction methodfor heavy oil in the Athabasca oil sands. The steaming procedure changes theelectrical resistivity of the oil reservoir, which creates a physical property contrastthat can theoretically be monitored using electromagnetic methods. This thesis setout to answer that question and the research has shown that EM is a promisingtool to detect and recover steam chambers as well as provide information about thesurrounding geology.The work done answered the specific questions posed at the start of this thesis:1. What survey designs allow detection of the steam chambers and how canthey be recovered using inversion?• The research showed that galvanic borehole methods and the combi-nation of surface inductive loops with borehole receivers are the mostpromising EM surveys for monitoring steam growth in the Athabascaoil sands. Recovery using inversion benefited from using active cellswhich limited resistivity changes to the reservoir and smoothing alongthe horizontal wells.2. How does the geologic background affect survey design and the feasibilityof using EM?• The overlying, conductive cap rock is a major impediment to using126EM surveys (both galvanic and inductive) at the surface, and therefore,borehole measurements were required to detect the steam chambers.Location within the Athabasca oil sands also matters: the conductiveoverburden at Leismer was significantly thicker compared to Aspen,meaning that the surface inductive transmitter and borehole receiversurvey used at Aspen could not detect the steam chambers at Leismer.3. Can the resistivity of the background models and steam chambers be relatedback to geology? How is this information useful for SAGD operations?• The airborne EM provided a wealth of geologic information aboutthe upper layers, including aquifer-related channels and the depth andthickness of the cap rock. The research showed that the resistivity ofthe steam chambers is affected by the temperature and salinity, as wellas other parameters, and thus indicates the presence of steam. Specif-ically, the EM results imaged a gap in the steam as a resistive region.Such information can be critical to SAGD operations: steaming can beadjusted to improve the steam-to-oil ratio and produce more oil.In this concluding chapter, I summarize the research and its impact on SAGD, aswell as outline new questions and future work.6.1 Feasibility of electromagneticsChapter 2 investigated how electric and electromagnetic methods can be used in theAthabasca oil sands to detect growing SAGD steam chambers. The research startedby using DC resistivity based on current industry practices. The results indicatedthat 3D inversions are necessary to mitigate artifacts that can arise from using 2Dinversions. The research also showed that by specifically designing a survey todetect a 3D anomaly, the same recovery can be achieved but using fewer data,thus decreasing data collection and computation time. However, the DC resistivityresults lacked resolution in both shape and amplitude.This motivated the use of electromagnetic methods, which greatly improved therecovered models. In all cases, a combination of borehole receivers with an EMtransmitter provided data that were highly sensitive to the steam chamber, and the127inversions recovered models with superior resolution in shape and better recoveryof the resistivity amplitude. In addition, it became feasible to distinguish the shapeof the steam chamber as growing irregularly. Of special significance was the resultobtained from using a surface transmitter and borehole receivers, which decreasesurvey costs but can still allow for a permanent installation. Because of the utilityand cost-effectiveness of this survey, it was further investigated for a field-basedexample in Chapter 3.6.2 Recovery using large surface transmitters andborehole receiversIn Chapter 3, I applied an EM survey using large surface loop transmitters and bore-hole receivers to a synthetic example based on the Aspen property in the Athabascaoil sands. Data measurements were limited to the vertical component of the electricfield within observation wells. The benefit of this survey design is that the elec-trodes can withstand the high-temperature SAGD environment, and the loop trans-mitters are easily deployed at the surface. Configurations with two transmitterswere examined and the research showed that they generated orthogonal excitationswithin the reservoir. Although each survey separately provided valuable informa-tion about the SAGD steam chambers, the combination of the two transmitterssubstantially reduced artifacts and produced an image with enhanced resolution.In this study, the location and extend of a no-growth area were discernible usingtwo transmitters, showcasing the ability of EM to image small details of the SAGDsteam chambers.Further research shows the impact of incorporating a priori information into theinversion. Directional smoothing based on the location of the horizontal injectorand producer wells provided better images. The addition of magnetic field datagreatly improves the shape and recovered resistivity and better defines distinctionbetween the three neighbouring chambers.Time-lapse examples showed that the EM survey design used here can readilymonitor chamber growth and at a greater frequency than typical seismic surveys.The ability to permanently install transmitters and receivers means data can becollected often and remotely. Combined with efficient inversion techniques and128a priori information, these EM methods allow for fast turn-around and practicallyreal-time results. This greatly impacts monitoring capabilities when combined withother surveys collected in the Athabasca oil sands.6.3 Improving recovered models by analyzing surveydesignChapter 4 is based on a field example where DC resistivity data were collectedin two vertical wells multiple times per day to monitor the growth of two steamchambers. A synthetic model was built based on the background geology and pop-ulated with steam chambers. The field-based surveys were used to investigate thesensitivity of the surveys to changes in the model. Calculating the approximatesensitivity is computationally fast and provided a first-order glimpse at the effi-cacy of the survey design and what a full 3D inversion can recover for differentmodel scenarios. Results using the standard DC resistivity surveys showed thatthe chambers are not recoverable for all scenarios. By using multi-frequency EM,the sensitivity to the reservoir is increased even though the survey layout did notchange. The inversion was able to recover the steam chambers using EM data. Fortime-lapse steam chamber growth, using multi-frequency EM allowed for betterrecovery of the chambers compared to using DC resistivity.6.4 Heavy oil exploration and monitoring using EMThe previous chapters investigated the feasibility of several EM methods to detectand image conductivity changes due to steam injection. Different surveys wereapplied to two field sites, showing that in each case, the EM surveys recover high-resolution information about the steam chambers. In Chapter 5, I show how sev-eral EM survey types can be applied to exploration and monitoring of a heavy oilregion. Airborne electromagnetic data were inverted to recover the backgroundresistivity structures at the Aspen property. The results showed that the airbornedata provide regional information about the layers above the heavy oil reservoir,including the thickness and uniformity of the cap rock. Because of the high con-ductivity of the overlying layers, the data are not sensitive to the reservoir itself.A surface survey using a large loop transmitter and surface receivers is used to re-129cover the reservoir before SAGD is implemented. The combination of the airborneand surface surveys allow for the recovery of a complete background model using3D inversion. Steam chambers are added to the reservoir and recovered in inver-sion using the same survey design as in Chapter 3. The work in this chapter placesthe previous chapters into context for SAGD development, production, and moni-toring, providing a start-to-finish methodology on how to use EM in the Athabascaoil sands.6.5 Future researchThe research presented in this thesis shows the feasibility of EM methods to mon-itor SAGD steam chambers and recovers the conductivity changes through 3D in-versions. While the work answered these questions, it has also raised new questionsand the research can benefit from future work.SAGD well pads have much infrastructure including steel-cased horizontal in-jector and producer wells. In addition, observation wells may or may not be cased.This thesis did not address the impact steel-cased wells can have on the electricand electromagnetic data measured using the proposed surveys but is a necessaryresearch topic to further understand the application of EM to SAGD monitoring.In order to do so, the casing must be included in the resistivity modelling as it isexpected to affect the EM data. Research on this can shed further light on howmuch casing affects the currents from EM sources and what the best practices arefor including it in the forward modelling and inversion of EM data.Furthermore, the work done in this thesis can benefit from the addition of otherdata collected. Joint inversion with seismic can provide complimentary informa-tion to better constrain the final models. The study of how steam injection changesconductivity can shed light on what other parameters can be included in the in-version, such as measured temperature and pressure in boreholes. In addition, thisthesis solely focused on conductivity but studies have shows that the conductivitymay be frequency-dependent. The impact of complex conductivity deserves to bestudied in terms of the proposed geophysical surveys in this thesis. By further un-derstanding the relationship between the EM data and the relevant physical proper-ties, recovered models can be better interpreted and provide enhanced information130to production engineers.The time-lapse inversion schemes used in this thesis were simple and the lit-erature contains many examples of improved time-lapse recovery of conductivitychanges. As SAGD steaming is a continuous process, the work would benefit fromincreased research into time-lapse inversion methodologies. Examples on how toimprove time-lapse recovery include altering the model objective function to notonly regularize in space but also in time and incorporate fluid flow into the inver-sion.Finally, the research presented in this thesis is not specific to SAGD steammonitoring. As mentioned at the start, steam is used for oil recovery in other re-gions besides the Athabasca oil sands and can injected using vertical wells too, asin cyclic steam simulation. In more recent years, steam injection has become amethod to recover contaminants in the subsurface and the research in this thesiscan be applied to those situations as well. 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