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Investigating the dependence of proton T₁ relaxation on pore size, pore fluid salinity, and pore fluid… Kanters, William Andrew 1996

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INVESTIGATING THE DEPENDENCE OF PROTON Tj RELAXATION ON PORE SIZE, PORE FLUID SALINITY, AND PORE FLUID pH IN WATER-WET AND OIL-WET SAND PACKS by WILLIAM ANDREW KANTERS B.Sc, University of Waterloo, 1993 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE in THE FACULTY OF GRADUATE STUDIES DEPARTMENT OF GEOLOGICAL SCIENCES We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA February, 1996 © William Andrew Kanters, 1996 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of &£0U?^'/^/)L SC<£<^Z-£~S The University of British Columbia Vancouver, Canada Date <f £/0l/27 DE-6 (2/88) Abstract The dependence of the proton nuclear magnetic resonance parameter, T l 5 on surface wettability, grain size, and pore fluid chemistry was investigated using laboratory prepared silica sand packs. A pulsed proton NMR spectrometer, with a proton Larmour frequency of 90 MHz, was used to obtain the Ti relaxation data. Pore fluid Ti data were found to be dependent on the surface wettability of the sand packs. An observed difference in T! of approximately 1 second was obtained between 100% water-wet and 100% oil-wet sand packs, when the pH of the pore fluid was neutral. This difference in T l f between the water-wet and oil-wet samples when saturated with distilled water, was observed for a range of different pore sizes. T! relaxation time was found to depend on sand pack grain size in both the water-wet and oil-wet samples. This indicated the presence of surface relaxation in the samples. Calculated surface relaxivities produced average values of 1.2 x 10"3 cm/s and 2.6 x lO^cm/s for the water-wet and the oil-wet samples respectively. Pore fluid chemistry was found to affect T! relaxation measurements in water-wet and oil-wet sand packs. Experimental results indicated that although Tj was unaffected by pore fluid salinity it was dependent on the pore fluid pH. Results showed that as pore fluid acidity increased, Ti relaxation times decreased in both the water-wet and the oil-wet sand packs. This enhanced relaxation at lower pH's was attributed to increased pore fluid relaxation at the grain surfaces. ii Table of Contents Abstract ii Table of Contents iii List of Tables v List of Figures vi Dedication vii Acknowledgments viii 1. Introduction 1 2. Background Information........................... .................—.................... ... 5 2.1 Fundamentals of Wettability 5 2.2 Wettability Measurement Techniques 6 2.2.1 Contact Angle Method 7 2.2.2 AmottMethod 8 2.2.3 USBMMethod. 8 2.2.4 Summary of Wettability Measurement Techniques 9 2.3 Nuclear Magnetic Resonance 10 2.3.1 NMR Background. 10 2.3.2 Longitudinal Relaxation (Ti) 14 2.3.3 Tj Relaxation Curve Interpretation 14 2.4 Mechanisms of Fluid Relaxation 17 2.4.1 Bulk Fluid Relaxation 18 2.4.2 Relaxation in Porous Media 18 2.5 Modeling Relaxation in Porous Media 19 3. Methods and Materials 22 3.1 Sample Material 22 3.2 Treating Sand for Surface Wettability 22 iii 33 NMR Sample Preparation. ... 26 3.3. 1 Sand Pack Preparation 26 3.3.2 Sand Pack Saturation 27 3.3.3 Saturating Solution Properties 30 3.4 NMR Apparatus and Measurements 32 3.5 Relaxation Data Inversion Techniques 33 4. Experimental Design and Results 34 4.1 Ti Relaxation in Sand Packs of Varying Grain Size 34 4.1.1 Pore Fluid: Distilled Water 34 4.1.2 Pore Fluid: pH 2, 0.02 MNaCl brine 38 4.2 Ti Dependence on Pore Fluid Salinity and pH 41 4.2.1 T} Dependence on Pore Fluid Salinity 41 4.2.2 Tj Dependence on Pore Fluid pH. 44 5. Discussion 47 5.1 Ti Relaxation in Sand Packs of Varying Grain Size 47 5.1.1 Pore Fluid: Distilled Water 47 5.1.2 Pore Fluid: pH 2, 0.02 MNaCl brine 58 5.2 Ti Dependence on Pore Fluid Salinity and pH 60 5.2.1 Tj Dependence on Pore Fluid Salinity 60 5.2.2 Tj Dependence on Pore Fluid pH : 62 5.3 Surface Relaxation in Porous Media at Low pH 64 6. Conclusions 68 7. Recommendations 70 8. References .. 71 Appendix A - Sample Information 76 Appendix B - T t Relaxation Curve tau Times 82 Appendix C - Sample Ti Relaxation Curves and Interpretation 86 Appendix D - Sp/Vp Calculations and p Estimates 141 iv List of Tables Table Page 3.1 Chemistry of Solutions used as Pore Fluids 31 4.1 Grain Size Data for Sand Used in Prepared Sand Packs 35 5.1 Pore Diameters Calculated from Grain Size Data 50 5.2 Results from Performing Linear Regression on a Plot of 1/Tj versus S/Vp 54 v List of Figures Figure Page 2.1 Sample Magnetic Moments and Net Magnetization of the Sample 11 2.2 Application of rf Pulse and Net Magnetization Rotation 13 2.3 Tj pulse sequence: a 180-X-90 sequence 15 2.4 Representative Tj Relaxation Curve 16 3.1 Outline of the Oil Wetting Process used to Create Oil-Wet Sands 24 3.2 Teflon Cell used to Prepare NMR Samples 28 3.3 High Pressure S aturation Cell Apparatus 29 4.1 Tj versus Grain Size, Pore Fluid: Distilled Water 36 4.2 Tj versus Grain Size, Pore Fluid: pH 2, 0.02 M NaCl 40 4.3 Tj versus Salinity Concentration, Pore Fluid: Distilled Water to 1.0 M NaCl 42 4.4 Bulk Tj for Various Salinity Solutions used in Figure 4.3 43 4.5 T, versus pH, Pore Fluid: pH 2 to 7 45 4.6 Bulk Tj for Various pH Solutions used in Figure 4.5 46 5.1 Tj versus r, A Comparison to show Linearity between Tj and r 51 5.2 p versus Grain Size, Pore Fluid: Distilled Water 53 5.3 1/Tj versus Sp/Vp, A Comparison to Determine p 55 5.4 p versus Grain Size, Pore Fluid: pH 2, 0.02 M NaCl 59 5.5 p versus Salinity Concentration, Pore Fluid: Distilled Water to 1.0 M NaCl 61 5.6 p versus pH, Pore Fluid: pH 2 to 7 65 vi To My Mom For all the help over the years, For being there when I needed You, For showing me what true strength is, For all the smiles and laughs, Thank You. vii Acknowledgments I would like to thank my committee members, Dr. Rosemary Knight, Dr. Alex MacKay, and Dr. Roger Beckie, for all their guidance and support. Rosemary, your enthusiasm and continual support for my work gave me the needed energy to keep at it. Alex, thank you for giving me all the time you did and providing laboratory facilities for me to perform my experiments. Roger, your insight and suggestions allowed for the project to develop smoothly. I would like to thank Paulette Tercier, Dave Butler, Kevin Jarvis, Jane Rea, and Mike Knoll from the Rock Physics Group at UBC for all their help during this project. Also, I would like to thank Irene Lees, Resa Estilaei, and Frank Linseisen, all from Hennings 100. Your help was greatly appreciated. The technicians of the Geological Sciences Department, Marc Baker, Bryon Cranston, Ray Rodway and Doug Poison, all had a hand at making the work presented here possible. Their support and ideas allowed for my work to proceed efficiently. Thanks goes out to all of you. I would also like to thank the office staff in the Geological Sciences Department, Theresa Karchewski, Donna Anderson, and Nancy Myrah. The three of you made dealing with the University much easier. I would like to thank all my friends, old and new, who have made being at UBC an experience for me. You were there when I needed to discuss my work, but more importantly you were there when I needed a break. Last, but definitely not least, I would like to thank NSERC for awarding me a PGS-A graduate scholarship and Imperial Oil for providing the funding for this work through a University Research Grant. viii 1. Introduction Wettability is a measure of the preference a pore surface has to be in contact with a particular fluid. It is an important characteristic of oil reservoirs because it will govern fluid distribution and fluid flow in the pore spaces. In oil reservoirs there are three main wettability types: water-wet, oil-wet, and neutral-wet. Describing a rock as oil-wet indicates that in the presence of two fluids, one of these being oil, the rock would spontaneously imbibe the oil. The ability to measure wettability is important to petroleum engineers that wish to maximize the performance of a producing field. There exists a number of qualitative and quantitative techniques that can be used to obtain information on the nature of a porous medium's wettability. Qualitative techniques provide only limited data on a reservoir's wettability and therefore are not widely used. Quantitative techniques provide more detailed information on the wettability of a surface. Three quantitative techniques are generally used: contact angle measurement, the Amott test, and the U.S. Bureau of Mines (USBM) technique. These three techniques, however, share two common disadvantages: they are labor intensive and they provide averaged, or idealized measurements of a porous medium's wettability. In an attempt to better measure wettability, research continues to improve existing techniques and to possibly develop new ones. A technique that was developed in the 1950's but has not been extensively used in wettability studies is proton nuclear magnetic resonance (NMR). NMR was first introduced by Bloch et al. [1946] and Purcell et al. [1946] and was used initially as a tool to investigate molecular scale mechanisms, such as structural bonding in molecules. Measurements on the molecular scale can be made with NMR because it measures the change in energy state of molecular nuclei. Wettability differences within a porous medium alter the amount of fluid-surface interaction that 1 occurs. It was therefore hypomesized"by"Brown andPatt [1956] that 'NMR may "be useful for detecting this change in the surface property. NMR has been used in a large number of fields since its introduction in 1946. It is used in the medical field for body imaging; for quality control and quality assurance in the food industry; and scientists, particularly chemists and physicists, use it to investigate topics ranging from the structure of a chemical bond to the amount of water in the ground. The versatility of NMR has led to its application in petrophysical studies. It has been used to estimate pore distributions in sandstone [Straley et al., 1991; Howard and Kenyon, 1992], to determine the degree of saturation in sandstone [Straley et al., 1991], to detect hydrocarbon contaminants in porous rocks [Hedberg et al., 1993], to predict the permeability of porous media [Borgia et al, 1992], and to measure pore surface wettability [Brown and Fatt, 1956; Williams and Fung, 1982]. Advancements in Magnetic Resonance Imaging (MRI), a spin-off from NMR, have allowed 3-dimensional mapping of fluid distributions in porous media [Baldwin, 1989]. The versatility of NMR is in part attributed to its ability to measure different parameters. One of the more commonly used NMR parameters is the relaxation time constant, T,. T, is the exponential time constant obtained as the longitudinal component of a sample's net magnetization returns to equilibrium after a disturbance. Tl relaxation is recognized to be sensitive to changes in wettability [Brown and Fatt, 1956; Hsu, 1994]. T! relaxation is affected by the wettability of a porous medium because fluids relax differently in confined spaces than when in bulk solution. In bulk solution, relaxation of the protons occurs due to energy being transferred from the protons to the system, or lattice. Fluid in a pore space continues to relax due to bulk relaxation, but relaxation at the fluid-surface boundary also occurs. Surface relaxation has been found to be much more efficient in removing excess energy from excited nuclei than bulk relaxation. As a result, Ti measurements made on fluids confined in a pore space will produce relaxation times significantly smaller than those obtained for bulk solutions. The nature 2 of the pores, such-as surface characteristics and geometry, as well as the type - of pore fluid, will determine the degree to which surface relaxation occurs. For example, the fluid-surface interactions in a water-wet system will differ significantly from that of an oil-wet system. It is for this reason that Tj data are useful for measuring changes in wettability. The sensitivity of T! relaxation to fluid-surface interactions was first demonstrated by Brown and Fatt [1956]. Brown and Fatt used an NMR apparatus to measure the proton relaxation of water-saturated water-wet and oil-wet sand packs. The oil-wet sands had been created using a silicone fluid SF 99 DriFilm, which is a reactive dimethylpolysiloxane used to yield water repellent coatings on silica surfaces. They found a linear relation between the Tj relaxation rate of the pore fluid and the quantity of oil-wet sand present in a sample. This demonstrated that NMR could be used as a tool to measure wettability differences in porous media. NMR as a tool to measure wettability was further studied by Williams and Fung [1982]. Williams and Fung used glass beads and pulverized sandstone as their porous media that were either treated with silicone or left untreated to obtain different surface conditions. They found that the oil-wet surfaces provided even greater relaxation than the water-wet surfaces, in apparent contradiction with the results of Brown and Fatt [1956]. Williams and Fung [1982] explained their enhanced relaxation at the oil-wet surface as due to the presence of methyl groups on the surface. These results did not support the use of NMR as a tool to measure wettability differences in porous media. In an attempt to clarify the conflicting results described above, a doctoral thesis was completed by Hsu [1994] to explore NMR relaxation as a measure of wettability. Hsu used glass and polymer beads, either clean or coated with one of five materials, to determine if Tj was affected by the composition of the oil-wetting film. His results showed that T x was dependent on the oil-wet film composition and demonstrated that Tj 3 data could be used to measure wettability differences in porous media provided factors, such as magnetic impurities in the oil-wet film, were negligible. Many factors can affect porous media wettability including crude oil composition, pore fluid chemistry, system temperature, and length of time over which the system has been allowed to interact. Previous investigations have shown that T\ is affected by some of these properties. The objective of this study was to improve the current understanding of how T, relaxation measurements depend on porous media wettability. Specifically, the dependence of Tj on pore size, pore fluid salinity, and pore fluid pH in water-wet and oil-wet sand packs was investigated. 4 2. Background Information 2.1 Fundamentals of Wettability Wettability is defined as "the tendency of one fluid to spread on or adhere to a solid surface in the presence of other immiscible fluids" [Craig, 1971]. This implies that in a water-wet system the rock has a preference for water to form a continuous film on the pore walls and cover the majority of the pore surface area. For an oil-wet rock, the grain surfaces prefer to be in contact with oil. Wettability is a measure of a rock's wetting preference and does not necessarily indicate which fluid is in contact with the rock [Anderson, 1986a]. For example, an oil-wet rock saturated with water would preferentially imbibe oil and displace the water even though water was originally in contact with the surface. Several factors govern the type of wettability in a rock-fluid system. These include crude oil composition, mineral surface charge, temperature, brine salinity, solution pH, pressure, aging time for fluid-surface contact, and fluid-reservoir history [Anderson, 1986a; Liu and Buckley, 1994; Jadhunandan and Morrow, 1995]. The more important of these factors are discussed below. Crude oil composition plays a key role in determining the likelihood of a surface becoming oil-wet. The surface-active agents in crude oil which affect wettability are believed to be the asphaltenes or the polar groups within the oil [Anderson, 1986a; Morrow, 1990]. Asphaltenes are the components of crude oil which do not dissolve in n-Heptane. Polar compounds, which contain a polar and a hydrocarbon end, generally include oxygen, nitrogen, and/or sulfur. Both the asphaltenes and the polar compounds are found within the heavier end members of hydrocarbons. This has made it difficult to 5 differentiate which of mese functional groups Is responsible for^ ^^m oil-wetted surfaces [Anderson, 1986a; Buckley, 1994]. A rock's surface charge, which is a function of mineralogical composition, also affects the surface wettability. This is because surface charge determines what type of fluid is adsorbed. For example, carbonate generally has a net positive surface charge at neutral pH, while at the same pH silica typically has a net negative charge [Stumm and Morgan, 1970]. Therefore, since oil has a net negative charge at neutral pH, due to the dissociation of carboxylic acids on the oil surface, it is more likely to be adsorbed on the carbonate surface than on the silica one [Buckley et al., 1987; Brown and Neustater, 1980]. The net surface charge of a mineral can be altered by the pore fluid in contact with the surface. By lowering the pH of a solution below 3.5 the surface of silica obtains a net positive charge [Stumm and Morgan, 1970]. As a result the surface will more likely be oil-wet than water-wet [Dubey and Doe, 1993]. The dependence of mineral surface charge on pH illustrates how some conditions will favor a water-wet system while other conditions will favor oil-wet conditions. Elevated temperatures also promote the wetting of a surface by oil. Work completed by Jadhunandan and Morrow [1991] showed that when a core is aged at higher temperatures stronger oil-wet conditions are created. These results were obtained by Jadhunandan and Morrow when Berea sandstone was aged with crude oil at room temperature, 50°C, and 80°C. The strongest oil-wet situations were obtained when the aging temperature was at 80°C. 2.2 Wettability Measurement Techniques Several different methods exist to measure wettability. The three most commonly used quantitative tests are: 1) contact angle measurement [Adamson, 1982]; 2) the Amott 6 method [Amott, 1958]; and 3) the U.S. Bureau of Mines (USBM) method [Donaldson er al, 1969]. Qualitative measurements also exist and include imbibition rates, microscope examination, flotation, and glass slide methods [Anderson, 1986b]. Methods for measuring fractional wettability - where a portion of the core is strongly oil-wet while the remainder of the system is strongly water-wet - are nuclear magnetic resonance (NMR) and dye adsorption [Anderson, 1986b]. Due to the scope of this study only the quantitative measurement techniques are reviewed below. Each of the three quantitative techniques have their advantages and disadvantages in how they obtain a wettability measurement. Contact angle measurements measure the angle which a drop of fluid makes on a specific surface; reflecting the wettability of the surface. Amott and USBM methods measure an average wettability of the core by either imbibition and forced displacement of a fluid (Amott test), or the work required for one fluid to displace another (USBM method). The next few sections will describe these in more detail. 2.2.1 Contact Angle Method The contact angle method measures the angle that is created at a fluid-solid interface. It is the most popular and commonly used technique to quantify wettability [Morrow, 1990]. Contact angle measurements can be made in a variety of different ways; these are reviewed by Neuman and Good [1979]. The contact angle measurement is ideal for situations where pure fluids and artificial cores are used since there is no possibility of the surface wettability being altered by surfactants or other compounds adsorbing to or desorbing from the surface. This technique has allowed for detailed studies on the effects of temperature, pressure, and brine chemistry on wettability and it is the only technique which allows for intermolecular forces to be measured [Fowkes, 1964]. 7 A disadvantage of the contact angle method is that the surface ;under study is usually a polished sample of the mineral being investigated. As a result, the .application of these results to reservoir conditions is questioned, since they do not account for roughness, heterogeneity, or the complex geometry present in reservoir rock. Other problems cited with contact angle measurements are the time required for a stable contact angle to be obtained and the hysteresis in the measurements [Anderson, 1986b]. 2.2.2 Amott Method The Amott method measures average core wettability by spontaneous imbibition and forced displacement of a fluid in the core. It is based on the principle that a wetting fluid will be spontaneously imbibed into a rock, thus displacing the non-wetting fluid. The Amott index, a ratio of the fluid volume displaced by imbibition alone to the total volume of fluid displaced by forced displacement, allows for the influence of other factors such as relative permeability, viscosity, and initial saturation to be minimized. A full description of this method is found in Amott [1959]. A major advantage of the Amott test is that actual reservoir fluids and cores are used in the test. Unlike the contact angle method, direct determination of the average wettability of the core can be made. Disadvantages of the Amott test are that the imbibition measurement can take anywhere from several hours to in excess of a month to complete. The test is also relatively insensitive to neutral wettability situations since spontaneous imbibition of either fluid can occur [Anderson, 1986a]. 2.2.3 USBMMethod The USBM Wettability Index measures the work required for one fluid to displace the other [Donaldson, 1969]. The test is based on the principle that the wetting fluid 8 :requires less energy to displace the"non-wetting fluid than the non-wetting fluid requires :to displace the wetting fluid. Specifically, the test is used to determine the work required for water to displace oil and for oil to displace water. By comparing these two values, a system's wettability can be estimated. An advantage of the USBM test is that it can be completed relatively quickly; four to eight cores can be tested within a few days. Also, native oil field brines and rock cores can be analyzed, these provide representative values for reservoir conditions. Disadvantages of the USBM test are that plug-sized samples are required to facilitate centrifuge spinning [Anderson, 1986b]. As well, the USBM test does not detect a mixed or fractional wetted core. 2.2.4 Summary of Wettability Measurement Techniques Limitations of each of the three quantitative techniques described above are apparent. The contact angle technique, although very popular, is limited by the use of prepared polished surfaces and pure solutions. Contact angle measurements also do not reflect porous media properties such as heterogeneity, roughness, and pore geometry. The Amott and USBM methods provide more information about representative reservoir rocks but are limited because they give average values for a fluid/rock system. Also, the time required to complete the Amott test can be quite long. A technique which could provide detailed information on the type and spatial distribution of wettability in geologic media is desired. A possible tool which could provide that information is nuclear magnetic resonance (NMR) [Brown and Fatt, 1956; Hsu, 1994; Borgia, Fantazzini, and Mesini, 1991]. 9 12.3 Nuclear Magnetic Resonance The following section provides a summary of NMR principles and techniques. A better understanding of how NMR works will make it apparent why NMR is applied in rock property investigations of porosity, permeability, wettability, and other petrophysical characteristics. This summary can be supplemented by referring to NMR texts such as Slichter [1963] or Fukushima and Roeder [1981]. 2.3.1 NMR Background NMR is a technique which monitors the change in energy state of molecular nuclei. To accomplish this, the nucleus must have a magnetic moment (M) which is the result of an interaction between the angular momentum of an atom's nucleus and the electric charge associated with the atom. Some nuclei which possess an intrinsic magnetic moment that are used in NMR research include 'H, 2 H , and 1 3 C . The magnetic moments of individual nuclei act independently and are randomly oriented, resulting in a net magnetic moment of zero for a substance. If these nuclei are placed in an external magnetic field (H0), such as the one present in an NMR spectrometer, the magnetic moments will become aligned parallel to this field. The reason for this alignment is that in this state the magnetic moments are in their lowest energy state. The magnetic moments create a Boltzman distribution with a small excess of magnetic moments aligned parallel to the positive axis of the external field (Figure 2.1). The net magnetic moment (M0) created parallel to the external field is a result of individual magnetic moments precessing about the external field. The magnetic moments of the nuclei are not static and resonate about the positive H D axis. The precession frequency, referred to as the Larmour frequency, depends on the type of nucleus being 10 (a) y / \ Net Magnetization, M CO Figure 2.1 : An illustration showing the magnetic moments of a sample. In (a) there is no external magnetic field and the net magnetization is zero. In (b) the presence of an external magnetic field (HQ) results in the alignment of the individual magnetic moments to create a net magnetization (M) [after Atkins, 1990] . 11 studied and the strength of the external magrieticTield. The Larmour frequency is "defined by the equation: co = ya0 2.1 where co is the Larmour frequency and y is the magnetogyric ratio. NMR measurements are made by removing the net magnetization of the sample from its lower energy state and then allowing it to relax back to this original state. To remove the sample from the lowest energy state a radiofrequency (rf) pulse is used. A rf pulse (Hj) provides energy to the sample which raises the energy state of the nuclei and results in a change to the net magnetic moment (Figure 2.2). H, is applied perpendicular to H 0 to cause rotation of the net magnetic moment away from H 0 in a plane perpendicular to Hp Proper functioning of the rf pulse requires that it be calibrated to the sample Larmour frequency. Once the correct frequency is obtained, the sample is said to be in resonance. The amount of rotation that the M 0 undergoes about the H! field depends on the duration of the radiofrequency pulse. In NMR, commonly used rotations are 90° and 180° pulses. This implies that Hx is applied long enough so that M 0 rotates 90° or 180° during the rf pulse. Once M 0 is rotated and Hi removed, the net magnetization will immediately begin to return to the lower energy state parallel to HQ. The return of M 0 to equilibrium is called relaxation and the time for this to occur is referred to as the relaxation time. A receiver coil is used to measure the net magnetic moment after rotation. The rf coil is oriented to measure the strength of the electromagnetic field (emf) in the horizontal, or x-y plane, which is perpendicular to HQ. The return of M 0 from the x-y plane to equilibrium is thought to be exponential with two time constants, T\ for the longitudinal component and T 2 for the transverse component. T! was the focus of this study and is discussed in detail below. 12 Figure 2.2 : An illustration showing how the rf pulse (Hj) is used to rotate the net magnetization of the sample. In (a) the rf pulse is used to cause a 90° rotation of the net magnetization. In (b) the sample magnetization is measured in the x-y plane using a receiver coil [after Atkins, 1990]. 13 , 2.3.2 Longitudinal Relaxation (TJ Ti relaxation time, or spin-lattice relaxation time, is the exponential time constant for the longitudinal relaxation (Mz) of the sample. Relaxation of the system is a result of an energy exchange between the nuclear spin system and the other degrees of freedom of the system, referred to as the lattice [Gladden, 1994]. Recall that the excess energy provided to the system by the rf pulse must be dissipated for relaxation to occur. The magnitude of the Ti relaxation time reflects the efficiency of energy transfer between the excited nuclei and the lattice. Measurements of T! relaxation are most commonly made with an inversion-recovery pulse sequence. This sequence consists of a 180° pulse followed by a 90° pulse applied after a delay time T. This is commonly referred to as a 180-T-90 pulse sequence and its purpose is to remove the system from equilibrium, allow relaxation over a period of time, and then bring the remaining net magnetization into the x-y plane for measurement using the receiver coil. The 180-1-90 sequence is shown in Figure 2.3. Measurements completed in this way allow for the creation of a relaxation curve when a range of % values are used in the pulse sequence. An example of a relaxation recovery curve is presented in Figure 2.4. 2.3.3 Tj Relaxation Curve Interpretation The relaxation curve derived from the inversion recovery experiments requires interpretation in order to obtain Tj relaxation constants. Several methods are available for interpretation of relaxation data [Kenyon et al., 1986; Munn and Smith, 1987]. This study used the nonnegative least squares (NNLS) algorithm of Lawson and Hanson [1974] as implemented by Whittall and Mackay [1989]. Details of this technique and its 14 M (a) Figure 2.3 : An illustration of the 180-X-90 pulse sequence. In (a) the net magnetization is rotated anti-parallel to the external magnetic field by a 180° pulse, (b) shows the relaxation of the net magnetization after time x. In (c) the remaining magnetization is rotated into the x-y plane by a 90° pulse for detection [after Atkins, 1990], 15 \ \ \ Each line represents the magnetization measured from one 180-T-90 pulse sequence. Figure 2.4 : A typical relaxation curve created using a finite number of 180-T-90 measurements. It is obvious from the curve that as time x increases, the amount of relaxation occurring between the 180° pulse and the 90° pulse increases [after Atkins, 1990]. 16 'limitations are presented by Hedberg et al. [1993] who suggest that theTSINLS algorithm provides no unique solution to the relaxation curve because it is composed of a finite number of inaccurate measurements. Instead of a unique solution from the NNLS algorithm the solution is generally composed of several Tj relaxation time constants. The number of T! values obtained reflects the characteristics of the porous media being studied. For example, a solution which consists of a single T, value indicates that the porous material under study is composed of a relatively homogenous pore network. A solution composed of several T\ values indicates a distribution of pore sizes within the porous solid. Porous media generally consist of a range of pore sizes rather than just one distinct size. Two classes are commonly used to represent Ti distributions; a discrete solution and a continuous distribution. A discrete solution is composed of isolated components which would be observed in homogeneous bulk fluids. For fluids confined in a porous medium a continuous distribution of T\ values is obtained. A continuous distribution of Tj data is therefore more representative of a porous medium than a discrete solution. In this study both discrete and continuous Tj distributions were calculated and presented. 2.4 Mechanisms of Fluid Relaxation Ti relaxation time has been discussed above strictly as a measure of the change in energy state of molecular nuclei. The mechanism of energy transfer from the excited nuclei to the lattice, as well as the mechanisms believed to cause surface relaxation are described below. 17 2.4.1 Bulk Fluid Relaxation Ti relaxation reflects the rate at which the nuclear spin system of a sample can redistribute the excess energy given to it by the 180-T-90 pulse sequence. The ability of a system to reach equilibrium after an rf pulse is characteristic of that system and provides information about the microscopic structure and dynamics of that sample. For a spin system to relax, there must exist a (random) local magnetic field which fluctuates at the appropriate frequency. This local magnetic field acts as an energy sink so that the excited nuclear spin system can dissipate energy [Gladden, 1994]. Detailed theories of relaxation are provided by Slichter [1963]. In a bulk solution, relaxation occurs as a result of the nuclear spin system exchanging energy with other degrees of freedom in the system. The excited nuclei interact with fluctuating local magnetic fields arising from the random motion of neighboring spins, ultimately leading to relaxation of the system [Kleinberg, 1994]. 2.4.2 Relaxation in Porous Media Fluids in porous media contain an additional energy sink which contributes to the relaxation of the sample's net magnetization. Fluids in confined spaces interact with the pore walls, resulting in relaxation. Measured T t relaxation in porous media therefore consists of both a bulk solution and a surface relaxation component [Senturia and Robinson, 1970]. Relaxation of fluids confined in porous media is usually much faster than that observed in bulk solution due to the possible interaction of the pore fluid with the grain surfaces [Brown and Fatt, 1956]. Two mechanisms have been proposed that cause surface relaxation in porous media. The first contains the pore fluid interactions with the bound water layer. Relaxation occurs because hydrogen in the bulk solution interact with, molecules of water 18 near the grain surface that have a restricted, or slowed motion. This' interaction.results in enhanced relaxation because the bound water will act as an energy sink for the protons in the bulk solution [Resing, 1972]. The second possible mechanism is the presence of paramagnetic ions on the surface. Paramagnetic ions cause enhanced relaxation due either to the much larger magnetic dipole of the electron compared to the proton, or through fluctuations of the electron magnetic moment resulting from its own relaxation [Korringa etal., 1962]. The presence of paramagnetic ions is believed to be the dominant mechanism that causes enhanced surface relaxation in porous media. This is supported by work completed by D'Orazio etal. [1990]. D'Orazio et al. measured T! relaxation times of water adsorbed on porous silica glass and calculated the surface relaxivity constant (p). A value for surface relaxivity (p) of 5 x 10"5 cm/s was obtained. This value is orders of magnitude smaller than the values of p obtained for clean sandstone. Generally, values of 1 x 10"3 cm/s to 3 x 10'3 cm/s are reported [Howard and Kenyon, 1992; Straley et al., 1991; Hedberg et al, 1993; Howard et al, 1993]. It is therefore believed that a small amount of impurities, such as iron and other metals found in "clean" sand and sandstone contributes greatly to the measured relaxation of fluid in porous media fKleinberg et al, 1994]. 2.5 Modeling Relaxation in Porous Media Measured Tj relaxation data are interpreted as the sum of all the rates of relaxation occurring in the pore fluid. Therefore, the measured magnetization, Mt(t), can be expressed as the sum of its components by the equation: N -i 2.2 i=l 19 where t is the recovery ;time and Aj is the amount of magnetization that has a relaxation time constant T^. A ; is proportional to the number of protons which have the same relaxation time, T i ; . In a porous material composed of spherical pores, two types of relaxation will take place: relaxation within the bulk solution and relaxation at the pore surface [Senturia and Robinson, 1970]. Generally, relaxation at the pore surface is much faster than bulk solution relaxation. If all magnetic relaxation were to take place at the pore surface, then relaxation would be most efficient. To quantify the probability of the excited nuclei diffusing from the pore body to the pore surface and undergoing relaxation, a dimensionless surface sink parameter, (pa /D), is used [Brownstein and Tarr, 1979]. The surface sink parameter is composed of the surface relaxivity parameter, the radius of the pore (a), and the self diffusion coefficient of the fluid (D). For water D is 2.43 x 10"5 cm/s at 24°C [Simpson and Carr, 1958]. the surface sink parameter is useful for estimating the type of relaxation occurring for a fluid in a porous medium. The general assumptions made to derive this parameter are: 1) diffusion from one pore to the other does not occur, 2) the pores are composed of simple geometric shapes, such as spheres or cylinders, and 3) p is constant throughout the sample. Using the surface sink parameter Brownstein and Tarr [1979] defined three possible diffusion regimes: slow, intermediate, and fast. The slow diffusion regime is identified with a value of pa / D > 10. In this case, proton relaxation occurs within the bulk fluid as well as at the grain surfaces. This is because proton diffusion is too slow to transfer all the excited nuclei within the fluid from the pore bodies to the pore walls. The intermediate diffusion regime occurs when 1 > pa / D > 10. The probability of the excited nuclei reaching the pore surface increases and surface relaxation becomes the dominant mechanism of relaxation. Fast diffusion occurs when pa / D « 1. In this situation, the excited nuclei within a pore have a very high probability of reaching the pore surface and relaxing during an NMR experiment. 20 The result Is a measured relaxation rate which is governed by surface relaxation mechani sms at the pore surfaces. The diffusion regime of a sample is governed by the values of p and the pore radius for a sample. To illustrate this, consider a situation where both values are quite large. In such a case the surface sink parameter would have a value that was quite large, indicating the system is in the slow diffusion regime. In order for a system to be in the fast diffusion regime it requires a small value for either the surface relaxivity or the pore radius. When the system is estimated to be in the fast diffusion regime, the "two-state fast-diffusion" model can be used. This model allows correlation between the pore surface to volume ratio and the measured Ti relaxation data. The "two-state fast-diffusion" model, originally proposed by Zimmerman and Brittin [1957] and further developed by Brownstein and Tarr [1977], defines pore fluids as being composed of two distinct components: a surface water phase with relaxation time Tis and a bulk water phase with relaxation time T l b . T l s and T l b are related to the measured relaxation (T^ by the equation: 1 a b — = — + — 2.3 Ti Tu Tib where a and b are the fractions of bound and bulk water. The constraint on this equation is that a + b = 1. Tj s is often found to be a much smaller quantity than T l b . Values for a and b are difficult to obtain so Equation 2.3 is often re-written in the form of: ± = p± + ± 2.4 T i V p Tit where ( p * Sp/Vp ) includes information on surface relaxation and its corresponding relaxation time Ti s . In this form, Equation 2.4 will provide information on either Sp/Vp or p, depending on what is known about the system. 21 3. Methods and Materials This section describes the materials and procedures used during this work. The sample properties and their preparation are discussed first, followed by a description of the NMR apparatus and the techniques used to interpret the relaxation data. 3.1 Sample Material Silica sand, known as Ottawa sand, was used in this study to create the porous sand packs. Ottawa sand has a high sphericity and roundness, with minimal amounts of impurities (<0.05% Fe203). These qualities made the sand well suited for this work. The high sphericity and roundness of the sand meant it could theoretically be packed with uniformity into the sample cells. Low quantities of impurities, especially Fe 20 3, meant that the contribution of the solid material would be negligible to the NMR measurements. To clarify this point, Fe is a paramagnetic ion; if it were present in large amounts in the sample, relaxation measurements would be greatly affected. To investigate the effect of wettability on T, relaxation data, sand was selected as the study material. Sand as the porous medium was most appropriate because: 1) complete oil-wetted sand grains could be obtained; 2) sand packs composed of one grain size would provide a system that had a unimodal pore size distribution; and 3) by varying the size of the sand grains, pore sizes could also be varied. 3.2 Treating Sand for Surface Wettability As discussed in Section 2.1, mineralogical composition influences the surface wetting characteristics of the sand. Silica sand at a neutral pH is generally water-wet. Therefore, to obtain oil-wet sands a treatment process was required. The oil-wetting 22 procedure used here was based on work completed by'Morrow "[1992] and Dubey and Doe [1993]. It contained a series of steps that are outlined in Figure 3.1. A more complete description of the process follows below. The first step in the process was to combine the various sand size fractions to be treated. This ensured that all the sand was treated similarly. Generally 25 to 40 ml of each grain size were used. The sand was divided so that all water-wet sand was placed in one container, while all oil-wet sand was placed in a second container. Sand grain surface-iron contamination was removed from the sand by washing the samples with a 0.1 M HC1 solution [Dubey and Doe, 1993]. The acid solution and the sand were left to interact over 48 hours, during which time the samples were stirred periodically. After 48 hours had elapsed, the HC1 solution was drained off and the sand was rinsed three times with distilled water. In the next step, the sand samples were placed in a pH 2.5, 0.02 M NaCl solution for 4 days. This was done because the oil-wetting tendency of a material can be affected by the type of solution it is exposed to before oil is introduced into the system [Dubey and Doe, 1993]. During the 4 day period, the samples were stirred frequently to ensure complete interaction between the solution and the sand. The solution was then drained off and the sand rinsed with distilled water to remove excess saline solution. Samples were then dried at 100°C for 24 hours. Sand intended to have a water-wet surface was removed from the procedure at this point. Performing the first 3 steps of the procedure on both batches of sand ensured that the only difference between the water-wet and oil-wet sands was exposure of the oil-wet sand to crude oil. No other factor could therefore contribute to any observed differences in Tj relaxation times between the samples. Oil-wetted surfaces on the remaining sand were created by exposure of the sand to crude oil. In these experiments two similar, but slightly different crude oils were used. Both crudes were from the Cold Lake Oil Field in Alberta, but differed from one another 23 Treatment Process used to create Water-Wet and Oil-Wet Sands ( Sand Sample ) i Wash Sand with 0.1 M HCI i Rinse sample with Dl Soak Sand in 0.02 M NaCl, Ph 2.5 Solution i Rinse sample with Dl i (Dry Sand in Oven]—*- [ Water-Wet Samples Add Sand to Crude Oil ) ( Sieve Sand J 1 Cook Sample 14 days @ 80°c) I ( Rinse Sand with n-Heptanej i Oil-wet Samples ] —( Sieve Sand ) Figure 3.1 : An outline of the process used in this work to create water-wet and oil-wet sands. (Dl is short for distilled water.) 24 In how they were:treated after extraction from the ground. One' crude was -shipped through the TransMountain Pipeline to the IOCO refinery in Port Moody, B.C., while the other crude was de-aired and de-watered, and then stored at the Imperial labs in Calgary. The main difference between the two crude oils was that diluent (approximately 27% by volume), which is used to lower the viscosity of crude oil, had been added to the oil that was shipped through the pipeline. The wetting properties of the crude oil are believed to be unaltered by the addition of diluent, since diluent is composed of light end hydrocarbons. Exposure of the sand tb the crude oil was completed by slowly adding the sand to the crude oil while the mixture was stirred. Sand added to the crude instead of vice versa ensured that each sand grain was in full contact with oil and no unsaturated sand pockets formed. The crude oil and sand mixture was then placed in a vacuum oven under 20 microns (500.0 mmHg) vacuum. The temperature was set at 60°C for one day, after which it was raised to 80°C where it was maintained for 2 weeks. Increasing the temperature in increments allowed the volatiles in the vacuum oven to reach equilibrium. A final aging temperature of 80°C was used because Jadhunandan and Morrow [1991] showed that this temperature was sufficient to produce oil-wet surfaces. After two weeks, the sand-oil mixture, which by that time resembled a hockey puck, was removed from the vacuum oven and the sand was separated from the oil. Due to the sample's low viscosity, it was necessary to separate the sand from the oil while the sample was still warm. To help liquify the sample and remove the excess crude oil from the sand n-Heptane was used. n-Heptane was added several times to the sample until no liquid crude remained mixed with the sand. n-Heptane does not alter the wettability condition of a sample since it only dissolves the fraction of crude oil which does not wet the surface [North, 1985]. Following the oil-wetting procedure, the originally translucent silica sand was now brown in color due to the oil-wet film. 25 The oil-wet and water-wet sands were then sieved to obtain the grain size fractions to be used in this study. Water-wet and oil-wet samples were "sieved to obtain grain sizes from 105 to 350 microns (U.S. mesh sizes 140 to 42 respectively). Sieving the oil-wet sand after it had been treated ensured that the size fractions of both the water-wet and oil-wet sands would correspond with each other. This prevented the possibility of the oil-wet sands being of slightly larger size due to the oil-wet film. To ensure that oil-wet sands were created by this procedure a simple 'float' test was conducted. This is a quick technique used to determine if oil-wet sands are produced [Anderson, 1986b; Hsu, 1994]. Complete oil-wetness was believed to have been obtained since all the oil-wet grains remained on the water surface. A similar test was undertaken with water-wet sand and all the grains sunk to the bottom of the container. This indicated that the two types of sand had distinctly different surface characteristics. 3.3 NMR Sample Preparation The following section describes the preparation, characterization, and saturation of the water-wet and oil-wet sand packs. All sand packs used in this study were created in the laboratory in order to maintain consistency between the samples. 3.3.1 Sand Pack Preparation Sand packs were prepared using Teflon sample holders to ensure the samples had a fixed porosity. With porosity and pore size fixed, any variations in the NMR relaxation data between the samples would be attributed to surface wettability differences. This was an important consideration since earlier work, in which porosity and pore size were not controlled, showed variations in T! relaxation data that could not be attributed to wettability differences alone [Kanters, 1994]. 26 The sample '[holders used were constructed of tetrafluoroethylene (PTFE) or Teflon. The composition of Teflon, [CF2-CF2]„, does not include any hydrogen ions which meant the sample holder would not contribute to the NMR signal. A schematic diagram of the Teflon sample holder is shown in Figure 3.2. The internal chamber of the sample holder, which contained the sand, was 0.7 cm in diameter and 1.5 cm in length, producing a total volume of 0.5770 cm .^ Tapered edges and a Teflon sleeve were used in the cell design to guarantee water tightness (Figure 3.2). Maintaining a fully saturated sample was important since NMR measurements are affected by saturation changes. Sand was packed into the Teflon cells in a deliberate way to obtain similar porosity and packing characteristics for all the samples. To pack the sand into the cells, a small portion of sand would be placed into the cell and compacted with a stainless steel rod, before more sand was added to the cell. The volume of sand added each time was approximately 1/5 the total sample cell volume; sand was therefore added and compacted five times for each sand pack. Sand pack porosities between 37% and 41% were obtained for the prepared samples. This 4% range in porosity for the samples was determined to be acceptable for the planned experiments. Porosity measurements were made using a helium porosimeter located in the Rock Physics Lab, University of British Columbia. Sample preparation information is presented in Appendix A. 3.3.2 Sand Pack Saturation A high pressure saturation apparatus was used to saturate the water-wet and oil-wet samples. A schematic of the apparatus is provided in Figure 3.3. Samples were saturated in the following way. Dry samples were placed in the sample chamber of the apparatus and a vacuum of 15 to 20 microns was established. The system was then sealed off and a de-aired solution was introduced into the system. The high pressure cell was then pressurized to 2000 psi for 6 to 10 hours to ensure saturation of the samples. 27 Teflon Sample Cell End Plug-Tapered End • End Cap Drilled holes • Teflon Filter (30-60 microns) Tapered End Complete Assembly 1 1 • 1 1 L _ 1 1 1 1 Sample Cylinder 0.7 cm 0.9 cm 0.9 cm 1.5 cm Sample Holder Positioning Rod / £ i Sample Cell Fitted with Teflon Sleeve Figure 3.2 : A schematic drawing of the Teflon Sample Holders used in the experiments. The blown up drawing on the left shows the three main parts: the end plug, the end cap, and the sample cylinder. On the right the holder is assembled as it would be once packed with sand. The drawing on the right shows how the positioning rod was used to lower the samples into the probe. 28 Quick Connectors ^ Cold Trap \ Vacuum Pump \ Vacuum Gauge Pressure Gauge Sample Chamber IIIIIIIIIIIINIIIIII Saturating ^ Solution Flask Hotplate Pressure Intensifier Figure 3.3 : A diagram of the pressure saturation apparatus. To saturate a sample, the sample is placed into the sample chamber and a vacuum is pulled on the system. Once a vacuum is established a de-aired solution is introduced. The pressure intensifier is then used to increase the pressure of the sytem to force fluid into the sample. 29 Once saturated, the samples were stored submerged in a beaker of saturating fluid until analysis with the NMR spectrometer. The beakers containing the submerged samples were covered with parafilm and stored at room temperature. 3.3.3 Saturating Solution Properties Several different solutions were used to saturate the water-wet and oil-wet samples: distilled water; a pH 2, 0.02 M NaCl brine; solutions varying in pH from 2 to 7 with no salinity; and solutions with NaCl concentrations ranging from 0.02 M to 1.0 M at neutral pH. The solution properties are listed in Table 3.1. The distilled water used in these experiments was obtained from a still located in room 328, Geological Sciences building, University of British Columbia. The feed for the still was deionized water. The pH of the distilled water was 5.2 and the conductivity was 0.2 mS/m (Table 3.1). The pH of the various saturating solutions was controlled using HC1 and NaOH. The pH was lowered by adding an appropriate amount of HC1. To raise the pH a small quantity of solid NaOH pellets were added. pH measurements were made with a Hanna Instruments 9025 microcomputer pH meter which had an accuracy of ± 0.01 pH units. pH measurements were made before and after the solution was de-aired. The various NaCl brines used were created by dissolving NaCl crystals in distilled water. For solutions that involved a change in salinity at a specified pH, the pH of the solution was first established and then the salt was added. All solutions were de-aired prior to being used to saturate the samples. De-airing was completed by bringing the solution to a boil and then cooling it off rapidly in a cold water bath. Agitation of the solution was minimized after being de-aired to avoid the reintroduction of air into the solution. The amount of water lost during boiling was measured and recorded. To maintain known concentrations of NaCl in the prepared 30 U) K) •— 01 8" s- ? >o a B . a * i -a , o. 8 c o f a . c r a 9? 9t c o " ro ro a o i TJ X | CO o c •a O J Oi 0 0 1 l o . O a-1 o o o p 0 0 oo 0 0 J O o o © © ro X Ol o » ra a Ol I P TO z o "Si [o ho a Ol li Ol o l Ol IS o Ol Oi t o | o * o o o © © o AO t o 0 0 o tO CO m 3 to fa a Ol o © tO as o ro a Ol o © Oi ro a J O © ro a Ol l i C/3 I o CA C/5 o o CO 5 s O J n ro a o o 3 3 5 CO •o zx, ta 3 a. o o 3 OL C o < «< o co s. ta 5' ca CO o c o 3 CO solutions, the water lost during Wiling was replaced with debarred distilled water once the solution had returned to room temperature. 3.4 NMR Apparatus and Measurements A pulsed proton NMR spectrometer was used in this study. The instrument is located in Lab 100, Hennings building, University of British Columbia. It consisted of a Bruker iron-core electromagnet and a SXP™ probe which has a dead time of 10 microseconds. The electromagnet has a magnetic field of 2.12 Tesla which translates into a Larmour frequency of 90 MHz for protons. The spectrometer was interfaced to an IBM PC which is used to control the NMR spectrometer. All samples were analyzed at room temperature (24°C ± 1°C). Samples were analyzed to obtain Ti and T 2 proton relaxation times. Ti data were gathered by completing a number of inversion recovery experiments, using a 180-X-90 sequence. The relaxation curve for Ti was created using 15 to 25 x values logarithmically spaced between 0.001 and 10 seconds (x sequences for individual samples are shown in Appendix B). T 2 data were obtained using the Carl-Purcell-Meyboom-Gill (CPMG) sequence for echo times of 200, 400, and 600 microseconds. Although T 2 data were collected, they are not further discussed but were archived for future analysis. To document any water loss from the samples during NMR measurements, sample weights were taken before and after analysis. Weights were measured with a Satorious scale that had an accuracy of ±0.0001 g. The scale is located in Lab 100, Hennings Building, University of British Columbia. Overall, the average sample saturation decreased by less than 1% during analysis. This was a negligible amount according to results from repeat 180-X-90 experiments. The repeat 180-X-90 experiments, performed at the beginning and end of the NMR measurements showed no change in the measured maximum amplitude of the net magnetization. This indicated that the amount 32 of water lost from the samples did not affect T.i measurements. More detailed information on sample saturation during the NMR experiments is provided in Table A.2 of Appendix A. 3.5 Relaxat ion Data Inversion Techniques T! relaxation data were interpreted using the nonnegative least squares (NNLS) inversion algorithms as applied by Whittall and MacKay (1989). The algorithms are encoded in computer programs available on the Physics computer, located in Hennings 100, University of British Columbia. In order to use these programs, NMR files were transferred from the IBM PC to the MicroVax E™ minicomputer in the Physics lab. Ti relaxation data were interpreted using the NNLS algorithm which was given an initial distribution of 160 Ti time constants, logarithmically spaced between 0.001 seconds to 10 seconds. 33 4. Exper imental Design and Results To investigate the study objectives, experiments were designed to determine if there is a measurable difference for pore fluid relaxation between 100% water-wet and 100% oil-wet sand packs. The following is a presentation of the results obtained from these experiments. 4.1 T i Relaxation in Sand Packs of V a r y i n g G r a i n Size Two sets of experiments were conducted to investigate the dependence of Tj on sand pack grain size. In the first experiment, water-wet and oil-wet sand packs were saturated with distilled water. In the second experiment, sand packs were saturated with a pH 2, 0.02 M NaCl brine. The results from these experiments are presented below. 4.1.1 Pore Fluid: Distilled Water In this experiment, T! relaxation measurements were made on 100% water-wet and 100% oil-wet sand packs that were saturated with distilled water. The sand packs analyzed were prepared using one of five different grain sizes, ranging from very fine to medium-sized sand. The five different grain sizes are listed in Table 4.1. For each group there existed a distribution of grain sizes limited by the size of the sieve screen used to separate the sands. Although Table 4.1 suggests a wider distribution in grain sizes for the groups composed of larger grains, this was not the case. Each group contained the same relative grain size distribution which was ± 9% of the group's mean grain size. The mean grain size of a group could therefore be used in calculations and as the identifier for that sand size. 34 Table 4.1 : Grain Size Data Wentworth Size Class U.S. Sieve Size Grain Diameter (microns) Average Grain Diameter (um) Very Fine Sand 140 - 120 105 - 125 115 Fine Sand 120 - 100 125-149 137 Fine Sand 80 - 100 149 -177 163 Fine Sand 70-80 177-210 194 Medium 50-60 250 - 300 275 Ti relaxation measurements were made on the above described samples using a pulsed proton NMR spectrometer. The Ti data obtained is presented in Figure 4.1 where the mean T! value (Ti(m e an)) for each sample is plotted against sand pack grain size. Ti(mean) accurately represents porous medium relaxation data [Kenyon et al., 1988; and Hedberg et al., 1993] and was calculated using the equation: tTuMTu) j =j=2 4.1 2>(TU) i=0 where the amplitude, A(Ti,), is proportional to the number of protons in the sample that have a relaxation time of T^. Ti ( m e a n ) values are used in porous media work because a porous medium can have a suite of Ti relaxation constants. Calculating T 1 ( m e a n ) values therefore provides an effective method to compare relaxation data between samples. In this study, T 1 ( m e an) values did not differ significantly from the dominant Ti relaxation constant. Nearly 95% of the samples showed strongly monoexponential T! distributions, implying that although Ti ( m ean) is used to represent a sample's relaxation data, it was usually calculated from the dominant T! relaxation constant. For comparison, Ti spectrums and T 1 ( m e a n ) values for all the samples are presented in Appendix C. 35 3 - r 2.5 73 e | L S + H 1 0.5 + Oil-Wet • O • • . • Water-Wet 1 1 1 1 1 1 1 0 50 100 150 200 250 300 350 Grain size (microns) Figure 4.1 : Mean Tj relaxation time versus grain size for the water-wet and oil-wet samples saturated with distilled water. The circles represent results obtained from oil-wet samples created using Cold Lake crude oil that had diluent added to it. The square symbols represent results obtained from oil-wet sand that was created using Cold Lake crude oil that was de-aired and de-watered. 36 The data presented in Figure 4.1 resulted from two separate experiments whose oil-wet samples differed in the type of crude oil used to make them. In the first experiment, depicted by circles in figure 4.1, the oil-wet samples were created using crude oil that had been transported through the pipeline. In the later experiment, the oil-wet sand was created using crude oil that had been obtained from the well head, shown as squares in Figure 4.1. Also, the Teflon cell design differed slightly between experiments. In the first experiment, a prototype Teflon cell was used that differed from that shown in Figure 3.2 by a smaller sample chamber volume and different end cap design. The prototype cell had a sample chamber volume of 0.4239 cm3 and two removable end caps that were not tapered. Agreement between the data from the two different experiments, especially data from the overlapping samples, created with sand 163 microns in diameter, suggested that the minor apparatus differences were unimportant. The data from the two experiments could therefore be compared as one data set. Figure 4.1 indicates a dependence of Tj relaxation time on surface wettability in the prepared sand packs. Ti relaxation times in the oil-wet sand packs were considerably higher than those for the water-wet porous media. The difference between the water-wet and oil-wet T! data exceeded 1 second for the suite of samples analyzed, which ranged in grain size from 115 microns to 275 microns. This suggested that T! relaxation data could be used as a tool to identify the wettability of a porous medium. An increase in sand pack grain size was accompanied by an increase in T! relaxation time. In the water-wet samples, an increase from 0.8 to 1.2 seconds was observed as grain size increased from 115 to 275 microns. In the oil-wet samples, T! increased from 1.8 to 2.7 seconds for the same increase in grain size. These results confirmed that Tj relaxation of pore fluids is positively correlated with a change in grain size, which corresponds to a change in pore size. Experimental error caused some variation in the data. The Tj relaxation time obtained for the water-wet sample, composed of grains 193 microns in diameter, varied 37 significantly from the other water-wet data. It is believed that an error during sample preparation, such as a change in sample porosity after the sample had been characterized, most likely caused this anomalous result. Therefore, this result was considered erroneous and was not included in data interpretation. A repeat of this sample was not completed because trends in the data had already been established by the other samples. Bulk fluid relaxation measurements were also made for the distilled water. Measurements of T l b ranged from 2.94 to 3.26 seconds (Appendix A - Table A.3). The lower values, near 2.95 seconds, were probably a result of analyzing water that was no longer completely de-aired because the values compare well with T i b values of 2.7 seconds reported by Seevers [1966] for water in equilibrium with air. The longer T l b values, 3.2 seconds, were more consistent with values previously reported for de-aired distilled water; Simpson and Carr [1958] reported a value of 3.3 seconds for distilled water free of oxygen. 4.1.2 Pore Fluid: pH2, 0.02 MNaCl brine To investigate a possible dependence of T t relaxation time on the saturating solution chemistry, experiments were conducted in which water-wet and oil-wet sand packs were saturated with a pH 2, 0.02 M NaCl solution. Selection of the saturating fluid was made based on experiments by Dubey and Doe [1993]. They found that a low pH, slightly saline solution created conditions which favored an oil-wet silica surface. Others also have reported that oil-wet situations are more likely to occur at low pH and low salinity [Buckley, 1994; Skauge and Fosse, 1994]. To investigate the effect of pore fluid chemistry on Ti relaxation, four water-wet and four oil-wet samples were prepared using sand grains 137, 163, 194, and 275 microns in diameter. Two duplicate samples, one water-wet and one oil-wet, were prepared to 38 assess reproducibility of the NMR measurements. Sand of 163 microns in diameter was selected as the size for the duplicate sample. Figure 4.2 plots T 1 ( m ean) values versus grain size data for this experiment. With a pH 2, 0.02 M NaCl pore fluid, the data showed no measurable difference in T! relaxation between the water-wet and oil-wet sand packs for the majority of grain sizes investigated, and no consistent dependence of T! on grain size. Specifically, values for the water-wet and the oil-wet samples are quite similar for all but the largest grain size analyzed which suggests that as grain size increases, Tj is less affected by pore fluid chemistry. Fewer data for the larger grain sizes does, however, prevent further conclusions from being made. The T t data obtained for the smaller grain sizes have no apparent trend and differ from those results presented earlier when the samples were saturated with distilled water. This suggests that pore fluid chemistry affects Tj relaxation measurements in water-wet and oil-wet sand packs. Bulk fluid relaxation times for the pH 2, 0.02 M NaCl solutions were also measured and T l b had values of 2.65 and 3.0 seconds. These values are slightly less than those obtained for distilled water. The bulk solutions no longer being completely de-aired is the probable cause for these lower results. This explanation was supported by work completed by Meiboom etal. [1957]. Meiboom etal. found that T l b was independent of pH and salinity in bulk solutions. The duplicate samples analyzed in this set of experiments had highly reproducible results. Tj relaxation times between the samples differed only slightly, 0.12 seconds for the water-wet and 0.15 seconds for the oil-wet samples. This illustrated that the laboratory-prepared sand packs were consistent for all the samples. 39 2.5 •a a | 1.5 • W H 1 0.5 + O O Water-Wet • Oil-Wet O 9 o o —\ 1 1 1 — 50 100 150 200 Grain size (microns) 250 300 350 Figure 4.2 : Mean relaxation time versus grain size for water-wet and oil-wet samples saturated with a pH 2,0.02 M NaCl solution. 40 4.2 Tj Dependence on Pore Fluid Salinity and pH The previous experiment had shown that a low pH, slightly saline pore fluid produced T! relaxation values quite different than those obtained for samples saturated with distilled water. Because both the pH and salinity of the pore fluid were changed, it was not clear which of these factors affected T! relaxation measurements. Therefore, additional experiments were conducted in which only the salinity or only the pH of the pore fluid was varied to investigate the apparent dependence of Ti on pore fluid chemistry in water-wet and oil-wet sand packs. Sand packs were prepared using only one grain size to remove the dependence of Tj on grain size which had been observed in the previous experiments. Sand packs were prepared using water-wet and oil-wet sand that was 163 microns in diameter. 4.2.1 Tj Dependence on Pore Fluid Salinity Water-wet and oil-wet samples were saturated with solutions which varied in NaCl concentration. The solutions used were distilled water, 0.02 M NaCl, 0.2 M NaCl, and 1.0 M NaCl. pH was maintained at 5.2 for all solutions. Detailed information on the saturating solutions is found in Table 3.1. Mean T, relaxation times versus pore fluid salinity are present in Figure 4.3. There is only minor change in Tj relaxation time as the pore fluid salinity increases. The oil-wet data remains relatively constant for all salinities, while a small increase in Tj for the water-wet samples is observed as pore fluid salinity increases. This small increase in Ti for the water-wet data stabilized at the higher salinities. It was therefore concluded that Tj was independent of pore fluid salinity in water-wet and oil-wet sand packs. Bulk solution relaxation times were measured for each of the four different salinities used (Figure 4.4). As the salinity increased from zero to 1.0 M NaCl, a slight 41 3 -r 2.5 a | 1.5 0.5 O O o • Oil-Wet O Water-Wet 0.00 0.01 0.10 1.00 NaCl Concentration (mol/L) Figure 4.3 : Mean Tj relaxation time versus pore fluid salinity for the water-wet and oil-wet samples. 42 Figure 4.4 : Mean bulk relaxation times (T lb) for the various NaCl solutions used to saturate the water-wet and oil-wet samples presented in Figure 4.3. 43 decrease in T l b was observed. This small decrease was thought to "be a result of experimental procedure and not indicative of a change in T l b with salinity.. This interpretation was made based on work completed by Meiboom et al. [1957] who found no change in T l b as solution salinity increased. Therefore, the average value of T l b , 3.1 seconds, could be calculated from the data and used in any calculations that require this value. 4.2.2 Tj Dependence on Pore Fluid pH Experiments to test for a possible Ti dependence on pH were conducted by varying the pH of the pore fluid. Solutions with pH values of 2, 3.5, 5.2, and 7 were used. Salinity was held at negligible levels for these solutions. Saturating solution properties are found in Table 3.1. A plot of pH versus T i ( m e a n ) is presented in Figure 4.5. An increase in Ti relaxation time was measured in both the water-wet and oil-wet samples as pore fluid pH increased. The water-wet samples showed an increase in Ti from 0.7 to 1.3 seconds with a change in pH from 2 to 7. In the oil-wet samples, Ti increased from 1.3 to 2.3 seconds over the same increase in pH. These data indicate that Tx relaxation is dependent on pore fluid pH, regardless of the system's wettability. Measurements of T l b were made for the various pH solutions. Results from these experiments are presented in Figure 4.6. T l b was found to be relatively constant over the pH range studied with relaxation times near 3.15 seconds for all solutions. This compared well with data reported by Meiboom et al. [1957] where constant values of T i b were found for solutions ranging in pH from 2 to 12. The independence of T i b on solution pH suggests that the observed changes in pore fluid Ti are caused by the fluid being confined in a porous medium. 44 2.5 + 2 + e § 1.5 H 1 0.5 O O o • Oil-Wet O Water-Wet 0 1 2 3 4 5 6 7 8 9 pH Figure 4.5 : Mean T, relaxation time versus pore fluid pH for the water-wet and oil-wet sand packs. 45 Figure 4.6: Mean bulk relaxation times (Tlb) for the various pH solutions used to saturate the water-wet and oil-wet samples presented in Figure 4.5. 46 5. Discussion The experimental results presented in the previous section demonstrated that T x could be used to determine wettability under certain conditions. When pore fluid was at a neutral pH, regardless of NaCl concentration, T! relaxation times reflected sand pack wettability. It was observed, however, that Ti was affected by pore fluid pH in both the water-wet and oil-wet systems. The results showed that when the pore fluid was acidic, differences in sand pack wettability were not clearly distinguished by T! relaxation data. A discussion of these results is presented below. 5.1 Tj Relaxation in Sand Packs of Varying Grain Size In this section, results of the investigation into the dependence of Tj relaxation on grain size are discussed. Discussion of the results from the distilled water experiments are presented first followed by the results from the low pH, slightly saline work. Tj will be shown to be a useful indicator of surface wettability providing the pore fluid is not acidic and saline. 5.1.1 Pore Fluid: Distilled Water Tx data for distilled water in water-wet and oil-wet porous media were found to be less than T i b measurements for bulk solutions of distilled water (Figure 4.1). T l b relaxation of the de-aired distilled water was 3.2 seconds, this was on average 2 seconds longer than the Ti measured for the water-wet samples and 1 second longer than Ti obtained for the oil-wet samples. The decrease in Ti from T l b for both the water-wet and 47 oil-wet samples'indicates that surface relaxation betweenthe pore fluid and the pore walls had occurred. This finding agrees with observations reported in previous studies [Brown and Fatt, 1956; Straley etal., 1991; and Hsu, 1994]. The decrease of T, from T l b as a result of the fluid being located within the pore spaces reflects the amount of surface interaction occurring between the pore fluid and the pore walls [Brown and Fatt, 1956]. Since the decrease in T! was less in the oil-wet system than in the water-wet samples, it was therefore concluded that less surface relaxation occurred at the oil-wet surface than at the water-wet surface. Confirmation that surface relaxation had occurred at both the water-wet and oil-wet surfaces was provided by experiments using different grain size samples. In Figure 4.1, T, showed a dependence on grain size in both the water-wet and the oil-wet samples. An explanation for this result is that as the sand pack grain size increases, the surface area to volume ratio decreases. This means that the number of sites available to provide surface relaxation for the pore fluid decreases, resulting in longer relaxation times. The amount of surface relaxation that occurred in the water-wet and oil-wet samples can be quantified using the surface relaxivity constant (p), which is a measure of the solid-liquid interaction. Equation 2.4, presented in Section 2.5, provides a method to calculate p. A limitation of Equation 2.4 is that the sample must be within the fast diffusion regime. The surface sink parameter proposed by Brownstein and Tarr [1979] unfortunately could not be used here to determine the diffusion regime of the samples because it requires a knowledge of p. The diffusion regime of the samples was instead established using 2 other criteria and the results were validated using the surface sink parameter. The criteria used were that: 1) the measured T, relaxation time must be longer than the time required for water molecules to diffuse from the pore centers to the pore walls, and 2) the relation between Tj and Sp/Vp must be linear. If these two conditions were satisfied, the samples relaxed within the fast diffusion regime. 48 With consideration to the first criterion, the time for a water molecule to diffuse from the pore center to the pore wall is determined using the following equation: r2 = 6Dt 5.1 where r is the mean squared distance traveled, D is the diffusion constant for water, and x is the time required for diffusion to occur. The two known values in Equation 5.1 are the diffusion coefficient for water and the mean squared distance traveled. For water at room temperature, D has a value of 2.43 x 10'5 cm2/s [Simpson and Carr, 1958]. The mean squared distance is equal to the pore radius because the variable of interest, %, is the time required for a water molecule to travel from the pore center to the pore wall. Unfortunately r is not readily known for the samples so it must be calculated from the grain size data. Spherical packing theory was used to obtain estimates of pore radii for the various sand packs analyzed. This theory is applicable since the sand grains used to prepare the sand packs had a high sphericity. From the sand pack porosity measurements of 37 to 41%, it was assumed that the samples had a simple hexagonal packing [Bourbie et al, 1987]. For simple hexagonal packing the maximum size of a sphere that could fit within a pore space is approximately half the size of the solid grains (pore diameter = 0.528 * grain diameter). This relationship was used to estimate the pore diameters presented in Table 5.1. Using the data in Table 5.1, Equation 5.1 could be used to estimate water molecule diffusion times. To obtain the maximum value for the diffusion time, the largest pore radius was selected and applied to Equation 5.1. A diffusion time of 0.36 seconds was obtained. This was less than half the shortest Tj relaxation time measured in the experiments, therefore, based on this criterion the samples analyzed fell within the fast diffusion regime. 49 Table 5.1 : Pore diameters Calculated from Grain Size Data Grain Size Pore Diameter * Pore Radius (microns) (microns) (cm) 115 60.7 3.04 x IO"3 137 72.3 3.62 x IO"3 163 86.1 4.31 x IO"3 194 102.4 5.12 x IO"3 275 145.2 7.26 x IO"3 * Pore Diameter = 0.528 * Grain Diameter (Grain diameters obtained from Table 4.1). The second of the two criteria considers the relationship between Ti and Sp/Vp. Assuming spherical pores, Sp/Vp reduces to 3/r where Sp is the surface area of the pores, V p is the volume of the pores, and r is the pore radius. From Equation 2.4 it is evident that 1/Ti is proportional to 3/r. Therefore, since Equation 2.4 is valid only when the system is in the fast diffusion regime, a linear relation between Tj and r would indicate that the samples are in the fast diffusion regime. A plot of Ti versus r is presented in Figure 5.1. A line of best fit is plotted for the water-wet and the oil-wet samples. The best-fit line has a high correlation coefficient, near 0.98, for both sample types. The second criterion is therefore satisfied and confirms that the samples were within the fast diffusion regime. Because both criteria indicate that Ti relaxation in the water-wet and oil-wet sand packs occurred within the fast diffusion regime, Equation 2.4 could be used to estimate the surface relaxivity of the samples. A third, less rigid, criterion can also be used to determine if relaxation occurred within the fast diffusion regime. This third method involves examination of the Tx relaxation curve. A monoexponential Tj relaxation curve strongly suggests that the system is in the fast diffusion regime [Kleinberg et al., 1994]. The relaxation curve data, presented in Appendix C, demonstrate that the majority of the 55 samples analyzed 50 2.5 4-•a § 1.5 + 0.5 o Water-Wet Oil-Wet CL 0.002 0.004 0.006 Pore Radius (cm) 0.008 0.01 Figure 5.1 : Mean T t relaxation versus pore radius for the water-wet and oil-wet samples saturated with distilled water. The linear trend of the data, shown by the best-fit line, indicated that relaxation in the samples was within the fast diffusion regime. 51 were monoexponeritial 'in character. This furmer confirms that the samples were In the fast diffusion regime and validated the use of Equation 2.4 to estimate p. Before Equation 2.4 could be used, however, an estimate of S p/V p was required. This was accomplished by relating the grain size and porosity data of each sample. As demonstrated above, S/V reduces to 3/r. If the known grain radius is used in this relation, S/V would be the surface to volume ratio with respect to the grains. This can be written as: where Sg is the grain surface, V g the grain volume, and d is the grain diameter. To obtain a value for Sp/Vp, several transformations are made. First, the surface area of the pores equals that of the grains, so Sp equals Sg. Second, V p is equivalent to the total volume less the volume of the grains (Vt - Vg). Dividing V p and (V,-Vg) by V t relates these values to the sample porosity. Therefore, S p/V p is equivalent to: where 0 is the porosity and Sp/Vp is the surface to volume ratio with respect to the pores. Calculated Sp/Vp ratios for the samples are found in Appendix D. Surface relaxivitjes can now be calculated from Equation 2.4 using the estimated Sp/Vp ratios and the measured Tj and Tj b data. The calculated values of p are presented in Figure 5.2 and indicate that the water-wet surface relaxivities exceed those of the oil-wet samples. This was expected since T! values for the water-wet samples were much shorter than oil-wet relaxation values. Data in Figure 5.2 demonstrate that p is not constant with pore size for either the water-wet or oil-wet samples. This was unexpected since p is thought to be a constant for homogeneous samples. Two factors were manipulated to determine a better estimate of p: the method used to estimate Sp/Vp and the effect of changing T l b . Adjustment of i = 2 = l Vg r d 5.2 6(1-6) dd 5.3 52 2.00E-03 T 1.50E-03 S 1.00E-03 2 v u s 5.00E-04 4-O.OOE+00 O o 8 O Water-Wet • Oil-Wet H 1 1 1 1— 50 100 150 200 250 Grain size (microns) 300 350 Figure 5.2 : Calculated surface relaxivity constants in relation to grain size for the water-wet and the oil-wet samples saturated with distilled water. 53 these factors did not remove the small variation 'in the estimated values of surface relaxivity. This was because p increased with grain size in the water-wet samples, and p decreased when grain size increased in the oil-wet samples. The contrasting trend between the water-wet and the oil-wet samples did not allow for a simple correction to be applied to the data. To investigate if a more consistent value of p could be obtained, a plot of 1/Tj versus Sp/Vp was made. This is shown in Figure 5.3. The relationship of 1/Tj to Sp/Vp in Equation 2.4 indicates that the slope of this line is equivalent to p and the y-intercept is equivalent to 1/T l b. In Figure 5.3 the best-fit line through the water-wet and the oil-wet data is plotted. Statistics of this line are presented in Table 5.2 and the fit indicated that T l b differed between the water-wet and oil-wet samples, and the values of p differed from those obtained when the y-intercept was fixed using the measured value of Ti b . Table 5.2 : Linear Regression Data for Figure 5.3 Sand Wettability 1 / Y-intercept T i b (s) Slope - p (cm/s) Correlation Coefficient (r) Water-wet 2.02 8.6 xlO"4 0.994 Oil-wet 3.85 3.6 x IO'4 0.979 The difference in T i b between the water-wet and oil-wet samples was unexpected since the pore fluid was distilled water for both. The values of T l b obtained from the best-fit lines, referred to as Tib(Predicted), were 2.0 seconds and 3.9 seconds for the water-wet and the oil-wet samples respectively. These both differed from the measured value for T i b of 3.2 seconds. Initially it might appear that the nature of the pore fluid had changed, resulting in the change in T l b . This was unlikely, however, since the difference between T l b ( p r e d i c t e d ) and T l b was quite large. The observed discrepancy in T l b ( p r e d i c t e d ) values was not resolved. 54 1.5 T 1.25 1 + g 5-0.75 + 0.5 0.25 p = 0.00086 cm/s Tlb = 2.02 s p = 0.00036 cm/s Tlb = 3.86 s H 1 0 0.02 0.04 0.06 0.08 0.1 Sp/Vp (1/microns) o Water-Wet • Oil-Wet Figure 5.3 : A plot of 1/Tj versus Sp/Vp for the water-wet and oil-wet sand packs saturated with distilled water. 55 Thesurface relaxivity values of Figure 5.3 differed from earlier results. This was because the values of p in Figure 5.3 were calculated using the measured values of Tu, while the values for p in Table 5.2 were determined using T^predicted)- Both methods of estimating p produced results that were in the same range. Unfortunately, the discrepancy in the Tlb(predicted) values for the water-wet and oil-wet data made the calculated values for surface relaxivities in Table 5.2 questionable. These values for p were therefore not used. The variation in p present in Figure 5.2 was assumed to be a result of a small amount of experimental error. A discussion of surface relaxivities was therefore based on the average values of p for the water-wet and oil-wet samples which were 1.2 x 10"3 cm/s and 2.6 x 10"4 cm/s respectively. The assumption that the samples are within the fast diffusion regime is confirmed by calculating the surface sink parameter, which, if less than one, indicates that relaxation occurs within the fast diffusion regime [Brownstein and Tarr, 1979]. A surface relaxivity of 1.2 x 10'3 cm/s and a pore radius of 7.3 x 10'3 cm/s were used to calculate the maximum value of pa / D for the samples. The calculated value for the surface sink parameter was 0.36, well below 1, confirming that relaxation occurred within the fast diffusion regime for the samples. The surface relaxivity value of 1.2 x 10"3 cm/s for the water-wet samples compares well with values previously cited. Values of 2.4 x 10"3 cm/s [Hedberg et al, 1993], 1.7 x 10"3 cm/s [Straley etal, 1991], and 1.0xl0"3cm/s [Howard and Kenyon, 1992] have been reported. Variation in p between studies is due to differences in experimental materials used. For example, sandstone which contains a minor amount of clay would yield results different from those obtained for clean sandstone, due to the larger surface area and paramagnetic ion content of the clay [Kleinberg, 1994]. Comparison of results from different experiments must therefore be made with caution, ensuring that the data were collected under the same experimental conditions. 56 The calculated surface relaxivity constant of .2.6 x IO*4 cm/s for the oil-wet samples was approximately 5 times less than that obtained for the water-wet samples. This smaller value of p indicated that less fluid-surface interaction was occurring than in the water-wet samples. It is difficult to compare the results from this study to previous studies because of differences in how the oil-wet system was created. Previous studies have used a variety of oils or synthetics to create the oil-wet surfaces [Brown and Fatt, 1956; Williams and Fung, 1982; Hsu, 1994]. This has caused surface relaxivities to differ from one experiment to the other. The following paragraph elaborates on this point. Relaxation of the pore fluid at the oil-wet surface is believed to be a result of paramagnetic impurities in the oil. Work by Hsu (1994) examined how the quantity of paramagnetic impurities in the wetting oil affected Ti relaxation measurements. Oil-wet samples were created using two crude oils that differed in the amount of paramagnetic ions present. The results showed that the amount of paramagnetic ions present in the oil directly affected Ti measurements. Specifically, oil-wet sand created using a crude oil with a high paramagnetic ion content had shorter Tj times than those of water-wet samples. This was completely opposite to the results obtained in this study, suggesting that using Ti to measure wettability may be complicated, since the amount of paramagnetic ions in crude oils is variable. Tx relaxation data in oil-wet systems are therefore specific to a particular system and caution must be taken when comparing results between experiments. Consequently, the results reported here are specific to oil-wet sands create using Cold Lake crude oil. This study has shown that T\ relaxation times for water-wet sand packs differs from Tx data in oil-wet sand packs when the pore fluid is distilled water. A discussion of how changes in pore fluid composition affect Ti relaxation in porous media follows below. 57 5J..2 PoreFluid:pH2, 0.02MNaCl brim Ti relaxation results for the water-wet and oil-wet samples saturated with a pH 2, 0.02 M NaCl brine in Figure 4.2 differed significantly from those obtained for sand packs saturated with distilled water. A change in pore fluid chemistry significantly affected measurements. To account for the results in Figure 4.2, T i b data were first examined. Because T l b of the pH 2, 0.02 M NaCl solution was similar to values obtained for distilled water, a change in bulk fluid relaxation did not cause the observed change in pore fluid relaxation when the solution is acidic and slightly saline. Surface relaxivities calculated from Equation 2.4 were examined next. Figure 5.4 presents the surface relaxivities for the water-wet and oil-wet samples. Unlike Figure 5.2, the values for p were scattered, ranging from 1.0 x 10"3 cm/s to 2.5 x 10"3 cm/s with no apparent dependence on grain size. Also, no consistent difference in p existed between the water-wet and oil-wet samples. A possible explanation of these results is that the oil-wet layer broke down and the sample reverted to a water-wet state. Two pieces of evidence, however, negate this possibility. First, a low pH, slightly saline condition has been found to more likely support an oil-wet surface than a system at higher pH [Liu and Buckley, 1994; Doe, 1994]. Second, a "float" test completed on the oil-wet grains in a pH 2, 0.02 M NaCl solution demonstrated no change in wettability over time, since the grains remained afloat for days. This evidence suggests that the oil-wet layer was stable and the measured Tj relaxation data reflect a change in the relaxation mechanisms of the system. 58 3 . 0 0 E - 0 3 2 . 5 0 E - 0 3 § 2 . 0 0 E - 0 3 4-c v 8 1 . 5 0 E - 0 3 + I u a 1 . 0 0 E - 0 3 5 . 0 0 E - 0 4 4-O . O O E + 0 0 O o 8 • • o + o O Water-Wet • Oil-Wet 5 0 100 150 2 0 0 2 5 0 Grain size (microns) 3 0 0 3 5 0 Figure 5.4 : Calculated surface relaxivity values for the water-wet and oil-wet samples saturated with a pH 2,0.02 M NaCl solution. 59 5.2 Tj Dependence on Pore Fluid Salinity and pH The set of experiments described above demonstrated that pore fluid composition affects Ti measurements in oil-wet and water-wet sand packs. Further experiments, discussed below, were necessary to determine which factor, either pH or salinity, caused the observed enhanced T! relaxation. 5.2.1 Tj Dependence on Pore Fluid Salinity Figure 4.3 presents the Ti data for water-wet and oil-wet sand packs saturated with various NaCl solutions. T! relaxation showed insignificant variation with a change in pore fluid salinity, indicating that pore fluid salinity has little affect on Ti relaxation in porous media. This result was confirmed by Bowers [personal communication] who found Ti to be independent of pore fluid NaCl concentration in systems with up to 100 000 ppm NaCl. Surface relaxivities for the water-wet and oil-wet samples were calculated using Equation 2.4, since all samples relaxed within the fast diffusion regime. Figure 5.5 presents calculated values of p which are relatively constant for the oil-wet samples but vary with salinity in the water-wet samples. The decrease in p for the water-wet samples as salinity increased was not considered to be significant since Ti data from Figure 4.3 for the water-wet samples did not show large variation with salinity. The change in p as salinity increased is therefore caused by the calculation of p from equation 2.4. For values of Ti near 1.0 second, the l/Ti term changes substantially with only small changes in Ti. As a result, the variation in p with salinity in the water-wet samples is not considered important. 60 2.00E-03 1.50E-03 E w £> ;? '8 1.00E-03 cu u .3 "c 9 5.00E-04 0.00E+00 O o o —I 1 1 — Dl 0.01 0.1 Salinity (mol/1 NaCl) O o Water-Wet • Oil-Wet Figure 5.5 : Calculated surface relaxivity values for the water-wet and oil-wet samples saturated with pore fluids that contained different amounts of NaCl. A decrease in surface relaxivity with the increase in pore fluid salinity was a result of slightly longer Tj relaxation times for these samples. 61 Average surface relaxivities for the water-wet and oil-wet samples are 9.4 x lO^cm/s and 2.7 x lO^cm/s respectively. These values were quite similar to the average values of p obtained for the water-wet and oil-wet samples saturated with distilled water. These results indicate that Ti relaxation in water-wet and oil-wet sand packs was not affected by pore fluid salinity. 5.2.2 Tj Dependence on Pore Fluid pH Figure 4.5 demonstrates the dependence of Ti relaxation on pore fluid pH; as pore fluid acidity increased, mean T! relaxation times decreased. This relation was observed in both water-wet and oil-wet samples. It would appear from Figure 4.5, however, that the oil-wet Ti times decreased by a larger proportion as pH decreased from 7 to 2 than did the water-wet T! times. This was not the case, since by normalizing the drop in T! for the water-wet and the oil-wet data, similar results were obtained. Normalization of the change in Ti was completed by dividing the total decrease in T 1 } as pH decreased from 7 to 2, by the average relaxation time for the water-wet or oil-wet samples. Decreases in Tx of 54% and 53% were calculated for the water-wet and oil-wet samples respectively. It was concluded that pore fluid pH has a similar affect on T! relaxation time in water-wet and oil-wet samples. There exists several possibilities to explain the decrease in Tj relaxation time with increased pore fluid acidity. These were: 1) a change in surface wettability, 2) an increase in bulk fluid relaxation, 3) a change in the self diffusion coefficient of water, and 4) an increase in surface relaxation. 62 The last (fourth) possibility-is thought to be the reason.for the observed results. The first 3 items, however, warrant an explanation of their unlikelihood to cause the decrease in Tx relaxation time. Each of the four possibilities are discussed below in sequence. 1. A Change in Surface Wettability Shorter Ti relaxation times would be obtained if the oil-wet film became unstable and broke down, reverting to a water-wet system. This did not occur, however, because T! decreased in both the water-wet and oil-wet samples similarly as acidity increased. If the change in Ti was due to a breakdown of the oil-wet layer, no change in Tj for the water-wet samples would have been observed. Also, "float" tests completed using the low pH solutions indicated that the oil-wet layer persisted and was stable. A change in surface wettability therefore did not cause shorter T\ relaxation times at low pH. 2. A change in Bulk Tlb Relaxation Bulk relaxation results are presented in Section 4.2.2. T l b did not change with fluid acidity thus dismissing this possibility as an explanation for the observed Ti data. 3. A change in the Self Diffusion Coefficient of Water Shorter Tj relaxation times could result from an increase in the self diffusion coefficient of water because an increase in D indicates that a greater number of excited nuclei would reach the pore walls during an NMR measurement. However, if a system is surface limited an increase in D would have no affect on T t measurements. This was shown by Latour et al. [1992] when Ti relaxation data for water-saturated sandstones showed negligible change as the self diffusion coefficient of the water was increased. An explanation for this observation is that in a surface-limited regime the surface relaxation sites are saturated, so an increase in the rate at which additional excited protons reach the surface would not affect the amount of relaxation occurring at the surface. Since the 63 samples analyzed in this study have been shown to relax within the fast diffusion regime, it was concluded that an increase in D does not explain the observed results. 4. A change in Surface Relaxation A change in surface relaxivity remains the only explanation for the observed Tj relaxation results at lower pore fluid pH. To determine the change in p as pore fluid acidity increased, Equation 2.4 was used to estimate p from the Ti data. Figure 5.6 presents the relation between p and pH for water-wet and oil-wet samples. Surface relaxivity values increased substantially as pore fluid pH decreased. For neutral pH pore fluids, p was similar to values obtained earlier in the distilled water and salinity experiments, with values of 1.2 x 10"3cm/s and 2.5 x 10"4cm/s for the water-wet and oil-wet samples respectively. As pH of the pore fluid decreased, p increased for both the water-wet and the oil-wet samples. At the lowest pH of 2, p was 2.0 x 10"3 cm/s for the water-wet samples and 8.3 x 10"4 cm/s for the oil-wet samples. The data suggest that a continuing decrease in pH would be accompanied by a further increase in p. A feature in Figure 4.5 and Figure 5.6 of particular interest is the similarity of Ti relaxation times and surface relaxivities between oil-wet samples at low pH and water-wet samples at neutral pH. This indicated that the amount of fluid-surface interaction is similar for oil-wet samples at low pH and water-wet samples at neutral pH. Knowledge of pore fluid pH is therefore required to properly estimate wettability conditions using T! data. 5.3 Surface Relaxation in Porous Media at Low pH This discussion would not be complete without addressing the possible relaxation mechanisms responsible for the observed changes in surface relaxation when pore fluid conditions are acidic. The two mechanisms believed to be responsible for surface 64 2.50E-03 x 2.00E-03 e * 1.50E-03 & ;? "B OS 3 y 1.00E-03 s 5.00E-04 + 0.00E+00 O o O Water-Wet • Oil-Wet pH Figure 5.6 : Calculated surface relaxivities for the water-wet and oil-wet samples saturated with different pH pore fluids. 65 relaxation in porous media are the existence of a bound water 'layer and the presence of paramagnetic ions. This section attempts to predict the effect of a decrease in pH on these two mechanisms. Relaxation at the fluid-solid interface caused by the bound water layer is thought to be a result of the rapid exchange between protons of surface OH groups, protons located in the first one or two monolayers of bound water, and protons in the remaining water [Clifford, 1975]. A decrease in pH causes an increase in the quantity of protons in the pore fluid, therefore an increased exchange rate of protons between the surface and the fluid may occur. This would result in increased relaxation with increased pore fluid acidity. As discussed above, however, the amount of relaxation observed for fluids on surfaces due to the bound water phenomenon would not be sufficient to account for the measured values for surface relaxation. Surface relaxation due to bound water was measured by D'Orazio [1990] to be on the order of 10"5 cm/s. This is two orders of magnitude less than that measured in this study for water-wet sand packs (10"3 cm/s). The question therefore arises whether the increase in surface relaxation caused by an increase in proton exchange with the bound water layer could cause a large enough overall change in the measured relaxation. Evidence to support or dismiss this possibility was not found in the literature. The second possible mechanism for enhanced fluid relaxation is the presence of paramagnetic ions in the sample. Paramagnetic ions are thought to cause enhanced relaxation due to the interaction of the pore fluid protons with the electron field of the ions [Kleinberg, 1994]. The exact nature of this interaction, however, is poorly understood. It is believed though that an increase in the number of protons in the pore fluid should have no effect on the amount of surface relaxation provided by the paramagnetic ions, because all the samples analyzed relaxed within the fast diffusion regime. Therefore, the amount of protons transferred from the bulk solution to the pore surface is already in excess of the amount of protons that can be relaxed at the 66 paramagnetic sites. Adding more protons, by lowering the pore fluid pH would only introduce additional protons to the already saturated paramagnetic sites. Based on available information, the increased surface relaxation observed when pore fluids are acidic can not be explained by the interaction of protons with paramagnetic ions. It has been demonstrated that relaxation at the bound water layer is the most probable mechanism responsible for the observed increase in surface relaxation when pore fluids are acidic. It is not known, however, if the increased acidity would affect relaxation caused by paramagnetic ions. Further experimentation is required to determine conclusively what mechanism is responsible for the results obtained. At present, determining the relaxation mechanism responsible for the observed results is of secondary importance to recognizing that enhanced relaxation occurs. With a knowledge that pore fluid acidity affects Ti data, the accuracy of interpreting data to measure wettability is greatly improved. 67 6 . Conclusions These experiments have contributed to a better appreciation of the usefulness of NMR in the measurement of wettability differences in porous media. T! relaxation times were measured for water-saturated water-wet and oil-wet sand packs to determine if surface wettability could be determined. T! was found to measure changes in wettability between 100% water-wet and 100% oil-wet sand packs under certain conditions. Ti measurements were dependent on pore size and pore fluid pH, but not on pore fluid NaCl content. The usefulness of unconsolidated sand as a porous medium was also demonstrated. Characteristics of the sand pack, such as porosity and pore size, require being constant throughout all experiments in order to obtain information on surface wettability. Consistency in the sample sand pack characteristics was obtained by using specially designed Telfon sample holders. Ti relaxation was shown to be dependent on sand pack wettability under certain pore fluid chemistry conditions. Measurements made on prepared sand packs saturated with distilled water showed that Ti was much shorter for water-wet samples then for oil-wet samples. The measured difference in T! relaxation time between the water-wet and oil-wet samples was approximately 1 second. Both water-wet and oil-wet T! data were found to be shorter than those of the bulk solution relaxation. The enhanced relaxation occurring for water in both the water-wet and oil-wet sand packs indicated the presence of surface relaxation. It was found that surface relaxivity in the oil-wet system was approximately 1/4 to 1/5 the value of surface relaxivity measured for the water-wet system. 68 A positive .relation between Tj relaxation time and pore size existed for both water-wet and oil-wet sand packs. Results showed that as pore size increased relaxation time of the pore fluid also increased. This was due to surface relaxation occurring at the water-wet and oil-wet surfaces. Tj was found to be independent of pore fluid salinity but dependent on pore fluid pH. It was found, that an increase in pore fluid acidity caused an increase in Tj relaxation rates. This was observed in both the water-wet and oil-wet samples. Enhanced relaxation at lower pH was attributed to a greater amount of surface relaxation at the grain surfaces within the porous sand packs. Increased surface relaxivity caused Tj measurements made on an oil-wet sample saturated with a low pH fluid were found to be similar to those obtained for a water-wet sample saturated with a neutral pH pore fluid. The results presented herein showed that T t relaxation is a useful measure of surface wettability, but that Ti data are dependent on certain properties of the saturated porous medium. Specifically, Ti measurements depend on the size of the pores and the pH of the pore fluid. A knowledge of both these properties is therefore required to estimate wettability conditions from T! relaxation data. 69 7 . Recommendations The recommendations outlined below are possible topics of research that this study has stimulated. Some of the suggestions may have in part been addressed in this study, but further research is required to fully interpret the meaning of these results. 1) The investigation into the dependence of T! on pore fluid chemistry should continue. This study demonstrated that Ti is affected by pore fluid pH when conditions are acidic. It is of interest whether basic pore fluid conditions would produce similar results. As well, only minor work was done combining salinity at various pH levels. Further experiments should be completed to determine if salinity contributes to overall T! relaxation measurements at different pore fluid pH. 2) Wettability is known to change over time due to different system conditions. Ti relaxation measurements may be useful for quantifying the changes that occur. Preliminary work not reported in this study indicated that T! does in fact change over time in oil-wet systems. It would be very useful to complete a detailed study to investigate this phenomenon. Such a study could be used to investigate the effect of pore fluid chemistry on T! at different time intervals. 3) It has been suggested that Ti directly depends on the quantity of paramagnetic ions in the oil-wetting film. Although some work has been completed on this topic by other researchers, additional work would prove useful. This possible dependence could be explored by performing a systematic study of how T! is affected by the quantity of paramagnetics in the oil-wet layer. 7 0 8 . References Adamson, A. W., 1982, Physical Chemistry of Surfaces, John Wiley & Sons, New York, 664 pgs. Amott, E., 1959, Observations Relating to the Wettability of Porous Rock, Petroleum Transactions, AIME, 216 : pgs. 156-162. Anderson, W. G., 1986a, Wettability Literature Survey-Part 1: Rock/Oil/Brine Interactions and the Effects of Core Handling on Wettability, Journal of Petroleum Technology, October: pgs. 1125-1144. Anderson, W. G., 1986b, Wettability Literature Survey-Part 2: Wettability Measurement, Journal of Petroleum Technology, November : pgs. 1246-1262. Atkins, P. W., 1990, Physical Chemistry, Oxford University Press, Oxford, 995 pgs. Baldwin, B. A. and Yamanashi, W. S., 1989, Detecting Fluid Movement and Isolation in Reservoir Core With Medical NMR Imaging Techniques, SPE Reservoir Engineering, May : pgs. 207-212. Bloch, F., Hansen, W. w. and Packard, M., 1946, Nuclear Induction, Physics Review, 69 : pg. 127. Borgia, G. C , Fantazzimi, P. and Mesini, E., 1991, Wettability effects on oil-water configurations in porous media: A nuclear magnetic resonance relaxation study, Journal of Applied Physics, 70 (12): pgs. 7623-7625. Borgia, G. C , Brighenti, G., Fantazzini, P., Fanti, G. D. and Mesini, E., 1992, Specific Surface and Fluid Transport in Sandstones Through NMR Studies, SPE Formation Evaluation, September : pgs. 206-210. Bourbie, T., Coussy, O. and Zinszner, B., 1987, Acoustics of Porous Media, Gulf Publishing Company - Book Division, Houston, 334 pgs. Brown, R. J. S. and Fatt, I., 1956, Measurements of Fractional Wettability of Oilfield Rocks by the Nuclear Magnetic Relaxation Method, Petroleum Transactions, AIME, 207 : pgs. 262-264. Brown, C. E. and Neustadter, E. L., 1980, The Wettability of'oilAvater/silica systems with reference to oil recovery, Journal of Canadian Petroleum, 19 : pgs. 100-110. 71 Brownstein, K. R. and Tarr, C. E., 1979, Importance of classical diffusion in NMR studies of water in biological cells, Physical Review A, 19 (6): pgs. 2466-2453. Buckley, J. S., Takamura, K. and Morrow, N. R., 1987, Influence of Electrical Surface Charges on the Wetting Properties of Crude Oils, SPE Paper Number 16964, pgs. 317-328. Clifford, J., 1975, Properties of Water in Capillaries and Thin Films, in WATER - A Comprehensive treatise. Plenum Press, New York, pgs. 75-131. Craig, F. F., 1971, The Reservoir Characteristics of Waterflooding, V. 3. Richardson, Texas. D'Orazio, F., Bhattacharja, S. and Halperin, W. P., 1990, Molecular Diffusion and Nuclear-Magnetic-Resonance Relaxation in Unsaturated Porous Silica Glass, Physical Review B, 42 (16): pgs. 9810-9818. Doe, P. H., 1994, Salinity Dependence in the Wetting of Silica by Oils. PROCEEDINGS The 3rd International Symposium on Evaluation of Reservoir Wettability and its Effect on Oil Recovery, Laramie, Wyoming. Donaldson, E. C , Thomas, R. D. and Lorenz, P. B., 1969, Wettability Determination and its Effect on Recovery Efficiency, Society of Petroleum Engineers Journal, 9 : pgs. 13-20. Dubey, S. T. and Doe, P. H., 1993, Base Number and Wetting Properties of Crude Oils, SPE Reservoir Engineering, August: pgs. 195-200. Fowkes, F. M., 1964, Attractive Forces at Interfaces, Industrial and Engineering Chemistry, 56 : pgs. 40-52. Fowkes, F. M., 1964, Contact Angle, Wettability, and Adhesion, in Advances in Chemistry Series. American Chemical Society, Washington, D.C, pgs. 99-111. Fukushima, E. and Roeder, S. B. W., 1981, Experimental Pulse NMR: A Nuts and Bolts Approach, Addison-Wesley Publishing Company, Inc., 539 pgs. Gladden, L. F., 1994, Nuclear Magnetic Resonance in Chemical Engineering: Principles and Applications, Chemical Engineering Science, 49 (20): pgs. 3339-3408. 72 Hedberg, S. A., Knight, R. J.., Mackay, A . X . and Whittall, K. P., 1993, The Use of Nuclear Magnetic Resonance for Studying and Detecting Hydrocarbon Contaminants in Porous Rocks, Water Resources Research, 29 (4): pgs. 1163-1170. Howard, J. J. and Kenyon, W. E., 1992, Determination of pore size distribution in sedimentary rocks by proton nuclear magnetic resonance, Marine and Petroleum Geology, 9 (139). Howard, J. J., Kenyon, W. E. and Straley, C , 1993, ProtonMagnatic Resonance and Pore Size Variations in Reservoir Sandstones, SPE Formation Evaluation, September : pgs. 194-200. Hsu, W. F., 1994, Wettability of Porous Media by Nuclear Magnetic Resonance Relaxation Methods. Ph.D. Thesis, Texas A&M. Jadhunandan, P. P. and Morrow, N. R., 1991, Spontaneous Imbibition of Water by Crude Oil/Brine/Rock Systems, In Situ, 15 (4): pgs. 319-345. Jadhunandan, P. P. and Morrow, N. R., 1995, Effect of Wettability on WaterfloodRecovery for Crude-Oil/Brine/Rock Systems, SPE Reservoir Engineering, February : pgs. 40-46. Kanters, W. A., 1994, Determination of porous media wettability using nuclear magnetic resonance techniques. Rock Physics Research Program, Volume 3, Paper H, University of British Columbia, Vancouver, Canada. Kenyon, W. E., Day, P. I., Straley, C. and Willemsen, J. F., 1986, Compact and Consistent Representation of Rock NMR datafor permeability estimation. 61 st Annual Technical Conference and Exhibition, paper 15643, New Orleans, La. Kenyon, W. E., Day, P. I., Straley, C. and Willemsen, J. F., 1988, A three-part study of NMR longitudinal relaxation properties of water-saturated sandstones, SPE Formation Evaluation, 3 (622). Kleinberg, R. L., Kenyon, W. E. and Mitra, P. P., 1994, Mechanism of NMR Relaxation of Fluids in Rock, Journal of Magnetic Resonance, Series A, 108 : pgs. 206-214. Korringa, J., Seevers, D. O. and Torrey, H. C , 1962, Theory of Spin Pumping and Relaxation in Systems with a Low Concentration of Electron Spin Resonance, Physical Review, 127 (4): pgs. 1143-1150. 73 Latour, L. L., Kleinberg, R. L.: and Sezgjner, A , 1992, Nuclear Magnetic Resonance Properties of Rocks at Elevated Temperatures, Journal of Colloid and Interface Science, 150 (2): pgs. 535-548. Lawson, C. L. and Hanson, R. J., 1974, Solving Least Squares Problems, Prentice-Hall, Englewood Cliffs, N.J. Liu, Y. and Buckley, J. S., 1994, Wetting Alteration by Adsorption from Crude Oil. PROCEEDINGS The 3rd International Symposium on Evaluation of Reservoir Wettability and its Effect on Oil Recovery, Lararmie, Wyoming. Meiboom, S., Luz, Z. and Gill, D., 1957, Proton Relaxation in Water, The Journal of Chemical Physics, 27 (6): pgs. 1411-1412. Morrow, N. R., 1990, Wettability and Its Effect on Oil Recovery, Journal of Petroleum Technology (SPE), 42 (12): pgs. 1476-1484. Munn, K. and Smith, D. M., 1987, A NMR Technique for the Analysis of Pore Structure: Numerical Inversion of Relaxation Measurements, Journal of Colloid and Interface Science, 119(1): pgs. 117-126. Neumann, A. W. and Good, R. J., 1979, Techniques of Measuring Contact Angles, Surface and Colloid Science, 11 : pgs. 31-91. North, F. K., 1985, Petroleum Geology, Allen & Unwin, Boston, 607 pgs. Purcell, E. M., Torrey, H. C. and Pound, R. V., 1946, Resonance absorption by nuclear magnetic moments in a solid, Physics Review, 69 : pgs. 37-38. Resing, H. A., 1972, NMR Relaxation of Adsorbed Molecules with Emphasis on Adsorbed Water, Advances in Molecular Relaxation Processes, 3 : pgs. 199-226. Seevers, D.O., 1966, A Nuclear Magnetic Method for Determining the Permeability of Sandstones, SPWLA 7th Annual Logging Symposium Proceedings, Paper L. Senturia, S. D. and Robinson, J. D., 1970, Nuclear Spin-Lattice Relaxation of Liquids Confined in Porous Solids, Soceity of Pertroleum Engineers Journal, 10 : pgs. 237-244. Simpson, J. H. and Carr, H. Y., 1958, Diffusion and Nuclear Spin Relaxation in Water, The Physical Review, Series 2, 111 (5): pgs. 1201-1202. 74 Skauge, A. and Fosse, B., 1994, A study ofthe Adhesion, Interfacial Tensions, andContact Angles for a Brine, Quartz, Crude Oil System. PROCEEDINGS The 3rd International Symposium on Evaluation of.Reservoir Wettability and its Effect on Oil Recovery, Lararmie, Wyoming. Slichter, C. P., 1963, Principles of Magnetic Resonance, Harper & Row, New York, 246 pgs. Straley, C , Morriss, C. E., Kenyon, W. E. and Howard, J. J., 1991, NMR in Partially Saturated Rocks: Laboratory Insights on the Free Fluid Index and Comparison with Borehole Logs. SPWLA 32nd Annual Logging Symposium, Paper C. Stumm, W. and Morgan, J. J., 1981, Aquatic Chemistry - An Introduction Emphasizing Chemical Equilibria in Natural Waters, John Wiley & Sons, New York, 780 pgs. Whittall, K. P. and Mackay, A. L., 1989, Quantitative interpretation of NMR relaxation data, Journal of Magnetic Resonance, 84 : pgs. 134-152. Williams, C. E. and Fung, B. M., 1982, The Determination of Wettability by Hydrocarbons of Small Particles byDeuteron T]p Measurement, Journal of Magnetic Resonance, 5 0 : pgs. 71-80. Zimmerman, J. R. and Brittin, W. E., 1957, Nuclear Magnetic Resonance Studies in Multiple Phase Systems: Lifetime of a Water Molecule in Adsorbing Phase on Silica Gel, Journal of Physical Chemistry, 61 : pgs. 1328-1333. 75 Appendix A This appendix contains detailed information for all the samples analyzed. For each of the samples the following information is given: 1) sample identity, 2) porosity calculations, 3) water content, and 4) general NMR data. The samples are organized into sections which correspond to the experiments conducted. For example, all the samples used in the pH experiments are grouped together. A legend is provided below to help interpret the tables. Legend General Symbols and Abbreviations * - indicates that the cell was re-packed after an earlier experiment WW - indicates that the sand was water-wet OW - indicates that the sand was oil-wet Table A.1 Sample ID Sample Holder ID Sample No. Vt W(empty) V(empty) W(full) V(full) W(sand) V(sand) Porosity Table A.2 Date Analyzed Tau Sequence Saturating Solution {5.2,0.02} W(before) Water Content: W(after) W(change) Saturation Change description of the sample which can be used to identify it. A marking etched into the base of the sample holder ID number assigned to sample for identification purposes The volume available for Sand packing in the Teflon Holder. Weight of the empty Teflon Sample holder Volume of the empty Teflon cylinder Weight of Teflon holder and sand Volume of Teflon holder and sand Weight of sand alone [W(full)-W(empty)] Volume of sand alone [Vs = V(full)-V(empty)] Sand pack porosity calculated by [Vv/Vt] Date the sample was analyzed using the NMR spectrometer Tau values used to define the relaxation curve (found in Appendix 3.2) Fluid used to saturated the sand packs represents the pH and NaCl concentration in Molarity. Weight of saturated sample before NMR measurements Predicted determined by [Vt * porosity * 1 g/cc] Measured determined by [W(before) - W(full)] Weight of saturated sample after NMR measurements Change in weight of samples during NMR analysis Change in saturation during NMR analysis calculated by [W(change) / Measured Water Content] Notes: 1) If a grain size measurement is absent from the Sample ID then it means the sample was created using grains that were 163 um in diameter. 2) The sections: Distilled Water, Exp#l; Distilled Water, Exp#2; and pH 2,0.02 M NaCl were used to complete the grain size work described in the text. The remaining two sections: Varying Salinity and Varying pH, were used to investigate TI dependence on pore fluid chemistry. 76 a 4 Cu 3 3 a . -£.8 8. d I z l | EC •3 =8: 2 5 aj 08 Q W s ro o t— <N O o oo v© s © OQ i r f 'a n * Ok 77 e cu E CU IM s cn es cu o CM •o e es C o e« E .o B O •a es u a «3 C <u i 7 3 <u s B ta B © 3 es H l l 0s-P. -T CN VO CO o VO od <o CO f -vo 95 3 2 CQ CN O © i O CN © • O 8 VO © vo co co d co CN r o vo vo VO CN r~ VO vo s vo CO d CO vo Ov s i CN t~ VO VO 3 oo VO 3 CN o I CN o I CN o » b E -1 . vo , BS ' a rc c I 8 \X M a "& a 78 ca E >> a a o o i-s f . « on Co s-' u a 0C cd i 0 0 •8 t/l "E. h l | 6 0 rc CO 8 •S M ca CQ <3\ r o oo oo CN CN d CN CN If C N IS! CQ ICQ CQ 121 o 3 §1 wo CN 8 a CN * 79 s a If & a , e o 00 i d 2 , 8. o 9 "I ca a! OQ O oo |<s o m >/-> oo 3 !<*> CN © CN © d | ,1 si 2 1 8 2 OQI © © o CN © i I cd W3 > 2 o 8 d 1^  s © © CN © © oo s CN P I<N1 ft CQ CQ CN 8 © «/-> 00 o 3 o 2 31 3 9 I S CN z CN O lis nss CN v i 5= o. i II i i i II « a. M a 80 CO c u S S o U . IS CO u 15 £ •o CN co •a •o <u ts CN CO •8 11 ON o •/•> ON © III WV ON i f . 6 551 Ico 9 ol O N I O CN c | .V .2 CO o .2 •c -g1 o o p. CO 3 CN ON s i CN U <=> pQ °.U «N H M 55 a. si CN I O N I CN ON I O fa « OQ C O > O c i i n r o CN ol </->[ ON I s O N I O CN \9 CN c i 8 DC • • "2 « co § "S W £ o H O O ^ — cN 8 1 A p p e n d i x B TI Relaxation Curve tau times This appendix contains the tau values used to define the inversion recovery relaxation curves. Three different sequences were used, identified as A, B and C. The reason for a change in sequences was to: 1) improve the characterization of the relaxation curve, 2) repeat specific tau times to check for a change in the sample, 3) reduce die time required for the TI inversion recovery analysis. Before point number 3 was completed tests were performed to determine if the TI relaxation constant would be effected. It was not and therefore the number of tau values used was reduced. Three tables are present in this Appendix: B.l , B.2, and B.3. The following information is given in the tables: 1) tau time 2) number of scans used, 3) time required for analysis, and 4) files in which the data was placed. 82 Table B.l - Tau values used to define Relaxation Curve A tau Sequence tau (mS) # Scans Used Required Time (min) Filename Header ID 1 1.00 24 4.3 rim ##.dtl 2 10.00 50 8.7 rlOm ##.dtl 3 100.00 50 8.7 rlOOm ##.dtl 4 1000.00 50 9.1 r1000m ##.dtl 5 10000.00 100 25.5 rlOs ##.dtl 6 1.50 24 4.3 rl500u ##.dtl 7 15.00 50 8.7 rl5m ##.dtl 8 150.00 50 8.7 rl50m ##.dtl 9 1500.00 50 9.3 r1500m ##.dtl 10 2.25 24 4.3 r2250u ##.dtl 11 22.50 50 8.7 r22m ##.dtl 12 225.00 50 8.8 r225m ##.dtl 13 2250.00 100 18.9 r2250m ##.dtl 14 3.50 24 4.3 r3500u ##.dtl 15 35.00 50 8.7 r35m ##.dtl 16 350.00 50 8.8 r350m ##.dtl 17 3500.00 100 20.0 r3500m ##.dtl 18 5.00 24 4.3 r5m ##.dtl 19 50.00 50 8.7 r50m ##.dtl 20 500.00 50 8.9 r500m ##.dtl 21 5000.00 100 21.3 r5000m ##.dtl 22 7.25 24 4.3 r7250u ##.dtl 23 72.50 50 8.7 r72m ##.dtl 24 725.00 50 9.0 r725m ##.dtl 25 7250.00 100 23.2 r7250m ##.dtl 26 CPMG200 50 9.2 cp2s ##.dtl 27 CPMG400 50 9.2 cp4s ##.dtl 28 CPMG600 50 9.2 cp5s ##.dtl Total Time: 285.7 minutes 4.8 hours Number of taus: 25 Notes: ## - is the sample number used to identify each file sample. 83 Table B.2 - .Tau values used to define Relaxation Curve B tau Sequence tau (mS) # Scans Used Required Time (min) Filename Header ID 1 250.00 50 8.8 r250m ##a.dtl 2 2000.00 100 18.7 r2000m ##.dtl 3 1.00 24 4.3 rim ##.dtl 4 10.00 50 8.7 rlOm ##.dtl 5 100.00 50 8.7 rlOOm ##.dtl 6 1000.00 50 9.1 rlOOOm ##.dtl 7 10000.00 100 25.5 rlOs ##.dtl 8 1.50 24 4.3 rl500u ##.dtl 9 15.00 50 8.7 rl5m ##.dtl 10 150.00 50 8.7 rl50m ##.dtl 11 1500.00 50 9.3 rl500m ##.dtl 12 8000.00 100 23.8 r8000m ##.dtl 13 2.50 24 4.3 r2500u ##.dtl 14 25.00 50 8.7 r25m ##.dtl 15 250.00 50 8.8 r250m ##b.dtl 16 2750.00 100 19.3 r2750m ##.dtl 17 4.00 24 4.3 r4m ##.dtl 18 40.00 50 8.7 r40m ##.dtl 19 400.00 50 8.8 r400m ##.dtl 20 4000.00 100 20.4 r4000m ##.dtl 21 6.25 24 4.3 r6250u ##.dtl 22 62.50 50 8.7 r625u ##.dtl 23 625.00 50 8.9 r625m ##.dtl 24 6000.00 100 22.1 r6000m ##.dtl 25 CPMG200 50 9.2 cp2s ##.dtl 26 CPMG400 50 9.2 cp4s ##.dtl 27 CPMG600 50 9.2 cp5s ##.dtl 28 250.00 50 8.8 r250m ##c.dtl Total Time: 302.4 minutes 5.0 hours Number of taus : 23 Notes: ## - is the sample number used to identify each file sample. 84 Table B.3 - Tau values used to define Relaxation Curve C tau Sequence tau (mS) # Scans Used Required Time (min) Filename Header ID 1 250.00 20 4.0 r250m ##a.dtl 2 1.00 12 2.7 rim ##.dtl 3 10.00 20 4.0 rlOm ##.dtl 4 100.00 20 4.0 rlOOm ##.dtl 5 1000.00 20 4.2 r1000m ##.dtl 6 5000.00 50 11.2 r5000m ##.dtl 7 2.50 12 2.7 r2500u ##.dtl 8 25.00 20 4.0 r25m ##.dtl 9 2000.00 50 9.9 r2000m ##.dtl 10 7500.00 50 12.3 r7500m ##.dtl 11 5.00 12 2.7 r5m ##.dtl 12 50.00 20 4.0 r50m ##.dtl 13 500.00 20 4.1 r500m ##.dtl 14 3000.00 50 10.3 r3000m ##.dtl 15 10000.00 50 13.3 rlOs ##.dtl 16 250.00 20 4.0 r250m ##b.dtl 17 CPMG200 50 9.2 cp2s ##.dtl 18 CPMG400 50 9.2 cp4s ##.dtl 19 CPMG600 50 9.2 cp5s ##.dtl 20 250.00 20 4.0 r250m ##c.dtl Total Time: 128.9 minutes 2.1 hours Number of taus : 15 Notes: ## - is the sample number used to identify each file sample. 85 Appendix C- Sample Tj Relaxation Curves and Interpretation This Appendix contains information about the samples discussed in the text. For each sample the following is given: 1) the Tj Relaxation curve, 2) the smoothed T, relaxation fit, and 3) the discrete T t data including the arithmetic mean value. The arithmetic mean was calculated using equation 4.1. This equation was: f —1=2. 4.1 l(mean) n «=0 To make finding a particular sample easier, samples are arranged according to the experiment. Sample numbering, therefore, will not be in sequence. The samples are arranged in the following sections: 1) Grain size Experiments - Pore Fluid : Distilled Water 2) Grain size Experiments - Pore Fluid : pH 2,0.02 M NaCl 3) Salinity Dependence Experiments 4) pH Dependence Experiments 86 Appendix~C.lGrain Size Experiments -'Pore Fluid : Distilled Water The samples contained in this section are the oil-wet and water-wet samples that were saturated with distilled water. Pore Fluid : Distilled water Number of Samples in Experiment Data Set : 12 Smoothed data created with fit relaxation of : 1% to 2% For easy reference to Figure 4.1, samples used to create the figure are shown in the diagram below. All sample numbers are placed in relation to where the data plots on Figure 4.1. Sample Number's Oil-Wet Samples 24 73 42/26 72 71 Water-Wet Samples 23 76 41/25 75 74 Grain Size (Microns) 115 137 163 194 275 Files in the following pages are listed from smallest to largest grain size. Water-wet samples are listed first, followed by the oil-wet samples. 87 Relaxation Curve Data Sample 23 1 T-2 3 T i m e ( s e c Smoothed TI Distribution Solution Discrete TI Solution and Select Parameters Sample ID Number 23 Tl(s) 0.004 0.689 1.199 Amplitude 36.20 660.58 346.48 Percent 3.5 63.3 33.2 CHI Squared for l e a s t squares f i t = 90.56 Number of non-Zero TI constants = 3 TI weighted arithmetic mean (sec) = 0.835 88 Relaxation CurveData Sample 76 T i m e ( s e c ) Smoothed TI Distribution Solution T i m e ( l o g ) Discrete TI Solution and Select Parameters T l ( s ) 0. 002 0.010 0.276 0.930 2.536 Sample ID Number Amplitude 14.11 9.13 48.42 1080.54 50.73 76 Percent 1.2 0.8 4.0 89.8 4.2 CHI Squared f o r l e a s t squares f i t = 4.43 Number of non-Zero TI constants = 5 TI weighted arithmetic mean (sec) = 0.954 89 Relaxation Curve Data j i i i Sample -4 1 ^ 3 2 3 T i m-e ( s e c ) Smoothed TI Distribution Solution J I L Time ( l o g ) Discrete TI Solution and Select Parameters Sample ID Number 41 Tl(s) 0. 016 0.492 1.119 Amplitude 5.16 266.57 945.39 Percent 0.4 21.9 77.7 CHI Squared f o r l e a s t squares f i t = 13.39 Number of non-Zero TI constants = 3 TI weighted arithmetic mean (sec) = 0.977 90 Relaxation Curve Data J L Sample 25 T i m e ( s e c ) Smoothed TI Distribution Solution Time ( l o g ) Discrete TI Solution and Select Parameters Sample ID Number : 25 Tl(s) Amplitude Percent 0.003 44.44 4.6 0.521 190.13 19.7 1.279 730.92 75.7 CHI Squared f o r le a s t squares f i t = 47.84 Number of non-Zero TI constants = 3 TI weighted arithmetic mean (sec) = 1.071 91 Relaxation Curve Data cm Smoothed TI Distribution Solution Discrete TI Solution and Select Parameters Sample ID Number 75 Tl(s) 0.156 1.547 3.875 Amplitude 13.33 1185.32 37.54 Percent 1.1 95.9 3.0 CHI Squared f o r lea s t squares f i t = 1.40 Number of non-Zero TI constants = 3 TI weighted arithmetic mean (sec) = 1.602 92 Relaxation Curve Data Smoothed TI Distribution Solution -i r Time ( l o g ) Discrete TI Solution and Select Parameters Sample ID Number : 74 Tl(s) Amplitude Percent 0.041 13.00 1.1 0.431 93.63 8.0 1.325 1068.97 90.9 CHI Squared f o r least squares f i t = 1.20 Number of non-Zero TI constants = 3 TI weighted arithmetic mean (sec) = 1.239 93 'Relaxation Curve Data CC T i m e ( s e c ) Smoothed TI Distribution Solution Time ( l o g ) Discrete TI Solution and Select Parameters Tl(s) 0. 003 0. 038 0.309 1.935 Sample ID Number : 24 Amplitude Percent 55.72 4.6 9.66 0.8 25.03 2.1 1118.87 92.5 CHI Squared f o r lea s t squares f i t = 41.46 Number of non-Zero TI constants = 4 TI weighted arithmetic mean (sec) = 1.797 94 Relaxation Curve Data Smoothed TI Distribution Solution - i r 1 0~a 1 0 Time ( l o g ) Discrete TI Solution and Select Parameters Sample ID Number 73 Tl(s) 0.120 2.034 Amplitude 21.97 1158.87 Percent 1.9 98.1 CHI Squared f o r le a s t squares f i t = 10.92 Number of non-Zero TI constants = 2 TI weighted arithmetic mean (sec) = 1.999 95 Relaxation Curve .Data T i m e ( s e c Smoothed TI Distribution Solution CC Discrete TI Solution and Select Parameters Tl(s) 0.002 0.118 2.177 Sample ID Number : 42 Amplitude Percent 5.24 0.4 25.65 2.1 1185.38 97.5 CHI Squared for lea s t squares f i t = 12.79 Number of non-Zero TI constants = 3 TI weighted arithmetic mean (sec) = 2.124 96 . Relaxation Curve Data ' Sample 26 t=n< ro T i m e ( s e c ) Smoothed TI Distribution Solution T i m e ( l o g Discrete TI Solution and Select Parameters Sample ID Number 26 Tl(s) 0.004 0. 369 2.275 Amplitude 53.50 17.29 982.01 Percent 5.1 1.6 93 . 3 CHI Squared f o r le a s t squares f i t = 81.15 Number of non-Zero TI constants = 3 TI weighted arithmetic mean (sec) = 2.128 97 Relaxation Curve Data T i m e ( s e c : Smoothed TI Distribution Solution Discrete TI Solution and Select Parameters Sample ID Number 72 Tl(s) 0.016 0. 069 2.357 Amplitude 5. 00 1.45 1146.20 Percent 0.4 0.1 99.4 CHI Squared f o r least squares f i t = 2.22 Number of non-Zero TI constants = 3 TI weighted arithmetic mean (sec) = 2.344 98 Relaxation Curve Data l m e Smoothed TI Distribution Solution Time ( l o g ) Discrete TI Solution and Select Parameters Sample ID Number 71 2 .702 Amplitude 18.56 1112.43 Percent 1.6 98.4 CHI Squared f o r least squares f i t = 5.37 Number of non-Zero TI constants = 2 TI weighted arithmetic mean (sec) = 2.660 99 Appendix C.2 -Grain Size Experiments - Pore Fluid : pH2,0.02 M NaCl The samples contained in this section are the oil-wet and water-wet samples that were saturated with a pH 2,0.02 M NaCl solution. Pore Fluid : pH 2,0.02 M NaCl Number of Samples in Experiment Data Set : 10 Smoothed data created with fit relaxation of : 1% to 2% For easy reference to Figure 4.2, samples used to create the figure are shown in the diagram below. All sample numbers are placed in relation to where the data plots in Figure 4.2. Sample Number's Oil-Wet 37 36/38 39 40 Samples Water-Wet 34 33/35 32 31 Samples Grain Size 115 137 163 194 275 (Microns) Files in the following pages are listed from smallest to largest grain size. Water-wet samples are listed first, followed by the oil-wet samples. 100 Relaxation Curve.Data T i m e ( s e c Smoothed TI Distribution Solution J L S a m p l e 34 ft A — s ! , 0"' 10"* 1 o" 1 Time ( l o g ) i 10" 10 Discrete TI Solution and Select Parameters Sample ID Number : 34 Tl(s) Amplitude 0.002 28.06 0.877 793.44 1.395 499.49 Percent 2.1 60.1 37.8 CHI Squared f o r least squares f i t = 98.35 Number of non-Zero TI constants = 3 TI weighted arithmetic mean (sec) = 1.055 101 Relaxation Curve Data T i m e ( s e c Smoothed TI Distribution Solution Discrete TI Solution and Select Parameters Sample ID Number 33 Tl(s) 0.103 0.454 0.965 Amplitude 9.89 208.20 1080.70 Percent 0.8 16. 0 83.2 CHI Squared f o r lea s t squares f i t = 116.07 Number of non-Zero TI constants = 3 TI weighted arithmetic mean (sec) = 0.876 102 Relaxation Curve Data T i m e ( s e c : Smoothed TI Distribution Solution Time ( l o g ) Discrete TI Solution and Select Parameters Sample ID Number : Tl(s) Amplitude 0.002 44.32 0.640 887.97 1.139 373.16 35 Percent 3.4 68.0 28.6 CHI Squared f o r l e a s t squares f i t = 62.07 Number of non-Zero TI constants = 3 TI weighted arithmetic mean (sec) = 0.761 103 Relaxation Curve Data T i m e ( s e c Smoothed TI Distribution Solution QJ CC Discrete TI Solution and Select Parameters Sample ID Number : 31 Tl(s) 0.411 1.298 Amplitude 91.58 1111.82 Percent 7.6 92 .4 CHI Squared f o r lea s t squares f i t = 11.07 Number of non-Zero TI constants = 2 TI weighted arithmetic mean (sec) = 1.230 105 Relaxation Curve Data Saraple 37 ra i 1 1 ~r r 0 1 2 3 * T i m e ( s e c ) Smoothed TI Distribution Solution e x Saraple 3 7 -A 1 1 i > -10"» IO-" 10"' ID' ID1 T i m e ( l o g ) Discrete TI Solution and Select Parameters Sample ID Number : 37 Tl(s) Amplitude Percent 0.939 1328.55 100.0 CHI Squared f o r lea s t squares f i t = 240.10 Number of non-Zero TI constants = 1 TI weighted arithmetic mean (sec) = 0.939 106 Relaxation Curve Data T i m e ( s e c Smoothed TI Distribution Solution T i m e ( l o g ) Discrete TI Solution and Select Parameters Sample ID Number 36 T l ( s 0. 01 0.738 1.131 Amplitude 40.79 156.48 1188.50 Percent 2.9 11.3 85.8 CHI Squared f o r l e a s t squares f i t = 53 0.54 Number of non-Zero TI constants = 3 TI weighted arithmetic mean (sec) = 1.054 1 0 7 Relaxation Curve Data T i m e ( s e c ) Smoothed TI Distribution Solution S a m p l e 38 ~1 t D" Time ( l o g ) Discrete TI Solution and Select Parameters Sample ID Number : 38 Tl(s) Amplitude Percent 0.903 1325.34 100.0 CHI Squared f o r le a s t squares f i t = 2 61.4 2 Number of non-Zero TI constants = 1 TI weighted arithmetic mean (sec) = 0.903 108 Relaxation Curve Data S a m p l e 3 9 T i m e ( s e c ! Smoothed TI Distribution Solution 1 1 1 -S a m p l e 3 9 A \ 1 1 1 1 0 - 5 10"' ID* ID 1 T i m e ( l o g ) Discrete TI Solution and Select Parameters Sample ID Number : 39 Tl( s ) Amplitude Percent 0.807 1375.67 100.0 CHI Squared f o r le a s t squares f i t = 503.19 Number of non-Zero TI constants = 1 TI weighted arithmetic mean (sec) = 0.807 109 Relaxation Curve Data T i m e ( s e c ) Smoothed TI Distribution Solution Time ( l o g ) Discrete TI Solution and Select Parameters Sample ID Number : 4 0 TI (s) 0. 002 0.413 1.840 Amplitude 12 .23 7.05 1198.83 Percent 1.0 0.6 98.4 CHI Squared f o r le a s t squares f i t = 47.41 Number of non-Zero TI constants = 3 TI weighted arithmetic mean (sec) = 1.814 110 Appendix C.3 - Salinity Dependence Experiments The samples contained in this section are oil-wet and water-wet samples that were saturated with various NaCl Solutions. Pore Fluid : Varying Salinity Number of Samples in Experiment Data Set : 8 Smoothed data created with fit relaxation of : 1% to 2% For easy reference to Figure 4.3, samples used in the figure are shown in the diagram below. Al l sample numbers are placed in relation to where the data plots in Figure 4.3. Sample Number's Oil-Wet Samples 42 86 102 105 Water-Wet Samples 41 87 103 106 Salinity (M NaCl) 0.02 0.2 1.0 Files in the following pages are listed from distilled water (Dl) to 1.0 M NaCl. Water-wet samples are listed first, followed by the oil-wet samples. Note that samples 41 and 42 can be found in Appendix C l , they are not reproduced here. Ill Relaxation Curve Data Smoothed TI Distribution Solution Time ( l o g ) Discrete TI Solution and Select Parameters Sample ID Number 87 Tl(s) 0. 001 0. 019 0.259 1.278 Amplitude 18.43 3 .85 67.73 1123.59 Percent 1.5 0.3 5.6 92.6 CHI Squared f o r lea s t squares f i t = 5.87 Number of non-Zero TI constants = 4 TI weighted arithmetic mean (sec) = 1.198 112 Relaxation Curve Data Smoothed TI Distribution Solution Discrete TI Solution and Select Parameters Sample ID Number : 103 Tl(s) 0.003 0.173 1.324 Amplitude 24.96 39.45 1391.89 Percent 1.7 2.7 95.6 CHI Squared f o r l e a s t squares f i t = 4.06 Number of non-Zero TI constants = 3 TI weighted arithmetic mean (sec) = 1.270 113 Relaxation Curve Data Smoothed TI Distribution Solution Time ( l o g ) Discrete TI Solution and Select Parameters Sample ID Number 86 Tl(s) 0. 063 2 .235 Amplitude 12.65 1171.58 Percent 1.1 98.9 CHI Squared f o r lea s t squares f i t = 4.34 Number of non-Zero TI constants = 2 TI weighted arithmetic mean (sec) = 2.212 115 Relaxation Curve Data J I 1 L_ T i m E ( s e c ) Smoothed TI Distribution Solution Time ( l o g Discrete TI Solution and Select Parameters Sample ID Number : 102 Tl(s) 0.001 0. 044 2.106 Amplitude 14.83 20.41 1303.62 Percent 1.1 1.5 97.4 CHI Squared for le a s t squares f i t = 3.93 Number of non-Zero TI constants = 3 TI weighted arithmetic mean (sec) = 2.052 116 Relaxation Curve Data Sample .105 Time ( s e c Smoothed TI Distribution Solution 1 0"' Time ( l o g ! Discrete TI Solution and Select Parameters Sample ID Number : 105 Tl(s) 0.004 0. 093 2 .135 Amplitude 17.17 11.59 1345.19 Percent 1.2 0.8 97.9 CHI Squared for lea s t squares f i t = 3.56 Number of non-Zero TI constants = 3 TI weighted arithmetic mean (sec) = 2.091 117 Appendix C.4 - pH Dependence Experiments The samples contained in this section are oil-wet and water-wet :samples .that were saturated with various pH strength solutions. Pore Fluid : Varying pH Number of Samples in Experiment Data Set : 8 Smoothed data created with fit relaxation of : 1% to 2% For easy reference to Figure 4.5, samples used in the figure are shown in the diagram below. Al l sample numbers are placed in relation to where the data plots in Figure 4.5. Sample Number's Oil-Wet Samples 77 79 42 83 Water-Wet Samples 78 80 41 84 PH 2 3.5 5.2 7 Files in the following pages are listed from low pH to high pH. Water-wet samples are listed first, followed by the oil-wet samples. Note that samples 41 and 42 can be found in Appendix C l , they are not reproduced here. 118 Relaxation Curve Data , 2D0 —| CD. az , s o -I Time ( s e c Smoothed TI Distribution Solution Sample "78 10"' 10"* 10"' Time ( i • g ' 1 0 * 1 0 ' Discrete TI Solution and Select Parameters Sample ID Number 78 Tl(s) 0. 054 0.183 0.761 Amplitude 10.32 34.16 1137.80 Percent 0.9 2.9 96. 2 CHI Squared for le a s t squares f i t = 19.63 Number of non-Zero TI constants = 3 TI weighted arithmetic mean (sec) = 0.738 119 Relaxation Curve Data S a m p l e 80 - 1 1 I 1. 5 2. 0 2. S 3. 0 0.5 1 . D T i m e ( s e c Smoothed TI Distribution Solution Time ( l a g ) Discrete TI Solution and Select Parameters Sample ID Number 80 T l ( s 0. 00 0. 357 0.749 Amplitude 10.84 194.95 963.19 Percent 0.9 16.7 82.4 2 .75 CHI Squared f o r l e a s t squares f i t = Number of non-Zero TI constants = 3 TI weighted arithmetic mean (sec) = 0.676 120 Relaxation Curve Data S a m p l e 84 1 2 3 4 T i m e ( s e c ) Smoothed TI Distribution Solution J I L T i m e ( l o g ) Discrete TI Solution and Select Parameters Sample ID Number : Tl(s) Amplitude 0.002 13.72 0.058 1.93 0.260 3.00 0.754 226.55 1.414 986.11 84 Percent 1.1 0.2 0.2 18.4 80.1 CHI Squared f o r least squares f i t = 2.20 Number of non-Zero TI constants = 5 TI weighted arithmetic mean (sec) = 1.272 121 Relaxation Curve Data 2 3 Time ( s e c ) Smoothed TI Distribution Solution Time ( l o g ) Discrete TI Solution and Select Parameters Tl(s) 0. 001 0.027 0.245 1.322 Sample ID Number Amplitude 18.85 1.39 13.86 1188.55 77 Percent 1.5 0.1 1.1 97.2 CHI Squared f o r le a s t squares f i t = 3.50 Number of non-Zero TI constants = 4 TI weighted arithmetic mean (sec) = 1.288 122 Relaxation Curve Data S a m p l e 79 T i m e i 6 s e c ' Smoothed TI Distribution Solution az Time ( l o g ) Discrete TI Solution and Select Parameters Sample ID Number TI (s) 0.133 1.787 79 Amplitude 22 . 06 1190.22 Percent 1.8 98.2 CHI Squared f o r le a s t squares f i t = 12.12 Number of non-Zero TI constants = 2 TI weighted arithmetic mean (sec) = 1.757 123 Relaxation Curve Data Smoothed TI Distribution Solution i i i 300 — Sample 83 4D0 — QJ - D 3 D 0 -— •4—' 1 1 CZL S 200 — -CC 1 DO — A 0 — 1 ' 10" ' 10"* 10" ' ID* 10' Time ( l o g ) Discrete TI Solution and Select Parameters Sample ID Number : 83 Tl(s) Amplitude Percent 0.004 4.14 0.4 0.065 8.50 0.7 2.335 1167.34 98.9 CHI Squared f o r l e a s t squares f i t = 6.01 Number of non-Zero TI constants = 3 TI weighted arithmetic mean (sec) = 2.310 124 AppendixC.S - Bulk Solution Samples The samples contained in this section are from Tj relaxation measurements made on bulk solution samples. Refer to Appendix A, Table A.3 for details on the sample properties. The data is presented in a similar order as in Table A.3. A Summary is given below. Fluid Properties Sample Numbers Distilled Water 27, 45, 51, 70, 85, and 95 pH 2, 0.02 M NaCl 30 and 47 0.02, 0.2, and 1.0 M NaCl 93, 111, and 110 respectively pH 2, 3.5, and 7 49 and 92,91, and 90 respectively 125 Relaxation Curve Data S a r a p l e 2 7 o T " T i m e ( s e c Smoothed TI Distribution Solution T i m e ( l o g ) Discrete TI Solution and Select Parameters Sample ID Number : 27 Tl(s) Amplitude Percent 0.008 19.85 3.0 3.027 644.48 97.0 CHI Squared f o r l e a s t squares f i t = 4.12 Number of non-Zero TI constants = 2 TI weighted arithmetic mean (sec) = 2.936 126 Relaxation - Curve Data Smoothed TI Distribution Solution j i : i_ T i m e ( l o g ) Discrete TI Solution and Select Parameters Sample ID Number 45 Tl( s ) 0.002 3.111 Amplitude 47.40 983.36 Percent 4.6 95.4 CHI Squared f o r lea s t squares f i t = 140.55 Number of non-Zero TI constants = 2 TI weighted arithmetic mean (sec) = 2.968 127 Relaxation Curve Data Sample 51 T i m e ( s e c Smoothed TI Distribution Solution T i m e ( l o g ) Discrete TI Solution and Select Parameters Sample ID Number 51 Tl(s) 3 .258 Amplitude 1528.52 Percent 100. 0 CHI Squared f o r l e a s t squares f i t = 93.96 Number of non-Zero TI constants = 1 TI weighted arithmetic mean (sec) = 3.258 128 Relaxation Curve Data T i m e ( s e c Smoothed TI Distribution Solution Discrete TI Solution and Select Parameters Sample ID Number 70 T l ^ s ^ Amplitude Percent 3.221 2.44 1150.92 0.2 99.8 CHI Squared f o r least squares f i t = 5.90 Number of non-Zero TI constants = 2 TI weighted arithmetic mean (sec) = 3.214 129 Relaxation CurveData T i m e ( s e c ) Smoothed TI Distribution Solution T i m e ( l o g ) Discrete TI Solution and Select Parameters Sample ID Number : 85 Amplitude 1559.99 Percent 100.0 CHI Squared f o r least squares f i t = 54.64 Number of non-Zero TI constants = 1 TI weighted arithmetic mean (sec) = 3.262 130 Relaxation Curve Data D 6.0 H Sample 9 5 T i m e ( s e c Smoothed TI Distribution Solution T i m e ( l o g Discrete TI Solution and Select Parameters Sample ID Number 95 TI (s 3 . 06 Amplitude 1185.01 Percent 100.0 CHI Squared f o r l e a s t squares f i t = 10.20 Number of non-Zero TI constants = 1 TI weighted arithmetic mean (sec) = 3.065 131 Relaxation Curve Data T i m e Smoothed TI Distribution Solution Discrete TI Solution and Select Parameters T l ( s ) 2.640 Sample ID Number Amplitude 809.87 30 Percent 100. 0 CHI Squared f o r lea s t squares f i t = 16.00 Number of non-Zero TI constants = 1 TI weighted arithmetic mean (sec) = 2.640 132 Relaxation CurveData T i m e ( s e c Smoothed TI Distribution Solution T i m e ( l o g ) Discrete TI Solution and Select Parameters Sample ID Number : 47 Tl(s) Amplitude Percent 2.987 1268.36 100.0 CHI Squared for least squares f i t = 83.51 Number of non-Zero TI constants = 1 TI weighted arithmetic mean (sec) = 2.987 133 Relaxa t ion Curve Da ta Sample 93 cu T i m e ( s e c ) Smoothed T I Distr ibut ion Solution T i m e ( l o g ) Discrete T I Solution and Select Parameters Sample ID Number 93 Tl(s) 3 .138 Amplitude 1318.60 Percent 100. 0 CHI Squared f o r lea s t squares f i t = 7.70 Number of non-Zero TI constants = 1 TI weighted arithmetic mean (sec) = 3.138 134 Relaxation Curve Data S a n p l e 1 1 1 T i m e ( s e c ) Smoothed TI Distribution Solution Discrete TI Solution and Select Parameters Sample ID Number : 111 Tl(s) 3. 083 Amplitude 1328.66 Percent 100.0 CHI Squared for least squares f i t = 14.87 Number of non-Zero TI constants = 1 TI weighted arithmetic mean (sec) = 3.083 135 Relaxation Curve Data T i m e ( s e c ) Smoothed TI Distribution Solution T i m e ( l o g ) Discrete TI Solution and Select Parameters Sample ID Number : 110 Tl(s) 3 .023 Amplitude 1346.23 Percent 100. 0 CHI Squared f o r lea s t squares f i t = 20.96 Number of non-Zero TI constants = 1 TI weighted arithmetic mean (sec) = 3.023 1 3 6 Relaxation Curve Data T i m e ( s e c Smoothed TI Distribution Solution T i m e ( l o g ) Discrete TI Solution and Select Parameters Sample ID Number 49 Amplitude 1166.17 Percent 100.0 CHI Squared f o r lea s t squares f i t = 137.15 Number of non-Zero TI constants = 1 TI weighted arithmetic mean (sec) = 3.110 137 Relaxation Curve Data T i m e ( s e c Smoothed TI Distribution Solution Discrete TI Solution and Select Parameters Sample ID Number 92 Tl(s) 3.014 Amplitude 1314.88 Percent 100.0 CHI Squared f o r l e a s t squares f i t = 9.71 Number of non-Zero TI constants = 1 TI weighted arithmetic mean (sec) = 3.014 138 Relaxation Curve Data T i m e ( s e c ) Smoothed TI Distribution Solution T i m e ( l o g ) Discrete TI Solution and Select Parameters Sample ID Number : 91 Tl(s) Amplitude Percent 3.119 1428.07 100.0 CHI Squared f o r least squares f i t = 10. Number of non-Zero TI constants = 1 TI weighted arithmetic mean (sec) = 3.1 139 Relaxation Curve Data T i m e ( s e c Smoothed TI Distribution Solution T i m e ( l e g ) Discrete TI Solution and Select Parameters Sample ID Number : 90 Amplitude 31.27 Percent 100.0 CHI Squared f o r least squares f i t = 9.3 5 Number of non-Zero TI constants = 1 TI weighted arithmetic mean (sec) = 3.149 140 Appendix D Sp/Vp Calculations and p Estimates This appendix contains information on sample Sp/Vp and surface relaxivity. Calculations of Sp/Vp and the surface relaxivity are presented in four tables. The tables are organized so that all the samples from a particular experiment are grouped together. The average sureface relaxivities are calculated for the waterwet and oilwet samples in each group. 141 Table D . l •;: Calculating, Surface Relaxivity fromS/V. Grain Size Experiments -.Pore.Fluid : distilled water tlbulk = 3.2 Water-Wet Samples Sample Grain (1-phi) Spore TI rho rho ID Size (urn) 6/d Porosity (Phi) Vpore (sec) (um/sec) (cm/s) 23 115 0.052 39.0 1.56 0.082 0.8 10.85 1.08E-03 76 137 0.044 40.9 1.44 0.063 1.0 11.63 1.16E-03 25 163 0.037 40.5 1.47 0.054 1.1 11.49 1.15E-03 41 163 0.037 38.0 1.63 0.060 1.0 11.84 1.18E-03 75 194 0.031 40.1 1.49 0.046 1.6 6.73 6.73E-04 74 275 0.022 38.2 1.62 0.035 1.2 14.01 1.40E-03 Average: 1.11E-03 Oil-Wet Samples Sample Grain Sgrain Porosity (1-phi) Spore TI rho rho ID Size (um) Vgrain (phi) (phi) Vpore (sec) (um/sec) (cm/s) 24 115 0.052 38.9 1.57 0.082 1.8 2.98 2.98E-04 73 137 0.044 38.9 1.57 0.069 2.0 2.73 2.73E-04 26 163 0.037 41.6 1.40 0.052 2.1 3.05 3.05E-04 42 163 0.037 38.0 1.63 0.060 2.1 2.64 2.64E-04 72 194 0.031 39.0 1.56 0.048 2.3 2.35 2.35E-04 71 275 0.022 39.2 1.55 0.034 2.7 1.87 1.87E-04 Average: 2.60E-04 Notes Sgrain/Vgrain is calculated using the relation S/V = 6/d Spore/Vpore is determined using (6 * ( 1 - phi))/ (d * phi) rho is the surface relaxivity determined from the equation: 1/T1 = rho (S/V)pore + 1/Tlbulk 142 . Table D . 2 : Calculating Surface Relaxivity..from S/V. Grain Size Experiments - Pore Fluid : pH 2, 0.02 MNaCl tlbulk= 3.0 Sample ID Grain Size (urn) 6/d Porosity (1-phi) (Phi) Spore Vpore TI (sec) rho (um/sec) rho (cm/s) 34 137 0.044 37.7 1.65 0.072 1.1 8.49 8.49E-04 33 163 0.037 37.1 1.70 0.062 0.9 12.95 1.30E-03 35 163 0.037 37.0 1.70 0.063 0.8 15.65 1.56E-03 32 194 0.031 37.8 1.65 0.051 0.6 25.66 2.57E-03 31 275 0.022 37.7 1.65 0.036 1.2 13.30 1.33E-03 Average: 1.52E-03 Oil-Wet Samples Sample ID Grain Size (urn) 6/d Porosity (1-phi) (phi) * Spore Vpore TI (sec) rho (um/sec) rho (cm/s) 37 137 0.044 37.2 1.69 0.074 0.9 9.90 9.90E-04 36 163 0.037 37.5 1.67 0.061 1.1 10.03 1.00E-03 38 163 0.037 37.6 1.66 0.061 0.9 12.67 1.27E-03 39 194 0.031 37.5 1.67 0.052 0.8 17.57 1.76E-03 40 275 0.022 36.9 1.71 0.037 1.8 5.84 5.84E-04 Average: 1.12E-03 Notes Sgrain/Vgrain is calculated using the relation S/V = 6/d Spore/Vpore is determined using (6 * ( 1 - phi))/ (d * phi) rho is the surface relaxivity determined from the equation: 1/T1 = rho (S/V)pore + 1/Tlbulk 143 Table D.3 : Calculating Surface Relaxivity from S/V. Investigating Salinity - Pore Fluid varies Grain Size: 163 Tlbulk= 3.1 Water-Wet Samples Sample ID Salinity (mol/1) 6/d Porosity (1-phi) (Phi) Spore Vpore TI (sec) rho (um/sec) rho (cm/s) 41 0.00 0.037 38.0 1.63 0.060 1.0 11.84 1.18E-03 87 0.02 0.037 39.8 1.51 0.056 1.2 9.38 9.38E-04 103 0.20 0.037 37.7 1.65 0.061 1.3 7.81 7.81 E-04 106 1.00 0.037 37.8 1.65 0.061 1.2 8.60 8.60E-04 Average: 9.41 E-04 Oil-Wet Samples Sample ID Salinity (mol/1) 6/d Porosity (1-phi) (Phi) Spore Vpore TI (sec) rho (um/sec) rho (cm/s) 42 0.0 0.037 38.0 1.63 0.060 2.1 2.64 2.64E-04 86 0.0 0.037 38.7 1.58 0.058 2.2 2.39 2.39E-04 102 0.2 0.037 38.6 1.59 0.059 2.1 2.99 2.99E-04 105 1.0 0.037 37.3 1.68 0.062 2.1 2.68 2.68E-04 Average: 2.67E-04 Notes Sgrain/Vgrain is calculated using the relation S/V = 6/d Spore/Vpore is determined using (6 * ( 1 - phi))/ (d * phi) rho is the surface relaxivity determined from the equation: 1/T1 = rho (S/V)pore + 1/Tlbulk 144 Table D.4 : Calculating Surface Relaxivity from S/V. Investigating pH - Pore Fluid : varies Grain Size: 163 Tlbulk= 3.1 Sample ID PH 6/d Porosity (1-phi) (Phi) Spore Vpore TI (sec) rho (um/sec) rho (cm/s) 78 2.0 0.04 40.6 1.46 0.054 0.7 19.17 1.92E-03 80 3.5 0.04 39.4 1.54 0.057 0.7 20.43 2.04E-03 41 5.0 0.04 38.0 1.63 0.060 1.0 11.67 1.17E-03 84 7.0 0.04 38.0 1.63 0.060 1.3 7.72 7.72E-04 Average: 1.47E-03 Oil-Wet Samples Sample ID PH 6/d Porosity (1-phi) (Phi) Spore Vpore TI (sec) rho (um/sec) rho (cm/s) 77 2.0 0.037 40.1 1.49 0.055 1.3 8.25 8.25E-04 79 3.5 0.037 37.9 1.64 0.060 1.8 4.09 4.09E-04 42 5.0 0.037 38.0 1.63 0.060 2.1 2.47 2.47E-04 83 7.0 0.037 37.8 1.65 0.061 2.3 1.82 1.82E-04 Average: 4.16E-04 Notes Sgrain/Vgrain is calculated using the relation S/V = 6/d Spore/Vpore is determined using (6 * ( 1 - phi))/ (d * phi) rho is the surface relaxivity determined from the equation: 1/T1 = rho (S/V)pore + 1/Tlbulk 145 

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