6th International Conference on Gas Hydrates

ONSET AND STABILITY OF GAS HYDRATES UNDER PERMAFROST IN AN ENVIRONMENT OF SURFACE CLIMATIC CHANGE - PAST.. Majorowicz, Jacek A.; Osadetz, Kirk; Safanda, Jan 2008

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Proceedings of the 6th International Conference on Gas Hydrates (ICGH 2008), Vancouver, British Columbia, CANADA, July 6-10, 2008.  ONSET AND STABILITY OF GAS HYDRATES UNDER PERMAFROST IN AN ENVIRONMENT OF SURFACE CLIMATIC CHANGE - PAST AND FUTURE Jacek A. Majorowicz ∗ NGC 105 Carlson Close Edmonton, AB, T6R 2J8 CANADA Kirk Osadetz Geological Survey of Canada 3303 - 33rd St. NW Calgary, AB, T2L2A7 CANADA Jan Safanda Institute of Geophysics Czech Academy of Sciences 141-31 Praha 4, CZECH REPUBLIC ABSTRACT Modeling of the onset of permafrost formation and succeeding gas hydrate formation in the changing surface temperature environment has been done for the Beaufort-Mackenzie Basin (BMB). Numerical 1D modeling is constrained by deep heat flow from deep well bottom hole temperatures, deep conductivity, present permafrost thickness and thickness of Type I gas hydrates. Latent heat effects were applied to the model for the entire ice bearing permafrost and Type I hydrate intervals. Modeling for a set of surface temperature forcing during the glacial-interglacial history including the last 14 Myr, the detailed Holocene temperature history and a consideration of future warming due to a doubling of atmospheric CO2 was performed. Two scenarios of gas formation were considered; case 1: formation of gas hydrate from gas entrapped under deep geological seals and case 2: formation of gas hydrate from gas in a free pore space simultaneously with permafrost formation. In case 1, gas hydrates could have formed at a depth of about 0.9 km only some 1 Myr ago. In case 2, the first gas hydrate formed in the depth range of 290 – 300 m shortly after 6 Myr ago when the GST dropped from -4.5 °C to -5.5. °C. The gas hydrate layer started to expand both downward and upward subsequently. More detailed modeling of the more recent glacial– interglacial history and extending into the future was done for both BMB onshore and offshore models. These models show that the gas hydrate zone, while thinning will persist under the thick body of BMB permafrost through the current interglacial warming and into the future even with a doubling of atmospheric CO2. Keywords: gas hydrates, gas hydrate stability, past and future climate change  ∗  Corresponding author: Phone: +1 780 438 9385 Fax +1 780 438 9385 E-mail: majorowicz@shaw.ca  NOMENCLATURE A, Rate of heat generation [μW/m3] Cv, Volumetric heat capacity [J/(m³·K)] K, Thermal conductivity [W/m.K] L, Latent heat in water/ice [ kJ/kg] T, Temperature [oC] t, Time [s] z, Depth [m] Ρ, Density [kg/m3] Φ, Fraction of the total volume occupied by ice/gas hydrate and other phases [%] Myr, million years INTRODUCTION The attempt to model the onset of ice bearing permafrost (IBP) formation, the formation of petroleum gas hydrate (GH) and modeling for the more detailed Holocene temperature history including a future warming due to the doubling of atmospheric CO2 requires knowledge of the surface temperature forcing environment. This needs to be derived from sources sometimes distant from the study area of the Canadian Arctic and specifically the Beaufort Mackenzie Basin (BMB) area where very thick GHs are located currently. Recent results of the analysis of the HolocenePleistocene temperature history using a 1D model that separated IBP and GH layers in an onshore setting during the last 600k years by Majorowicz, Osadetz and Safanda 2008 [1] showed that GH can be stable through interglacial intervals despite large variations in surface temperatures due to the buffering effect of the IBP and the retardation of GH dissociation due to latent heat effects. That work did not include an analysis of the origin, growth and persistence of the GH and IBP layers. It is essential to understand the origin, growth and persistence of sub-permafrost GH accumulations, as a function of temperature history, to determine if a geological natural gas resource model can be formulated. Our analysis will use the characteristics of IBP and GH origin, growth and persistence, as a function of temperature history, to simultaneously constrain the models of past environments that led to the initiation, growth and persistence of the linked occurrences of both IBP and GH accumulations in the subsurface of the Canadian Arctic. The work will also address the risks posed by global and regional temperature  change, as well as providing a tool that will assist the appraisal of risks related to surface imposed changes on the GH layer. In order to model conditions for the IBP formation due to cooling of the surface and following GH formation considering latent heat ‘delay’ effects (due to deeper formation conditions) we need to know surface conditions in the past. To understand better the formation and history of petroleum GHs in terrestrial IBP regions we have performed numerical modeling of the surface forcing due to general cooling trend started in late Miocene and more detailed glacial-interglacial history and future climate change. Persistent GH layers in a terrestrial environment of thick IBP in cold regions sequester methane and impede its migration into the atmosphere. The Mallik site in the Mackenzie Delta is an excellent example of such GH deposits situated in the large area of deep GH Type I stability in the onshore and offshore (Figure1) under continental and continental relic IBP (accumulated during the Pliestocene marine low-stand prior to the Holocene sea level rise). More detailed descriptions can be found in a collection of works edited by Dallimore and Collett 2005 [2]. Judge and Majorowicz, 1992 [3], Majorowicz and Hannigan 2000 [4] and Majorowicz and Smith 1999 [5]. These works describe the geothermal environment of the BMB hydrates and Mallik site in particular.  Figure 1: Depth to GH base of Type I GHSZ in Mackenzie Delta (modified from [4]). Modelling herein is for northern Richards Island and offshore (near the centre of figure). We model the onset of permafrost formation and subsequent GH formation in the changing surface  temperature environment for the BeaufortMackenzie (BMB). We also model terrestrial BMB GH thickness variations below an icebearing IBP layer in response to past and future surface temperature changes onshore and offshore in BMB using a 1D thermal model that assumes no water or gas flow. SURFACE TEMPERATURE HISTORY Our evidence for past temperatures comes mainly from isotopic considerations (especially δ18O). Our models of surface forcing of temperature are based on Muller, and MacDonald 2000 [6] and Frakes et al., 1992 [7]. Recent surface forcing uses a detailed Holocene glacial-interglacial history compiled from other sources by Taylor et al. 2005 [8]. We also consider the implications of a warmer future based on a doubling of atmospheric CO2, which results in a local mean surface temperature increase of 2o C/100 yrs as postulated by the IPCC Report 2007 [9]. The analysis of the paleoclimatic data for the Phanerozoic and specifically for the last tens of Myrs from the above sources and ones in the References show: Sixty-five to one hundred Myr ago average global temperatures were the highest during the last ~200 Myr (Fig.2). This obviously prevented the formation of large scale ice sheet. Forests extended all the way to the poles. Temperature also peaked 50-52 Myr ago, when atmospheric CO2 ranged 1125-3000 ppm. By 20 Myr ago, CO2 dropped to about 400 ppm [10]. The Paleocene-Eocene Thermal Maximum (Fig.2) could have been caused by abrupt releases of methane hydrates under the bottom of the ocean. During that time the Arctic Ocean may have reached levels more typically associated with modern temperate (i.e. mid-latitude) oceans. Following the Paleocene to early Eocene peak warming the climate cooled variably towards the Pleistocene glacial environment. However, 3 to 6 Myr ago, globally averaged temperatures were still higher than today with surface temperature at poles higher than present temperatures. The Northern Hemisphere likely had no continental glaciers [6,7].  The Brown University [11] 5 Myr record of temperatures in the eastern equatorial Pacific (EEP), located off the coast of South America shows that surface temperatures were 27° C, 5 Myr ago. Surface temperatures are 23° C today. In between, they found a pattern of steady cooling, roughly one degree Celsius every Myr. This finding, [11], contradicts the long-standing notion that rapid glacier growth in the high northern latitudes about 3 Myr ago alone set off the dramatic cooling of the global climate. The finding shows instead that those glaciations were part of a long-term cooling trend.  Figure 2: History of the surface forcing of the last 65 Myr (modified from [12]). Climate during the following 3 Myr before present changed dramatically in response to astronomical effects (Milankovitch cycles) caused changes in surface forcing. These resulted in cycles of glacials and interglacials within a gradually deepening ice age. The growth and retreat of continental ice sheets in the Northern Hemisphere occurred at 2 frequencies; 41 kyr and 100 kyr (Figure 3). The gradual intensification of this ice age over the last 3 Myr has been associated with declining concentrations of the CO2 which partly influences this change in temperatures. El Nino was continual rather than intermittent until 3 Ma. Significant amplification of the response of climate to orbital forcing began 3 Myr ago, resulting in drastic oscillations between ice ages and warmer periods over the past 1 Myr (Figure 3).  than the onset time for the IBP. The equilibrium IBP thickness is some 250 m for a GST of -5 °C. It means that the IBP, a potentially impermeable seal for any potential gas migrating upward, existed for a long time before p-T conditions permitted the first hydrate formation. Figure 3: More detailed history of the last 5.5 Myr of surface forcing (modified from [12]). P-T TIME ENVELOPE AND FORMATION OF PERMAFROST AND GAS HYDRATE PRELIMINARY CONSIDERATIONS We can use the temperature history shown in Figure 2 and Figure 3 in considering the IBP and GH formation. If the equivalent Vostok ∆T temperature of 0 °C indicated for the present time corresponds to the present ground surface temperature of -6 °C at Mallik, then during the period 6–3.5 Myr ago corresponds to ground surface temperature (GST) oscillations at Mallik between -6 °C and -4 °C. The oscillation period seems to be close to 41 ka, like that observed between 2.5 - 1 Myr ago. The range of GSTs between -6 °C and -4 °C is critical for GH formation as shown in preliminary test for the steady-state in Figure 4. -20  -15  -10  -5  0  5  10  15  20  0  0  depth, m  300  300  Steady-state profiles 60 mW/m2 frozen - thawed conductivity 3.4 x 2.1 W/(m.K) water ice liquidus = -0.000715 *z(m)-0.064*CNaCl (g/L) 9 g NaCl,  600  900  600  900  1200 solidus  water ice liquidus  1200  hydrate phase curve 8.9*ln(z)-50.1  1500  1500 -20  -15  -10  -5 0 5 temperature, °C  10  15  20  Figure 4: Steady-state profiles corresponding to Mallik –Richards Is. area geothermal model The model curve (T-z) approaches the GH phase curve from above for the ground surface temperature (GST) of -5 °C at the depth of about 300 m. According to the above, the GH could not have formed when the GST was higher than -5 °C. Before 6 Myr ago the climate was even warmer, which means that the first GH deposits might have formed around 6 Myr or later, which is different  The geotherm corresponding to the GST of -5 °C crosses the GH phase curve at about 300 m, just below its intersection with the IBP phase curve at 250 m. This means that GH could have formed immediately below the IBP base. Because the geotherm and the phase curve are nearly parallel in this range of p-T, even a small downward shift of the geotherm means a large broadening of the zone with the p-T conditions favorable for GH formation. Therefore, by gradual cooling between 10 and 5-6 Myr, some 250 m of IBP could had formed before the temperature decrease allowed for the first GH formation, at the depth of 300 m. Further surface cooling below -5 °C caused the IBP base to descend into the layer already occupied by GH. For 30% porosity and 60% GH saturation, the remaining water available to freeze occupied not 30%, but only 12% of the whole volume and the latent heat released by its freezing was 2.5 times smaller than in the IBP interval above the GH. The question is, “what had happened with the methane in the uppermost 300 m, if any gas was initially collected under the IBP?” We will attempt to simulate the 41 ka cycles with the GST oscillating between -6 °C and -4 °C, where the initial temperature profile was a steadystate one with a GST of -4 °C. The steady-state profile for the GST of -6 °C, which represents the lower temperature limit within the cycle may never be reached, as that cycle’s period is too short. It is assumed that 20.5 ka is the end of the cold part of the cycle after the GST jumps from -4 °C to -6 °C. The more recent surface climate history for the end of the Wisconsinan and Holocene is after Taylor et al. 2005 [8]. Pleistocene surface history of glacials and interglacials is after Muller and MacDonald 2000 [6].  METHOD  Solving the transient heat conduction equation gives the temporally dependent subsurface temperature change in response to surface forcing: Cv ∂T/∂t = ∂[K(∂T/∂z)]/∂z + A  (1)  where T is the temperature, K is the thermal conductivity, Cv is the volumetric heat capacity, A is the rate of heat generation per unit volume, z is the depth, and t is the time in a one-dimensional, layered geothermal model. We employed a computer code to simulated temporal subsurface temperature changes in response to surface forcing by Safanda et al. 2004 [13]. Within the model Equation (1) is solved numerically by an implicit finite-difference method similar to that described by Galushkin 1997 [14]. The upper boundary condition is the temporally varying GST and the lower boundary condition is a constant heat flow density at 15 km depth. The depth grid steps are: 2, 5, 10, 50, 100, 250 and 500 m in the depth layers at 0-100, 100-1500, 1500-2000, 2000-2500, 2500-5000, 5000-10000, 10000-15000 m, respectively. Time steps vary between 0.5 to 50 yrs, depending on the amplitude of GST changes. The finite-difference scheme of equation (1) on the depth and time grids.zk-1 , zk , zk+1 ,... and ...tn , tn+1 ,....., respectively, has a form: Cv,k n (Tkn+1 – Tkn) / (tn+1 – tn) = 2Kk+1n (Tk+1n+1 – Tkn+1)/[Δzk+1(Δzk + Δzk+1)] n 2Kk (Tkn+1 – Tk-1n+1)/[Δzk(Δzk + Δzk+1)] + Ak where the subscript k and the superscript n denote values at the kth depth step and the nth time step, respectively; Δzk = zk - zk-1 ; Kk+1n = Δzk+1 /[ ∫z k z k+1 dz/kn(z)]. This difference scheme, together with the upper and lower boundary conditions lead to a system of difference equations for unknown values Tk-1n+1 , Tkn+1 , Tk+1n+1 (where the subscript k and the superscript n denotes a value at the k-depth step and the n-th time step) within a tri-diagonal matrix, which was solved by the forward method of Peaceman and Rachford 1955 [15]). To estimate effective thermal conductivity values and volumetric heat capacity, it was necessary to consider the respective geometric and arithmetic averages of the constituent values for the rock matrix, water, ice and GH in proportion to their volumetric fractions [14], [16]. A consumption or  release of the latent heat, L, in water/ice (334 kJ.kg-1) and GH (430 kJ.kg-1) accompanying either thawing or freezing was included. The effects of interstitial ice and GH were accounted for using apparent heat capacity according to Carslaw & Jaeger 1959 [17], when the volumetric heat capacity is increased in the depth sections of the model where the thawing and freezing occurs, i.e. where the temperature is within the thawing range between the temperature of solidus TS , and liquidus, TL , at the actual simulation time step. The liquidus and solidus temperatures of water/ice and GH are depth and hydrostatic pressure dependent [14] and solidus temperatures were 0.2 °C lower than liquidus temperatures. A contribution to the heat capacity from the latent heat = ρΦL/(TL-TS) was considered, where ρ is the density of either ice or GH and Φ is a fraction of the total volume occupied by these phases. In the IBP zone we infer the 30% rock matrix porosity to be fully occupied by water at temperatures above TL, and by ice at temperatures below TS. Within the GH stability zone the GH saturation in matrix porosity was inferred to be 60%. For the model to be tractable, the model IBP and GH stability zones are assumed not to overlap, which follows common observation in the study area that GHs are not generally found within the IBP [1]. The salt concentration 9 g/L was considered constant with depth and the p-T phase curves were adjusted to this value. Numerical code performance was tested by comparing model results against the analytical solidification problem solution [17], where the molten half-space at liquidus temperature, 1300o C, is in contact with a solid half-space at zero temperature and releases the latent heat of 477 kJkg-1 in the temperature range 1100-1300o C. Comparison of the differences between the numerical and analytical temperature profiles were found to be within about 20 oC. If we assume that the magnitude of the difference is proportional to the temperature range, i.e. to the contrast at the contact of the molten and solid half-spaces, the error expected for the IBP and GH numerical simulations should be about 100 times smaller (i.e. tenths of a °C) because of the scale of both the temperature range and surface temperature variations that are used in our simulations. A similar error range was estimated by halving the time and/or depth steps.  Our model uses deep heat flow, thermal conductivity, present IBP, Type I GH thicknesses and a surface melting temperature (-0.576oC) that considers groundwater salinities (9 g/L). It employs latent heat effects throughout the IBP and GH layers, which improves upon previous models [8]. The models are constrained by deep heat flow from bottom hole temperatures determined from deep wells [18], [19], and thermal conductivity, latent heat, present IBP thickness and observed present Type I GH thicknesses [20], [21]. The models consider the pressure–depth dependence of ice assuming hydrostatic and GH thawing points over the entire expected extent of the IBP and GH layers according to Sloan 1998 [22]. Previously published models have considered only a thin layer using a constant dissociation temperature [8]. In simulating the temporal subsurface changes in models with vertically separated occurrence of IBP and GH, a consumption/release of the latent heat during decay/formation of IBP or GH was considered separately. This means that in IBP zone, only the latent heat and p-T phase curve of water ice were taken into account, and in the GH zone only latent heat and p-T phase curve of the GH is considered. The division into IBP and GH zones was prescribed in the model explicitly. The above conditions may not be appropriate in models of possible simultaneous IBP and GH occurrence. In such cases it is prescribed at each depth point, which fraction of the pore space can be occupied by water ice and which by GH. Then the code checks independently the p-T conditions for IBP and for GH in each depth point, in each time step and increases the volumetric heat capacity [17]. For example, in the Mallik case, where a porosity of 30% was assumed, the prescribed pore fraction of GH in the uppermost 250 m was zero and that of IBP 100%, because as the preliminary calculations had shown, IBP forms prior to hydrate. On the contrary, below 250 m the GH forms first. For the 60% saturation of the pore space by GH this means that the ratio of pore fractions occupied by GH and IBP is 60: 40 at this depth. MODEL FOR THE 14 M.Y. HISTORY OF SURFACE TEMPERATURE CHANGE – RESULTS  We have simulated the downward propagation of the surface warming and cooling attending the cyclical glacial and interglacial models for the eastern Richards Island location (Figure 1). The dependence of the thermal conductivity on water/ice content and the specific heat of the rock section on the porosity and the proportion of interstitial water and ice are important. Accounting for the effect of the latent heat necessary to thaw the interstitial ice in the IBP layer, is crucial for matching observations at realistic time rates. In the absence of this heat sink provided by thawing ice in the IBP, the subsurface warming would proceed much faster. Individual computational models use the characteristics of IBP and GH formation and dissipation, as functions of temperature history, constrained by present temperature observations and current IBP and GH layer thicknesses. All models account for latent heat by means of the apparent specific heat, which is a standard treatment. The model also considers diffusive heat flow related to surface-subsurface coupling. As Figure 4 illustrates, GH formation can start only when the long-term GSTs drops below -5 °C. The temperature dropped below -5 °C (+1 °C of the equivalent Vostok temperature) not before 10 Myr ago. There was a warm period (25 to 15 Myr ago) with maybe no IBP in Mallik. We considered the variation between -4 to -6 °C, because according to Figure 3 this is a typical variation for the time period 3.5 to 5 Myr ago. For later stages of the 41 ka cycle, the amplitude can be twice as large, e.g. -6 °C to -10 °C or -8 °C to 12 °C, close to the transition to 100 ka era some 700 to 900 ka ago. We have used a stepwise approximation of the surface temperature with a length of the step 1 Myr between 14 and 6 Myr ago and 0.5 Myr between 6 and 2.5 Myr. From 2.5 Myr ago we consider the 41 ka cycle and from the 0.9 Myr the 100 ka cycle. Case 1 - Gas hydrate formation controlled by the geological gas entrapment conditions In Case 1 we allow occurrence of GH only in the geologically confined area under a geologically impermeable seal.  We relate our model to the above cited findings. The division into IBP and GH zones was prescribed in the model explicitly. We have vertically separated the occurrence of IBP and GH. A consumption/release of latent heat during the decay/formation of IBP or GH is considered separately. It means that in IBP zone, only the latent heat and p-T phase curve of water ice were taken into account, and in the GH zone it was only latent heat and p-T phase curve of GH.  -3  -2.5  -2  -1.5  -1  -0.5  0 0  Mallik - permafrost and gas hydrate simulation  100 ka cycles  -2 -4  41 ka cycles  -6  0  -8 -10  200  -12 -14  400 depth, m  -16 600  the observed permafrost base  surface temperature gas hydrate considered permafrost base only below 900 m gas hydrate base below 900 m  800  1000 the observed gas hydrate base  1200 -3  -2.5  -2  -1.5 -1 time, Myr  -0.5  0  Figure 5: Surface temperature and bases of the IBP and the GH in the last 3 Myr according to numerical simulation of the last 14 Myr subsurface temperature forcing – Case 1 model. GH formation was considered below 900 m only. The GH did not form even during the coldest 41 ka cycles (from -11.5 °C to -7.5 °C), because the steady-state geotherm corresponding to the mean surface temperature of the cycle, -9.5 °C, crosses the GH stability curve just above 900 m (see Figure 4) and duration of the cold phase of the cycle with surface temperature of -11.5 °C is too short (20.5 ka) for the temperature to cool close to the steady-state curve corresponding to -11.5 °C. The simulated bases of IBP, 541 m, and GH, 1060 m, are slightly above its observed positions in Mallik, 600 m and 1107 m, respectively, at present. In our previous simulations [2], the bases appeared deeper, at 600 m and 1165 m. The main reason is probably the shorter duration of the cold phase of the glacial, (75 ka instead of 90 ka), considered in the latest simulations. The length of the whole glacial cycle circa 100 ka, is consistent other sources and the length of the interglacial is 25 ka. The surface temperatures during the glacial,  surface temperature, °C  This is a probable situation for case of the Beaufort-Mackenzie (BMB) GHs as shown by stratigraphic sections in the Mallik boreholes [1]. At Mallik, the interbedded character of the GH bearing strata indicates a lithologic control on GH occurrence. GH layers occur in coarse-grained sandstone beds separated by thin non-hydratebearing, fine-grained siltstone and claystone beds. The gas and GH at Mallik appears to be entrapped in association with the diastrophic structure. The fault bounding the structure is the likely conduit for migration of the gas into the GH stability zone (GHSZ). Two general types of gas were observed in the Mallik wells. Microbial gas is characterized by high C1/(C2+C3) ratios (>1000) and methane carbon isotopic ratios between -70 to -93‰. Thermogenic gas is wetter and has carbon isotopic ratios for methane of around -35 to -45‰. The carbon isotopic ratios for ethane and propane of this thermogenic gas are -31‰ and -26‰ respectively. Methane isotopic compositions of 12 GH samples averaged -42.7‰ and clearly indicate a thermogenic source according to Lorenson et al., 2004 [23]. Thermogenic gas likely migrated up along listric-normal growth faults from larger depths where gas generation is possible due to availability of the source rock and thermal conditions (thermogenic gas generation envelope temperatures are likely in 4-5km in the area of study). The deep upward migrating gas could have been trapped in the anticline and or tilted fault blocks and turned into GH when cooling took place. Such a hypothesis has some grounds in the coincidence of GH occurrences above the deep known hydrocarbon reserves as estimated by Majorowicz and Osadetz 2001 [24].  -15 °C, and the interglacial were the same as that of previous model 3 by Majorowicz, Osadetz and Safanda 2008 [2] modified from Taylor et al. (2005, Fig. 3b) [8].  – 300 m, separated from the IBP base at the depth of 250 m by a 40 m thick unfrozen zone. -6  -10  -8  -6  -4  -2  depth, m  0  41 ka cycles  0 200 Mallik - permafrost and gas hydrate simulation  depth, m  the observed permafrost base  600  gas hydrate considered only below 900 m  surface temperature permafrost base gas hydrate base  800  1000  the observed gas hydrate base  1200 -14  -12  -10  -8 -6 time, Myr  -4  -2  Figure 6: 14 Myr history of surface temperature forcing, IBP and GH base depth variation – Case 1 model Case 2 - considering simultaneous occurrence of permafrost and gas hydrate In case 2 we allow the simultaneous occurrence of IBP and GH. This has some geological grounds as the geological seals commonly seen in the BMB area are not widely available [1]. The numerical simulation of the subsurface temperature response to changes of the surface temperature forcing was done for the last 14 Myr (Figures7-10). The GST history is the same as in Case 1 model shown in Figure 6. The profiles shown in Fig. 7 correspond to times 20, 10,000, 20,000 and 42,500 years after the cooling and to time 20 years after the consequent warming. Analysis of the results shown in Fig. 7 is very informative. The curve for time 42,500 years (5.9575 Myr ago) shows the moment when the first GH starts to form at in the depth interval 290  2  4 0  0  200  5.99998 Myr ago 5.99 Myr ago 5.98 Myr ago 5.9575 Myr ago 5.49998 Myr ago  gas hydrate phase curve 8.9*ln(z)-50.1  100  200  300  300  400  400 solidus  water ice liquidus  0 500 -2 -6 -4 -2 0 2 4 temperature, °C -4 -6 Figure 7: Transient temperature-depth profiles as -8 a response to the GST cooling from -4.5 °C to -5.5 -10 °C 6 Myr ago (and to all previous GST history -12 -14 since 14 Myr ago) followed by warming back to -16 4.5 °C 5.5 Myr ago. surface temperature, °C  100 ka cycles  400  0  100  The plot of the whole 14 Myr history of surface forcing effects on IBP and GH is shown in Figure.6 -12  -2  Response to GST jumps from -4.5 ° to -5.5 °C 6 Myr ago and back to -4.5 °C 5.5 Myr ago  Despite our use of quite general surface temperature history (Figure 2 and Figure 3), agreement between the model and the observation on present observation on state of GH and IBP is reasonably good.  -14  -4  0  In the times of warm climate, like before 14 Myr ago, when GST at the Mallik site was +1 °C, the subsurface temperatures were above p-T phase curves of both IBP and GH at all depths (for the geothermal model with basal heat flow of 60 mW/m2 and conductivity of 2.1 W/(m.K)). With the onset of a gradual cooling at 14 Myr ago, when the GST dropped below the solidus temperature of IBP, the IBP started to propagate from the surface downward. However, for the model considered (30% porosity), with all the pore water frozen, thermal conductivity of the frozen rock 3.4 W/(m.K) and the latent heat of water freezing 0.334 MJ/kg) the temperatures stay above the p-T phase curve of GH until the GST drops to -5.5 °C. A GST of -5 °C was not low enough for GH formation in this geothermal model. It is questionable, what could have happened with the methane contained in the freezing rock. If all pore water had frozen, it could not have escaped to the surface and might have been pushed downward below the downward migrating IBP base or escaped to the sides of the IBP body and then migrated upward. Such IBP ‘weak’ thermokarst areas underlie water bodies of the present Mackenzie River Delta. Figure 7 shows the situation after the GST cools from -4.5 °C to -5.5 °C 6 Myr ago, preceded by the whole GST history since 14 Myr ago. The T-z  500  profile started to move downward and touched the p-T phase curve of the GH at the depth interval 290 - 300 m 42.5 ka after the GST drop (light blue profile in Fig.7 for time 5.9575 Myr ago). At that moment, the IBP base was at the depth of 250 m. It means that there was an unfrozen depth section (250 – 290 m) separating IBP from hydrate. With further subsurface cooling, the zone occupied by GH propagated not only downward, but also upward and after another 100 ka the upper GH boundary touched the IBP base at the depth of 255 m. Upward spreading of the GH zone stopped at this moment, because all pore space in overlying IBP was occupied by frozen water. Nevertheless, this contact of IBP with GH, which stopped upward growth of the GH layer, does not stop downward migration of the IBP layer, because the model considers 60% saturation of the pore space by hydrate. The rest of 40% of the pore space (12% of the whole volume) was occupied by water, which could have frozen with subsequent cooling. This scenario and consequences following from it for IBP and GH occurrence were taken into account by considering separately the porosity available for water ice and for the hydrate. For the ice, it was 30% above the line of the IBP–GH contact at approximately 250 m and 12% below it. Similarly, the porosity available for the GH above the line of contact at 250 m was considered to be 0% and below it 18% (60% saturation in 30% porosity rock). This opened the possibility to treat the latent heat released/consumed in the solidusliquidus zones of IBP (0.334 MJ/kg) and GH (0.430 MJ/kg) independently and appropriately. The thermal conductivity in the zone of simultaneous occurrence of IBP and GH was estimated at 2.7 W/(m.K). It is lower value than that for pure IBP (3.4 W/(m.K) because of the presence of GH with a low conductivity 0.45 W/(m.K) at the expense of water ice with conductivity 2.2 W/(m.K). According to the GST history used in the simulations, this first GH, which started to form at time 5.9575 Myr ago reached its maximum thickness 130 m (between 250 – 380 m) shortly after the next GST change from -5.5 °C to -4.5 °C, which occurred 5.5 Myr ago. The same is true with the IBP, which penetrated into the GH only 9 m (250 – 259 m). As can be seen in Fig.8, following that GST warming, the last GH disappeared in the  depth range 310 – 340 m at time 5.472 Myr ago when it was separated from the IBP base at the depth of 240 m by a 70 m thick melted zone. The GH formed again shortly after the next decrease of the GST from -5.0 °C to -5.5 °C 4.5 Myr ago. Since this moment, the GH survived all the following GST variations. Its upper constraint at 250 m was always within the GH stability zone and its maximum extent to 990 m was reached during the most recent glacials. Depth variations of the IBP and GH upper and lower boundaries during the last 14 Myr are depicted in Figure 9 and in detail for the last 3 Myr in Figure 10. Also shown are variations of these parameters for the Case 1 Model, where the GH formation was restricted to the depth below 900 m only, and simultaneous occurrence of IBP and GH was not possible. The shallower position of both IBP and GH in this model is caused by lower conductivity of the IBP in the zone of its simultaneous occurrence with GH below 250 m. It is also evident from Figure 10 that depth variations of both the IBP and GH basis are larger in Case 2 than Case 1 during the 41 ka and 100 ka cycles. The most probable reason for the larger variations of the IBP base is a smaller damping effect of the latent heat release/consumption at the base due to a smaller amount of freezing/ melting water/ice. Most of the pore water is bounded in the GH, which is stable in this depth range. The smaller damping effect at the IBP base also means that the subsurface temperature changes propagate faster to the GH base and that these cause its larger depth variations compared to Model –Case 1. The Case 2 model assuming presence of methane in the whole rock, or at least below 250 m, before the onset of cooling 14 Myr ago predicts the following subsurface temperature-GH and IBP changes resulting from the gradual climate cooling since this time: (1) IBP thickness did not exceed 200 m before the time 6 Myr ago (2) GST temperatures higher than -5.5 °C prevailing before the time 6 Myr ago did not enable the GH to form (3) First GH formed in the depth range 290 – 300 m shortly after the time 6 Myr ago when the GST dropped from -4.5 °C to -5.5. °C and started to spread both downward and upward. After another  100 ka, the upper GH boundary touched the IBP base propagating downward at the depth of 255 m  m, separated from the IBP base at the depth of 240 m by a 70 m thick melted zone. -14  0  2  5.49998 Myr ago 5.49 Myr ago 5.472 Myr ago 5.46 Myr ago  depth, m  400  depth, m  800  hydrate considered only below 900 m in Case 1  the gas hydrate base observed at present  -12  -10  -8 -6 time, Myr  -4  -2  0  Figure 9: Depth variations of the IBP and GH upper and lower boundaries during the last 14 Myr for Case 2 compared with results of Case 1, where the GH formation was restricted to the depth below 900 m. The indicated upper GH boundary above 250 m shown in Figs 9-10 is a formal one. It was calculated according to the p-T phase curve. In reality, no GH was considered there because all pore space above 250 m is occupied by water ice and GH cannot form in a region already occupied by ice.  300  400  400 water ice liquidus  500  500 2  hydrate base - Case 1 hydrate base - Case 2 hydrate upper boundary - Case 2 according to the p-T curve the real one limited by permafrost at 250 m  -14  300  -2 0 temperature, °C  0 -2 -4 -6 -8 -10 -12 -14 -16  the permafrost base observed at present  600  1200  200  -4  Mallik - a simultaneous occurrence of permafrost and gas hydrate below 250 m  1000  100  gas hydrate phase curve 8.9*ln(z)-50.1  -6  0  200  0  solidus  -2  41 ka cycles  Response to GST jumps from -5.5 ° to -4.5 °C 5.5 Myr ago  200  -4  4  0  100  -6  permafrost base - Case 1 permafrost base - case 2  0  The simultaneous occurrence also implies lower conductivity in this zone, which means higher temperature gradient, which shifts the IBP and GH basis upward, above their position observed currently. -2  -8  100 ka cycles  The Case 2 model provides no mechanism enabling methane to escape to the earth surface from below the IBP lid formed 14 Myr ago. It is forecast of simultaneous occurrence of IBP and GH below 250 m is, however, not generally observed [1].  -4  -10  surface temperature  (5) Shortly after the definitive GH formation, the downward migrating IBP base and upward migrating upper GH boundary met at the depth of about 250 m. Since that moment, IBP below 250 m could have “used” only that part of the pore water, which was not bounded in hydrate.  -6  -12  4  Figure 8: Transient temperature-depth profiles as a response to the sudden GST warming from -5.5 °C to -4.5 °C 5.5 Myr ago and to all previous GST changes since 14 Myr ago. The profiles correspond to times 20, 10 000, 28 000 and 40 000 years after the warming. Curve for time 28 000 years (5.472 Myr ago) shows the moment when the last GH disappears in the depth interval 310 – 340  Modeling of the recent onshore-offshore BMB 0.5 Myr history plus future climate change More detailed histories of IBP and GH variations for models of surface forcing of the last 0.5 Myr and into the future are shown in Figs 11-12. The models are based on the surface temperature forcing effect on IBP and GHs, which currently have observed bases at about 600 m and about 1160-1170 m, respectively. The detailed terrestrial case model considers the climatic history proposed by Taylor et al. (2005, their Fig. 3b [8]). This model (model 3 described by us previously [2], where the considered length of the glacial cycle was 115 ka) employs a frozen thawed conductivity varying from 3.4 (frozen) to 2.1 (unfrozen) W/(m·K). In Figs 11-12 we also consider future warming projected by the IPCC 2007 projections [9]. Surface temperature will change dramatically accompanying the projected doubling of atmospheric CO2 resulting in future climate warming during the next 300 years. We  surface temperature, °C  (4) First GH disappeared after subsequent warming and formed definitively shortly after GST drop from -5 °C to -5.5 °C at time 4.5 Myr ago. Since this moment, the GH survived all the following GST variations. Its upper constraint at 250 m was always within the GH stability zone and its maximum extent to 990 m was reached during the most recent glacials.  predict the consequences of such a mean surface temperature change, from -6° C to 0° C, considering past history followed by gradual warming, at a rate of 2° C per century. -2.5  -2  -1.5  -1  0 -2 -4 -8 -10  temperature  -12 0  -14 -16  200  surface temperature, °C  -6  41 ka cycles  permafrost base - Case 1 permafrost base - Case 2  560  580 10  5 model 3 - Taylor's history (-15°C to -2°C 13.5 ka ago, to -5°C 8 ka ago, to -6°C 4.5 ka ago + future change ( from -6°C to 0°C in 300 yrs)  0  0 model 6 -Taylor's history+sea transgression (only in the 5th cycle) (from -15°C to -2°C 13.5 ka ago, to +1°C 8 ka ago = sea transgression) + future change ( from +1°C to +7°C in 300 yrs)  -5  -10  future  -15  -20  -20 460  480  500  520 time, ka  540  560  580  Figure 11: Model considering sea transgression and related temperature changes from land to subsea (warmer). Mallik, model 3, model 6, frozen-thawed conductivity 3.4 x 2.1  460  480  500  520  540  560  580  1000  gas hydrate considered only below 900 m in Case 1  0 Top of the gas hydrate layer at 900 m  200  the gas hydrate base observed at present  -2.5  -2  -1.5 -1 time, Myr  -0.5  400  600 permafrost  base  800 Holocene future 13.5 ka  5th glacial  1000  -3  0  Figure 10: Detailed part of depth variations from Figure 9 for the IBP and GH upper and lower boundaries for the last 3 Myr before present. The model simulation that considers the Holocene marine transgression was also considered (Figs 11-12) as related to the situation existing in the Beaufort Sea. It is compared to our previous ‘terrestrial case’ model [2]. We have used the Taylor 1999 [25] and Taylor et al., 2005 [8] surface temperature model for Mallik (model 3 [2]), but in the 5th glacial considered a warming from -2°C to +1°C (instead of cooling to -5°C according to Taylor’s onshore model) 8 ka ago + the future warming starting at present from +1°C to +7°C in 300 years. Marine transgression occurred during the previous interglacials, however, it is not considered in our models due to a lack of good data for such events. The future warming of the sea bottom was assumed for the extreme global warming case scenario [9], (Figure 11).  200  model 3 -Taylor's history+future climate change model 6 -Taylor's history+sea transgression (only in the 5th cycle)+future change  400  1200  top of permafrost  1200  end of the 5th cycle  hydrate base - Case 1 hydrate base - Case 2 hydrate upper boundary Case 2 - according to the p-T curve the real one - limited by permafrost at 250 m  -10  Holocene 13.5 ka  0  800  -5  5th glacial  -15  the permafrost base observed at present  600  540  5  depth, m  depth, m  400  520  Model 3 and 6. Top of the gas hydrate layer at 900 m  0  100 ka cycles  500  end of the 5th cycle  Mallik - simultaneous occurrence of permafrost and gas hydrate below 250 m  -0.5  480  10  temperature, °C  -3  Mallik, model 3, model 6, frozen-thawed conductivity 3.4 x 2.1  460  600 800 1000 1200  gas hydrate base  1400  1400 460  480  500  520 time, ka  540  560  580  Figure 12: Consequences in changes in GH and IBP as related to model in Fig. 11 (transgression plus global warming). It is a fact that the host rock responds to the ice/water volumetric changes during the freezing/thawing cycles in the IBP. If the IBP thaws at its base only, like in the Mallik case, no water can migrate downward from the surface, such that the 8% of the pore space, which was occupied by ice before melting and should be empty now. It could be that during the freezing/thawing cycles the pore space changes. This would mean that the land surface could rise and fall by some 7-8 m during the glacial cycles, if the IBP base varied by 300 m and the porosity was 30%. We account for the effective specific heat changes connected with this effect (without considering the above mentioned surface subsidence or uplift). Fortunately, the results differ  negligibly from the simulations, where the effect of the negative dilation of the rock as a result of the thawing was not considered - the attending bases of the IBP and the GHs differ from the previous simulations by tens of centimeters only. Figure 13 shows the T-z profiles corresponding to model based on Taylor's surface temperature history interrupted by sea transgression + future warming. -15  -10  -5  0  5  10  15  20  depth, m  0  300  300  600  600  Present time 103.5 ka of the 5th cycle 300 years in the future (2300 A.D.)103.8 ka of the 5th cycle end (115 ka) of the 5th cycle (13500 A.D.)  1200  hydrate phase curve for 50 m deep sea transgression  900  1200  hydrate phase curve 8.9*ln(z)-50.1  1500  1500 -15  -10  -5  0 5 10 temperature, °C  15  20  DISCUSSION AND CONCLUSIONS Historical surface temperature forcing as well as geological control have significant implications for both IBP and GHs model results that consider latent heat effects of water/ice and GH formation and dissipation and 14Myr GST history.  25  0  900  cycle variations, in spite of the accelerated surface warming accompanying climate change.  Our model, in which we considered a stepwise approximation of the GST with a length of the step 1 Myr between 14 and 6 Myr ago and 0.5 Myr between 6 and 2.5 Myr followed from 2.5 Myr ago by the 41 ka cycles and from 0.9 Myr by the 100 ka cycles, shows that the onset of GH formation always comes after IBP formation begins. IBP, provides a potentially impermeable seal for any upward gas migration and this is inferred to have existed long before the p-T conditions enabled formation of the first GH.  25  Figure 13: T-z profiles corresponding to model based on Taylor's surface temperature history interrupted by sea transgression + future warming). In calculating the model, which simulates a Holocene marine transgression, the change of the GH P(z)-T phase curve due to the increase of the hydrostatic pressure after the transgression is not considered, as a first approximation, since the water depth is shallow. The phase curve corresponding to the sea depth of 50 m is shown in Fig.13 by a dashed line. After the 50 m sea level increase, the GH phase boundary would shift by about 25 m down. Heat released during the GH crystallization would probably increase the temperature in that zone. But the changes would not be dramatic. The future predictions for the ‘terrestrial case’ (Fig.12) show that hypothesizing a time corresponding to the "natural" end of this interglacial, about 11.5 ka in the future, the model predicts that the IBP will have thawed by ~150 m from below and 70-80 m from the surface. The predicted accompanying GH layer thinning is very small, and within the range of previous natural  The two scenarios proposed, i.e.; Case 1: formation of GH from natural gas previously entrapped under a deep geological seal Case 2: formation of GH from gas in all of the free pore space simultaneous with IBP formation; The results of these two models indicate two entirely different GH generation onset times for depending on model assumptions. For Case 1: GHs could have formed at 0.9 km only some 0.9 Myr ago. For Case 2: the first GH formed in the depth range 290 – 300 m shortly after 6 Myr ago when the GST dropped from -4.5 °C to -5.5. °C and started to spread both downward and upward. In case 2, after all the pore water had frozen, methane contained in the freezing rock could be prevented from escaping to the surface by a IBP seal and this methane might have been pushed downward below the downward migrating IBP base. It is also possible that this methane could have escaped to the sides of the IBP seal and then migrated upward. Detailed models of recent of ~102 kyr cycles in the BMB area shows that GH layer thickness generally increases during colder intervals (i.e.  glacial) and decreases during warmer intervals (i.e. interglacial). In the more recent glacial history of the ~100 ka cycles these variations are ~0.2 km for the IBP and about 0.1 km for the GH layer. Where the IBP layer is thick it is unlikely that sub-IBP GHs disappeared entirely during previous interglacial intervals, nor are they expected to disappear prior to the ‘natural’ end of the current interglacial. In regions of thick terrestrial IBP like the Mackenzie Delta, GH layers can act as a persistent sink for methane from deep thermogenic sources and petroleum systems, and as a barrier to the migration of methane into the atmosphere.  observations of methane isotopic compositions from ice cores for the “clathrate gun” hypothesis of Sowers et al 2006 [28]. This study shows that thermal modeling is essential for the understanding of the origin, growth and persistence of sub-IBP GH accumulations, as a function of temperature history. It can help to determine and distinguish the features of the GH geological natural gas resource model, which have both climate and resource implications. REFERENCES  This is also true for the offshore BMB case where hydrates can and have probably existed under relic IBP despite marine transgression, as illustrated in our 1D model where the 5th glacial warms from 2°C to +1°C (instead of cooling to -5°C according to onshore model of Taylor’s [8]). Likewise the impact of future climatic change attending a doubling of atmospheric CO2 does not completely destabilize the GH layer. In all models, the predicted future GH layer thinning is very small, and within the range of previous natural cycle variations, in spite of the accelerated surface warming accompanying climate change and large thinning of the relic offshore IBP, which our models suggest thin to 0.05km at the future natural interglacial (i.e. 5th ) cycle ). The hypothesis that GHs destabilize rapidly in response to environmental change, late in glacial intervals, and that they serve, at other times, as a sink for, and barrier to the migration of, methane into the atmosphere applies mainly to marine nonIBP GHs [26,27], which may be more easily destabilized than are the terrestrial sub-IBP GHs we modeled. Our study shows that sub-IBP GHs below thick IBP vary in thickness in response to surface temperature history changes, but that terrestrial thermal inertia conserves both IBP and sub-IBP GHs delaying and reducing methane release. Terrestrial thermal inertia also imposes a phase-delay between surface temperature warming and the subsequent onset of GH dissociation, making it unlikely that terrestrial GHs below thick IBP could rapidly reinforce climate warming events, consistent with the hypothesis. The implications of latent heat effects and thermal inertia for submarine GHs remain to be determined, however, our model results appear consistent with the implications of recent  [1] Majorowicz JA, Osadetz KG, Safanda J. Modeling temperature profiles considering the latent heat of physical-chemical reactions in permafrost and gas hydrates – the Mackenzie Delta terrestrial case. Proceedings of the Ninth International Conference On Permafrost Fairbanks 2008 (in press) [2] Dallimore SR, Collett TS, editors. Scientific results from the Mallik 2002 gas hydrate production research well program, Mackenzie Delta, Northwest Territories, Canada. 2005 Geol. Surv. Canada Bull.; 585: 140p. CD and Charts. [3] Judge AS, Majorowicz JA. Geothermal conditions for gas hydrate stability in the Beaufort-Mackenzie area - the global change aspect. 1992 Paleogeography Paleoclimatology and Paleoecology, Global & Planetary Change Section; 98: 251-263. [4] Majorowicz JA., Hannigan PK. Stability zone of natural gas hydrates in a permafrost – bearing region of the Beaufort –Mackenzie basin - Study of a feasible energy source. Nat. Res. Res. 2000; 9: 3-25. [5] Majorowicz JA, Smith SL. Review of ground temperatures in the Mallik field area: a constraint to the methane hydrate stability. In: Dallimore SR, Uchida T, Collett TS editors. JAPEX/JNOC/GSC Mallik 2L-38 Gas Hydrate Research Well, Mackenzie Delta, Northwest Territories, Canada. Geological Survey of Canada Bulletin 1999; 544: 45-56. [6]Muller R.A, MacDonald GJ. Ice ages and astronomical causes: data, spectral analysis, and mechanisms. Berlin: Springer Praxis, 2000. [7] Frakes LA, Francis JE, Syktus JI. Climate models of the Phanerozoic. Cambridge: Cambridge Univ. Press, 1992.  [8] Taylor AE, Dallimore SR, Hyndman R Wright JF. Comparing the sensitivity of permafrost and marine gas hydrate to climate warming. In: Dallimore SR, Collett TS editors. Scientific Results from the Mallik 2002 Gas Hydrate Production Research Well Program, Mackenzie Delta, Northwest Territories, Canada. Geological Survey of Canada, Bulletin 2005; 585:130 and CD paper 52. [9] Intergovernmental Panel on Climate Change Fourth Assessment Report Climate Change: SynthesisReport2007: http://www.ipcc.ch/pdf/assessmentreport/ar4/syr/ar4_syr_spm.pdf [10]Climate Change - Carbon dioxide, Polsson. K. 2007 http://www.islandnet.com/~kpolsson/climate/carbo ndioxide.htm [11] Lawrence, KT, Liu Z, Herbert TD  Evolution of the Eastern Tropical Pacific Through Plio-Pleistocene Glaciation. 2006 Science; 312:79-83. [12]Geologic temperature record 2008: http://en.wikipedia.org/wiki/Temperature_record [13] Safanda J, Szewczyk J, Majorowicz JA. Geothermal evidence of very low glacial temperatures on the rim of the Fennoscandian ice sheet. Geophys. Res.Lett. 2004; 31: L07211. [14] Galushkin Yu. Numerical simulation of permafrost evolution as a part of sedimentary basin modeling: permafrost in the PlioceneHolocene climate history of the Urengoy field in the West Siberian basin. Can.J.Earth Sci.1997; 34: 935-948. [15] Peaceman DW, Rachford HH. The numerical solution of parabolic and elliptic differential equations. Journal of the Society for Industrial and Applied Mathematics 1955;3: 28-41. [16] Nixon JF. Thermal simulation of subsea saline permafrost. Can.J.Earth Sci. 1986;23: 20392046. Sloan, ED. Clathrate hydrates of natural gases. 2nd ed., New York: Marcel Dekker Inc.,1998. [17]Carslaw HS, Jaeger JC. Conduction of heat in solids. Oxford: Oxford University Press, 1959, 2nd ed. [18] Majorowicz JA, Judge A, Jones FW. Deep subpermafrost thermal regime in the Mackenzie Delta basin, northern Canada, - Analysis from petroleum bottom-hole temperature data. Geophysics1990; 55: 362-371.  [19] Taylor AE, Burgess M, Judge A, Allen VS. Canadian Geothermal Data Collection Ä Northern Wells 1981. Geothermal Series, Earth Physics Branch, E.M.R., Canada 1982; 13: 153p. [20] Henniges J, Huenges E, Burkhard H. In situ thermal conductivity of gas hydrate bearing sediments of the Mallik 5L-38 well. J. Geophys. Res. 2005; 110: B11206 [21] Wright JF, Nixon FM, Dallimore SR., Henninges J, Cote MM. Thermal conductivity of sediments within the gas hydrate bearing interval at the Mallik 5L-38 gas hydrate production well. In: Dallimore SR, Collett TS editors. Scientific Results from the Mallik 2002 Gas Hydrate Production Research Well Program, Mackenzie Delta, Northwest Territories, Canada. Geological Survey of Canada, Bulletin 2005; 585: 129-130. [22] Sloan ED. Clathrate hydrates of natural gases, 2nd ed., New York: Marcel Dekker Inc., 1998. [23] Lorenson TD, Collett TS, Whiticar MJ. Origin of gases in permafrost assossiated gas hydrate – Examples from Alaska and Canada. Hedeberg Conerence, Vancouver, 2004. http://www.searchanddiscovery.net/documents/abs tracts/2004hedberg_vancouver/extended/lorenson/ lorenson.htm. [24] Majorowicz JA, Osadetz K.G. Basic geological and geophysical controls bearing on gas hydrate distribution and volume in Canada. AAPG Bulletin 2001; 85/7:1211-1230. [25]Taylor AE, Modelling the thermal regime of permafrost and gas hydrate deposits to determine the impact of climate warming. Mallik field area. in: Dallimore SR, Uchida T, Collett TS editors. JAPEX/JNOC/GSC Mallik 2L-38 Gas Hydrate Research Well, Mackenzie Delta, Northwest Territories, Canada. Geological Survey of Canada Bulletin 1999; 544:391-401. [26]Nisbet EG, The end of the ice age. Can. J. Earth Sci. 1990; 27: 148 - 157. [27]Nisbet EG, Have sudden large releases of methane from geological reservoirs occurred since the Last Glacial Maximum, and could such releases occur again? Phil. Trans. R. Soc. Lond. A 2002;360: 581-607. [28]Sowers T. Late Quaternary atmospheric CH4 isotope record suggests marine clathrates are stable. Science 2006; 31: 838-840. ACKNOWLEDGMENTS This work has been supported by the Earth Sciences Sector Gas Hydrates Fuel of the Future Program.  

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