6th International Conference on Gas Hydrates

NUMERICAL STUDY ON PERMEABILITY HYSTERESIS DURING HYDRATE DISSOCIATION IN HOT WATER INJECTION Konno, Yoshihiro; Masuda, Yoshihiro; Takenaka, Tsuguhito; Oyama, Hiroyuki; Ouchi, Hisanao; Kurihara, Masanori 2008

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   NUMERICAL STUDY ON PERMEABILITY HYSTERESIS DURING HYDRATE DISSOCIATION IN HOT WATER INJECTION   Yoshihiro Konno ∗, Yoshihiro Masuda and Tsuguhito Takenaka Department of Geosystem Engineering, School of Engineering University of Tokyo Eng. Bldg. No.4, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656 JAPAN  Hiroyuki Oyama National Institute of Advanced Industrial Science and Technology (AIST) Tsukisamu-higashi, Toyohira-ku, Sapporo 062-8517 JAPAN  Hisanao Ouchi and Masanori Kurihara Japan Oil Engineering Co. Ltd. 1-7-3 Kachidoki, Chuo-ku, Tokyo 104-0054 JAPAN   ABSTRACT Hot water injection is a production technique proposed to gas recovery from methane hydrate reservoirs. However, from a practical point of view, the injected water experiences a drop in temperature and re-formation of hydrates may occur in the reservoir. In this work, we proposed a model expressing permeability hysteresis in the processes between hydrate growth and dissociation, and studied hydrate dissociation behavior during hot water injection. The model of permeability hysteresis was incorporated into the simulator MH21-HYDRES (MH21 Hydrate Reservoir Simulator), where the decrease in permeability with hydrate saturation during hydrate growth process was assumed to be much larger than the decrease during hydrate dissociation process. Laboratory hydrate dissociation experiments were carried out for comparison. In each experiment, we injected hot water at a constant rate into a sand-packed core bearing hydrates, and the histories of injection pressure, core temperature, and gas/water production rates were measured. Numerical simulations for the core experiments showed the re-formation of hydrates led to the increase in injection pressure during hot water injection. The simulated tendencies of pressure increase varied markedly by considering permeability hysteresis. Since the experimental pressure increases could not be reproduced without the permeability hysteresis model, the influence of permeability hysteresis should be considered to apply hot water injection to hydrate reservoirs.   Keywords: methane hydrate, gas production, hot water injection, permeability hysteresis, numerical simulation                                                          ∗ Corresponding author: Phone: +81 3 5841 7061 Fax +81 3 5841 7035 E-mail: konno@kelly.t.u-tokyo.ac.jp Proceedings of the 6th International Conference on Gas Hydrates (ICGH 2008), Vancouver, British Columbia, CANADA, July 6-10, 2008.  NOMENCLATURE  Ag Specific surface area of gas particles [0.375 mm-1] AHS Specific surface area of hydrate particles [0.375 mm-1] C Specific heat [J·kg-1·K-1] D Depth from a reference level [m] ef  Gas fugacity at V-H-Lw equilibrium [MPa] gf  Gas fugacity in pore space [MPa] g Acceleration of gravity [9.80665 m2·s-1] h Enthalpy [J·kg-1] KB Hydrate dissociation rate constant [mol m-2·MPa-1·s-1] Kgen Hydrate formation rate constant [0.31 mol m-2·Pa-1·s-1] kD Absolute permeability [m2] kD0 Absolute permeability at SH=0 [m2] krl Relative permeability to phase (l) [fraction] krw° End-point water permeability [fraction] krg° End-point gas permeability [fraction] m Power of SwD N Permeability reduction index Nhys Permeability reduction index during hydrate re-formation / dissociation n Power of (1 – SwD) in& Net generation rate of component (i) per 1m3 of sediment during hydrate dissociation /formation and water freezing/ice melting process (i = CH4, H2O) [mol·s-1·m-3] idissocn ,&  Generation rate of component (i) due to hydrate dissociation per 1m3 of sediment (i = CH4, H2O) [mol·s-1·m-3] lprodn ,&  Production rate of phase (l) per 1m3 of sediment [mol·s-1·m-3] p pressure [Pa] HQ&  Heat sink rate due to hydrate dissociation per 1m3 of sediment [W·m-3] IQ&  Heat sink rate with ice-water phase transition per 1m3 of sediment [W·m-3] saltsQ&  Heat generation rate with salt dissolution into water per 1m3 of sediment [W·m-3] extQ&  Heat sink rate to outside at the system boundary per 1m3 of sediment [W·m-3] lprodQ ,&  Heat sink rate with production of phase (l) per 1m3 of sediment [W·m-3] Rinj. Injection rate of hot water [ml/min] SH_hys The hydrate saturation at the reformation SH_norm The normalized hydrate saturation in re-formation / dissociation process  Siw Irreducible water saturation [fraction] Sl Saturation of phase (l) [fraction] Srg Residual gas saturation [fraction] T Temperature [K] Tinj. Temperature of injected water [K] t Time [s] U Internal energy [J kg-1] xi Mole fraction of component (i) in water phase (i = MeOH, salts) [fraction] φ Porosity [fraction] effλ  Effective thermal conductivity of sediment, [W·m-1·K-1] µ Viscosity [Pa·s] ρ  Mass density [kg·m-3] ρ  Molar density [mol·m-3]  Subscripts g Gas phase H Hydrate phase I Ice phase R Sand grain (rock matrix) w Water phase  INTRODUCTION Methane hydrate is a crystalline solid composed of water and methane. The total amount of methane gas in this solid form may surpass the total conventional gas reserve. And some individual methane hydrate accumulations may contain significant and concentrated resources [1]. That indicates the potential as a future energy resource. Hot water injection is one of gas production methods from hydrate reservoirs [2]. In this method, hydrate re-formation and permeability reduction may occur when the gas and water generated by dissociation of hydrates flow through the reservoir. These phenomena lead to the increase in injection pressure and may be the trigger of formation fracturing. So, the understanding of hydrate re-formation and permeability reduction is critical for application of the method. Sakamoto et al. reported permeability change by hydrate re-formation and concluded that the permeability changed rapidly when the hydrate saturation exceeded a threshold [3] [4]. In this study, we considered that the permeability change has hysteresis in the processes between hydrate formation and dissociation. We modeled the permeability hysteresis and incorporated the model into the original developed simulator: MH21-HYDRES (MH21 Hydrate Reservoir Simulator). Thorough the comparison between numerical simulation and experimental data, the permeability hysteresis model was validated.   THEORY OF SIMULATOR Governing equations The MH21-HYDRES is a compositional simulator solving the equations of mass balances for methane, water, methanol and salts, and one energy balance equation. The mass and energy balances equations are as follows:  Mass balance equations: For methane components: ( ) godCHggggrgD nnDgpkk,4 pr&& −+ ∇−∇∇ ρµρ・( )gg St φρ∂∂=  (1)  For water components: ( ) ∇−∇−−∇ DgpxxkkwwwsaltsMeOHwrwD ρµρ )1(・  [ ])1()1( ,2saltsMeOHwwwprodsaltsMeOHOHxxStnxxn−−∂∂=−−−+φρ&& (2)  For methanol components: ( )( )wMeOHwwprodMeOHwwwMeOHwrwDSxtnxDgpxkkφρρµρ∂∂=− ∇−∇∇ ・,& (3)  For salts components: ( )  ・ wprodsaltswwwsaltswrwD nxDgpxkk,&− ∇−∇∇ ρµρ  ( )wsaltsw Sxt φρ∂∂=  (4)  Energy balance equation: ( )( ) ( ) ∇−∇⋅∇+∇⋅∇= ++−∂∂∑∑∑===gwlllllrlDleffgwllllsaltsHIllllRRDgpkkhTUSTCSTCt,,,,1ρµ ρλρρφρφ ∑=+−+−−gwllprodextsaltsIH QQQQQ,,&&&&&  (5) Permeability hysteresis during hydrate re- formation / dissociation  The permeability of hydrate reservoirs can change due to presence of hydrates. Masuda et al. have proposed a following model to express this phenomenon [5].  ( )NHDD Skk −= 10  (6)  In dissociation process, as is common in depressurization method, this model is supported by experimental data [6]. On the other hand, in re-formation / dissociation process, the permeability can change more rapidly than that of just dissociating process. We modeled this rapid change of permeability as:  ( ) ( )hysNnormHNhysHDD SSkk __0 11 −−=  (7)  hysHhysHHnormH SSSS___ 1−−=  (8)  where SH_hys is the hydrate saturation at the re-formation and SH_norm is the normalized hydrate saturation in re-formation / dissociation process. In this model, the permeability reduction index of re-formation/dissociation process Nhys is larger than N in Eq. (6). Figure 1 shows this permeability hysteresis in the processes between hydrate formation and dissociation.   00.10.20.30.40.50.60.70.80.910 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1Hydrate saturationkD/kD0Dissociation process (N = 2)Re-formation / dissociationprocess (Nhys = 10)kD/kD0 Figure 1  Permeability reduction ratio vs. SH.  Relative permeability The gas and water relative permeabilities were modeled as follows:  Gas relative permeability:  nwDorgrg Skk )1( −=  (9)  Water relative permeability:  mwDorwrw Skk =  (10)  rgiwiwHwwD SSSSSS −−−−= 11  (11)  Figure 2 shows the gas and water relative permeability curves used for this study. Parameters in Eq. (9) and (10) were set as Table 1. Residual gas saturation was used as a matching parameter for gas production.   00.10.20.30.40.50.60.70.80.910 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1Water saturationRelative permeabilityGas Water Figure 2  Relative permeability curves.  Table 1 Parameters for relative permeability.   Parameter Value krg° 1.0 krw° 0.2 n 2 m 3 Siw 0.15 Srg 0.45  Hydrate formation / dissociation Clarke-Bishnoi equation was used to model hydrate dissociation [7].   ( )geHSHBCHdissoc ffASKn −= φ4,&  (12)  Hydrate formation was modeled based on the work of Malrgaonkar et al. [8].  ( )geggwgenCHform ffASSKn −= φ4,&  (13)  EXPERIMENTAL Apparatus and procedure Artificial methane hydrate cores were prepared for experiments. The core length and diameter were 150 mm and 50 mm respectively. The core was packed into the rubber sleeve. The rubber sleeve thickness was 10 mm. The core holder as shown in Figure 3 was used for the dissociation experiments. The core was maintained at constant pressure and temperature. Hot water was injected from one side of the core and the pressure of the other end was kept constant. Figure 4 shows the position of the sensor. The volumes of gas and water produced, temperatures of inside and outside of the core and pressures at the both ends of the core were measured.   Rubber sleeveTap for sensorWater tank for confining pressureWater tank for axial pressureMovable end plugPressure vesselCoolant jacketFixed end plugThermal insulator  Figure 3 The schematic diagram of core holder.  T0 T4P1 P225 mm 10 mm25.5 mmT5Rubber sleeveInjection  Figure 4 The position of the sensor.  SIMULATION DETAILS Grid system A cylindrical coordinate system was used. The hydrate core and rubber sleeve were divided into 7 x 30 grids. Figure 5 shows the schematic grid system. Boundary conditions such as heat transfer were set to reproduce the experimental conditions.    Figure 5  The schematic grid system.  Model settings Parameter studies (Run 1-3) and comparison studies (Run e1, 2) were conducted. These simulations have differences in models: re-formation and hysteresis models are considered or not. Table 2 shows the model differences between these simulations.   Table 2. Model settings.  Run No Re-formation model Hysteresis model Run 1 With With Run 2 With Without Run 3 Without Without Run e1 With With Run e2 With Without  Input data Table 3 shows the input data for simulations. The data were based on the experiment. The permeability reduction index N and Nhys were decided by comparison with the experiment.  Table 3. Input data.   Run 1, 2, 3 Run e1, 2 φ 0.4 0.4 kD0 (mD) 3000 3000 SH 0.70 0.76 Sw 0.30 0.20 Sg 0.0 0.04 Pi (MPa) 8.1 8.1 Ti (K) 281.15 281.15 Rinj. (ml/min) 10 9.43 Tinj. (K) 303.15 Follow the schedule  (about 300) N 2 2 Nhys 8 8  RESULTS AND DISCUSSION The effect of hydrate re-formation and permeability hysteresis We studied the effect of hydrate re-formation and permeability hysteresis using parameter studies with three different conditions (Run 1-3). Figure 6 shows the comparison of injection pressures of these three Runs. Through the comparison between Run 2 and Run 3, it was found that the reduction of differential pressure was delayed due to re-formation of hydrates. But the value of differential pressure was almost the same whether hydrates re-form or not. On the other hand, in Run 1 with permeability hysteresis, the differential pressure increased and decreased rapidly since the processes between re-formation and dissociation of hydrates caused rapid change of permeability. The comparison of cumulative gas produced in Figure 7 shows that re-formation and permeability hysteresis had a limited effect on gas productivity as long as hot water could be injected. However, the large injection pressure may be critical problem for application of the method.  7.07.58.08.59.09.50 20 40 60 80 100 120 140 160 180 200Time [min]Pressure [MPa]Run1 Run2 Run3  Figure 6  The comparison of injection pressures.  0246810120 20 40 60 80 100 120 140 160 180 200Time [min]Cumulative gas produced [NL]Run1 Run2 Run3  Figure 7  The comparison of cumulative gas produced.  Comparison between the simulation and the experiment We conducted comparison study between the simulation and the experiment. Injection pressure, cumulative gas produced and temperatures of inside of the core were compared. Figure 8 shows the comparison of injection pressure. Measured injection pressure showed the rapid increase and decrease. The simulation with permeability hysteresis model (Run e1) reproduced the rapid change of the injection pressure. In contrast, the simulation without permeability hysteresis model (Run e2) could not reproduce this tendency. In the experiment, reductions of injection pressure were seen at 35 min and 55 min. It was considered that heterogeneity of the core caused the some reductions. Figure 9 shows the comparison of cumulative gas produced. The difference among models was not obvious, however, the simulation with the permeability hysteresis model reproduced the measured data. Figure 10 shows the comparison of temperatures of inside of the core. The simulation with permeability hysteresis model reproduced the tendency of measured data. Figure 11 shows the profiles of hydrate saturation, gas saturation, pressure and temperature at 20 min, 50 min, 100 min and 200 min. In Figure 11, hot water was injected from the left end of the core. Hydrates were dissociated from left to right side of the core and re-generated at low temperature region. At 50 min when the injection pressure reached maximum value, hydrate saturation rose up to 0.79, and pressure dropped rapidly in hydrate saturated region. At 100 min when the injection pressure dropped to initial value, hydrates of center of the core disappeared and gas broke through the core.                7.07.58.08.59.09.510.00 20 40 60 80 100 120 140 160 180 200Time [min]Pressure [MPa]Exp. Run e1 Run e2 Figure 8  The comparison of injection pressures.  02468101214160 20 40 60 80 100 120 140 160 180 200Time [min]Cumelative gas produced [NL] Exp. Run e1 Run e2 Figure 9  The comparison of cumulative gas produced.  2802852902953003050 20 40 60 80 100 120 140 160 180 200Time [min]Temperature [K]T1 (Exp.) T2 (Exp.) T3 (Exp.)T1 (Run e1) T2 (Run e1) T3 (Run e1) Figure 10  The comparison of temperatures.                Figure 11  The profiles of hydrate saturation, gas saturation, pressure and temperature. 20 min 50 min 100 min 200 minSHSgP (MPa)T (K)0 0.850 0.58 10280 300CONCLUSION We modeled permeability hysteresis in the processes between formation and dissociation of hydrates. Developed model was incorporated into the simulator: MH21-HYDRES, and a comparison study between simulation and experiment was conducted to validate the model. The simulator with permeability hysteresis model reproduced the rapid change of injection pressure measured by the experiment. Injection pressure increased to value a few MPa higher than the initial pressure since re-formation of hydrates caused permeability reduction. Simulations showed that re-formation and permeability hysteresis had limited effect on gas productivity as long as hot water could be injected. However, the large injection pressure may be a critical problem for application of the method.  ACKNOWLEDGMENT This work was done as a research project under the Research Consortium for Methane Hydrate Resources in Japan (MH21 Research Consortium) on the National Methane Hydrate Exploitation Program by the Ministry of Economy, Trade and Industry (METI). We would like to thank the Ministry of Economy, Trade and Industry (METI) who financially supported this research.  REFERENCES [1] Milkov A.V. Global estimates of hydrate-bound gas in marine sediments: how much is really out there?. Earth-Science Reviews 2004; 66:183-197. [2] Masuda Y, Kurihara M, Ohuchi H, Sato T. A Field-Scale Simulation Study on Gas Productivity of Formations Containing Gas Hydrates, In: Proceedings of the Fourth International Conference on Gas Hydrates, Yokohama, 2002. [3] Sakamoto Y, Komai T, Kawamura T, Minagawa H, Tenma N, Yamaguchi T. Laboratory-scale experiment of methane hydrate dissociation by hot-water injection and numerical analysis for permeability estimation in reservoir: Part 1 - Numerical study for estimation of permeability in methane hydrate reservoir. INTERNATIONAL JOURNAL OF OFFSHORE AND POLAR ENGINEERING 2007; 17(1):47-56. [4] Sakamoto Y, Komai T, Kawamura T, Minagawa H, Tenma N, Yamaguchi T. Modification of permeability model and history matching of laboratory-scale experiment for dissociation process of methane hydrate: Part 2 - Numerical study for estimation of permeability in methane hydrate reservoir. INTERNATIONAL JOURNAL OF OFFSHORE AND POLAR ENGINEERING 2007; 17(1):57-66. [5] Masuda Y, Fujinaga Y, Naganawa S, Fujita K, Sato T, Hayashi Y. Modeling and Experimental Studies on Dissociation of Methane Gas Hydrates in Berea Sandstone Cores, In: Proceedings of the 3rd International Conference on Gas Hydrates, Salt Lake City, 1999. [6] Masuda Y, Konno Y, Kurihara M, Ouchi H, Kamata Y, Ebinuma T, Narita H. Validation Study of Numerical Simulator Predicting Gas Production Performance from Sediments Containing Methane Hydrates, In: Proceedings of the Fifth International Conference on Gas Hydrates, Trondheim, 2005. [7] Clarke M, Bishnoi P.R. Determination of the Activation Energy and Intrinsic Rate Constant of Methane Gas Hydrate Decomposition. The Canadian Journal of Chemical Engineering 2001; 79:143-147. [8] Malegaonkar M.B., Dholabhai P.D., Bishnoi P.R. Kinetics of Carbon Dioxide and Methane Hydrate Formation. The Canadian Journal of Chemical Engineering 1997; 75:1090-1099. 

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