International Conference on Gas Hydrates (ICGH) (6th : 2008)

RELATIVE PERMEABILITY CURVES DURING HYDRATE DISSOCIATION IN DEPRESSURIZATION Konno, Yoshihiro; Masuda, Yoshihiro; Sheu, Chie Lin; Oyama, Hiroyuki; Ouchi, Hisanao; Kurihara, Masanori Jul 31, 2008

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Proceedings of the 6th International Conference on Gas Hydrates (ICGH 2008), Vancouver, British Columbia, CANADA, July 6-10, 2008.  RELATIVE PERMEABILITY CURVES DURING HYDRATE DISSOCIATION IN DEPRESSURIZATION Yoshihiro Konno ∗ , Yoshihiro Masuda and Chie Lin Sheu 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 Depressurization is thought to be a promising method for gas recovery from methane hydrate reservoirs, but considerable water production is expected when this method is applied to the hydrate reservoir of high initial water saturation. In this case, the prediction of water production is a critical problem. This study examined relative permeability curves during hydrate dissociation by comparing numerical simulations with laboratory experiments. Data of gas and water volumes produced during depressurization were taken from gas recovery experiments using sand-packed cores containing methane hydrates. In each experiment, hydrates were dissociated by depressurization at a constant pressure. The surrounding temperature was held constant during dissociation. The volumes of gas and water produced, the temperatures inside of the core, and the pressures at the both ends of the core were measured continuously. The experimental results were compared with numerical simulations by using the simulator MH21-HYDRES (MH21 Hydrate Reservoir Simulator). The experimental results showed that considerable volume of water was produced during hydrate dissociation, and the simulator could not reproduce the large water production when we used typical relative permeability curves such as the Corey model. To obtain good matching for the volumes of gas and water produced during hydrate dissociation, the shape of relative permeability curves was modified to express the rapid decrease in gas permeability with increasing water saturation. This result suggests that the connate water can be easily displaced by hydrate-dissociated gas and move forward in the hydrate reservoir of high initial water saturation. Keywords: methane hydrate, gas production, depressurization, relative permeability  ∗  Corresponding author: Phone: +81 3 5841 7061 Fax +81 3 5841 7035 E-mail: konno@kelly.t.u-tokyo.ac.jp  NOMENCLATURE C Specific heat [J·kg-1·K-1] D Depth from a reference level [m] g Acceleration of gravity [9.80665 m2·s-1] h Enthalpy [J·kg-1] kD Absolute permeability [m2] kD0 Absolute permeability at SH=0 [m2] krl Relative permeability to phase (l) [fraction] N Permeability reduction index Ng Index of gas relative permeability Nw Index of water relative permeability n& i 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] n& dissoc , i Generation rate of component (i) due to hydrate dissociation per 1m3 of sediment (i = CH4, H2O) [mol·s-1·m-3] n& prod ,l Production rate of phase (l) per 1m3 of sediment [mol·s-1·m-3] p pressure [Pa] Q& H Heat sink rate due to hydrate dissociation per 1m3 of sediment [W·m-3] Q& I Heat sink rate with ice-water phase transition per 1m3 of sediment [W·m-3] Q& salts Heat generation rate with salt dissolution into water per 1m3 of sediment [W·m-3] Q& ext Heat sink rate to outside at the system boundary per 1m3 of sediment [W·m-3] Q& prod ,l Heat sink rate with production of phase (l) per 1m3 of sediment [W·m-3] Sl Saturation of phase (l) [fraction] Siw Irreducible water saturation [fraction] Srg Residual gas saturation [fraction] Sw,m Effective water saturation [fraction] T Temperature [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] λeff  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. Depressurization is a promising method for gas production from methane hydrate reservoirs, both from economic and ecological perspectives. But, in the hydrate reservoir of high initial water saturation, considerable water production may become a problem of application of the method. So the prediction of water production is one of the most important issues. In this study, numerical simulations were done using the original developed simulator: MH21-HYDRES (MH21 Hydrate Reservoir Simulator) [2] to examine relative permeability curves during hydrate dissociation by comparing numerical simulations with laboratory experiments. 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: ⎞ ⎛ k D k rg ρ g ( ∇・⎜ ∇p g − ρ g g∇D )⎟ + n& CH 4 − n& prod , g ⎟ ⎜ μg ⎠ ⎝ ∂ = (ρ g φ S g ) (1) ∂t For water components: ⎞ ⎛ k k ρ (1 − x MeOH − x salts ) (∇p w − ρ w g∇D )⎟⎟ ∇・⎜⎜ D rw w μw ⎠ ⎝ + n& H 2O − (1 − x MeOH − x salts )n& prod , w (2) ∂ = [ρ wφS w (1 − x MeOH − x salts )] ∂t  For methanol components: ⎛k k ρ x ⎞ ∇・⎜⎜ D rw w MeOH (∇p w − ρ w g∇D )⎟⎟ μw ⎝ ⎠ ∂ − x MeOH n& prod , w   = (φρ w x MeOH S w ) ∂t  (3)  For salts components: ⎞ ⎛k k ρ x ∇・⎜⎜ D rw w salts (∇p w − ρ w g∇D )⎟⎟ − x salts n& prod , w μw ⎠ ⎝ ∂ = (φρ w x salts S w ) (4) ∂t Energy balance equation: ⎛ ⎞⎫⎪ ∂ ⎧⎪ ⎨(1 − φ )ρ R C R T + φ ⎜⎜ ∑ S l ρ l C l T + ∑ S l ρ l U l ⎟⎟⎬ ∂t ⎪⎩ l = w, g ⎝ l = I , H , salts ⎠⎪⎭ ⎛ ⎞ k k ρ = ∇ ⋅ (λ eff ∇T ) + ∇ ⋅ ⎜⎜ ∑ hl D rl l (∇p l − ρ l g∇D )⎟⎟ μl ⎝ l = w, g ⎠ & & & & & (5) − Q H − Q I + Q salts − Qext + ∑ Q prod ,l l = w, g  Permeability reduction in porous media containing hydrates The permeability of hydrate reservoirs can change due to presence of hydrates. Masuda et al. have proposed a following model to express this phenomenon [2]. Figure 1 shows the permeability reduction ratio. The permeability reduction index N is an empirical parameter. In this study, N was set as 2.  k D = k D 0 (1 − S H )  N  (6)  Corey model: Gas relative permeability is modeled as follow: ⎧ 1 2 2 ⎪ ⎧ ⎫ ⎪⎛⎜ 1 − S rg − S w,m ⎞⎟ ⎪ ⎛⎜ S w,m − S iw ⎞⎟ ⎪ 1 − k rg = ⎨ ⎜ ⎟ ⎨ ⎜ ⎟ ⎬ ⎪⎝ 1 − S rg − S iw ⎠ ⎪⎩ ⎝ 1 − S rg − S iw ⎠ ⎪⎭ ⎪ 0 ⎩ S w,m < Siw S iw ≤ S w,m < 1 − S rg  (7)  1 − S rg ≤ S w,m Water relative permeability is modeled as follow:  0 ⎧ ⎪⎛ S − S ⎞ 4 ⎪ iw ⎟ k rg = ⎨⎜ w,m ⎜ 1 − S rg − S iw ⎟ ⎪⎝ ⎠ ⎪⎩ 1  S w,m < Siw S iw ≤ S w,m < 1 − S rg  (8)  1 − S rg ≤ S w,m  In this study, residual gas saturation was set as 0.1 and irreducible water saturation was set as 0.2.  1 N=2  0.9 0.8  N=6  0.7 kD/kD0  Two different relative permeability models were used for comparison studies. One model is Corey model [3] typically used in a conventional reservoir simulation. The other model was derived from Kozeny-Carman model [4]. In the model derived from Kozeny-Carman model, we assumed that hydrates occupy from the capillary walls and gas/water flows the center of capillaries. Through comparison studies between experiments and simulations, the shape of relative permeability derived from Kozeny-Carman model was modified. These relative permeability models are as follows:  0.6  N=10  0.5  The model derived from Kozeny-Carman model: Gas relative permeability is modeled as follow:  {  0.4  (  krg = (1 − S w,m ) 1 − S w,m  0.3 0.2  )}  2 Ng  (9)  0.1 0 0  0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9  1  Water relative permeability is modeled as follow:  Hydrate saturation  Figure 1 Permeability reduction ratio vs. SH. Relative permeability curves  krw = S w,m  Nw  (10)  Theoretically, Ng and Nw are 1 and 2 respectively. In this study, Ng and Nw were used as matching parameters for gas and water production.  Sw,m is the effective water saturation defined as follow: T5  S w ,m  10 mm  25 mm  Sw = 1 − SH − SI  (11)  25.5 mm  T4  T0  Figure 2 shows these relative permeability curves.  P1  P2 Rubber sleeve  1  Kozeny Carman model_ Nw=2, Ng=1  0.9  Figure 4 The position of the sensor.  Corey_Siw=0.2, Srg=0.1  0.8  krg  0.7  Conditions Table 1 shows the experimental conditions. Two experiments with different production pressure were conducted.  kr  0.6 0.5 0.4  krw  0.3 0.2  Table 1 Experimental conditions.  0.1 0 0  0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Sw,m  1  Figure 2 Relative permeability curves. 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 by depressurization. The core was maintained at constant pressure and temperature. One side of the core was depressurized at constant pressure to produce gas and water. 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. Water tank for axial pressure  Tap for sensor  Exp. 1 10.5 285.85 6.1 40.5 59.4 11.4 29.2  Exp. 2 10.4 285.65 4.1 39.6 27.2 24.6 48.2  SIMULATION DETAILS Grid system A cylindrical coordinate system was used. The hydrate core and the rubber sleeve were divided into 7 x 30 grids. Figure 5 shows the schematic grid system.  Movable end plug Pressure vessel  Rubber sleeve Water tank for confining pressure  Initial pressure / MPa Initial temperature / K Production pressure / MPa Porosity / % Hydrate saturation / % Gas saturation / % Water saturation / %  Coolant jacket  Figure 5 The schematic grid system.  Thermal insulator  Fixed end plug  Figure 3 The schematic diagram of core holder.  Simulation conditions Initial input data were based on the measured data (Table 1). Boundary conditions such as heat transfer were set to reproduce the experimental conditions. The index of gas relative permeability Ng in Eq. (9) and the index of water relative permeability Nw in Eq. (10) were set as matching parameters for gas and water production.  12 P1 (Exp.)  Pressure [MPa]  10  P1 (Sim.)  8 6 4 2 0 0  20  40  60  80  100  120  140  160  180  200  Time [min]  Figure 8 Comparison of pressure. (Exp. 1) 287 286 Temperature [K]  RESULTS Figure 6 and 7 show the comparison of cumulative gas and water produced in Exp. 1 respectively. The production volume of gas was overestimated and the production volume of water was underestimated in the case of Corey model. On the other hand, the production volumes of gas and water could be reproduced by the simulator using the model derived from Kozeny-Carman model when the indexes of gas and water relative permeability were set as 4 and 2. In this simulation conditions, the predictions agreed with the measured pressure and temperatures (Figure 8, 9). Figure 10 and 11 show the comparison of cumulative gas and water produced in Exp. 2 respectively. The measured data were reproduced by the simulator using the model derived from Kozeny-Carman model when the indexes of gas and water relative permeability were set as 8 and 2. Both experiments showed that considerable volume of water was produced during hydrate dissociation, especially at early stage of hydrate dissociation.  T1 (Exp.)  T2 (Exp.)  T3 (Exp.)  T1 (Sim.)  T2 (Sim.)  T3 (Sim.)  285 284 283 282 281 280 0  20  40  60  80  100  120  140  160  180  200  Time [min]  Figure 9 Comparison of temperatures. (Exp. 1) 10 Exp. Sim. (Kozeny Carman model_Nw=2, Ng=4) Sim. (Corey model)  14 12  Cumulative Gas Produced [NL]  Cumulative Gas Produced [NL]  16  10 8 6 4 2 0  Exp. 8  Sim. (Kozeny Carman model_Nw=2, Ng=8)  6  4  2  0 0  20  40  60  80  100  120  140  160  180  200  0  20  40  Time [min]  Figure 6 Comparison of cumulative gas produced. (Exp. 1)  80  100  Figure 10 Comparison of cumulative gas produced. (Exp. 2)  90  100 Exp.  80  Cumulative Water Produced [ml]  Cumulative Water Produced [ml]  60 Time [min]  Sim. (Kozeny Carman model_Nw=2, Ng=4)  70  Sim. (Corey model)  60 50 40 30 20 10 0  90 80 70 60 50 40 30 Exp.  20  Sim. (Kozeny Carman model_Nw=2, Ng=8)  10 0  0  20  40  60  80  100  120  140  160  180  Time [min]  Figure 7 Comparison of cumulative water produced. (Exp. 1)  200  0  20  40  60  80  Time [min]  Figure 11 Comparison of cumulative water produced. (Exp. 2)  100  DISCUSSION Figure 12 shows the relative permeability curves used for the comparisons. Gas permeability decreased rapidly with increasing water saturation in both experiments. In the initial conditions of experiments, water occupied a large part of the effective pores and was the continuous phase. On the other hand, initial gas was the discontinuous phase. In depressurization method, gas generated by hydrate dissociation appears in all pores independently of their size, and this gas is discontinuous and immobile in Lw-H region. So, at early stage of hydrate dissociation, water in effective pores is easily displaced by gas generated. After that, gas phase becomes high saturation due to the continuous supply of gas from hydrates and gets connected. It suggests that considerable volume of water may be produced during hydrate dissociation by depressurization, especially at early stage of hydrate dissociation in Lw-H region. 1  krw_Nw=2 krg_Ng=4 krg_Ng=8  0.9 0.8 0.7  kr  0.6 0.5 0.4 0.3 0.2 0.1 0 0  0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Sw,m  1  Figure 12 Relative permeability curves used for comparisons. CONCLUSION Relative permeability curves during hydrate dissociation by depressurization were examined through comparison with numerical simulations and experimental data for fluid production. The experimental results showed that considerable volume of water was produced during hydrate dissociation. The simulator reproduced the large water production when we used the model that gas permeability decreased rapidly with increasing water saturation. Temperatures of inside and outside of the core and pressure at the end of the core were also reproduced by the simulator. This result suggests that the connate water can be easily displaced by hydrate-dissociated gas and move forward in the hydrate reservoir of high initial water saturation.  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 hydratebound gas in marine sediments: how much is really out there?. Earth-Science Reviews 2004; 66:183-197. [2] 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. [3] Corey A.T. The interrelation between gas and oil relative permeabilities. Producers Monthly 1954; 19:38-41. [4] Carman P.C. Flow of gases through porous media. London: Butterworths, 1956.  

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