Numerical Simulation and Analysis of Water Phase Effect on Methane

Article pubs.acs.org/IECR

Numerical Simulation and Analysis of Water Phase Effect on Methane Hydrate Dissociation by Depressurization Jia-Fei Zhao, Chen-Cheng Ye, Yong-Chen Song,* Wei-Guo Liu, Chuan-Xiao Cheng, Yu Liu, Yi Zhang, Da-Yong Wang, and Xu-ke Ruan Key Laboratory of Ocean Energy Utilization and Energy Conservation of Ministry of Education, School of Energy and Power Engineering, Dalian University of Technology, Dalian 116024, P. R. China ABSTRACT: The gas hydrate dissociation process is always accompanied by water production and water transfer, which may affect gas generation rate. In this study, in order to analyze the water phase effect in the process of dissociation in porous media, a two-dimensional (2-D) axisymmetric simulator is developed to model methane hydrate dissociation in porous media by depressurization. Mass transport, intrinsic kinetic reaction and energy conservation are included in the governing equations, which are discretized by finite difference method and are solved in the implicit pressure-explicit saturation (IMPES) method. Then, a series of simulations are performed to study the relationship among changes of water saturation, temperature, pressure and hydrate saturation in laboratory-scale methane dissociation by depressurization, water transfer in porous media for different outlet pressure and bath temperature, and the sensitivity analysis to water saturation. These results suggest that the front dissociation interface is wrapped in an area where water saturation is distributed in a gradient. As the water moves, the water phase plays an important role in late stage thermal conduction. Higher water saturation may lead to higher gas generation rate in the late stage. The water-unsaturated condition is also forecasted by the simulator. The implications of the data are discussed in detail.

1. INTRODUCTION Gas hydrates are solid crystalline compounds in which gas molecules are lodged within the lattices of ice crystal structures.1,2 Vast amounts of CH4 are trapped in gas hydrates, and a significant effort has begun to evaluate hydrate deposits as a potential energy source.3−5 The key problem in the production of methane from the hydrate layer will be the dissociation of in situ hydrates. There are at least three means by which commercial production of natural-gas hydrates might eventually be achieved, all of which alter the thermo-dynamic conditions in the hydrate stability zone such that the gas hydrate decomposes.6−9 Depressurization taking place the section by pumping, especially within the free gas below the bottom simulating reflector, has been quoted by many researchers as the most economically viable option.10−12 Laboratory-scale hydrate experiments and simulations have been undertaken for predicting the behavior of hydrate dissociation in porous media. Yousif et al.13 performed the experiments on the hydrate formation and dissociation in Berea sandstone cores through depressurization method and established an isothermal model to interpret the results. Masuda14 developed a two-phase, gas−water numerical finitedifference simulator to model their depressurization experiment results. In the simulator, the Kim−Bishnoi equation was used to determine the dissociation rate, when the permeability of hydrate-bearing sandstone was assumed to be the function of hydrate saturation. Furthermore, heat transfer by conduction and convection within the sandstone containing hydrate was considered. Sun et al.15 developed a simulator for methane hydrate dissociation in porous media with the ice phase considered. This laboratory scale is usually beneficial to analyze fundamental principles. Moreover, researchers have © 2012 American Chemical Society

done the numerical simulations about sensitivity analysis in porous media such as temperature, pressure, and permeability. The results show that those factors could obviously affect the course of hydrate dissociation. Kambiz et al.16 developed a comprehensive Users' Def ined Subroutine for analysis of hydrate dissociation process into the FLUENT code. Different core temperatures and various outlet valve pressures in the core were simulated. Kambiz showed that increasing the surrounding temperature increases the rate of gas and water production as a result of a faster rate of hydrate dissociation, and decreasing the outlet valve pressure increases the rate of hydrate dissociation; therefore, the rate of gas and water production increases. Moridis investigated the sensitivity of gas production to different initial hydrate saturation and intrinsic permeability using the TOUGH+HYDRATE simulator. Moridis17 pointed out that a lower initial hydrate saturation leads to a higher gas production because of the larger effective initial permeability to water. Masanori et al.18 targeting the methane hydrate (MH) bearing units C and D of the Mt. Elbert Formation in the Alaska North Slope Field, predicted cumulative gas production by the methods of depressurization, a combination of depressurization and wellbore heating, and hot water huff and puff. Masanori suggested that the effect of the wellbore heating becomes smaller as the initial temperature of the reservoir becomes higher. Received: Revised: Accepted: Published: 3108

September 6, 2011 December 27, 2011 January 9, 2012 January 9, 2012 dx.doi.org/10.1021/ie202035n | Ind. Eng.Chem. Res. 2012, 51, 3108−3118

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media, which is important for understanding methane hydrate dissociation mechanism inside sediments in nature. The water transfer course when the core is water-unsaturated is also predicted by the simulator.

In addition, gas hydrates dissociation process is always accompanied by water transfer behavior in porous media, which may affect the effectiveness of dissociation. 19 Research on the sensitivity analysis of water saturation will be beneficial to understand the natural gas hydrates dissociation condition. Chuvilin20 was the first one to pay close attention to the water transfer behavior in gas hydrate formation processes in porous media, he and his partners observed that the appearance of clay particles in sands strongly changes the character of hydrate accumulation, decreasing water transfer during hydrate formation. After that, Kneafsey,21 Jin Shigeki,22 Kawasaki Tatsuji,23 and Peng Zhang19 performed the experiments on water transfer of gas hydrates formation and dissociation processes by means of experiments. Kneafsey, using CT (computed tomography) technology, found that water saturation changes affected the density much more strongly than hydrate formation, dissociation, gas pressure changes, or mechanical processes. Jin Shigeki determined the spatial distribution of the natural gas hydrates in sedimentary layers with a microfocus X-ray CT apparatus. Kawasaki Tatsuji also observed methane hydrate dissociation behavior in methane hydrate bearing sediments by X-ray CT scanner. Peng Zhang, using a novel apparatus with three pF-meter sensors, detected water content and temperature changes inside porous media successfully. Then, he studied water transfer characteristics inside nonsaturated media during methane hydrate formation and dissociation processes and water changes on the top, middle, and bottom locations of experimental media during the reaction processes. It showed that there were obvious methane hydrate formation configuration differences among different media. Minagawa24 used proton nuclear magnetic resonance (NMR) to measure pore size distribution of sediment in order to characterize methane hydrate-bearing sediment by pore size distribution and permeability. Sand sediment with different grain size distributions was measured as fundamental research and for application of natural methane hydrate bearing sediment. Furthermore, Sakamoto25 conducted an experimental study on consolidation and gas production behavior during MH dissociation by depressurization. On the basis of experimental results, Sakamoto carried out numerical simulation for MH dissociation process for depressurization and optimized relative permeability curves that dominated gas−water production behavior. However, few have developed numerical simulations focusing on this factor and analyzing it systematically. Therefore, in this study, in order to study the water phase on methane hydrate dissociation by depressurization, a laboratory-scale two-dimensional (2-D) axisymmetrical depressurization simulator was developed. The radial boundary heat conduction that causes hydrate dissociation adjacent to the wall is taken into consideration. The effect of water transfer on heat conduction and dissociation has been discussed. These models also apply new amendment formulas, such as calculation of relative permeability. Therefore, water transfer and water phase on methane hydrate dissociation by depressurization can be more accurately presented. Water-unsaturated core is a media in which initial water saturation is less than its bound water saturation. Methane hydrate water transfer characteristics during methane hydrate dissociation process are different in water-saturated media than they are in water-unsaturated

2. HYDRATE DISSOCIATION MODEL The general governing equations for hydrate dissociation in porous media have been derived by combining the continuity equation, the equation of motion, energy conversion equation, kinetic reaction equation, and the equation of state for three components (gas, water, and hydrate). These equations are based on the following assumptions: • Porous media are homogeneous, and solid phase (hydrate and porous) media are incompressible and stagnant. • Two-phase flow accords with Darcy’s law. The absolute permeability of porous media is the function of hydrate saturation. The relative permeability of gas and liquid determines the flow behavior of two-phase fluid. • Gas does not dissolve in water. • There is no ice phase during the whole dissociation. 2.1. Mass Conservation Equations. The cylindrical geometry is chosen to study the gas production by depressurization. The simulation for laboratory scale case can predict the behavior of gas production and the pressure, saturation, and temperature profile. The nomenclature and principles were cited by Liang.26 Equations 1−3 describe the mass balance of gas, water, and hydrate.

−

−

∂ 1 ∂ (r ρgvgr) − (ρ vgx ) + qġ + ṁ g ∂x g r ∂r ∂ = (φρgSg) ∂t

(1)

∂ 1 ∂ (r ρw vwr) − (ρ vwx ) + qẇ + ṁ w ∂x w r ∂r ∂ = (φρw S w ) ∂t

(2)

∂ (φρ hSh) (3) ∂t where r is the radial distance, ρg is the density of gas, ρw is the density of water, ρh is the density of hydrate, vgr is the radial velocity of gas, vwr is the radial velocity of water, vgx is the axial velocity of gas, vwx is the axial velocity of water, ϕ is the porosity, Sg is the saturation of gas, Sw is the saturation of water, and Sh is the saturation of hydrate. The boundary change of gas q̇̇g, the mass of gas for hydrate formation or dissociation ṁ g, the radial change of gas (1/r)(∂/∂r)(rρgvgr) and the axial change of gas (∂/∂x)(ρgvgx) combine total change of gas. The boundary change of water qw, the mass of water for hydrate formation or dissociation ṁ w, the radial change of water (1/r)(∂/∂r)(rρwvwr) and the axial change of water (∂/∂x)(ρwvwx) combine total change of water. The mass of hydrate for hydrate formation or dissociation is the total change of hydrate. The three-phase saturation meets the following equation: ṁ h =

Sg + S w + Sh = 1 3109

(4)

dx.doi.org/10.1021/ie202035n | Ind. Eng.Chem. Res. 2012, 51, 3108−3118


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The heat consumption in terms of hydrate dissociation q̇h is calculated as follows:

The velocities of gas and water are expressed by Darcy’s law; the equation for Darcy’s velocity is as follows:

vi = −

Kk ri ∇Pi μi

qḣ = ṁ h ΔHD

(i = g , w) (5)

where ṁ h is the mass of hydrate for hydrate formation or dissociation. ΔHD is the enthalpy change of hydrate for hydrate formation or dissociation and is calculated expressed as follows:

where Pi is pressure difference between gas and water and μi is the viscosity of gas or water. The relative permeabilities, krw and krg, of water and gas are calculated based on Corey’s model and expressed as follows:

⎛ Sw ⎞n w − S wr ⎜ Sw + Sg ⎟ k rw = ⎜ ⎟ ⎜ 1 − S wr − Sgr ⎟ ⎝ ⎠ ⎛ Sg ⎞ng − S gr ⎟ ⎜ Sw + Sg ⎟ k rg = ⎜ ⎜⎜ 1 − S wr − Sgr ⎟⎟ ⎝ ⎠

ΔHD = (446.12 × 103) − 132.638T

ṁ g Hg + ṁ w H w + ṁ h Hh = ṁ h ΔHd

(6)

dHi =

(7)

∂Hi ∂Hi dT + dPi − C pidT + σidPi ∂T ∂Pi (14)

∂Hs dT − CPSdT (15) ∂T where Cpi is the specific heat under constant pressure of phase i and σi is gas throttle coefficient of phase i. By the van der Waals equation, we calculate the gas throttle coefficient. Based on the data of Tester,28 the throttle coefficient of methane is given by dHs =

(8)

⎛ ∂Hg ⎞ ⎟ ≈ − 1.5 × 104 σg = ⎜⎜ ⎟ ⎝ ∂Pg ⎠T

(16)

2.3. Kinetics Equations. According to the dissociation reaction of hydrate, we can obtain the following equations:

ṁ h = ṁ g

NhM w + Mg Mg

(17)

NM ṁ w = ṁ g h w Mg

1 ∂ ⎛⎜ ∂T ⎞⎟ ∂ ⎛⎜ ∂T ⎞⎟ r λc + λc r ∂r ⎝ ∂r ⎠ ∂x ⎝ ∂x ⎠ ∂ − (r ρgvgrhg + r ρwrh w ) ∂r ∂ (ρ vgx hg + r ρwx h w ) + qġ hg + qẇ h w − ∂x g

(18)

where Nh is a coefficient of the decomposition reaction. On the basis of the model of Kim and Bishnoi,29 the gas productivity of hydrate dissociation reaction is

ṁ g = kdMgA(fe − f )

(19)

where kd is the reaction constant and f and fe are gas fugacity and equilibrium reaction fugacity, which are usually replaced by local gas pressure Pg and equilibrium pressure Pe, respectively. Equilibrium pressure is calculated using the eq 20.

+ qḣ + qiṅ ∂ = [(1 − Φ)ρshs + Φ(Shρ hhh + Sg ρghg ∂t

⎛ 9459 ⎞ Pe = 1.15 exp⎜49.3185 − ⎟ Te ⎠ ⎝

(9)

The conductivity coefficient of core λc is calculated as follows:

λc = λ s(1 − Φ) + Φ(λhhh + λ gSg + λ wS w )

(13)

(i = h , g , w)

2.2. Energy Conservation Equations. The energy balance eq 9 includes the following terms on the left-hand side of equations: the conductive (1/r)(∂/∂r)(rλc (∂T/∂r)) + (∂/∂x)(λc (∂T/∂x)) and the convective −(∂/∂r)(rρgvgrhg + rρwrhw) − (∂/∂x)(ρgvgxhg + rρwxhw) heat transfer, the heat input/output in terms of injection/production of gas q̇ghg and water q̇whw, and the heat consumption in terms of hydrate dissociation q̇h and heat input from surrounding q̇in. The right-hand side of the equation is the change in the enthalpy of the gas hg, water hw, hydrate hh, and sandstone hs.

+ S w ρw h w )]

(12)

The decomposing latent heat of hydrate is defined as Selim27 does, where ΔHD is enthalpy change of hydrate dissociation.

where Swr is the water residual saturation, Sgr is the gas residual saturation, and nw and ng are empirical constants. Equation 8 describes the absolute permeability of porous media with the presence of hydrate. In the equation, n is the permeability reduction index.

K = K 0(1 − Sh)n

(11)

(20)

⎛ ΔE ⎞ kd = k 0 exp⎜ − a ⎟ ⎝ RT ⎠

(10)

where λs is the conductivity coefficient of stone, λh is the conductivity coefficient of hydrate, λ g is the conductivity coefficient of gas, and λw is the conductivity of water.

(21)

According to ref 30, k0 = 3.6 × 10 mol·m ·Pa·s, −(ΔEa/R) = 9752.73 K. In eq 19, A is the interface area between hydrate and fluid phases, which is estimated using Amyx’s method31 in 4

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Figure 1. Schematic of hydrate core sample, computational grid, and location of different sections.

this paper.

Initial conditions are follows:

T = T0

Φ3e 2K

(22)

Φe = Φ(1 − Sh)

(23)

A=

Sg = Sg0

S w = S w0

(0 ≤ r ≤ R , 0 ≤ x ≤ L)

(26)

∂P = 0 (x = L ) ∂x ∂P ∂T = 0 (r = 0, R 0) = 0 (r = 0) ∂r ∂r

P = P0 (x = 0)

(24)

qiṅ = αA(Tb − T ) (r = R 0) ∂T = 0 (x = 0, L) (27) ∂x 2.5. Comparison of Numerical Simulation with Experiment Data. Masuda14 conducted the experiment by using a Berea sandstone core sample with a cylindrical geometry to investigate hydrate dissociation induced by depressurization. The experiment conditions are summarized in Table 1. Some assumptions that the core sample is homogeneous and the initial distributions of phase saturation, pressure, and temperature are uniform in the core sample are made. For the simulation, as shown in Figure 1, the 2-D axisymmetrical core is equally divided into 10 blocks in radial direction and 60 blocks in axial direction. Figure 2 shows that the simulated gas production largely matches the experimental data (see Table 1). The simulation

Here, Pc takes the format of the following function:32 Pce in eq 25 is nominal capillary pressure.

⎛ Sw ⎞nc − S wr ⎟ ⎜ Sw + Sg Pc ⎟ e = ⎜ Pc ⎜ 1 − S wr ⎟ ⎝ ⎠

Sh = Sh0

The following boundary conditions are imposed:

The pressure difference between the gas phase and water phase is Pc, defined as follows:

Pc = Pg − Pw

P = P0

(25)

2.4. Initial and Boundary Conditions. In this paper, the simulation based on Masuda’s14 experiment results is used as the base case. The core is submerged in water bath, the temperature of the water bath is 275.45 K, which is the same as the temperature of the inner core, and the sediment in the core is water-saturated. Because the decomposition reaction absorbs heat, when outlet pressure is reduced to 2.84 MPa, the gas hydrate begins dissociating. As shown in Figure 1, the outlet valve is defined on the left of the core. On all the walls and the right side of the core, on-slip boundary condition is assumed. Free convective heat transfer between the circumferential wall and the surrounding is assumed, and the boundary condition for the ends of the core is adiabatic. Table 1 shows the initial conditions for the simulation. Table 1. Experimental Conditions in the Hydrate Dissociation Experiment by Masuda14 param.

value

core length, L core length, L intrinsic porosity, Φ0 outlet pressure, P0 core pressure, Pc core temp., T0 hydrate saturation, Sh water saturation, Sw gas saturation, Sg bath temp., Tb intrinsic permeability, K

30 cm 5.1 cm 0.182 2.84 MPa 3.75 MPa 275.45 K 0.443 0.35 0.207 275.45 K 97.98 md

Figure 2. Cumulative gas production comparison between the experimental data and the simulation results.

predicts that the core sample generates about 9033 cm3 of methane gas when all the hydrate in the core dissociates. 3111



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Masuda,14 however, reported generation of about 9067 cm3 of methane gas, which is slightly higher than the simulation results. It is seen that the experimental data is higher than the simulated results at the beginning (before 95 min). There are two reasons that may cause the difference. One reason is that because the pressure of core is 3.75 MPa, which is much higher than the outlet pressure (see Table 1), the cumulative gas production of the experiment tends to bigger than the simulated result. The other one is that, in the simulation condition, the hydrate saturation in the core is set to be a mean value. However, in the real hydrate formation situation inside the core, the hydrate saturation near the outlet part is always higher than the inside part, due to gas concentration and porous media permeability. Figure 3 shows variations of the temperature at points (a−c) of the core sample and the comparison between the simulated

simulation results and the experimental data are due to these approximations.

3. RESULTS AND DISCUSSION This section reports how the water effect acts on the cause of hydrate dissociation by depressurization. It compares distributions of temperature, pressure, hydrate saturation, and water saturation to analyze the relationship between the front interface movement and the water saturation change in the core. Furthermore, it simulates the cause of water saturation change to discuss water transfer. Finally, it studies the effects of different initial water saturation on hydrate dissociation to discover the effects on gas generation and the reasons for them. 3.1. Dissociation Interface and Water Saturation. The simulated distributions of temperature, hydrate saturation, and water saturation are presented in this section. The temperature of water bath is 275.45 K, the outlet pressure is 2.84 MPa, the initial temperature of core inside is 275.45 K, the initial pressure of core inside is 3.75 MPa, the initial hydrate saturation is 0.443, and the initial water saturation is 0.35. When gas hydrate dissociation reaches the 60 min mark, the dissociation interface is almost located in the middle of the core. At this location, the relationship among the front dissociation interface, phase saturation, and temperature can easily be observed. Figure 4 shows that hydrate saturation distribution near the outlet port part (0−0.16 m core length) is mainly affected by temperature distribution, and hydrate saturation distribution of the front dissociation interface (0.16−0.22 m) is affected by distribution of water saturation gradient change. Comparing parts a and b of Figure 4 (0−0.16 m), hydrate saturation

Figure 3. Simulation and experimental comparison of temperature variations at different sections.

results with experiment data.14 As the hydrate dissociates, the temperatures in all the points of the core sample for both simulation and experimental data decrease to the minimum, and then, they increase and approach the surrounding temperature. This is because hydrate dissociation is an endothermic process and the free convective heat transfer at the wall boundary cannot supply sufficient heat for a rapid dissociation reaction. However, there are some quantitative differences between the simulated results and the experimental data. The relative deviation between the simulated results and the experimental data is 25%, after 95 min the relative deviation of all three sections is below 14%. Before 95 min, relative deviations are all beyond 36%. It is conjectured that steam breakthrough phenomena may happen before 95 min. In that case, the heat conduction and heat transfer would be strengthened at this part of core in the experiment situation. When the hydrate dissociates, it absorbs heat from the bigger part of core and makes the temperature of section a increase slowly. In addition, the core is merged in the water bath (the temperature is higher), and so, the temperature of simulation around 273.8 K between 30 and 70 min is higher than that in the experiment data. Similarly, the temperature of section c will drop faster than the simulated result before 95 min. Besides, the value of such as overall heat transfer coefficients for natural convection to the surrounding and typical material properties may not fit the fact. The differences between the

Figure 4. Simulated distribution of (a) temperature, (b) hydrate saturation, (c) water saturation, and (d) pressure, at 60 min. 3112



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distribution is similar to temperature distribution. Because, as shown in Figure 4c, in this part the water saturation is nearly unchanged, it just slowly declines to 0.25 (bound water saturation). However, temperature is the dominating cause of dissociation. In addition, water saturation change happens right after the hydrate saturation change as the dissociation course goes on. Comparing parts b and c of Figure 4, the positions of hydrate front interfaces and water saturation change are inosculated. Additionally, the pressure change area takes up some of the same space as the front dissociation interface area. Comparing parts b and d of Figure 4, the positions of hydrate front interfaces and pressure change are similar (0.13−0.16). However, in the back part of core, they are different, especially between 0.18 and 0.3, and pressure change does not present the hydrate dissociation near wall of the core, rather water saturation change does. Therefore, the front interface is in an area where water saturation distributes in gradient. Figure 5 shows the water saturation, hydrate saturation, temperature, and pressure distributions at 140 min. As the

temperature; thus, the temperature near cylindrical surface of core is higher. Data in Figure 4b shows that the dissociation front interface reaches the middle of core length at 60 min. Though hydrate saturation near the outlet port goes down, the hydrate saturation stays in 0.443 at the closed end of core (right side of the core) as the initial hydrate saturation. 3.2. Water Transfer. In porous media, when the velocity is not high, water flow follows Darcy's law (see eq 5). Through water saturation, core porosity, and density of water under different temperatures and gridding volumes, the distribution of water content at different times could be calculated. To study the process of water transfer, the changes of water saturation at different times are simulated. Similarly, the temperature of water bath is 275.45 K, the outlet pressure is 2.84 MPa, the initial temperature of core inside 275.45 K, the initial pressure of core inside is 3.75 MPa, the initial hydrate saturation is 0.443, and the initial water saturation is 0.35. Figure 6 shows the distribution of water saturation from 40 to 80 min. At the beginning of dissociation process, water stays

Figure 6. Simulated distribution of water saturation at (a) 40 min, (b) 60 min, and (c) 80 min.

at the core, and the water saturation remains unchanged at 0.35 (initial water saturation). When the pressure comes down, the hydrate begins to dissociate, and water is produced simultaneously at the outlet port. The water produced there is driven out of the core by gas pressure. Then, the water saturation comes down gradually until bound water saturation (0.25). The finding that water is driven by gas is logical. Because the velocity of water transfer is slower than that of gas transfer in the porous media (through eq 5 water has higher viscosity compared to that of gas). Moreover, unit volume methane hydrate usually produces a lot of gas but little water in the meantime. Large amounts of gas would drive out the water. As dissociation continues, water saturation comes down and gas saturation increases simultaneously. Data in Figure 6a also shows that the line of front dissociation interface is not perpendicular to the core axis. These results are understandable because the upward side could easily get heat from the core wall, which is immersed in a

Figure 5. Simulated distribution of (a) temperature, (b) hydrate saturation, (c) water saturation, and (d) pressure, at 140 min.

dissociation goes on, the temperature level has a higher effect than water saturation after the front interface reached the end of the core. As shown in Figure 5, water saturation is very close to bound saturation in the whole core, and the pressure also falls to 2.8 MPa. Though water saturation still affects the dissociation course, its effect lessens gradually. The predictions correspond with the real experiment situation shown in Figure 4a. When the temperature near the outlet port (left side of core) goes down, the temperature near the dissociation interface is lower. Additionally, the cylindrical surface of the core (upward side of core) is heated at a constant 3113



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constant temperature water bath. This made hydrate near upward side dissociate faster and produce more water. Furthermore, the pressure at the opened end of the core is lower, which made water flow to the outlet port. Therefore, under changes in temperature and pressure, water saturation distribution slants in gradient. Figure 7 shows the distribution of gas saturation from 40 to 80 min. Contrary to the results shown in Figure 7, the

Figure 8. Simulated distribution of water saturation: (a) initial temperature is 275 K at 60 min; (b) initial temperature is 275.45 K at

Figure 7. Simulated distribution of gas saturation at (a) 40 min, (b) 60 min, and (c) 80 min.

saturation of methane gas increases gradually. Obviously, the gas saturation is higher at the outlet of the core and the position near the wall of core. This is because, the methane hydrate dissociates fast at this place as was mentioned previously. Compared with Figure 6, the course of gas driving water is present. In order to analyze the effects of bath temperature and outlet pressure on water transfer, simulations with different bath temperatures and outlet pressures are performed. In these simulations, bath temperature or outlet pressure is the unique variable, other initial conditions can be found at Table 1. Figure 8 represents the distribution of water saturation with different bath temperatures (275 K, 275.45 K, and 276 K) at 60 min. These figures show that higher bath temperatures lead to quicker water transfer. From Figure 8, in case of 276 K, the water saturation change area almost reaches the end of the core. Under such temperature, the wall effect is clearly shown. Figure 9 shows simulations with different outlet pressures (2.7 MPa, 2.84 MPa, and 3 MPa); lower outlet pressure promotes water transfer. As shown in Figure 9, the water saturation change area reaches the middle of the core, which is slower than the case of 276 K. 3.3. Water Sensitivity Analysis. The characteristics of water flow usually affect the rate of gas production, and initial water saturation is one of the most important characteristics. This factor will affect phase velocity and heat conduction. The simulation conditions almost coincide with Table 1, except for initial water saturation. Through different initial water

Figure 9. Simulated distribution of water saturation with initial outlet pressure of (a) 2.7 MPa, (b) 2.84 MPa, and (c) 3 MPa, at 60 min.

saturation amounts, water sensitivity analysis is divided into three groups. Figure 10 shows the simulated distribution of water pressure (MPa), when initial Sw = 0.30 (a), Sw = 0.35 (b), and Sw = 0.40 (c) at 80 min. As seen from Figure 10a, at the beginning of dissociation process, gas generation rate rises quickly at the beginning, grows relatively more slowly later (5−20 min), and gradually increases growth rate (between 20−100 min). Then, in the middle period of time (100−160 min), the rate of these three situations drops sharply one by one. As a result, the rate (Sw = 0.40) gradually climbs to the head of these three situations. In last period of time (after 160 min), all rates come down slowly and tend to be identical. Data in Figure 10b shows 3114



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Figure 10. (a) Gas generation rate time evolution for different initial water saturation cases; (b) cumulative gas production time evolution for different initial water saturation cases.

that though the higher initial water saturation the slower cumulative gas production, the cumulative gas production in these three cases reached nearly 9000 cm3 in the end. It is shown that lower initial water saturation only benefits gas generation rate at the beginning (before 80 min), but it negatively relates to cumulative production. To investigate the cause of differences among these three cases before 100 min, the simulated distribution of pressure with different initial water saturation is analyzed at 100 min, as shown in Figure 11. At this time, the case with Sw = 0.30 gets

Figure 12. Simulated distribution of core temperature with (a) initial Sw = 0.30, (b) initial Sw = 0.35, and (c) initial Sw = 0.40, at 160 min.

Figure 13. Simulated distribution of core hydrate saturation with (a) initial Sw = 0.30, (b) initial Sw = 0.35, and (c) initial Sw = 0.40, at 160 min.

groups are simulated. Though when Sw = 0.30, the core is under the best temperature environment for decomposition in the middle period of time (see Figure 10); as shown in Figure 12, the hydrate saturation still remains 0.443 where the core length is 0.30 m. The gas production rate when Sw = 0.40 catches up and rises to be the fastest case. This is because when Sw = 0.40, certain parts of the hydrate still remain to be decomposed, which causes gas generation rate to be at the highest level between 100 min and 160 min (see Figure 10). After that, heat transfer would govern the course of dissociation while pressure remains constant. Because methane dissociation reaction is an endothermic process, the temperature of the core would drop. However, heat transfer benefits

Figure 11. Simulated distribution of water pressure with (a) initial Sw = 0.30, (b) initial Sw = 0.35, and (c) initial Sw = 0.40, at 100 min.

the fastest pressure transfer; the pressure reaches 3.4 MPa where core length is 0.3 m. As shown in eq 19, a larger pressure difference causes faster dissociation. Those results suggest that, at the first period of time (before 100 min) in Figure 10a, higher water saturation leads to lower pressure transfer, which causes lower gas generation rate in this period. To investigate the cause of differences among these three cases between 80 min and 120 min, the distribution of core temperature at 160 min (see Figure 12) and distribution of core hydrate saturation at 160 min (see Figure 13) of these three 3115



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from water compared with gas. Methane hydrate in the core can absorb more heat from the tube wall if the water saturation is higher. Equations 19 and 21 show that higher temperature causes faster dissociation. As a result, higher water saturation leads to higher gas generation rate in the last period of time (after 160 min). From these three stages, the first stage (before 100 min) leads the whole process. Pressure is the major influential element. Though temperature condition also affects gas generation, there is only slight difference at the tail end of the core (see Figure 12). Actually, the reason that gas generation rate (Sw = 0.40) gradually climbs to the head of these three situations is because certain parts of hydrate still remain to be decomposed, which can attribute to the up-stage dissociation result. In the course of hydrate dissociation, conduction and conviction affect the distribution of core temperature. The thermal conductivity of water is higher than that of methane gas; thus, increasing the water saturation is beneficial to the thermal conductivity of core. However, water phase transfer is slow in the porous media; the convective heat transfer of gas phase is stronger than water phase. In other words, higher water saturation obstructs convective heat transfer. In Figure 12, when Sw = 0.30, the core is under the best temperature environment for decomposition at 160 min. This proves that convection plays a more important role in the course of hydrate dissociation. Thus, in order to increase the velocity of gas generation rate, how to strengthen the gas flow and draw water out of core is a point of view. 3.4. Forecast for Water-Unsaturated Core. As mention previously, characteristics of water flow affect the course of hydrate dissociation. When the core is water-saturated, gas will drive water to the outlet. The saturation of water will gradually decrease into bound saturation, because water will obstruct pressure transfer and slow down the velocity of dissociation. However, if the core is water-unsaturated, the pore will absorb the water. This would change the flow of water and cause heat to transfer differently. In the formal experiment situation, the water saturation is 0.35, which outstrips the water bound saturation (0.25). Here, the initial water saturation is 0.15 below the bound saturation. Because, in this situation, the attraction is stronger than the repulsive force between the water and the pore, water saturation would increase slowly. Furthermore, methane gas bubbles seem to cause no obvious effects on water saturation change. Therefore, this simulation assumes that the bigger difference in values between real-time water saturation and bound saturation, the quicker the pore absorbs water. Water will remain fixed in the core until it saturates beyond the bound saturation. Similarly, the simulation considers the process of heat transfer and mass transfer. The temperature of the water bath is 275.45 K, the outlet pressure is 2.84 MPa, the initial temperature of core inside 275.45 K, the initial pressure of core inside is 3.75 MPa, and the initial hydrate saturation is 0.44 Figure 14 shows the distribution of water saturation from 40 to 80 min when the initial water saturation is 0.15. At the 40 min point, water saturation changes happen in the middle of the core. Water saturation rises slowly as the course of dissociation begins, and the value is higher near the outlet. Then, in the 60 min and 80 min periods, water saturation gradually reaches 0.23, which is almost bound saturation, 0.25, but hardly exceeds, at the outlet part. The water saturation cannot

Figure 14. Simulated distribution of water saturation at (a) 40 min , (b) 60 min, and (c) 80 min, when the initial water saturation is 0.15.

increase quickly, mainly because the unit volume methane hydrate releases water less than unit volume. In addition, gas drives the water to the outlet when the water saturation beyond the bound saturation.

4. CONCLUSION Based on the analytical and simulated investigations presented in this paper, the following conclusions can be drawn: 1. Water phase has a clearly influential effect in dissociation course. The front dissociation interface occurs in an environment of water saturation gradient. 2. As dissociation continues, the effect of water will lessen slowly and temperature will dominate that course gradually. 3. When pressure comes down, dissociated water is driven by gas, and the water saturation comes down into bound water saturation from the dissociation interface to the outlet port. 4. Because the water phase slows down pressure transfer at the beginning of dissociation, especially when initial water saturation is higher, the higher initial water saturation leads to a slower rate of hydrate dissociation at the beginning. However, this rate of hydrate dissociation would rise and even catch up to the rate of the lowest initial water saturation in the middle period. 5. In the course of hydrate dissociation, conduction and conviction affect the distribution of core temperature. However, convection plays a more important role in the course of hydrate dissociation. 6. Water saturation rises until it reaches bound saturation; when the core is water-unsaturated, the saturation is higher near the outlet part. Future studies should consider large scale water movement, and heat transfer and pressure transfer affected by changes to water qualities in different water phases.

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Corresponding Author

*Telephone: +86 411 84706722. Fax: +86 411 84706722. E-mail: [email protected], [email protected]. 3116



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ACKNOWLEDGMENTS This study has been supported by National Natural Science of China (Grant No. 51006017), National High Technology Research and Development Program of China (Grant No. 2006AA09209-5), State Key Development Program for Basic Research of China (Grant No. 2009CB219507), and Natural Science Foundation of China (Grant No. 50736001).

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NOMENCLATURE As = reaction ratio surface area (m2). C = specific heat (J/(kg·K−1)). H = enthalpy of phase (J/kg). K = absolute permeability (md). k = relative permeability of gas or water. k0 = intrinsic reaction constant. M = molecular weight. ṁ = mass of phase for hydrate formation or dissociation (kg/(s·(m3)−1)). N = permeability reduction factor, N = 15. Nh = hydrate number. nc = empirical constants in eq 23, nc = 0.65. ng = empirical constants in eq 7, ng = 0.4. nw = empirical constants in eq 6, nw = 0.2. P = pressure (Pa). Pc = capillary pressure (Pa). Pce = Enter pressure in eq 26, Pce = 1 KPa. Pe = equilibrium pressure (Pa). P0 = outlet pressure (Pa). q̇ = energy source (J). R = universal gas constant, R = 8.31 (J/(mol·K−1)). r = radial distance (m). S = saturation of phase. Sgr = gas residual saturation. Swr = water residual saturation. T = temperature (K). Tb = surrounding temperature (K). Te = equilibrium temperature (K). t = time (s). u = velocity of fluid phase (m/s). x = axis distance (m).

Symbols

Φ = porosity. Φe = efficient porosity. μ = viscosity (Pa s). λ = conductivity coefficient (w/(m·K−1)). ρ = density of phase (kg/m3). σ = gas throttle coefficient. Subscripts

g = gas phase. h = hydrate phase. in = heat from surrounding. s = sandstone phase. w = water phase.

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Numerical Simulation and Analysis of Water Phase Effect on Methane

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