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Energy and entropy analyses of hydrate dissociation in different scales of hydrate simulator
Energy 102 (2016) 176e186
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Energy and entropy analyses of hydrate dissociation in different scales of hydrate simulator Jing-Chun Feng a, b, c, d, 1, Yi Wang a, b, d, 1, Xiao-Sen Li a, b, d, * a
Key Laboratory of Gas Hydrate, Guangzhou Institute of Energy Conversion, Chinese Academy of Sciences, Guangzhou 510640, PR China Guangzhou Center for Gas Hydrate Research, Chinese Academy of Sciences, Guangzhou 510640, PR China c University of Chinese Academy of Sciences, Beijing 100083, PR China d Guangdong Key Laboratory of New and Renewable Energy Research, Development and Application, Guangzhou 510640, China b
a r t i c l e i n f o
a b s t r a c t
Article history: Received 8 January 2016 Received in revised form 13 February 2016 Accepted 14 February 2016 Available online xxx
To investigate the effect of the reservoir scale on hydrate dissociation by depressurization in conjunction with warm water stimulation with dual horizontal wells, experiments of hydrate dissociation by such method have been carried out in CHS (Cubic Hydrate Simulator) and PHS (Pilot-scale Hydrate Simulator). The results show that there is little difference of temperature variation during the depressurizing stage with different scales of hydrate simulator. However, during the constant-pressure stage (the injection stage), the difference is obvious, and the heat transfer rate in the PHS is faster than that in the CHS. Additionally, the system entropy production during the injection stage is the largest, implying that the injection stage is the main source of energy consumption. Moreover, both the ratio of the amount of the dissociated gas in the PHS to that in the CHS and the ratio of the entropy production for hydrate dissociation with the PHS to that with the CHS approximately equal to the volume ratio of the PHS to the CHS. © 2016 Elsevier Ltd. All rights reserved.
Keywords: Hydrate Depressurization Thermal stimulation Horizontal well Reservoir scale Entropy analysis
1. Introduction Natural gas hydrate is widely distributed in the permafrost regions and the offshore oceanic regions, where the local environments of high pressure and low temperature are satisfied. In nature, gas hydrate exists as an ice-like solid in which the guest molecule (mainly methane) is encapsulated in the hydrogen-bonding cages comprised by water molecules [1,2]. Accurate estimation of the amount of gas hydrate on the earth is challenging, and the common perception is that the total carbon content in gas hydrate is more than twice as much as that in all of the conventional fossil fuels [3]. If 1 cubic meter of gas hydrate is dissociated at standard pressure and temperature, 164 m3 of gas and 0.8 m3 of water can be produced. The previous studies [4,5] indicate that the energy density of methane hydrate is 2e5 times larger than that of the conventional natural gas, and 10 times larger than the other kinds of unconventional gas sources, such
* Corresponding author. Key Laboratory of Gas Hydrate, Guangzhou Institute of Energy Conversion, Chinese Academy of Sciences, Guangzhou 510640, PR China. Tel.: þ86 20 87057037; fax: þ86 20 87034664. E-mail address: [email protected] (X.-S. Li). 1 These authors contributed equally to this work. http://dx.doi.org/10.1016/j.energy.2016.02.081 0360-5442/© 2016 Elsevier Ltd. All rights reserved.
as shale gas and coal bed gas. Generally, methane hydrate is considered to be a potential energy resource on account of the huge gas reserves in hydrate resource and the high density of methane hydrate [6,7]. Moreover, gas hydrate has been widely applied in the process of carbon dioxide capture [8e10], hydrogen storage [11] and flow assurance of the seabed pipeline [12]. Gas hydrate is dissociated when the stable condition of pressure and temperature is disturbed [13]. Up to now, the conventional research methods for hydrate dissociation are depressurization [14e18], thermal stimulation [19e22], inhibitor injection [23e25], and carbon dioxide replacement [26]. From the perspectives of high energy ratio, high production efficiency, and the avoidance of ice blockage and hydrate re-formation, the combination of depressurization and thermal stimulation is regarded to be a profitable method for hydrate dissociation [27e29]. Due to the huge energy loss with the increase of water injection temperature, Feng et al. [30] reported that high temperature (beyond 40 C) injection was not economic for hydrate dissociation, and they further indicated [31] that the optimal injected temperature for hydrate dissociation in a 5.83 L cubic hydrate simulator was 38e39 C by using the evaluation methods of entropy production minimization and energy ratio maximization. The hydrate dissociation behavior and the production performance of the hydrate reservoir are strongly
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affected by the scale of hydrate reservoir. The numerical research of Tang et al. [32] showed that the controlling mechanism of hydrate dissociation in the reservoir of small scale is kinetic-controlled. Whereas the controlling factor of hydrate dissociation in large scale hydrate reservoir is fluid flow. In addition, the analytical modeling of Wang et al. [33] also indicates that hydrate dissociation in the large scale hydrate reservoir is strongly dependent on the characteristics of heat transfer, mass transfer, and fluid flow. Both the experimental and numerical analyses of Li et al. [34] showed that the kinetic limitation was weak for hydrate dissociation by depressurization in a 117.8 L hydrate simulator. In general, the hydrate reservoir scale is an important factor which affects gas production from the hydrate-bearing reservoir. Up to now, the investigation of reservoir scale for hydrate dissociation mainly focuses on the vertical well configuration and the behaviors of gas and water production. There is short of the investigation of the effect of reservoir scale on horizontal well configuration and the optimization of the operating condition during hydrate dissociation. Therefore, the research of the effect of reservoir scale on the optimization of the operating condition for hydrate dissociation, especially with the horizontal well system, is desperately needed. Hydrate dissociation is an irreversible process during the laboratory-scale experiment. For the irreversible process, entropy analysis, which is the application of the second law of thermodynamics, has been considered as an efficient way that shows the sources of energy losses and what modifications should be conducted to increase the energy efficiency [35]. Entropy generation is proportional to the lost work in an irreversible process, and the entropy generation is contribute to explain the optimal conditions for energy losses [36]. The method of entropy generation minimization which means the minimization of energy consumption, has been widely used in the optimal processes of the cogeneration plant [37], the distillation [38], the heat convection in porous media [39], the heat engines [40], and so on. Based on the minimum entropy generation theory, Feng et al. [31] has obtained the optimal temperature range for hydrate dissociation in a 5.83 L reactor with the dual horizontal wells. However, there is lack of the evolution of the entropy generation with different scales of reservoir.
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The main purposes of this work are the investigations of the evolutions of hydrate dissociation behaviors and entropy production under different scales of hydrate reservoir. Hydrate samples were synthesized in a 5.83 L CHS (Cubic Hydrate Simulator) and a 117.80 L PHS (Pilot-scale Hydrate Simulator). Considering the advantage of horizontal well pattern over the vertical well pattern [41,42], the dual horizontal wells were set as the production scenario. The pressure and temperature condition of hydrate formation and dissociation were originated from the exploration data of hydrate accumulation in the South China Sea. The behaviors of gas production, water production, hydrate dissociation, and entropy production in different scales of hydrate reservoir were obtained. 2. Experimental apparatus and process 2.1. Experimental apparatus The schematic of the two apparatus are shown in Fig. 1. The CHS is a cubic hydrate simulator with the side length of 180.00 mm. The diameter of the PHS is 500.00 mm and the height of the PHS is 600.00 mm. As shown in Table 1, the inner volume of the CHS and the PHS is 5.83 and 117.80 L, respectively. The components of the two apparatus are similar. The differences are that the volume of the PHS is almost 20 times larger than that of the CHS, and the PHS is placed in a cold room. As shown in Fig. 1, the high pressure reactor made from stainless steel 316 is the core of the apparatus. An inlet pressure transducer and an outlet pressure transducer are placed in the bottom and top of the reactor, respectively. The CHS is immersed in a water bath (15e30 C, ±0.1 C) to ensure the Table 1 Parameters of methane hydrate formation in the CHS and PHS.
Inner Volume (L) Pore Volume (mL) Bath Temperature (k) P0 (MPa) Pend (MPa) Tend (k)
Fig. 1. Schematic of the CHS and PHS.
CHS
PHS
5.83 2752.00 281.15 20.05 13.400 281.85
117.80 51,360.00 281.15 19.63 13.70 281.87
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stability of the required temperature environment. Both the water jacket (15e30 C, ±0.1 C) around the PHS and the resident cold room (8e30 C, ±2 C) are performed as the safeguard to guarantee the required temperature condition. Two gas flow meters are used to meter the amount of the injected and the produced methane gas, respectively. The temperature and the amount of water injection are controlled by a heater and a metering pump, respectively. The amount of the produced water is measured by a balance. The working pressure is adjusted by a back-pressure regulator. Figs. 2 and 3 give the schematic diagram for the inner design and well configuration of the CHS and PHS, respectively. As described in Fig. 2, the inner space of the CHS is evenly divided into 4 isometric regions by 3 horizontal layers. The injection well (Well HC) is set on the lowest layer (Layer C), and the production well (Well HA) is placed on the uppermost layer (Layer HA). There are 25 (5 5 ¼ 25) thermal couples evenly distributed on each of the horizontal layer. Thus, a total of 75 (25 3 ¼ 75) thermal couples are installed in the CHS. As shown in Fig. 3, the inner design and the well configuration in the PHS is similar to that in the CHS. The difference is that there are 49 (7 7 ¼ 49) thermal couples on each of the horizontal layer, and the total thermal couples in the PHS is 147 (49 3 ¼ 147).
immediately. Table 2 shows the detailed parameters of hydrate dissociation. To begin with, the upper horizontal well was opened for hydrate dissociation. When the pressure in the reactors declined to 4.7 MPa, warm water was injected into the reservoir from the lower horizontal well. The water injection rate for the CHS was 20 mL/min. Based on the scaling-up modeling, the corresponding water injection rate for the PHS was 207 mL/min [43]. During the injection process, the pressures in the reactor were kept as constant (4.70 MPa) until the end of the dissociation experiments. The detailed information of hydrate formation and dissociation also has been introduced in the previous studies [20,27,31,41].
2.2. Experimental process
where Qh is the quantity of heat performed for hydrate dissociation. Qres is the quantity of heat releasing from the cooling down of the reservoir. Qenv is the quantity of heat exchanging with the surrounding environment. Qgp and Qwp are the quantity of heat applied for gas production and water production, respectively. The detailed calculation methods of the items in Eq. (1) are as follows:
Table 1 gives the specific parameters for hydrate formation in the two reactors. Firstly, the two reactors were suffused with silica sands. The grain size of those silica sands ranges from 300 to 450 mm. After sands filling, both the porosity of the CHS and PHS are 48%. Then, the precalculated amount of deionized water and pure methane gas were injected into the two reactors, making the pressures in the reactors increase to approximately 20 MPa [31,41]. All the outlets were kept closed afterwards. When the pressures in the reactors decrease to the desired value, the formation process was terminated. The hydrate dissociation experiments followed the completion of hydrate formation
3. Determination of entropy production 3.1. Depressurization process According to the law of conservation of energy, the energy equation for the system during the depressurization is described as Eq. (1).
Qh þ Qres þ Qenv þ Qgp þ Qwp ¼ 0
Qh ¼ Nh DHh
(1)
(2)
where Nh is the molar quantity of hydrate dissociation, and DHh stands for the dissociation heat of hydrate, which is used as 54.1 kJ/ mol in this work [31].
Fig. 2. Inner design and well configuration in the CHS.
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179
Fig. 3. Inner design and well configuration in the PHS.
Table 2 Conditions of methane hydrate dissociation in the CHS and PHS.
Initial Gas Saturation Initial Water Saturation Initial Hydrate Saturation Production Pressure(MPa) Injection Temperature(k) Injection Rate (mL/min)
Qres
Qres ¼
Cs mso;j þ Cg mgo;j þ Cw mwo;j T1;j T0;j
(4)
j¼1
CHS
PHS
58.00% 12.00% 30.00% 4.70 311.38 20.00
60.00% 10.00% 30.00% 4.70 311.38 207.00
¼ Cs mso þ Cg mgo þ Cw mwo ðT1 T0 Þ
j¼n X
where mso,j, mgo,j, and mwo,j are the mass of the tiny part of the silica sand, methane gas, and water, respectively. n is 75 and 147 for the CHS and the PHS, respectively. T1,j and T0,j are the temperatures of the tiny part at the end and the initial point of the depressurization process, respectively.
Qgp ¼ Cg mgp ðT3 T2 Þ (3)
where Cs, Cg, and Cw are the specific heat of the silica sand, methane gas, and water, respectively. mso, mgo, and mwo are the corresponding original mass of the silica sand, methane gas, and water in the reservoir before the depressurization process. T0 and T1 are the temperatures of the reservoir at the beginning and the ending points of the depressurization process. The distributions of sand, gas, and water in the reservoir at the end of the depressurization process are irregular. In order to explain the temperature in the reactor as accurate as possible, the reservoir can be divided into n tiny parts in accordance with the distribution of the thermocouples, and the distributions of sand, gas, and water in each tiny part can be considered to be uniform. As shown in Figs. 2 and 3, n is 75 and 147 for the CHS and the PHS, respectively. The temperature and mass distributions of gas, water, and hydrate in each tiny part can be regarded as identical, and the central position of each tiny part is assumed to be the location of the corresponding thermal couple. Therefore, the temperature measured by each thermal couple can be considered to be the temperature of the corresponding tiny part, and Eq. (3) can be transformed to the following equation [31]:
(5)
where mgp is the mass of the produced gas. T2 and T3 are the temperatures at the outlet in the initial and the end of the depressurization process, respectively. On account of the variation of T3 over time, the total amount of produced gas is divided into several parts (m) to describe the temperature at the wellhead as accurate as possible. During each part of gas production, the temperature variation at the outlet can be neglected. Therefore, the temperature at the outlet can be considered as constant during each small part of gas production, and Eq. (5) can be transformed to the following equation:
Qgp ¼
iX ¼m
Cg mgp;i T3;i T2
(6)
i¼1
where mgp,i is the mass of the small part of produced gas, and T3,i is the corresponding temperature at the outlet. Similarly, the quantity of heat applied for water production can be expressed as follows:
Qwp ¼ Cw mwp ðT3 T2 Þ ¼
i¼m X i¼1
Cw mwp;i T3;i T2
(7)
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Combining and solving Eqs. (1), (2), (4), (6) and (7) simultaneously, Qenv can be obtained for the depressurization process. For the depressurization process, the entropy production in the whole system (DSsystem) from the starting point to the ending point is shown in Eq. (8).
DSsystem ¼ DShyd þ DSgp þ DSwp þ DSres þ DSew þ DSenv
(8)
where DShyd is the entropy change of the hydrate in the reservoir caused by phase transformation. DSgp and DSwp are the entropy productions due to gas and water production, respectively. DSres represents the entropy production of the reservoir due to temperature change. DSew is the entropy production due to the volumetric change of gas in the gas production process. DSenv is the entropy production of the environment. The specific calculation processes for these items are as follows:
DShyd ¼
DSgp ¼
Qh N DHh ¼ h Tequ Tequ
i¼m X
Cg mgp;i ln
i¼1
DSwp ¼
i¼m X
(10)
T3;i T2
(11)
ZT1 DSres ¼ DSso þ DSgo þ DSwo ¼
Cs mso þ Cg mgo þ Cw mwo dT T
T0
T ¼ Cs mso þ Cg mgo þ Cw mwo ln 1 T0 ¼
Qinj ¼ Qws þ Qwp ¼ Cw mws ðT1 T4 Þ þ Cw mwp ðT3 T4 Þ ¼
j¼n X
i¼m X Cw mws;j T1;j T4 þ Cw mwp;i T3;i T4
j¼n X T1;j Cs mso;j þ Cg mgo;j þ Cw mwo;j ln T0;j j¼1
where T4 is the initial temperature of the injected water. wdescribed as the following equation: j¼n X Qwd ¼ Cw mwd T1 Tequ ¼ Cw mwd;j T1;j Tequ
where Tequ is the equilibrium temperature of hydrate dissociation at the working pressure (4.7 MPa). Consequently, the quantity of heat exchanging with the surrounding environment during the injection process can be acquired by combining and solving Eqs. (2), (4), (6) and (15)e(17) simultaneously. For the injection process, the entropy production of the total system from the initial to the ending point is drawn as follows:
þ DSpump
j¼1
(18) (12)
Pe DSew ¼
V2
dV V1
Tenv
Qenv Tenv
The computational methods of DShyd, DSgp, DSres, DSew, and DSenv in Eq. (18) are similar to Eqs. (9), (10), and (12)e(14). The detailed information of the other items in Eq. (18) is explained as follows:
(13) ZT1
where V1 and V2 are the volumes of the gas in the reservoir with high pressure and under the standard condition, respectively. Tenv is the temperature of the environment.
DSenv ¼
(17)
j¼1
DSsystem ¼ DSinj þ DShyd þ DSres þ DSgp þ DSwd þ DSenv þ DSew
j¼n Y T1;j ¼ Cs mso;j þ Cg mgo;j þ Cw mwo;j ln T0;j
Z
(16)
i¼1
j¼1
T3;i T2
Cw mwp;i ln
i¼1
(9)
There is an assumption that the amount of water production is from water injection [31], and the amount of water from hydrate dissociation stayed in the reservoir, because the amount of water injection is far larger than that of water from hydrate dissociation and the pore space of the reservoir is large enough for the accommodation of the water from hydrate dissociation. The calculation methods of Qh, Qres, and Qgp in Eq. (15) are similar to Eqs. (2), (4) and (6) in the depressurization process. For the water injection process, the majority of the injected water was produced out, and the rest amount of water stayed in the reservoir and occupied the space left by hydrate dissociation and gas production. Therefore, the quantity of water originating from water injection can be divided into two parts, which can be described in the following equation:
DSinj ¼ DSws þ DSwp ¼ T4
¼
j¼n X
Cw mws;j ln
j¼1
(14)
¼ Cw mws;j ln
i¼m X T3;i Cw mws dT þ Cw mwp;i ln T T4 i¼1
i¼m T1;j X T3;i þ Cw mwp;i ln T4 T4 i¼1
j¼n Y T1;j j¼1
T4
þ
i¼m X i¼1
Cw mwp;i ln
T3;i T4
(19)
3.2. Injection process Based on the law of energy conservation, the energy equation for the injection process can be explained as Eq. (15).
Qh þ Qres þ Qinj þ Qenv þ Qgp þ Qwd ¼ 0
DSwd ¼
j¼n X j¼1
Cw mwd;j ln
j¼n Y T1;j T1;j ¼ Cw mwd;j ln Tequ T j¼1 equ
(20)
(15)
here Qres is the quantity of heat used for heating the reservoir, and Qinj is the quantity of heat originating from water injection. Qwd is the quantity of heat required for heating the water from hydrate dissociation. The rest items in Eq. (15) are similar to that in Eq. (1).
DSpump ¼
Wpump Ppump t ¼ Tenv Tenv
(21)
where Ppump is the power of the metering pump, and it was measured by a power meter. t is the duration of water injection.
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4. Results and discussions 4.1. Evolution of pressure and temperature Fig. 4 shows the evolution of pressure during the dissociation experiment in the CHS and PHS. As shown in Table 1, the reservoir temperatures after hydrate formation in the CHS and PHS are approximately 281.85 K, hence the corresponding dissociation pressure is 6.10 MPa [30]. Namely, there is no hydrate dissociation when the pressure is higher than 6.10 MPa. Fig. 4 shows that the dissociation experiment can be divided into three stages: (1) Stage 1, from point C1 to C2 in the CHS and from point P1 to P2 in the PHS; (2) Stage 2, from point C2 to C3 in the CHS and from point P2 to P3 in the PHS; (3) Stage 3, from point C3 to the end in the CHS and from point P3 to the end in the PHS. There is no hydrate dissociation in Stage 1 because the pressures in the reactors are higher than the corresponding equilibrium pressure. During Stage 2, the pressures start to decrease below the equilibrium pressure, and the slopes of the pressure curves for the CHS and the PHS are approximately the same. During the third stage, the pressures in the CHS and the PHS are kept as 4.7 MPa until the end of the experiment. Fig. 5 depicts the temperatures at the wellheads. Because the temperature T-3 in the CHS and the temperature T-28 in the PHS were influenced by the heat exchange with the boundary [30,44], the temperatures T-8 and T-27 were selected as the representative temperature at the wellhead in the CHS and the PHS, respectively. It shows that in the CHS, the temperatures basically keep stable during the initial period of the first stage, whereas it shows a mild increase in the later period of the first stage due to the released heat from hydrate re-formation [30]. The similar trend of temperature variation occurs in the PHS. Moreover, as seen in Fig. 5, during the second stage, on account of the endothermic effect of hydrate dissociation, the temperatures at the wellheads approximately decline synchronously in the CHS and PHS. This means that the difference of temperature variation is small with the increase of reservoir scale during the depressurization period (Stages 1 and 2). Because the heat was injected into the reservoir, the temperature ascending phenomenon emerges gradually in the CHS and the PHS. As shown in Fig. 5, the temperature increase of T-8C in the CHS occurs at point D (t ¼ 88.19 min), which represents the onset of hydrate dissociation at the location of 8C. The time interval of point D and the starting point of Stage 3 in the CHS is 4.04 min, during which the injected heat was absorbed by the reservoir.
Fig. 4. Evolution of pressure during dissociation experiments in the CHS and PHS.
Fig. 5. Evolution of temperate at points (8A, B, C) in the CHS and points (27A, B, C) in the PHS during dissociation experiments.
Similarly, the ascending trend of T-27C initiates at point H (t ¼ 127.82 min), and the duration from the starting point of the injection stage to point H in the PHS is 20.15 min. As shown in Fig. 5, the ascending point of temperature T-8B is point E (t ¼ 115.56 min), which indicates that the onset of hydrate dissociation in Layer B in the CHS. The similar staring point of temperature increase in Layer B in the PHS is point I (t ¼ 193.03 min). The time interval between point H and I is 65.21 min, which is 2.38 times longer than that of the time interval between point D and E (27.37 min). In addition, the distance between Layer C and Layer B in the CHS and the PHS is 45 and 150 mm, respectively. That is, the distance between Layer C and Layer B in the PHS is 3.33 times further than that in the CHS. Therefore, the moving rate of the heat front from the lowest layer to the middle layer in the PHS (2.3 mm/ min) is higher than that in the CHS (1.6 mm/min). It can be concluded that the heat transfer rate in the PHS is higher than that in the CHS. This is because the distance between the injection well and the water bath in the PHS is farther than that in the CHS. This results in that the heat exchange rate of the injected heat and the water bath in the PHS is slower than that in the CHS. Accordingly, the reservoir in the PHS is heated faster than that in the CHS. Fig. 5 shows that the initial points of temperature increase for T-8A and T-27A are point F (t ¼ 165.27 min) and point J (t ¼ 236.93 min), respectively. The time intervals between point E and F as well as point I and J are 49.71 min and 43.90 min, respectively. This distinction is small, which is on account of the fact that the majority areas of the reservoir are in high temperature when the hydrate in Layers B and C have been dissociated completely, which reduces the corresponding heat loss. Fig. 6 describes the spatial distributions of temperatures in the CHS and PHS at the ending points of Stage 1, 2, and 3, respectively. Fig. 6a and d show the spatial distributions of temperature at the ending point of Stage 1 in the CHS and PHS, respectively. As seen, the temperatures in the CHS and PHS are basically uniform. In addition, the temperatures are almost equals to the environmental temperature (281.15 K), which confirms the above conclusion that there is no hydrate dissociation during Stage 1. Fig. 6b and e give the temperature spatial distributions at the end of Stage 2 in the CHS and the PHS, respectively. As shown, the temperatures in the CHS and the PHS are uniform and they are approximately identical with the equilibrium temperature (279.25 K). This illustrates that the descending trends of the temperatures in the CHS and the PHS are approximately in the
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Fig. 6. Spatial distribution of temperature at the end of each stage in the CHS and PHS.
same pace, which verifies the above conclusion that the difference of the temperature transfer during the depressurizing period is small with the increase of the reservoir scale. Fig. 6c and f show the spatial distributions of temperatures at the end of Stage 3 in the CHS and the PHS, respectively. As shown in Fig. 6c, the heat transfers along the injection well, and the hightemperature region climbs from the bottom to the top of the reservoir. Moreover, the temperatures in the entire region are approximately above the equilibrium temperature, which indicates that the hydrate in the CHS has been dissociated completely. Fig. 6f shows the similar temperature characteristic in the PHS. The difference is that the temperatures in the regions near the two horizontal wells in the PHS are higher than the temperatures in the corresponding regions of the CHS. This indicates that the heat transfer area in the PHS is broader than that in the CHS, which verifies the above conclusion that there is less energy loss through the boundary in the PHS. 4.2. Gas production
Fig. 7. Evolution of cumulative volume of gas production during dissociation experiments.
Fig. 7 shows the evolution of the cumulative volume of gas production (Vp) over time in the CHS and PHS. It is shown that the volume ratio of the final cumulative volume of gas production from the PHS to that from the CHS is approximately 20. As noted, the volume ratio of the PHS (117.80 L) to that of the CHS (5.83 L) is 20.19. Namely, the final cumulative volume of gas production by depressurization in conjunction with warm water stimulation with dual horizontal wells is significantly influenced by the scale of the reservoir. During the second stage, there is very small
difference between the variation tendency of the gas production rate for the PHS and that for the CHS, which results from the fact that the gas production rate in the depressurizing period is mainly controlled by the depressurizing rate [30]. During the third stage, the growth rates of gas production for both of the CHS and the PHS are remarkably lower than that during the second stage. In addition, the durations of the second stage and the third stage for the CHS are 15.21 min and 115.5 min, respectively. This
J.-C. Feng et al. / Energy 102 (2016) 176e186
indicates that the duration in the third stage is 7.59 times longer than that in the second stage for the CHS. Similarly, the duration in the third stage is 30.76 times longer than that in the second stage for the PHS. This means that the duration of hydrate dissociation in the constant-pressure stage (the injection stage) is much longer than that in the depressurizing stage, which shortens the overall efficiency of the whole gas production process. Therefore, the improvement of the gas production efficiency in the injection stage plays an important effect in the enhancement of the overall efficiency of gas production. Furthermore, this effect strengthens with the increase of the reservoir scale. The final slopes of the gas production curve for both the CHS and the PHS are approximately 0, which indicates that the hydrate in the reservoir has been dissociated completely. Fig. 8 shows the final cumulative volumes of gas production during the first, second, and the third stages as well as the corresponding ratio of gas production in the PHS to that in the CHS. In the first stage, all of the produced gas is from the free gas. In the second stage, the produced gas is the mixture of the free gas and the dissociated gas. In the third stage, all of the produced gas is originated from hydrate dissociation. As shown, the volume ratios of gas production for the PHS to that for the CHS during the first, second, and the third stages are 20.38, 10.98, and 20.21, respectively. The ratio of the inner volume of the PHS to that of the CHS is 20.19, which approximately equals to the ratio of Vp(PHS) to Vp(CHS) during the third stage. This result indicates that the dissociated gas is significantly affected by the scale of the reservoir. Although the volume of the dissociated gas accounts for a large part of the total produced gas, the gas production time in the third stage is quite long. Hence, the average gas production rate (QP) during the three stages is calculated, and it is shown in Fig. 9. As shown, for the CHS, the average gas production rates during the first, second, and third stages are 1.93, 5.29, and 1.08 L/min, respectively. Similarity, the average gas production rates for the PHS during the first, second, and third stages are 33.51, 60.22, and 5.77 min, respectively. This result indicates that the average gas production rate during the second stage is the largest for both the CHS and the PHS, which is due to the quick phase transformation under the effect of depressurization. The average gas production rate during the third stage is the minimum during the three stages, which confirms the above conclusion that the improvement of the gas production efficiency during the injection stage plays a leading role in the enhancement of the whole gas production efficiency.
Fig. 8. Final cumulative volumes of gas production during three stages and corresponding ratio of gas production in the PHS to that in the CHS.
183
Fig. 9. Average gas production rate during three stages.
4.3. Entropy production Fig. 10 shows the system entropy production (DSsys) during the first and the second stage for the CHS and the PHS as well as the corresponding ratio of the DSsys (PHS) to the DSsys (CHS). As shown, for both the CHS and the PHS, the system entropy production during the first stage is higher than that in the second stage. This indicates that during the free gas release stage, more energy is lost by the irreversible process, and this amount of energy is not consumed for hydrate dissociation. Namely, there is less anergy in the mixed gas release stage compared to that in the free gas release stage. The ratios of the DSsys (PHS) to the DSsys (CHS) in the first and the second stages are 23.75 and 10.35, respectively. This manifests that entropy production in the mixed gas release stage is less affected by the reservoir scale. Fig. 11 gives the system entropy production (DSsys) during the injection stage, and the corresponding ratio of the DSsys (PHS) to the DSsys (CHS). Comparing Figs. 10 and 11, it can be found that the entropy production during the third stage is far larger than that during the first two stages for both the CHS and the PHS. This means that the dissociated gas release stage is the main source of entropy production and the total energy lost by the irreversible process during this stage is the largest. In other word, the anergy in the injection stage is the largest and the amount of wasted energy is not applied for hydrate dissociation.
Fig. 10. System entropy production in Stage 1 and Stage 2 and corresponding ratio of entropy production in the PHS to that in the CHS.
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4.4. Energy ratio and thermal efficiency Energy ratio and thermal efficiency are common indicators that assess the efficiency of gas production from the hydrate reservoir. Energy ratio is described as the ratio of the combustion heat of the methane gas to the total input energy, which can be explained by Eq. (22):
h¼
Fig. 11. System entropy production in Stage 3 and corresponding ratio of entropy production in the PHS to that in the CHS.
VP Mgas Cw Minj Tinj T
(22)
where Vp is the cumulative volume of produced methane gas, and Mgas (37.6 MJ/m3) is the combustion heat of the methane. Minj is the cumulative mass of injected water. Tinj and T are the temperatures of the injected water and the environment, respectively. Thermal efficiency is the indicator that means the ratio of the heat employed for hydrate dissociation to the total input energy, which can be defined as the following equation:
Nh DHh Cw Minj Tinj T
This is because huge amount of energy is lost by the heat absorption of the reservoir and the heat exchange with the environment during the process of heat injection. The ratio of the DSsys (PHS) to the DSsys (CHS) in the third stage is 32.33, which indicates that entropy production in the injection stage is strongly affected by the reservoir scale. The above mentioned analysis indicates that the improvement of the production efficiency in the injection stage plays a leading role in the enhancement of the whole production efficiency. Moreover, the previous studies [30,45] reported that the constant-pressure production stage necessitates heat injection distinctly. Consequently, the effect of the injected heat on hydrate dissociation with the variation of reservoir scale requires to be well understood. The entropy production for hydrate dissociation is an import factor that affects the hydrate dissociation behavior. Fig. 12 shows the entropy production for hydrate dissociation (DShyd) during the injection stage. As shown in Fig. 12, the DShyd during the injection stages for the CHS and the PHS stages are 1048.10 and 20990.49 J/K, respectively. The ratio of DShyd for the PHS to that for the CHS is 20.03, which is pretty close to the volume ratio of the PHS to the CHS. This indicates that the entropy production for hydrate dissociation is directly proportional to the scale of the hydrate reservoir.
where DHh is the dissociation heat of the methane hydrate, and Nh is the mol of the dissociated hydrate. Figs. 13 and 14 give the evolutions of the energy ratio and the thermal efficiency during the injection stage for the CHS and the PHS. As shown in Fig. 13, both the energy ratios for the CHS and the PHS initially increase and then decrease continuously over time. Fig. 13 shows that the peak value of energy ratio emerges later in the PHS than that in the CHS, and the peak values of energy ratio for the CHS and the PHS are 71.81 and 60.39, respectively. After the peak value, the energy ratio for the PHS is higher than that for the CHS, which is resulted from the fact that the distance between the injection well and the boundary increases with the enlargement of the reservoir, and the corresponding heat loss through the boundary gets less accordingly. The final energy ratio for the PHS (10.17) is lower than that for the CHS (16.24). This is caused by the fact that the duration for the completion of hydrate dissociation for the PHS is pretty longer than that for the CHS, and there is only a small amount of gas production in the later period for the PHS. Therefore, during this period, the injected heat is mainly lost by the heat absorbing
Fig. 12. Entropy production for hydrate dissociation during injection stage.
Fig. 13. Evolution of energy ratio for injection process.
x¼
(23)
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185
for the CHS and PHS decrease continuously over time. During the initial period, the energy ratio and the thermal efficiency for the PHS are higher than that for the CHS, due to the less energy loss in the PHS. Acknowledgments This work is supported by National Science Fund for Distinguished Young Scholars of China (51225603), National Natural Science Foundation of China (51406210), Key Arrangement Programs of the Chinese Academy of Sciences (KGZD-EW-301-2), and International S&T Cooperation Program of China (2015DFA61790) which are gratefully acknowledged. References
Fig. 14. Evolution of thermal efficiency for injection process.
effect of the reservoir and the heat diffusion through the boundary, rather than applied for hydrae dissociation. As shown in Fig. 14, the thermal efficiencies for both the CHS and the PHS decrease continuously over time. In the initial period, the thermal efficiency for the PHS is higher than that for the CHS, indicating that more proportion of the injected heat in the PHS is employed for hydrate dissociation. Subsequently, the thermal efficiencies for both the CHS and the PHS decrease to very low level. The final thermal efficiencies for both the CHS and the PHS are 0.89 and 0.58, respectively, which indicates that the final thermal efficiency decreases with the increase of the reservoir scale.
5. Conclusion In this work, the experiments of hydrate dissociation by depressurization in conjunction with warm water stimulation with the dual horizontal wells were carried out in the CHS and the PHS. The conclusions can be drawn as follows: The difference of temperature variation is small with the increase of reservoir scale during the depressurization period, whereas, the heat transfer rate in the PHS is higher than that in the CHS during the injection period. Moreover, the ratio of the cumulative volume of the dissociated gas in the PHS to that in the CHS approximately equals to the volume ratio of the PHS to the CHS. The average gas production rate during the injection stage is the smallest, indicating the improvement of the gas production efficiency during the injection stage plays a leading role in the enhancement of the overall efficiency of gas production. Entropy analysis shows that the system entropy production during the mixed gas release stage is the smallest, and the entropy production in the mixed gas release stage is less affected by the reservoir scale. Additionally, the entropy production during the injection stage is far larger than that during the depressurization stage for both the CHS and the PHS, which means that the dissociated gas release stage is the main source of entropy production. The ratio of entropy production for hydrate dissociation with the PHS to that with the CHS is pretty close to the volume ratio of the PHS to the CHS, indicating that the entropy production for hydrate dissociation is directly proportional to the scale of the hydrate reservoir. The energy ratios for the CHS and the PHS initially increase and then decrease continuously over time, and the thermal efficiencies
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Contents lists available at ScienceDirect
Energy journal homepage: www.elsevier.com/locate/energy
Energy and entropy analyses of hydrate dissociation in different scales of hydrate simulator Jing-Chun Feng a, b, c, d, 1, Yi Wang a, b, d, 1, Xiao-Sen Li a, b, d, * a
Key Laboratory of Gas Hydrate, Guangzhou Institute of Energy Conversion, Chinese Academy of Sciences, Guangzhou 510640, PR China Guangzhou Center for Gas Hydrate Research, Chinese Academy of Sciences, Guangzhou 510640, PR China c University of Chinese Academy of Sciences, Beijing 100083, PR China d Guangdong Key Laboratory of New and Renewable Energy Research, Development and Application, Guangzhou 510640, China b
a r t i c l e i n f o
a b s t r a c t
Article history: Received 8 January 2016 Received in revised form 13 February 2016 Accepted 14 February 2016 Available online xxx
To investigate the effect of the reservoir scale on hydrate dissociation by depressurization in conjunction with warm water stimulation with dual horizontal wells, experiments of hydrate dissociation by such method have been carried out in CHS (Cubic Hydrate Simulator) and PHS (Pilot-scale Hydrate Simulator). The results show that there is little difference of temperature variation during the depressurizing stage with different scales of hydrate simulator. However, during the constant-pressure stage (the injection stage), the difference is obvious, and the heat transfer rate in the PHS is faster than that in the CHS. Additionally, the system entropy production during the injection stage is the largest, implying that the injection stage is the main source of energy consumption. Moreover, both the ratio of the amount of the dissociated gas in the PHS to that in the CHS and the ratio of the entropy production for hydrate dissociation with the PHS to that with the CHS approximately equal to the volume ratio of the PHS to the CHS. © 2016 Elsevier Ltd. All rights reserved.
Keywords: Hydrate Depressurization Thermal stimulation Horizontal well Reservoir scale Entropy analysis
1. Introduction Natural gas hydrate is widely distributed in the permafrost regions and the offshore oceanic regions, where the local environments of high pressure and low temperature are satisfied. In nature, gas hydrate exists as an ice-like solid in which the guest molecule (mainly methane) is encapsulated in the hydrogen-bonding cages comprised by water molecules [1,2]. Accurate estimation of the amount of gas hydrate on the earth is challenging, and the common perception is that the total carbon content in gas hydrate is more than twice as much as that in all of the conventional fossil fuels [3]. If 1 cubic meter of gas hydrate is dissociated at standard pressure and temperature, 164 m3 of gas and 0.8 m3 of water can be produced. The previous studies [4,5] indicate that the energy density of methane hydrate is 2e5 times larger than that of the conventional natural gas, and 10 times larger than the other kinds of unconventional gas sources, such
* Corresponding author. Key Laboratory of Gas Hydrate, Guangzhou Institute of Energy Conversion, Chinese Academy of Sciences, Guangzhou 510640, PR China. Tel.: þ86 20 87057037; fax: þ86 20 87034664. E-mail address: [email protected] (X.-S. Li). 1 These authors contributed equally to this work. http://dx.doi.org/10.1016/j.energy.2016.02.081 0360-5442/© 2016 Elsevier Ltd. All rights reserved.
as shale gas and coal bed gas. Generally, methane hydrate is considered to be a potential energy resource on account of the huge gas reserves in hydrate resource and the high density of methane hydrate [6,7]. Moreover, gas hydrate has been widely applied in the process of carbon dioxide capture [8e10], hydrogen storage [11] and flow assurance of the seabed pipeline [12]. Gas hydrate is dissociated when the stable condition of pressure and temperature is disturbed [13]. Up to now, the conventional research methods for hydrate dissociation are depressurization [14e18], thermal stimulation [19e22], inhibitor injection [23e25], and carbon dioxide replacement [26]. From the perspectives of high energy ratio, high production efficiency, and the avoidance of ice blockage and hydrate re-formation, the combination of depressurization and thermal stimulation is regarded to be a profitable method for hydrate dissociation [27e29]. Due to the huge energy loss with the increase of water injection temperature, Feng et al. [30] reported that high temperature (beyond 40 C) injection was not economic for hydrate dissociation, and they further indicated [31] that the optimal injected temperature for hydrate dissociation in a 5.83 L cubic hydrate simulator was 38e39 C by using the evaluation methods of entropy production minimization and energy ratio maximization. The hydrate dissociation behavior and the production performance of the hydrate reservoir are strongly
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affected by the scale of hydrate reservoir. The numerical research of Tang et al. [32] showed that the controlling mechanism of hydrate dissociation in the reservoir of small scale is kinetic-controlled. Whereas the controlling factor of hydrate dissociation in large scale hydrate reservoir is fluid flow. In addition, the analytical modeling of Wang et al. [33] also indicates that hydrate dissociation in the large scale hydrate reservoir is strongly dependent on the characteristics of heat transfer, mass transfer, and fluid flow. Both the experimental and numerical analyses of Li et al. [34] showed that the kinetic limitation was weak for hydrate dissociation by depressurization in a 117.8 L hydrate simulator. In general, the hydrate reservoir scale is an important factor which affects gas production from the hydrate-bearing reservoir. Up to now, the investigation of reservoir scale for hydrate dissociation mainly focuses on the vertical well configuration and the behaviors of gas and water production. There is short of the investigation of the effect of reservoir scale on horizontal well configuration and the optimization of the operating condition during hydrate dissociation. Therefore, the research of the effect of reservoir scale on the optimization of the operating condition for hydrate dissociation, especially with the horizontal well system, is desperately needed. Hydrate dissociation is an irreversible process during the laboratory-scale experiment. For the irreversible process, entropy analysis, which is the application of the second law of thermodynamics, has been considered as an efficient way that shows the sources of energy losses and what modifications should be conducted to increase the energy efficiency [35]. Entropy generation is proportional to the lost work in an irreversible process, and the entropy generation is contribute to explain the optimal conditions for energy losses [36]. The method of entropy generation minimization which means the minimization of energy consumption, has been widely used in the optimal processes of the cogeneration plant [37], the distillation [38], the heat convection in porous media [39], the heat engines [40], and so on. Based on the minimum entropy generation theory, Feng et al. [31] has obtained the optimal temperature range for hydrate dissociation in a 5.83 L reactor with the dual horizontal wells. However, there is lack of the evolution of the entropy generation with different scales of reservoir.
177
The main purposes of this work are the investigations of the evolutions of hydrate dissociation behaviors and entropy production under different scales of hydrate reservoir. Hydrate samples were synthesized in a 5.83 L CHS (Cubic Hydrate Simulator) and a 117.80 L PHS (Pilot-scale Hydrate Simulator). Considering the advantage of horizontal well pattern over the vertical well pattern [41,42], the dual horizontal wells were set as the production scenario. The pressure and temperature condition of hydrate formation and dissociation were originated from the exploration data of hydrate accumulation in the South China Sea. The behaviors of gas production, water production, hydrate dissociation, and entropy production in different scales of hydrate reservoir were obtained. 2. Experimental apparatus and process 2.1. Experimental apparatus The schematic of the two apparatus are shown in Fig. 1. The CHS is a cubic hydrate simulator with the side length of 180.00 mm. The diameter of the PHS is 500.00 mm and the height of the PHS is 600.00 mm. As shown in Table 1, the inner volume of the CHS and the PHS is 5.83 and 117.80 L, respectively. The components of the two apparatus are similar. The differences are that the volume of the PHS is almost 20 times larger than that of the CHS, and the PHS is placed in a cold room. As shown in Fig. 1, the high pressure reactor made from stainless steel 316 is the core of the apparatus. An inlet pressure transducer and an outlet pressure transducer are placed in the bottom and top of the reactor, respectively. The CHS is immersed in a water bath (15e30 C, ±0.1 C) to ensure the Table 1 Parameters of methane hydrate formation in the CHS and PHS.
Inner Volume (L) Pore Volume (mL) Bath Temperature (k) P0 (MPa) Pend (MPa) Tend (k)
Fig. 1. Schematic of the CHS and PHS.
CHS
PHS
5.83 2752.00 281.15 20.05 13.400 281.85
117.80 51,360.00 281.15 19.63 13.70 281.87
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stability of the required temperature environment. Both the water jacket (15e30 C, ±0.1 C) around the PHS and the resident cold room (8e30 C, ±2 C) are performed as the safeguard to guarantee the required temperature condition. Two gas flow meters are used to meter the amount of the injected and the produced methane gas, respectively. The temperature and the amount of water injection are controlled by a heater and a metering pump, respectively. The amount of the produced water is measured by a balance. The working pressure is adjusted by a back-pressure regulator. Figs. 2 and 3 give the schematic diagram for the inner design and well configuration of the CHS and PHS, respectively. As described in Fig. 2, the inner space of the CHS is evenly divided into 4 isometric regions by 3 horizontal layers. The injection well (Well HC) is set on the lowest layer (Layer C), and the production well (Well HA) is placed on the uppermost layer (Layer HA). There are 25 (5 5 ¼ 25) thermal couples evenly distributed on each of the horizontal layer. Thus, a total of 75 (25 3 ¼ 75) thermal couples are installed in the CHS. As shown in Fig. 3, the inner design and the well configuration in the PHS is similar to that in the CHS. The difference is that there are 49 (7 7 ¼ 49) thermal couples on each of the horizontal layer, and the total thermal couples in the PHS is 147 (49 3 ¼ 147).
immediately. Table 2 shows the detailed parameters of hydrate dissociation. To begin with, the upper horizontal well was opened for hydrate dissociation. When the pressure in the reactors declined to 4.7 MPa, warm water was injected into the reservoir from the lower horizontal well. The water injection rate for the CHS was 20 mL/min. Based on the scaling-up modeling, the corresponding water injection rate for the PHS was 207 mL/min [43]. During the injection process, the pressures in the reactor were kept as constant (4.70 MPa) until the end of the dissociation experiments. The detailed information of hydrate formation and dissociation also has been introduced in the previous studies [20,27,31,41].
2.2. Experimental process
where Qh is the quantity of heat performed for hydrate dissociation. Qres is the quantity of heat releasing from the cooling down of the reservoir. Qenv is the quantity of heat exchanging with the surrounding environment. Qgp and Qwp are the quantity of heat applied for gas production and water production, respectively. The detailed calculation methods of the items in Eq. (1) are as follows:
Table 1 gives the specific parameters for hydrate formation in the two reactors. Firstly, the two reactors were suffused with silica sands. The grain size of those silica sands ranges from 300 to 450 mm. After sands filling, both the porosity of the CHS and PHS are 48%. Then, the precalculated amount of deionized water and pure methane gas were injected into the two reactors, making the pressures in the reactors increase to approximately 20 MPa [31,41]. All the outlets were kept closed afterwards. When the pressures in the reactors decrease to the desired value, the formation process was terminated. The hydrate dissociation experiments followed the completion of hydrate formation
3. Determination of entropy production 3.1. Depressurization process According to the law of conservation of energy, the energy equation for the system during the depressurization is described as Eq. (1).
Qh þ Qres þ Qenv þ Qgp þ Qwp ¼ 0
Qh ¼ Nh DHh
(1)
(2)
where Nh is the molar quantity of hydrate dissociation, and DHh stands for the dissociation heat of hydrate, which is used as 54.1 kJ/ mol in this work [31].
Fig. 2. Inner design and well configuration in the CHS.
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179
Fig. 3. Inner design and well configuration in the PHS.
Table 2 Conditions of methane hydrate dissociation in the CHS and PHS.
Initial Gas Saturation Initial Water Saturation Initial Hydrate Saturation Production Pressure(MPa) Injection Temperature(k) Injection Rate (mL/min)
Qres
Qres ¼
Cs mso;j þ Cg mgo;j þ Cw mwo;j T1;j T0;j
(4)
j¼1
CHS
PHS
58.00% 12.00% 30.00% 4.70 311.38 20.00
60.00% 10.00% 30.00% 4.70 311.38 207.00
¼ Cs mso þ Cg mgo þ Cw mwo ðT1 T0 Þ
j¼n X
where mso,j, mgo,j, and mwo,j are the mass of the tiny part of the silica sand, methane gas, and water, respectively. n is 75 and 147 for the CHS and the PHS, respectively. T1,j and T0,j are the temperatures of the tiny part at the end and the initial point of the depressurization process, respectively.
Qgp ¼ Cg mgp ðT3 T2 Þ (3)
where Cs, Cg, and Cw are the specific heat of the silica sand, methane gas, and water, respectively. mso, mgo, and mwo are the corresponding original mass of the silica sand, methane gas, and water in the reservoir before the depressurization process. T0 and T1 are the temperatures of the reservoir at the beginning and the ending points of the depressurization process. The distributions of sand, gas, and water in the reservoir at the end of the depressurization process are irregular. In order to explain the temperature in the reactor as accurate as possible, the reservoir can be divided into n tiny parts in accordance with the distribution of the thermocouples, and the distributions of sand, gas, and water in each tiny part can be considered to be uniform. As shown in Figs. 2 and 3, n is 75 and 147 for the CHS and the PHS, respectively. The temperature and mass distributions of gas, water, and hydrate in each tiny part can be regarded as identical, and the central position of each tiny part is assumed to be the location of the corresponding thermal couple. Therefore, the temperature measured by each thermal couple can be considered to be the temperature of the corresponding tiny part, and Eq. (3) can be transformed to the following equation [31]:
(5)
where mgp is the mass of the produced gas. T2 and T3 are the temperatures at the outlet in the initial and the end of the depressurization process, respectively. On account of the variation of T3 over time, the total amount of produced gas is divided into several parts (m) to describe the temperature at the wellhead as accurate as possible. During each part of gas production, the temperature variation at the outlet can be neglected. Therefore, the temperature at the outlet can be considered as constant during each small part of gas production, and Eq. (5) can be transformed to the following equation:
Qgp ¼
iX ¼m
Cg mgp;i T3;i T2
(6)
i¼1
where mgp,i is the mass of the small part of produced gas, and T3,i is the corresponding temperature at the outlet. Similarly, the quantity of heat applied for water production can be expressed as follows:
Qwp ¼ Cw mwp ðT3 T2 Þ ¼
i¼m X i¼1
Cw mwp;i T3;i T2
(7)
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Combining and solving Eqs. (1), (2), (4), (6) and (7) simultaneously, Qenv can be obtained for the depressurization process. For the depressurization process, the entropy production in the whole system (DSsystem) from the starting point to the ending point is shown in Eq. (8).
DSsystem ¼ DShyd þ DSgp þ DSwp þ DSres þ DSew þ DSenv
(8)
where DShyd is the entropy change of the hydrate in the reservoir caused by phase transformation. DSgp and DSwp are the entropy productions due to gas and water production, respectively. DSres represents the entropy production of the reservoir due to temperature change. DSew is the entropy production due to the volumetric change of gas in the gas production process. DSenv is the entropy production of the environment. The specific calculation processes for these items are as follows:
DShyd ¼
DSgp ¼
Qh N DHh ¼ h Tequ Tequ
i¼m X
Cg mgp;i ln
i¼1
DSwp ¼
i¼m X
(10)
T3;i T2
(11)
ZT1 DSres ¼ DSso þ DSgo þ DSwo ¼
Cs mso þ Cg mgo þ Cw mwo dT T
T0
T ¼ Cs mso þ Cg mgo þ Cw mwo ln 1 T0 ¼
Qinj ¼ Qws þ Qwp ¼ Cw mws ðT1 T4 Þ þ Cw mwp ðT3 T4 Þ ¼
j¼n X
i¼m X Cw mws;j T1;j T4 þ Cw mwp;i T3;i T4
j¼n X T1;j Cs mso;j þ Cg mgo;j þ Cw mwo;j ln T0;j j¼1
where T4 is the initial temperature of the injected water. wdescribed as the following equation: j¼n X Qwd ¼ Cw mwd T1 Tequ ¼ Cw mwd;j T1;j Tequ
where Tequ is the equilibrium temperature of hydrate dissociation at the working pressure (4.7 MPa). Consequently, the quantity of heat exchanging with the surrounding environment during the injection process can be acquired by combining and solving Eqs. (2), (4), (6) and (15)e(17) simultaneously. For the injection process, the entropy production of the total system from the initial to the ending point is drawn as follows:
þ DSpump
j¼1
(18) (12)
Pe DSew ¼
V2
dV V1
Tenv
Qenv Tenv
The computational methods of DShyd, DSgp, DSres, DSew, and DSenv in Eq. (18) are similar to Eqs. (9), (10), and (12)e(14). The detailed information of the other items in Eq. (18) is explained as follows:
(13) ZT1
where V1 and V2 are the volumes of the gas in the reservoir with high pressure and under the standard condition, respectively. Tenv is the temperature of the environment.
DSenv ¼
(17)
j¼1
DSsystem ¼ DSinj þ DShyd þ DSres þ DSgp þ DSwd þ DSenv þ DSew
j¼n Y T1;j ¼ Cs mso;j þ Cg mgo;j þ Cw mwo;j ln T0;j
Z
(16)
i¼1
j¼1
T3;i T2
Cw mwp;i ln
i¼1
(9)
There is an assumption that the amount of water production is from water injection [31], and the amount of water from hydrate dissociation stayed in the reservoir, because the amount of water injection is far larger than that of water from hydrate dissociation and the pore space of the reservoir is large enough for the accommodation of the water from hydrate dissociation. The calculation methods of Qh, Qres, and Qgp in Eq. (15) are similar to Eqs. (2), (4) and (6) in the depressurization process. For the water injection process, the majority of the injected water was produced out, and the rest amount of water stayed in the reservoir and occupied the space left by hydrate dissociation and gas production. Therefore, the quantity of water originating from water injection can be divided into two parts, which can be described in the following equation:
DSinj ¼ DSws þ DSwp ¼ T4
¼
j¼n X
Cw mws;j ln
j¼1
(14)
¼ Cw mws;j ln
i¼m X T3;i Cw mws dT þ Cw mwp;i ln T T4 i¼1
i¼m T1;j X T3;i þ Cw mwp;i ln T4 T4 i¼1
j¼n Y T1;j j¼1
T4
þ
i¼m X i¼1
Cw mwp;i ln
T3;i T4
(19)
3.2. Injection process Based on the law of energy conservation, the energy equation for the injection process can be explained as Eq. (15).
Qh þ Qres þ Qinj þ Qenv þ Qgp þ Qwd ¼ 0
DSwd ¼
j¼n X j¼1
Cw mwd;j ln
j¼n Y T1;j T1;j ¼ Cw mwd;j ln Tequ T j¼1 equ
(20)
(15)
here Qres is the quantity of heat used for heating the reservoir, and Qinj is the quantity of heat originating from water injection. Qwd is the quantity of heat required for heating the water from hydrate dissociation. The rest items in Eq. (15) are similar to that in Eq. (1).
DSpump ¼
Wpump Ppump t ¼ Tenv Tenv
(21)
where Ppump is the power of the metering pump, and it was measured by a power meter. t is the duration of water injection.
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181
4. Results and discussions 4.1. Evolution of pressure and temperature Fig. 4 shows the evolution of pressure during the dissociation experiment in the CHS and PHS. As shown in Table 1, the reservoir temperatures after hydrate formation in the CHS and PHS are approximately 281.85 K, hence the corresponding dissociation pressure is 6.10 MPa [30]. Namely, there is no hydrate dissociation when the pressure is higher than 6.10 MPa. Fig. 4 shows that the dissociation experiment can be divided into three stages: (1) Stage 1, from point C1 to C2 in the CHS and from point P1 to P2 in the PHS; (2) Stage 2, from point C2 to C3 in the CHS and from point P2 to P3 in the PHS; (3) Stage 3, from point C3 to the end in the CHS and from point P3 to the end in the PHS. There is no hydrate dissociation in Stage 1 because the pressures in the reactors are higher than the corresponding equilibrium pressure. During Stage 2, the pressures start to decrease below the equilibrium pressure, and the slopes of the pressure curves for the CHS and the PHS are approximately the same. During the third stage, the pressures in the CHS and the PHS are kept as 4.7 MPa until the end of the experiment. Fig. 5 depicts the temperatures at the wellheads. Because the temperature T-3 in the CHS and the temperature T-28 in the PHS were influenced by the heat exchange with the boundary [30,44], the temperatures T-8 and T-27 were selected as the representative temperature at the wellhead in the CHS and the PHS, respectively. It shows that in the CHS, the temperatures basically keep stable during the initial period of the first stage, whereas it shows a mild increase in the later period of the first stage due to the released heat from hydrate re-formation [30]. The similar trend of temperature variation occurs in the PHS. Moreover, as seen in Fig. 5, during the second stage, on account of the endothermic effect of hydrate dissociation, the temperatures at the wellheads approximately decline synchronously in the CHS and PHS. This means that the difference of temperature variation is small with the increase of reservoir scale during the depressurization period (Stages 1 and 2). Because the heat was injected into the reservoir, the temperature ascending phenomenon emerges gradually in the CHS and the PHS. As shown in Fig. 5, the temperature increase of T-8C in the CHS occurs at point D (t ¼ 88.19 min), which represents the onset of hydrate dissociation at the location of 8C. The time interval of point D and the starting point of Stage 3 in the CHS is 4.04 min, during which the injected heat was absorbed by the reservoir.
Fig. 4. Evolution of pressure during dissociation experiments in the CHS and PHS.
Fig. 5. Evolution of temperate at points (8A, B, C) in the CHS and points (27A, B, C) in the PHS during dissociation experiments.
Similarly, the ascending trend of T-27C initiates at point H (t ¼ 127.82 min), and the duration from the starting point of the injection stage to point H in the PHS is 20.15 min. As shown in Fig. 5, the ascending point of temperature T-8B is point E (t ¼ 115.56 min), which indicates that the onset of hydrate dissociation in Layer B in the CHS. The similar staring point of temperature increase in Layer B in the PHS is point I (t ¼ 193.03 min). The time interval between point H and I is 65.21 min, which is 2.38 times longer than that of the time interval between point D and E (27.37 min). In addition, the distance between Layer C and Layer B in the CHS and the PHS is 45 and 150 mm, respectively. That is, the distance between Layer C and Layer B in the PHS is 3.33 times further than that in the CHS. Therefore, the moving rate of the heat front from the lowest layer to the middle layer in the PHS (2.3 mm/ min) is higher than that in the CHS (1.6 mm/min). It can be concluded that the heat transfer rate in the PHS is higher than that in the CHS. This is because the distance between the injection well and the water bath in the PHS is farther than that in the CHS. This results in that the heat exchange rate of the injected heat and the water bath in the PHS is slower than that in the CHS. Accordingly, the reservoir in the PHS is heated faster than that in the CHS. Fig. 5 shows that the initial points of temperature increase for T-8A and T-27A are point F (t ¼ 165.27 min) and point J (t ¼ 236.93 min), respectively. The time intervals between point E and F as well as point I and J are 49.71 min and 43.90 min, respectively. This distinction is small, which is on account of the fact that the majority areas of the reservoir are in high temperature when the hydrate in Layers B and C have been dissociated completely, which reduces the corresponding heat loss. Fig. 6 describes the spatial distributions of temperatures in the CHS and PHS at the ending points of Stage 1, 2, and 3, respectively. Fig. 6a and d show the spatial distributions of temperature at the ending point of Stage 1 in the CHS and PHS, respectively. As seen, the temperatures in the CHS and PHS are basically uniform. In addition, the temperatures are almost equals to the environmental temperature (281.15 K), which confirms the above conclusion that there is no hydrate dissociation during Stage 1. Fig. 6b and e give the temperature spatial distributions at the end of Stage 2 in the CHS and the PHS, respectively. As shown, the temperatures in the CHS and the PHS are uniform and they are approximately identical with the equilibrium temperature (279.25 K). This illustrates that the descending trends of the temperatures in the CHS and the PHS are approximately in the
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Fig. 6. Spatial distribution of temperature at the end of each stage in the CHS and PHS.
same pace, which verifies the above conclusion that the difference of the temperature transfer during the depressurizing period is small with the increase of the reservoir scale. Fig. 6c and f show the spatial distributions of temperatures at the end of Stage 3 in the CHS and the PHS, respectively. As shown in Fig. 6c, the heat transfers along the injection well, and the hightemperature region climbs from the bottom to the top of the reservoir. Moreover, the temperatures in the entire region are approximately above the equilibrium temperature, which indicates that the hydrate in the CHS has been dissociated completely. Fig. 6f shows the similar temperature characteristic in the PHS. The difference is that the temperatures in the regions near the two horizontal wells in the PHS are higher than the temperatures in the corresponding regions of the CHS. This indicates that the heat transfer area in the PHS is broader than that in the CHS, which verifies the above conclusion that there is less energy loss through the boundary in the PHS. 4.2. Gas production
Fig. 7. Evolution of cumulative volume of gas production during dissociation experiments.
Fig. 7 shows the evolution of the cumulative volume of gas production (Vp) over time in the CHS and PHS. It is shown that the volume ratio of the final cumulative volume of gas production from the PHS to that from the CHS is approximately 20. As noted, the volume ratio of the PHS (117.80 L) to that of the CHS (5.83 L) is 20.19. Namely, the final cumulative volume of gas production by depressurization in conjunction with warm water stimulation with dual horizontal wells is significantly influenced by the scale of the reservoir. During the second stage, there is very small
difference between the variation tendency of the gas production rate for the PHS and that for the CHS, which results from the fact that the gas production rate in the depressurizing period is mainly controlled by the depressurizing rate [30]. During the third stage, the growth rates of gas production for both of the CHS and the PHS are remarkably lower than that during the second stage. In addition, the durations of the second stage and the third stage for the CHS are 15.21 min and 115.5 min, respectively. This
J.-C. Feng et al. / Energy 102 (2016) 176e186
indicates that the duration in the third stage is 7.59 times longer than that in the second stage for the CHS. Similarly, the duration in the third stage is 30.76 times longer than that in the second stage for the PHS. This means that the duration of hydrate dissociation in the constant-pressure stage (the injection stage) is much longer than that in the depressurizing stage, which shortens the overall efficiency of the whole gas production process. Therefore, the improvement of the gas production efficiency in the injection stage plays an important effect in the enhancement of the overall efficiency of gas production. Furthermore, this effect strengthens with the increase of the reservoir scale. The final slopes of the gas production curve for both the CHS and the PHS are approximately 0, which indicates that the hydrate in the reservoir has been dissociated completely. Fig. 8 shows the final cumulative volumes of gas production during the first, second, and the third stages as well as the corresponding ratio of gas production in the PHS to that in the CHS. In the first stage, all of the produced gas is from the free gas. In the second stage, the produced gas is the mixture of the free gas and the dissociated gas. In the third stage, all of the produced gas is originated from hydrate dissociation. As shown, the volume ratios of gas production for the PHS to that for the CHS during the first, second, and the third stages are 20.38, 10.98, and 20.21, respectively. The ratio of the inner volume of the PHS to that of the CHS is 20.19, which approximately equals to the ratio of Vp(PHS) to Vp(CHS) during the third stage. This result indicates that the dissociated gas is significantly affected by the scale of the reservoir. Although the volume of the dissociated gas accounts for a large part of the total produced gas, the gas production time in the third stage is quite long. Hence, the average gas production rate (QP) during the three stages is calculated, and it is shown in Fig. 9. As shown, for the CHS, the average gas production rates during the first, second, and third stages are 1.93, 5.29, and 1.08 L/min, respectively. Similarity, the average gas production rates for the PHS during the first, second, and third stages are 33.51, 60.22, and 5.77 min, respectively. This result indicates that the average gas production rate during the second stage is the largest for both the CHS and the PHS, which is due to the quick phase transformation under the effect of depressurization. The average gas production rate during the third stage is the minimum during the three stages, which confirms the above conclusion that the improvement of the gas production efficiency during the injection stage plays a leading role in the enhancement of the whole gas production efficiency.
Fig. 8. Final cumulative volumes of gas production during three stages and corresponding ratio of gas production in the PHS to that in the CHS.
183
Fig. 9. Average gas production rate during three stages.
4.3. Entropy production Fig. 10 shows the system entropy production (DSsys) during the first and the second stage for the CHS and the PHS as well as the corresponding ratio of the DSsys (PHS) to the DSsys (CHS). As shown, for both the CHS and the PHS, the system entropy production during the first stage is higher than that in the second stage. This indicates that during the free gas release stage, more energy is lost by the irreversible process, and this amount of energy is not consumed for hydrate dissociation. Namely, there is less anergy in the mixed gas release stage compared to that in the free gas release stage. The ratios of the DSsys (PHS) to the DSsys (CHS) in the first and the second stages are 23.75 and 10.35, respectively. This manifests that entropy production in the mixed gas release stage is less affected by the reservoir scale. Fig. 11 gives the system entropy production (DSsys) during the injection stage, and the corresponding ratio of the DSsys (PHS) to the DSsys (CHS). Comparing Figs. 10 and 11, it can be found that the entropy production during the third stage is far larger than that during the first two stages for both the CHS and the PHS. This means that the dissociated gas release stage is the main source of entropy production and the total energy lost by the irreversible process during this stage is the largest. In other word, the anergy in the injection stage is the largest and the amount of wasted energy is not applied for hydrate dissociation.
Fig. 10. System entropy production in Stage 1 and Stage 2 and corresponding ratio of entropy production in the PHS to that in the CHS.
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4.4. Energy ratio and thermal efficiency Energy ratio and thermal efficiency are common indicators that assess the efficiency of gas production from the hydrate reservoir. Energy ratio is described as the ratio of the combustion heat of the methane gas to the total input energy, which can be explained by Eq. (22):
h¼
Fig. 11. System entropy production in Stage 3 and corresponding ratio of entropy production in the PHS to that in the CHS.
VP Mgas Cw Minj Tinj T
(22)
where Vp is the cumulative volume of produced methane gas, and Mgas (37.6 MJ/m3) is the combustion heat of the methane. Minj is the cumulative mass of injected water. Tinj and T are the temperatures of the injected water and the environment, respectively. Thermal efficiency is the indicator that means the ratio of the heat employed for hydrate dissociation to the total input energy, which can be defined as the following equation:
Nh DHh Cw Minj Tinj T
This is because huge amount of energy is lost by the heat absorption of the reservoir and the heat exchange with the environment during the process of heat injection. The ratio of the DSsys (PHS) to the DSsys (CHS) in the third stage is 32.33, which indicates that entropy production in the injection stage is strongly affected by the reservoir scale. The above mentioned analysis indicates that the improvement of the production efficiency in the injection stage plays a leading role in the enhancement of the whole production efficiency. Moreover, the previous studies [30,45] reported that the constant-pressure production stage necessitates heat injection distinctly. Consequently, the effect of the injected heat on hydrate dissociation with the variation of reservoir scale requires to be well understood. The entropy production for hydrate dissociation is an import factor that affects the hydrate dissociation behavior. Fig. 12 shows the entropy production for hydrate dissociation (DShyd) during the injection stage. As shown in Fig. 12, the DShyd during the injection stages for the CHS and the PHS stages are 1048.10 and 20990.49 J/K, respectively. The ratio of DShyd for the PHS to that for the CHS is 20.03, which is pretty close to the volume ratio of the PHS to the CHS. This indicates that the entropy production for hydrate dissociation is directly proportional to the scale of the hydrate reservoir.
where DHh is the dissociation heat of the methane hydrate, and Nh is the mol of the dissociated hydrate. Figs. 13 and 14 give the evolutions of the energy ratio and the thermal efficiency during the injection stage for the CHS and the PHS. As shown in Fig. 13, both the energy ratios for the CHS and the PHS initially increase and then decrease continuously over time. Fig. 13 shows that the peak value of energy ratio emerges later in the PHS than that in the CHS, and the peak values of energy ratio for the CHS and the PHS are 71.81 and 60.39, respectively. After the peak value, the energy ratio for the PHS is higher than that for the CHS, which is resulted from the fact that the distance between the injection well and the boundary increases with the enlargement of the reservoir, and the corresponding heat loss through the boundary gets less accordingly. The final energy ratio for the PHS (10.17) is lower than that for the CHS (16.24). This is caused by the fact that the duration for the completion of hydrate dissociation for the PHS is pretty longer than that for the CHS, and there is only a small amount of gas production in the later period for the PHS. Therefore, during this period, the injected heat is mainly lost by the heat absorbing
Fig. 12. Entropy production for hydrate dissociation during injection stage.
Fig. 13. Evolution of energy ratio for injection process.
x¼
(23)
J.-C. Feng et al. / Energy 102 (2016) 176e186
185
for the CHS and PHS decrease continuously over time. During the initial period, the energy ratio and the thermal efficiency for the PHS are higher than that for the CHS, due to the less energy loss in the PHS. Acknowledgments This work is supported by National Science Fund for Distinguished Young Scholars of China (51225603), National Natural Science Foundation of China (51406210), Key Arrangement Programs of the Chinese Academy of Sciences (KGZD-EW-301-2), and International S&T Cooperation Program of China (2015DFA61790) which are gratefully acknowledged. References
Fig. 14. Evolution of thermal efficiency for injection process.
effect of the reservoir and the heat diffusion through the boundary, rather than applied for hydrae dissociation. As shown in Fig. 14, the thermal efficiencies for both the CHS and the PHS decrease continuously over time. In the initial period, the thermal efficiency for the PHS is higher than that for the CHS, indicating that more proportion of the injected heat in the PHS is employed for hydrate dissociation. Subsequently, the thermal efficiencies for both the CHS and the PHS decrease to very low level. The final thermal efficiencies for both the CHS and the PHS are 0.89 and 0.58, respectively, which indicates that the final thermal efficiency decreases with the increase of the reservoir scale.
5. Conclusion In this work, the experiments of hydrate dissociation by depressurization in conjunction with warm water stimulation with the dual horizontal wells were carried out in the CHS and the PHS. The conclusions can be drawn as follows: The difference of temperature variation is small with the increase of reservoir scale during the depressurization period, whereas, the heat transfer rate in the PHS is higher than that in the CHS during the injection period. Moreover, the ratio of the cumulative volume of the dissociated gas in the PHS to that in the CHS approximately equals to the volume ratio of the PHS to the CHS. The average gas production rate during the injection stage is the smallest, indicating the improvement of the gas production efficiency during the injection stage plays a leading role in the enhancement of the overall efficiency of gas production. Entropy analysis shows that the system entropy production during the mixed gas release stage is the smallest, and the entropy production in the mixed gas release stage is less affected by the reservoir scale. Additionally, the entropy production during the injection stage is far larger than that during the depressurization stage for both the CHS and the PHS, which means that the dissociated gas release stage is the main source of entropy production. The ratio of entropy production for hydrate dissociation with the PHS to that with the CHS is pretty close to the volume ratio of the PHS to the CHS, indicating that the entropy production for hydrate dissociation is directly proportional to the scale of the hydrate reservoir. The energy ratios for the CHS and the PHS initially increase and then decrease continuously over time, and the thermal efficiencies
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