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Sensitivity analysis of gas production from Class I hydrate reservoir by depressurization
Energy 39 (2012) 281e285
Contents lists available at SciVerse ScienceDirect
Energy journal homepage: www.elsevier.com/locate/energy
Sensitivity analysis of gas production from Class I hydrate reservoir by depressurization Xingxing Jiang*, Shuxia Li, Lina Zhang Department of Petroleum Engineering, China University of Petroleum (East China), Qingdao, Shandong 266555, China
a r t i c l e i n f o
a b s t r a c t
Article history: Received 9 August 2011 Received in revised form 23 December 2011 Accepted 10 January 2012 Available online 11 February 2012
A 3D numerical model for gas production from hydrate reservoirs is developed, which considers kinetics of dissociation, heat and multiphase fluid flow. Three components (gas, water and hydrate) and three phases (gas, water and hydrate) are considered in the model. The equations are spatially discretized by a finite difference method. IMPES method is used to solve the mass balance equations and temperature is solved implicitly. Based on the model, gas production from Class I hydrate reservoir (with underlying free gas) under constant bottom-hole pressure was simulated. The sensitivity analysis of the factors including development parameters and reservoir parameters were performed. Results show that hydrate dissociation rate increases with the increases of initial reservoir temperature. The larger the absolute permeability is, the higher the hydrate dissociation rate is. Hydrate dissociation rate is significantly improved, when dissociation rate constant increases. However, higher initial reservoir pressure and bottom-hole pressure will lead to lower hydrate dissociation rate. Research results provide theoretical support for hydrate production. Ó 2012 Elsevier Ltd. All rights reserved.
Keywords: Hydrate reservoir Depressurization Numerical model Sensitivity studies
1. Introduction With oil and gas resources of the growing tension, looking for the new and replacement energy is imminently. In recent years, Natural gas hydrate (NGH) found in the sea and permafrost is recognized as the most important energy resource because of its large reserve, clean and high energy efficiency. Gas hydrates are solid crystalline compounds of natural gas molecules, which are encaged within a crystal structure composed of water molecules. Hydrate exists in low temperature and high pressure [1] and [2]. At present, hydrate accumulations have been divided into three main classes [3]: Class I (underlying free gas), Class II (underlying free-water) and Class III (single hydrate zone). In addition, Class IV pertains specifically to oceanic accumulations, and involves disperse, low-saturation hydrate deposits that lack confining geologic strata [4]. Class I deposits are relatively easy to induce hydrate dissociation because of the proximity to equilibrium at the hydrateegas interface [5]. Currently, three main methods are proposed to exploit hydrate: depressurization, thermal stimulation, inhibitor injection [6,7,8,9]. In comparison, depressurization is a relatively inexpensive and economical method.
* Corresponding author. Tel.: þ86 1386 4892 917; fax: þ86 532 8698 1936. E-mail address: [email protected] (X. Jiang). 0360-5442/$ e see front matter Ó 2012 Elsevier Ltd. All rights reserved. doi:10.1016/j.energy.2012.01.016
At present, scholars have done a lot of research on numerical simulation of NGH by depressurization. A series of mathematical model have been developed at home and abroad, including analytical model and numerical model, from one-dimension to three-dimension, from one single phase to multiphase. With the continuous research, model is more and more perfect. Holder et al. [7] developed a 3D single phase model which applied the heat conduction equation and considered the change of temperature during the NGH dissociation. Then Burshears et al. [10] expanded the Holder’s model and considered two phase flow. Yousif et al. [11] applied kinetic model, but without considering the effect of temperature change on hydrate dissociation. Moridis et al. [12] added EOSHYDR2 module to Tough2, which can simulate gas production in the cases of complex formation. Ahmadi et al. [13] established an axisymmetric model, considering dissociation kinetics and gas-water two phase flow. S. H. tabatabaie [14] proposed an analytical model for calculating gas production rate under a constant bottom-hole pressure. A. Shahbazi [15] developed a three-dimensional numerical model and simulated gas production from Class III hydrate reservoirs. On the basis of the mathematical model, combined with the characteristics of NGH, a 3D numerical model was developed. This model is used to simulate the development of Class I hydrate reservoir. The sensitivity analysis of the factors including development parameters and reservoir parameters were performed. The
282
X. Jiang et al. / Energy 39 (2012) 281e285
results can provide theoretical basis for the development of hydrates in the future. 2. Mathematical model According to the mechanism of gas hydrate dissociation and basic fundamentals of fluid flow in porous media [16] and [17], we established a three-dimensional Cartesian numerical model involving three phase (hydrate, water and gas) and three components (hydrate, water, gas). Hypothesis: Kinetics of hydrate dissociation is considered and hydrate dissociates gas and water; Gaswater two phase flow follows Darcy’ Law; Heat transfer through convection and conduction is considered; The diffusion and dissolve of gas are ignored.
Fig. 1. The geologic model.
2.1. Mass balance equations The mass balance equations of three components are as follows:
rg kkrg V, Vpg mg
!
v _g ¼ frg Sg þ qg þ m vt
_ h ¼ m _g m
(1) _g _w ¼ m m
r kkrw v _w ¼ V, w Vpw þ qw þ m ðfrw Sw Þ mw vt
(2)
v _h ¼ m ðfrh Sh Þ vt
(3)
nh Mw þ Mg Mg
(10)
nh Mw Mg
(11)
2.4. Equilibrium model
2.2. Energy balance equation
Natural gas hydrate laboratory of China University of Petroleum does a lot of experiments to measure the relationship of the equilibrium hydration pressure Pe and temperature T. Equilibrium points of NGH were determined using graphical method. The following relation can be obtained by fitting the experimental data.
Pe ¼ 8 1013 e0:1052T
"
V, leff VT þ V,
Cw rw kkrw
mw
Vpw þ
Cg rg kkrg
mg
!
#
Vpg ,T
v _ h ,DHh þ qw Cw T þ qg Cg T ¼ m Ceff ,T vt
(4)
Ceff ¼ ð1 fÞrR CR þ f Sw rw Cw þ Sh rh Ch þ Sg rg Cg
2.5. Absolute permeability model
(5)
Hydrate dissociation in porous media can change the pore structure, causing the changes of permeability. Therefore, the relationship between hydrate saturation and the reservoir permeability must be considered. In this paper, Masuda’s formula was adopted [20] and [21].
(6)
k=k0 ¼ ð1 Sh ÞN
where,
leff ¼ ð1 fÞlR þ f Sw lw þ Sg lg þ Sh lh
(12)
(13)
2.6. Relative permeability model 2.3. Dissociation kinetic model The transition between hydrate and gas and water can be written as [18]:
CH4 ,nh H2 O0CH4 þ nh H2 O
(7)
The Kim-Bishnoi model is adopted, as follows [19]:
_ g ¼ Kd As ðpe pÞ m
(8)
As ¼ fSh AHS
(9)
AHS ¼ 300; 000 m1 According to dissociation of chemical formula, calculate the mass of gas hydrate decomposed and the decomposition water.
The relative permeability was considered with the modification of Brooks-Corey model [22]. Table 1 Parameters of the model. Property
Hydrate layer
Free gas layer
Initial temperature, K Initial pressure, MPa Thickness, m Absolute permeability, md Porosity, fraction Water saturation, Sw, fraction Initial hydrate saturation, Sh, fraction Initial gas saturation, Sg, fraction Area, m2 Bottom-hole pressure, MPa Dissociation rate constant, mol/(m2 KPa s)
283 7.8 12 20 0.3 0.2 0.6 0.2 21 10 4 4.4 1012
6 20 0.3 0.3 0 0.7 21 10
X. Jiang et al. / Energy 39 (2012) 281e285
283
Fig. 4. Gas release rate with varying absolute permeability. Fig. 2. Gas release rate with varying initial hydrate reservoir pressure.
8 > < krg
*
ng
¼ k0rg Seg * nw krw ¼ k0rw Sew > : pc ¼ pce Se* nc w
(14)
depressurization. In order to investigate parametric sensitivity during production from Class I deposits, a Class I hydrate reservoir (Fig. 1) is established. The area of the geologic model is 210 m 210 m and its thickness is 18 m (hydrate layer 12 m, free gas layer 6 m). The system is discretized in 21 21 6 ¼ 2, 646 gridblocks in (x, y, z). A well is located at the center of the geologic model. Related parameters of the model are listed in Table 1.
where,
8 Sg > > Seg ¼ > > > S þ g Sw 8 > > 8 sffiffiffiffiffiffiffiffiffiffi > Seg Segr > > * Sw > > e e > > fe k0 < < Sg ¼ 1 S e Se > < Sw ¼ 0 Sg þ Sw pce ¼ pce wr gr , , f0 k e e > Sw Swr > > : > > Se ¼ Sgr e* > gr : Sw ¼ 1 S e Se > > f f ¼ þ S e 0 g Sw > S þ S g w > wr gr > > > Swr > > : Sewr ¼ Sg þ Sw
4. Sensitivity studies
(15)
The equations are spatially discretized by a finite difference method. IMPES method is used to solve the mass balance equations and temperature is solved implicitly. A fast convergence and high accuracy incomplete LU decomposition, preconditioned conjugate gradient method is adopted.
In this section, the effects of key reservoir parameters and operating conditions have been studied on gas release rate in the hydrate reservoir. 4.1. Effect of initial hydrate reservoir pressure For Class I hydrate reservoir, Fig. 2 shows the gas release rate have a mild dependence on initial hydrate reservoir pressure. At the early stage, as reservoir pressure increases, gas release rate decreases. This is contrary to conventional gas reservoir. Because the higher initial reservoir pressure causes pressure drop slowly. Then, equilibrium pressure is reached more difficult. Finally, gas release rate in the reservoir is small.
3. Reservoir model 4.2. Effect of initial reservoir temperature In 1960s, gas production from Messoyakha gas field in Siberian by Depressurization technology [23]. The Messoyakha field is a typical Class I hydrate reservoir. Results indicate very high potential for producing gas from Class I hydrate reservoir using
In Fig. 3, it’s obvious that gas release rate depends strongly on hydrate reservoir temperature. In contrast with the effect of initial
Fig. 3. Gas release rate with varying initial hydrate reservoir temperature.
Fig. 5. Gas release rate with varying dissociation rate constant.
284
X. Jiang et al. / Energy 39 (2012) 281e285
was used to examine the effect of large number parameters on performance of hydrate reservoir. Though the sensitivity studies, we can draw the following conclusions: 1. During the constant bottom-hole production period, gas release rate increases gradually to peak and then reduces. 2. For Class I hydrate reservoir, the effect of initial reservoir temperature, absolute permeability, dissociation rate constant and bottom-hole pressure on gas release rare is bigger. 3. For Class I hydrate reservoir, gas release rate increases with the increases of initial reservoir temperature. The bigger the absolute permeability is, the higher the gas release rate is. Hydrate dissociation rate is significantly improved, when dissociation rate constant increases. High initial reservoir pressure and bottom-hole pressure will lead to low hydrate dissociation rate. 4. For Class I hydrate reservoir, when initial hydrate reservoir temperature is very low, gas production from hydrates is recommended by the combination of heat injection and depressurization.
Fig. 6. Gas release rate with varying bottom-hole pressure.
reservoir pressure, this plot shows that reservoir temperature increases, gas release rate increases. Gas and water released from hydrate need absorb heat. As we all know, the higher reservoir temperature is, the reservoir energy is greater. In addition, as reservoir temperature increases, the corresponding equilibrium pressure increases. Therefore, hydrate dissociates faster, as shown in Equation (8). When initial hydrate reservoir temperature is very low, gas production from hydrates is recommended by the combination of heat injection and depressurization.
Acknowledgment This work is financially supported by Numerical Simulation of Natural Gas Hydrate Production by Depressurization and Thermal Stimulation (Grant No.GZH201100310) and the Fundamental Research Funds for the Central Universities (Grant No. 09CX05001A). Nomenclature porosity, fraction k permeability, mm2 krg gas relative permeability, fraction water relative permeability, fraction krw k0rg relative permeability endpoint value of gas phase, fraction
f
4.3. Effect of absolute permeability Permeability can reflect the seepage of the porous media. It is the important factor of influencing gas release rate. Fig. 4 shows that gas release rate increases with absolute permeability. This was expected because big absolute permeability results in fast gas flow, so the pressure declines fast. As a result, hydrate dissociates faster. The result is identical with Moridis’ studies [24]. 4.4. Effect of dissociation rate constant Fig. 5 presents the effect of dissociation rate constant from 0.44 1012to 44 1012 mol/(m2 KPa s) on gas release rate. With higher dissociation rate constant, hydrates dissociate faster. Dissociation constant changes an order of magnitude will result in distinct hydrate dissociation rate. 4.5. Effect of bottom-hole pressure Fig. 6 shows gas release rate when bottom-hole pressure is changed. Initially, the effect is not significant, because gas production of this stage is mainly from free gas. Then, the differential pressure between reservoir pressure and equilibrium pressure grows big. As expected, the lower bottom-hole pressure is, the greater peak of gas release rate is. So gas release rate depends strongly on the degree of pressure reduction. However, increasing hydrate dissociation rate results in a decrease of reservoir temperature. Ultimately, gas release rate decreases faster at later times. 5. Conclusions A three-dimensional, three phase, three component mathematical model was developed, which can be applied to predict gas production from Class I hydrate reservoir. In addition, this model
k0rw k0 N Sg Sw Sh Sgr Sgw
rg rw rh
pg pw pe p0ce pc pwf T
mg mw
_g m _w m _h m Cg Cw Ch CR
lg
relative permeability endpoint value of water phase, fraction permeability when hydrate saturation is 0, mm2 the permeability reduction index, fraction gas saturation, fraction water saturation, fraction hydrate saturation, fraction irreducible gas saturation, fraction irreducible water saturation, fraction density of gas, g/cm3 density of water, g/cm3 density of hydrate, g/cm3 pressure of gas, 0.1 MPa pressure of water, 0.1 MPa critical pressure, 0.1 MPa gas entry pressure for modified Brooks-Corey capillary pressure function, 0.1 MPa capillary pressure, 0.1 MPa flowing wellbore pressure, 0.1 MPa reservoir temperature, K viscosity of gas, mPa s viscosity of water, mPa s mass rate of gas produced per unit volume, g/(cm3 s) mass rate of water produced per unit volume, g/(cm3 s) mass rate of hydrate decomposed per unit volume, g/(cm3 s) heat capacity of gas, J/(g K) heat capacity of water, J/(g K) heat capacity of hydrate, J/(g K) heat capacity of rock, J/(g K) thermal conductivity of gas, W/(cm K)
X. Jiang et al. / Energy 39 (2012) 281e285
lw lh lR kd Mg Mw nh ng nw nc DHh
thermal conductivity of water, W/(cm K) thermal conductivity of hydrate, W/(cm K) thermal conductivity of rock, W/(cm K) dissociation rate constant, mol/(KPa m2 s) molecular weights of gas, g/mol molecular weights of water, g/mol hydrate number (5.75), dimensionless gas phase index, dimensionless water phase index, dimensionless capillary force index, dimensionless heat of dissociation of hydrate, J/mol
References [1] Makogon YF. Hydrates of hydrocarbons. Tulsa: Pennwell Books; 1997. pp. 482. [2] Zhu Haiyan, Liu Qingyou, Deng Jingen, Wang Guorong, Xiao Xiaohua, Jiang Zhenglu, et al. Pressure and temperature preservation techniques for gas-hydrate-bearing sediments sampling. Energy 2011;36:4542e51. [3] Moridis GJ. Numerical studies of gas production from class 2 and class 3 hydrate accumulations at the Mallik Site, Mackenzie Delta, Canada. SPE; 2004:88039. [4] Moridis GJ, Reagan MT, Boyle K, Zhang K. Sensitivity analysis of gas production from Class 2 and Class 3 hydrate deposits. OTC; 2008:19554. [5] Alp Doruk, Parlaktuna Mahmut, Moridis GJ. Gas production by depressurization from hypothetical Class 1G and Class 1W hydrate reservoirs. Energy Conversion Manage 2007;48:1864e79. [6] Li Gang, Li XiaoSen, Wang Yi, Zhang Yu. Production behavior of methane hydrate in porous media using huff and puff method in a novel threedimensional simulator. Energy 2011;36:3170e87. [7] Holder GD, Angert PF. Simulation of gas production from a reservoir containing both gas hydrate and free natural gas. SPE; 1982:11105. [8] McGuire PL. Recovery of gas from hydrate deposits using conventional technology. SPE; 1982:10832.
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[9] Sung Wonmo, Lee Hoseob, Kim Sunjoon. Numerical study for production performances of a methane hydrate reservoir stimulated by inhibitor injection. Energy Sources 2003;25:845e56. [10] Burshears M, O’Brien TJ, Malone RD. A multi-phase, multi-dimensional, variable composition simulation of gas production from a conventional gas reservoir in contact with hydrate. SPE; 1986:15246. [11] Yousif MH, Abass HH, Selim MS, Sloan ED. Experimental and theoretical investigation of methane-gas-hydrate dissociation in porous media. SPE; 1991:18320. [12] Moridis GJ. Numerical studies of gas production from methane hydrates. SPE; 2003:87330. [13] Ahmadi G, Ji C, Smith DH. Natural gas production from hydrate dissociation: an axisymmetric model. J Pet Sci Eng 2007;58:245e58. [14] Tabatabaie SH, Pooladi-Darvish M. Analytical solution for constant pressure production from hydrate-capped gas reservoir, Canadian International Petroleum Conference (2009), pp. 189. [15] Shahbazi A, Pooladi-Darvish M. Behavior of depressurization in type III hydrate reservoirs. SPE; 2010:137047. [16] Ge JL. Basic fundamental of fluid flow in porous medium. Beijing: Petroleum Industry Press; 1982. [17] Li S. Basic reservoir numerical simulation. China Petroleum University Press; 2008. [18] Sloan ED. Clathrate hydrate of natural gases. New York: Marcel Dekker, Inc; 1998. [19] Kim HC, Bishnoi PR, Heidemann RA, Hrizvi SSH. Kinetics of methane hydrate decomposition. Chem Eng Sci 1987;42:1645e53. [20] Masuda Y. Modeling and experimental studies on dissociation of methane gas hydrates in Berea sandstone cores, Proceedings of Third International Conference on Gas Hydrates, Salt Lake City, Utah, USA (1999). [21] Nazridoust K, Ahmadi G. Computational modeling of methane hydrate dissociation in a sandstone core. Chem Eng Sci 2007;62:6155e77. [22] Lake LW. Enhanced oil recovery. Upper Saddle River, NJ: Prentice-Hall Inc; 1989. [23] Grover T. Analysis of reservoir performance of the Messoyakha gas hydrate reservoir. SPE; 2008:114375. [24] Moridis GJ, Reagan MT, Boyle K, Zhang K. Evaluation of a deposit at the PBUL106 site, North Slope, Alaska, for a potential long-term test of gas production from Hydrates. SPE; 2010:133601.
Contents lists available at SciVerse ScienceDirect
Energy journal homepage: www.elsevier.com/locate/energy
Sensitivity analysis of gas production from Class I hydrate reservoir by depressurization Xingxing Jiang*, Shuxia Li, Lina Zhang Department of Petroleum Engineering, China University of Petroleum (East China), Qingdao, Shandong 266555, China
a r t i c l e i n f o
a b s t r a c t
Article history: Received 9 August 2011 Received in revised form 23 December 2011 Accepted 10 January 2012 Available online 11 February 2012
A 3D numerical model for gas production from hydrate reservoirs is developed, which considers kinetics of dissociation, heat and multiphase fluid flow. Three components (gas, water and hydrate) and three phases (gas, water and hydrate) are considered in the model. The equations are spatially discretized by a finite difference method. IMPES method is used to solve the mass balance equations and temperature is solved implicitly. Based on the model, gas production from Class I hydrate reservoir (with underlying free gas) under constant bottom-hole pressure was simulated. The sensitivity analysis of the factors including development parameters and reservoir parameters were performed. Results show that hydrate dissociation rate increases with the increases of initial reservoir temperature. The larger the absolute permeability is, the higher the hydrate dissociation rate is. Hydrate dissociation rate is significantly improved, when dissociation rate constant increases. However, higher initial reservoir pressure and bottom-hole pressure will lead to lower hydrate dissociation rate. Research results provide theoretical support for hydrate production. Ó 2012 Elsevier Ltd. All rights reserved.
Keywords: Hydrate reservoir Depressurization Numerical model Sensitivity studies
1. Introduction With oil and gas resources of the growing tension, looking for the new and replacement energy is imminently. In recent years, Natural gas hydrate (NGH) found in the sea and permafrost is recognized as the most important energy resource because of its large reserve, clean and high energy efficiency. Gas hydrates are solid crystalline compounds of natural gas molecules, which are encaged within a crystal structure composed of water molecules. Hydrate exists in low temperature and high pressure [1] and [2]. At present, hydrate accumulations have been divided into three main classes [3]: Class I (underlying free gas), Class II (underlying free-water) and Class III (single hydrate zone). In addition, Class IV pertains specifically to oceanic accumulations, and involves disperse, low-saturation hydrate deposits that lack confining geologic strata [4]. Class I deposits are relatively easy to induce hydrate dissociation because of the proximity to equilibrium at the hydrateegas interface [5]. Currently, three main methods are proposed to exploit hydrate: depressurization, thermal stimulation, inhibitor injection [6,7,8,9]. In comparison, depressurization is a relatively inexpensive and economical method.
* Corresponding author. Tel.: þ86 1386 4892 917; fax: þ86 532 8698 1936. E-mail address: [email protected] (X. Jiang). 0360-5442/$ e see front matter Ó 2012 Elsevier Ltd. All rights reserved. doi:10.1016/j.energy.2012.01.016
At present, scholars have done a lot of research on numerical simulation of NGH by depressurization. A series of mathematical model have been developed at home and abroad, including analytical model and numerical model, from one-dimension to three-dimension, from one single phase to multiphase. With the continuous research, model is more and more perfect. Holder et al. [7] developed a 3D single phase model which applied the heat conduction equation and considered the change of temperature during the NGH dissociation. Then Burshears et al. [10] expanded the Holder’s model and considered two phase flow. Yousif et al. [11] applied kinetic model, but without considering the effect of temperature change on hydrate dissociation. Moridis et al. [12] added EOSHYDR2 module to Tough2, which can simulate gas production in the cases of complex formation. Ahmadi et al. [13] established an axisymmetric model, considering dissociation kinetics and gas-water two phase flow. S. H. tabatabaie [14] proposed an analytical model for calculating gas production rate under a constant bottom-hole pressure. A. Shahbazi [15] developed a three-dimensional numerical model and simulated gas production from Class III hydrate reservoirs. On the basis of the mathematical model, combined with the characteristics of NGH, a 3D numerical model was developed. This model is used to simulate the development of Class I hydrate reservoir. The sensitivity analysis of the factors including development parameters and reservoir parameters were performed. The
282
X. Jiang et al. / Energy 39 (2012) 281e285
results can provide theoretical basis for the development of hydrates in the future. 2. Mathematical model According to the mechanism of gas hydrate dissociation and basic fundamentals of fluid flow in porous media [16] and [17], we established a three-dimensional Cartesian numerical model involving three phase (hydrate, water and gas) and three components (hydrate, water, gas). Hypothesis: Kinetics of hydrate dissociation is considered and hydrate dissociates gas and water; Gaswater two phase flow follows Darcy’ Law; Heat transfer through convection and conduction is considered; The diffusion and dissolve of gas are ignored.
Fig. 1. The geologic model.
2.1. Mass balance equations The mass balance equations of three components are as follows:
rg kkrg V, Vpg mg
!
v _g ¼ frg Sg þ qg þ m vt
_ h ¼ m _g m
(1) _g _w ¼ m m
r kkrw v _w ¼ V, w Vpw þ qw þ m ðfrw Sw Þ mw vt
(2)
v _h ¼ m ðfrh Sh Þ vt
(3)
nh Mw þ Mg Mg
(10)
nh Mw Mg
(11)
2.4. Equilibrium model
2.2. Energy balance equation
Natural gas hydrate laboratory of China University of Petroleum does a lot of experiments to measure the relationship of the equilibrium hydration pressure Pe and temperature T. Equilibrium points of NGH were determined using graphical method. The following relation can be obtained by fitting the experimental data.
Pe ¼ 8 1013 e0:1052T
"
V, leff VT þ V,
Cw rw kkrw
mw
Vpw þ
Cg rg kkrg
mg
!
#
Vpg ,T
v _ h ,DHh þ qw Cw T þ qg Cg T ¼ m Ceff ,T vt
(4)
Ceff ¼ ð1 fÞrR CR þ f Sw rw Cw þ Sh rh Ch þ Sg rg Cg
2.5. Absolute permeability model
(5)
Hydrate dissociation in porous media can change the pore structure, causing the changes of permeability. Therefore, the relationship between hydrate saturation and the reservoir permeability must be considered. In this paper, Masuda’s formula was adopted [20] and [21].
(6)
k=k0 ¼ ð1 Sh ÞN
where,
leff ¼ ð1 fÞlR þ f Sw lw þ Sg lg þ Sh lh
(12)
(13)
2.6. Relative permeability model 2.3. Dissociation kinetic model The transition between hydrate and gas and water can be written as [18]:
CH4 ,nh H2 O0CH4 þ nh H2 O
(7)
The Kim-Bishnoi model is adopted, as follows [19]:
_ g ¼ Kd As ðpe pÞ m
(8)
As ¼ fSh AHS
(9)
AHS ¼ 300; 000 m1 According to dissociation of chemical formula, calculate the mass of gas hydrate decomposed and the decomposition water.
The relative permeability was considered with the modification of Brooks-Corey model [22]. Table 1 Parameters of the model. Property
Hydrate layer
Free gas layer
Initial temperature, K Initial pressure, MPa Thickness, m Absolute permeability, md Porosity, fraction Water saturation, Sw, fraction Initial hydrate saturation, Sh, fraction Initial gas saturation, Sg, fraction Area, m2 Bottom-hole pressure, MPa Dissociation rate constant, mol/(m2 KPa s)
283 7.8 12 20 0.3 0.2 0.6 0.2 21 10 4 4.4 1012
6 20 0.3 0.3 0 0.7 21 10
X. Jiang et al. / Energy 39 (2012) 281e285
283
Fig. 4. Gas release rate with varying absolute permeability. Fig. 2. Gas release rate with varying initial hydrate reservoir pressure.
8 > < krg
*
ng
¼ k0rg Seg * nw krw ¼ k0rw Sew > : pc ¼ pce Se* nc w
(14)
depressurization. In order to investigate parametric sensitivity during production from Class I deposits, a Class I hydrate reservoir (Fig. 1) is established. The area of the geologic model is 210 m 210 m and its thickness is 18 m (hydrate layer 12 m, free gas layer 6 m). The system is discretized in 21 21 6 ¼ 2, 646 gridblocks in (x, y, z). A well is located at the center of the geologic model. Related parameters of the model are listed in Table 1.
where,
8 Sg > > Seg ¼ > > > S þ g Sw 8 > > 8 sffiffiffiffiffiffiffiffiffiffi > Seg Segr > > * Sw > > e e > > fe k0 < < Sg ¼ 1 S e Se > < Sw ¼ 0 Sg þ Sw pce ¼ pce wr gr , , f0 k e e > Sw Swr > > : > > Se ¼ Sgr e* > gr : Sw ¼ 1 S e Se > > f f ¼ þ S e 0 g Sw > S þ S g w > wr gr > > > Swr > > : Sewr ¼ Sg þ Sw
4. Sensitivity studies
(15)
The equations are spatially discretized by a finite difference method. IMPES method is used to solve the mass balance equations and temperature is solved implicitly. A fast convergence and high accuracy incomplete LU decomposition, preconditioned conjugate gradient method is adopted.
In this section, the effects of key reservoir parameters and operating conditions have been studied on gas release rate in the hydrate reservoir. 4.1. Effect of initial hydrate reservoir pressure For Class I hydrate reservoir, Fig. 2 shows the gas release rate have a mild dependence on initial hydrate reservoir pressure. At the early stage, as reservoir pressure increases, gas release rate decreases. This is contrary to conventional gas reservoir. Because the higher initial reservoir pressure causes pressure drop slowly. Then, equilibrium pressure is reached more difficult. Finally, gas release rate in the reservoir is small.
3. Reservoir model 4.2. Effect of initial reservoir temperature In 1960s, gas production from Messoyakha gas field in Siberian by Depressurization technology [23]. The Messoyakha field is a typical Class I hydrate reservoir. Results indicate very high potential for producing gas from Class I hydrate reservoir using
In Fig. 3, it’s obvious that gas release rate depends strongly on hydrate reservoir temperature. In contrast with the effect of initial
Fig. 3. Gas release rate with varying initial hydrate reservoir temperature.
Fig. 5. Gas release rate with varying dissociation rate constant.
284
X. Jiang et al. / Energy 39 (2012) 281e285
was used to examine the effect of large number parameters on performance of hydrate reservoir. Though the sensitivity studies, we can draw the following conclusions: 1. During the constant bottom-hole production period, gas release rate increases gradually to peak and then reduces. 2. For Class I hydrate reservoir, the effect of initial reservoir temperature, absolute permeability, dissociation rate constant and bottom-hole pressure on gas release rare is bigger. 3. For Class I hydrate reservoir, gas release rate increases with the increases of initial reservoir temperature. The bigger the absolute permeability is, the higher the gas release rate is. Hydrate dissociation rate is significantly improved, when dissociation rate constant increases. High initial reservoir pressure and bottom-hole pressure will lead to low hydrate dissociation rate. 4. For Class I hydrate reservoir, when initial hydrate reservoir temperature is very low, gas production from hydrates is recommended by the combination of heat injection and depressurization.
Fig. 6. Gas release rate with varying bottom-hole pressure.
reservoir pressure, this plot shows that reservoir temperature increases, gas release rate increases. Gas and water released from hydrate need absorb heat. As we all know, the higher reservoir temperature is, the reservoir energy is greater. In addition, as reservoir temperature increases, the corresponding equilibrium pressure increases. Therefore, hydrate dissociates faster, as shown in Equation (8). When initial hydrate reservoir temperature is very low, gas production from hydrates is recommended by the combination of heat injection and depressurization.
Acknowledgment This work is financially supported by Numerical Simulation of Natural Gas Hydrate Production by Depressurization and Thermal Stimulation (Grant No.GZH201100310) and the Fundamental Research Funds for the Central Universities (Grant No. 09CX05001A). Nomenclature porosity, fraction k permeability, mm2 krg gas relative permeability, fraction water relative permeability, fraction krw k0rg relative permeability endpoint value of gas phase, fraction
f
4.3. Effect of absolute permeability Permeability can reflect the seepage of the porous media. It is the important factor of influencing gas release rate. Fig. 4 shows that gas release rate increases with absolute permeability. This was expected because big absolute permeability results in fast gas flow, so the pressure declines fast. As a result, hydrate dissociates faster. The result is identical with Moridis’ studies [24]. 4.4. Effect of dissociation rate constant Fig. 5 presents the effect of dissociation rate constant from 0.44 1012to 44 1012 mol/(m2 KPa s) on gas release rate. With higher dissociation rate constant, hydrates dissociate faster. Dissociation constant changes an order of magnitude will result in distinct hydrate dissociation rate. 4.5. Effect of bottom-hole pressure Fig. 6 shows gas release rate when bottom-hole pressure is changed. Initially, the effect is not significant, because gas production of this stage is mainly from free gas. Then, the differential pressure between reservoir pressure and equilibrium pressure grows big. As expected, the lower bottom-hole pressure is, the greater peak of gas release rate is. So gas release rate depends strongly on the degree of pressure reduction. However, increasing hydrate dissociation rate results in a decrease of reservoir temperature. Ultimately, gas release rate decreases faster at later times. 5. Conclusions A three-dimensional, three phase, three component mathematical model was developed, which can be applied to predict gas production from Class I hydrate reservoir. In addition, this model
k0rw k0 N Sg Sw Sh Sgr Sgw
rg rw rh
pg pw pe p0ce pc pwf T
mg mw
_g m _w m _h m Cg Cw Ch CR
lg
relative permeability endpoint value of water phase, fraction permeability when hydrate saturation is 0, mm2 the permeability reduction index, fraction gas saturation, fraction water saturation, fraction hydrate saturation, fraction irreducible gas saturation, fraction irreducible water saturation, fraction density of gas, g/cm3 density of water, g/cm3 density of hydrate, g/cm3 pressure of gas, 0.1 MPa pressure of water, 0.1 MPa critical pressure, 0.1 MPa gas entry pressure for modified Brooks-Corey capillary pressure function, 0.1 MPa capillary pressure, 0.1 MPa flowing wellbore pressure, 0.1 MPa reservoir temperature, K viscosity of gas, mPa s viscosity of water, mPa s mass rate of gas produced per unit volume, g/(cm3 s) mass rate of water produced per unit volume, g/(cm3 s) mass rate of hydrate decomposed per unit volume, g/(cm3 s) heat capacity of gas, J/(g K) heat capacity of water, J/(g K) heat capacity of hydrate, J/(g K) heat capacity of rock, J/(g K) thermal conductivity of gas, W/(cm K)
X. Jiang et al. / Energy 39 (2012) 281e285
lw lh lR kd Mg Mw nh ng nw nc DHh
thermal conductivity of water, W/(cm K) thermal conductivity of hydrate, W/(cm K) thermal conductivity of rock, W/(cm K) dissociation rate constant, mol/(KPa m2 s) molecular weights of gas, g/mol molecular weights of water, g/mol hydrate number (5.75), dimensionless gas phase index, dimensionless water phase index, dimensionless capillary force index, dimensionless heat of dissociation of hydrate, J/mol
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