Front. Energy Power Eng. China 2009, 3(2): 152–159 DOI 10.1007/s11708-009-0017-x
REVIEW ARTICLE
Lin ZUO, Lixia SUN, Changfu YOU
Latest progress in numerical simulations on multiphase flow and thermodynamics in production of natural gas from gas hydrate reservoir
© Higher Education Press and Springer-Verlag 2009
Abstract Natural gas hydrates are promising potential alternative energy resources. Some studies on the multiphase flow and thermodynamics have been conducted to investigate the feasibility of gas production from hydrate dissociation. The methods for natural gas production are analyzed and several models describing the dissociation process are listed and compared. Two prevailing models, one for depressurization and the other for thermal stimulation, are discussed in detail. A comprehensive numerical method considering the multiphase flow and thermodynamics of gas production from various hydratebearing reservoirs is required to better understand the dissociation process of natural gas hydrate, which would be of great benefit to its future exploration and exploitation. Keywords numerical simulation, natural gas hydrate, dissociation, thermodynamics, multiphase flow
1
Introduction
Hydrocarbon hydrates are attracting increasing attention as a potential alternative energy resource because of the sheer size of the world reserve and the ever increasing energy demand. The world reserve of natural gas trapped in hydrates, both in oceanic sediments and under permafrost regions where low temperatures and high pressures promote the hydrate formation, is estimated to be several times bigger than the known reserves of conventional natural gas and oil combined [1]. Current estimates of the world natural gas Received October 10, 2008; accepted December 15, 2008
✉
Lin ZUO, Lixia SUN, Changfu YOU ( ) Key Laboratory for Thermal Science and Power Engineering of Ministry of Education, Department of Thermal Engineering, Tsinghua University, Beijing 100084, China E-mail:
[email protected]
reserve in hydrates is 0.71015 – 21015 m3, and the best estimate is 11015 – 51015 m3 [2]. Since the scientific well program started in 1998 in the Mallik gas hydrate field, located at the northeastern edge of Canada’s Mackenzie Delta, five methane hydrate-bearing zones have been explored as ideal sites for field tests of gas production from a natural gas hydrate reservoir. As one of the most concentrated gas hydrate reservoirs in the world and the first place for large scale field tests, Mallik plays a significant role in certifying the studies and corresponding processes of hydrate-originating production at present. Many countries have made large amounts of investment in natural gas hydrate studies, as shown in Table 1. Table 1 Research project of natural gas hydrates in the world [3] year
event
1970
beginning of natural gas production from hydrate reservoirs in Messoyakha, Russia
1982
first research project of natural gas hydrates in America (8 million US dollars)
1995
first research project of natural gas hydrates in Japan (10 million US dollars)
1996
first research project of natural gas hydrates in India (5 million US dollars)
1999
first research project of natural gas hydrates in Korea (5 million US dollars)
2001
second research project of natural gas hydrates in Japan (200 million US dollars)
2001
second research project of natural gas hydrates in America (50 million US dollars)
2004
research project of natural gas hydrates in China (50 million US dollars)
2004
second research project of natural gas hydrates in India (18 million US dollars)
2005
second research project of natural gas hydrates in Korea (83 million US dollars)
2005
third research project of natural gas hydrates in America (150 million US dollars)
Lin ZUO et al. Production of natural gas from gas hydrate reservoir
Gas hydrates are solid crystal compounds in which gas molecules are lodged within the lattices of ice crystals. Under suitable conditions, the following reaction takes place: G þ nH2 O ¼ G$nH2 O,
(1)
where n is the hydration number and G refers to a kind of gas. Particularly, when the gas is methane (CH4) the hydration number equals six and the compounds are methane hydrates, which represent the majority of natural gas hydrates. Current studies conducted focus on the natural gas production from hydrate dissociation mainly by depressurization, thermal stimulation, and inhibitor injection. In depressurization, the pressure of the fluids in contact with hydrates is lowered, pushing hydrates out of the stability region and leading to decomposition. Because no extra heat is introduced into the reservoir, the heat for decomposition must be supplied from the surroundings. Besides, the presence of a free-gas zone beneath the hydrate may be essential to the success of the depressurization. In thermal stimulation, heat is introduced into a hydrate-bearing reservoir, causing destabilization of hydrate particles, by the injection of hot fluids, including water, brine, or steam, or by involving a downhole process, such as in-situ combustion or electric /electromagnetic heating [4]. However, the economic cost associated with such methods calls for careful planning and engineering. Injecting inhibitors causes hydrate decomposition by shifting the thermodynamic equilibrium, but this method is limited to small volumes because of the high cost of inhibitors. Figure 1 schematically shows the equilibrium curve and the methods of hydrate dissociation [5].
processes and provide technical criteria for the selection of promising hydrate-bearing zones for commercial gas production. For these reasons, this paper focuses on the different numerical models of natural gas production from hydrate reservoirs and current simulation results. Moreover, some recommendations are proposed for further development of numerical studies about natural gas hydrate dissociation.
2
Numerical simulations of natural gas production from hydrate reservoirs play a significant role in predicting gas hydrate behavior during dissociation, in supporting the design for field experiments of hydrate gas production, and in evaluating hydrate-bearing zones with appropriate production methods. In addition, with numerical simulations, researchers are able to identify the controlling
Numerical models
The existing models proposed for gas production from hydrate dissociation can be divided into models based on thermal method and models based on depressurization. Generally, hydrate-bearing reservoirs, which may also contain free gas or water, are in the equilibrium state with high pressure and low temperature. When the equilibrium is undermined by depressurization, thermal stimulation or inhibitor injection, the hydrates are no longer stable and begin to dissociate into natural gas and water (or ice forms in some specific sediments because of the rapid temperature drop caused by the strong endothermic reaction of hydrate dissociation). The process of hydrate dissociation then expands owing to heat and mass transfer. As a result, the reservoir can be divided into the zone where the dissociation has finished, dominated by the multiphase flow in porous medium and heat convection; the zone with undissociated hydrates, with free gas or water in some cases, dominated by heat conduction and convection if free gas or water exist; and the zone called the dissociation front, where hydrates are dissociating. Some models determine this front by the equilibrium curve of pressure and temperature and describe this zone with mass and energy conservations. Moreover, the kinetics of hydrate dissociation is used in more comprehensive models to describe this zone. 2.1
Fig. 1 Schematic representation of the hydrate dissociation methods [5]
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Thermal models
Holder and Angert [6] developed a thermal based model to simulate the production from a hydrate zone adjacent to a conventional gas reservoir. In this model, the conservations of mass and energy of gas phase are included but the water production from hydrate dissociation is ignored. Mcguire [7] developed two analytical thermal models in 1982, which represented the upper and lower bounds on gas hydrate production and determined the effects of porosity, bed thickness, and injection temperature on hydrate dissociation process. Selim and Sloan [8] studied hydrate dissociation in a semi-infinite, hydrate-filled porous medium. They developed an analytical thermal model using a continuity equation, Darcy’s Law, and energy balance equations for the dissociated and undissociated phases. The system of equations that describe Selim’s model [8] is shown below.
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Mass balance: ∂g ∂ðg ug Þ f þ ¼ 0, ∂t ∂x
(2)
where, Φ is the porosity of hydrate reservoir, ρg the density of gas, ug the velocity of gas, t the time, and x the distance from well. Darcy’s Law for gas: ug ¼ –
k ∂p , ∂x
2.2
∂T1 ∂ ∂2 T þ ðg Cpg ug T1 Þ ¼ kh1 21 , ∂t ∂x ∂x
(4)
where ρ1, T1, and Cp1 are the density, the temperature, and the heat capacity of zone 1, respectively; Cpg, the heat capacity of gas; and kh1, the thermal conductivity of zone 1. Heat balance in undissociated zone (zone 2): ∂T2 ∂2 T ¼ α2 22 , ∂t ∂x
(5)
where T2 is the temperature of zone 2; and α2, the thermal diffusivity of zone 2. Ideal gas law: g ¼
p , RT1
(6)
where R is the gas constant. Mass balance at the dissociation interface: FH H
dx þ g ug ¼ 0, dt
(7)
where ρH is the density of hydrate; and FH, the mass fraction of gas in hydrate. Heat balance at the dissociation interface: kh2
∂T2 ∂T dx – kh1 1 ¼ fH QH , ∂x ∂x dt
Depressurization models
(3)
where, k is the permeability of gas, μ the viscosity of gas, and p the pressure. Heat balance in dissociated zone (zone 1): 1 Cp1
appropriate values of parameters, such as permeability and heat capacity in different zones, to include the effect of water existing during the dissociation, this model is used to analyze hydrate dissociation for conditions of local chemical equilibrium driven by thermal stimulation. The boundary conditions of temperature are set for different exploitation situations while those of pressure are set according to the initial conditions of hydrate reservoirs.
(8)
Models based on depressurization method are also proposed. Burshears et al. [9] used a 3D, two-phase simulator to address the questions regarding the feasibility of producing gas from hydrates when a conventional gas reservoir is in contact with a hydrate cap. They assumed that the dissociation of hydrates is affected by depressurization. The temperature at any point on the hydrate-gas interface was assumed to be the equilibrium dissociation temperature at the local pressure. The kinetic reaction is not included in this model. Yousif et al. [10] developed a 1D, three-phase numerical finite difference simulator to simulate gas production from hydrates in a Berea sandstone sample in the laboratory. Several experiments were conducted in the laboratory to validate the model. Ahmadi et al. [11,12] conducted many investigations on modeling the process of hydrate dissociation by depressurization. A one-dimensional axisymmetric model [11] as shown in Fig. 2 was developed to describe natural gas production from methane hydrate dissociation in a confined reservoir by depressurization. They accounted for the heat sink from hydrate dissociation and solved the convection-conduction heat transfer in the gas and hydrate zones. This model assumed that the water produced in the dissociation was stagnant and the effect of water in the dissociated zone was limited to the decrease in porosity and the increase in heat capacity of the porous medium. Heat is supplied by gas convection to the dissociation interface because of the endothermic nature of the hydrate dissociation process. Furthermore, heat conduction is negligible compared to convection.
where kh2 is the thermal conductivity of zone 2; and QH, the heat of hydrate dissociation. Hydrate dissociation curve: B pD ¼ exp A – (9) TD where pD is the equilibrium pressure; TD, the temperature; and A, B, the coefficients derived from experiments. This model is limited to only one dimension and only includes the flow of gas. Besides, it ignores the water produced from hydrate dissociation, the heat convection and the kinetic reaction of hydrate dissociation. With
Fig. 2
Schematic of an axisymmetric hydrate reservoir [11]
Lin ZUO et al. Production of natural gas from gas hydrate reservoir
A more complicated model is proposed by Nazridoust and Ahmadi [12]. Based on their earlier work, they provided a 3D model including multi-phase flow, and completed the equation of energy conservation. The governing equations used to solve the multiphase flow conditions during the hydrate dissociation process are outlined as follows: The continuity equations for different phases: ∂ ðf S Þ þ r$k uD;k ¼ m_ k , ðk ¼ H,g,wÞ ∂t 0 k k
(10)
where Φ0 is the porosity of hydrate reservoir; ρk, the density of different phases; uD,k, the velocity of different phases; Sk, the volume fraction of different phases; m_k , the mass flow rate of different phases; and H, g, w, the hydrate, gas, and water. Darcy’s Law for flow in porous medium: uD;k ¼ –
KD Krk rp, ðk ¼ g,wÞ k
(11)
where KD is the absolute permeability of hydrate reservoir; Krk, the relative permeability of different phases; μk, the viscosity of gas; and p, the pressure. The equation of energy balance: ∂ ½ð1 – f0 ÞR CR T þ f0 SH H CH T þ f0 Sw w Uw ∂t þ f0 Sg g Ug þ r$ðg hg uD;g þ w hw uD;w Þ ¼ r$ðK0 rT Þ – QH ,
(12)
where ρR, and CR are the density and the heat capacity of rock in reservoirs, respectively; CH, the heat capacity of hydrate; Uw, the internal energy of water; Ug, the internal energy of gas; hg, the specific enthalpy of gas; hw, the specific enthalpy of water; T, the temperature; K0, the effective conductivity coefficient; and QH, the heat of hydrate dissociation. For the saturation of various phases: SH þ Sw þ Sg ¼ 1,
(13)
The mass generation rate of gas per unit volume of porous medium by dissociation: m_ g ¼ kB Mg AHS f0 SH ½pe ðT Þ – p, p£pe ,
(14)
where pe is the equilibrium pressure; kB, the coefficient of dissociation; Mg, the molecular weight of gas; and AHS, the reaction area of per volume hydrate. The equilibrium curve: log10 ðpe Þ ¼ AðT – T0 Þ þ BðT – T0 Þ2 þ C,
(15)
where A, B, and C are the coefficients of curve; and T0, the standard temperature which is 273.15 K. This 3D model includes three continuity equations for phases of gas, water and hydrate. In the equation of energy
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balance, both conduction and convection are under consideration, which contributes to the presence of the effective conductivity coefficient. The kinetic reaction model of hydrate dissociation is used to determine the mass flow rate of different phases. Although this model is more comprehensive than the one-dimensional axisymmetric model, experimental data are still necessary to determine parameters that significantly affect the prediction of the hydrate dissociation process. In depressurization simulation, the boundary conditions vary with different exploitation settings while the tempature boundary conditions are determined by hydrate reservoirs. 2.3
Numerical methods and property parameters
Many methods have been proposed to solve the system of partial differential equations of the models shown above. Ahmadi [11] linearized the partial differential equations of a 2D model and obtained three key nonlinear coupled equations to determine the temperatures and pressures by an iterative scheme. In the work of Zuo and You [13], a more effective iteration method, which solves the equations separately, was proposed and an important parameter, which determines the velocity of the dissociation front, was obtained and varied with time, instead of being a constant in Ahmadi’s work. To solve more comprehensive models, the FLUENT code with a users’ defined subroutine (UDS) of hydrate dissociation process was used [12]. Tsimpanogiannis and Lichtner [14] introduced a similarity variable to recast the equations, and solved numerically a transcendental equation with only one unknown variable. With the center difference scheme, Feng et al. [15] numerically solved the system of equations. Moridis and co-workers [16] developed the EOSHYDR2 module for the general-purpose TOUGH2 simulator, which models hydrate dissociation, phase behavior and fluid flow for complex conditions. The integral finite difference method was used to solve the system of equations, which deals with heat and up to four mass components (i.e., water, methane, hydrate, and watersoluble inhibitors such as salts or alcohols) that are partitioned among four possible phases (gas, liquid, ice or hydrate phases). Moreover, the property parameters needed in the systems of equations are derived from experiments and geophysical investigations conducted by many researchers, and a typical set of property parameters is listed in Table 2. 2.4
Dissociation kinetics
In the systems of equations listed above, a reservoir under exploitation is divided into two zones by the dissociation front and the equations of energy balance and relative phase permeabilities which are different in two zones. As a result, the equations of the whole reservoir cannot be determined until the dissociation front is found. There are
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Table 2
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Typical property parameters [12]
parameter
value
initial porosity r0
0.182
absolute permeability Kd/ mD
97.98
core temperature T/ K
275.45
initial pressure p/ MPa
3.75
initial hydrate saturation
0.465
initial water saturation
0.351
initial gas saturation Note: 1 mD = 9.8710
0.206 –16
m
2
two models, i.e., the equilibrium curve and the kinetic reaction, to predict the location of the dissociation front. In the equilibrium model, the system is composed of heat and two mass components (CH4 and H2O) that are distributed among four possible phases: the gas phase, the aqueous phase, the solid ice phase and the solid hydrate phase. The system always exists at equilibrium, with the occurrence of the various phases and phase transitions determined by the distribution of temperature and pressure. One of the available equilibrium curves is Eq. (15) and the values of A, B and C can be obtained using the least square error fit to the equilibrium pressure-temperature data of methane hydrate [17]. In the kinetic model, the system is composed of heat and three mass components: CH4, H2O, and CH4$nH2O. As opposed to the equilibrium model, the hydrate is not treated as a thermodynamic state of CH4 and H2O but as a third distinct compound. In this case the solid hydrate phase is considered to be composed exclusively of the CH4$nH2O component. Phase changes and transitions are determined by a kinetic rate of dissociation or formation, which acts as a source term and is given by the equation of Kim et al. [18]: dmH E (16) ¼ K0 exp – F Aðf – f Þ, dt RT A e where f and fe are the values of fugacity for the pressure at temperature T in the gas phase and at equilibrium, respectively; E is the hydration activation energy; K0 is the hydration reaction constant; A is the surface area for the reaction; FA is the area adjustment factor [dimensionless], which accounts for deviations from the assumption of grain sphericity used in calculating A [19]; and R is the universal gas constant. The values of K0 and E can be determined from laboratory data in pure hydrate systems [18] and in hydrate-bearing medium [20]. Kowalsky and Moridis [21] compared the kinetic and equilibrium models in simulating gas hydrate dissociation process, and analyzed the response simulated using both models in various settings and the sensitivity to factors such as the initial hydrate saturation, the hydrate reaction surface area and the numerical discretion. They found that though some differences are observed at early times, the
calculated responses for both models are remarkably similar for large-scale systems undergoing thermal stimulation and depressurization. However, for modeling shortterm processes, kinetic limitations can be important, and neglecting them may lead to significant over-prediction of hydrate dissociation. Assuming the validity of the current kinetic model, though some shortcomings still exist, the use of the equilibrium model appears to be preferred for simulating the dissociation of gas hydrates, given that the computational demands for the kinetic model far exceed those for the equilibrium model.
3
Current numerical results
Many studies have been conducted to predict gas production from hydrate dissociation process with the models. The gas production from reservoirs with free gas or water zones underlying the gas hydrate deposits by depressurization is possible, and in reservoirs of gas hydrates with no underlying free gas or water zones, thermal stimulation is also a feasible way to produce natural gas from hydrate reservoirs. 3.1
Results of depressurization models
The many works focusing on the issues of the effects of different boundary conditions and initial states on gas production by depressurization [11,12,22] shared the following conclusions: First, hydrate dissociation rate is sensitive to the physical and thermal conditions of a hydrate reservoir, the heat supply from the environment, and the outlet valve pressure; Second, the porosity and the relative permeability are important factors affecting hydrate dissociation and gas generation process; Third, increasing the surrounding temperature increases the rate of gas and water production due to a faster rate of hydrate dissociation; Fourth, decreasing the outlet valve pressure increases the rate of hydrate dissociation and, therefore, the rate of gas and water production increases; And finally, for a fixed down hole pressure, the distance of dissociation front from the well increases roughly proportional to the square root of time, and the production rate decreases with time. Some studies are conducted to investigate hydrate dissociation process. In the work of Bai et al. [23], the numerical results for a 3D hydrate reservoir showed that at the beginning of depressurization, gas can be produced effectively from the hydrate reservoir. With the depletion of the reservoir energy due to endothermic process of hydrate dissociation, the gas production rate decreases rapidly. Then, methods such as thermal stimulation and inhibitor injection should be used with depressurization. As a result, two-well systems, involving a combination of depressurization (at the production well) and thermal stimulation (at the injection well, where hot fluids are
Lin ZUO et al. Production of natural gas from gas hydrate reservoir
injected), appear to be substantially superior to single-well systems (only one low pressure well as the production well) [24]. Some researchers also calculated the hydrate gas production rate with free gas or water. The group of Moridis [25] simulated the natural gas production rate of hydrate reservoirs containing water or gas and showed that in a hydrate reservoir with free water, hydrates contribute up to 65% of the production rate and up to 45% of the cumulative volume of produced gas; the corresponding numbers for a hydrate reservoir with free gas are 75% and 54%. Depressurization in reservoirs with gas hydrates underlain by aquifers inevitably leads to large amounts of water produced [24]. With that consideration, single horizontal wells appear to have an advantage over single vertical wells by delaying water going up and leading to higher contributions of CH4 from dissociation to the production gas stream. Moreover, numerical models of depressurization have been built combined with experimental data by Feng et al. [15] as shown in Fig. 3. It was found that the intrinsic dissociation kinetics constant in real conditions was in the order of 102 mol/(m$Pa$s), which was three orders lower than that derived from bulk hydrate dissociation. It was suggested that hydrate dissociation kinetics had a great effect on gas production for the laboratory scale hydrate reservoir, while it had little effect on a field scale reservoir which was dominated by the flowability under the pressure drive.
Fig. 3 Experimental and simulated cumulative gas produced from depressurization experiments [15]
3.2
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the decomposition of natural gas hydrate, and the boundary effect. There also exists dissociation front in natural gas hydrate dissociation process by thermal stimulation. Due to the way of hot media injection, the hydrate near the injection end is almost decomposed, whereas most of the hydrate near the exit end is not decomposed, exhibiting a high saturation. The primary parameter affecting dissociation is the heat flux provided to the hydrate face. As the location of dissociation front moves away from the wellbore, the face area becomes larger resulting in a decrease in the effective heat flux. Reduction in heat flux reduces the speed of dissociation. Moridis et al. [24] used the EOSHYDR2 model to numerically simulate gas production for conditions of reservoirs without free gas or water zones. Sensitivity studies indicated that gas production from hydrate accumulations increases with gas hydrate saturation, hydrate initial temperature, and circulating water temperature in the well. Hydrate dissociation is also related to the thermal conductivity of the system, the method of heat addition, and the pressure at which the well is kept. Gas production is less sensitive to the rock and gas hydrate specific heat and the permeability of media. However, unlike the situation of depressurization models, the permeability factor affecting hydrate dissociation in thermal stimulation models is still under a case-by-case examination. Using the thermal model of Selim and Sloan [8], Tsimpanogiannis and Lichtner [14] found that low dissociation region permeability, corresponding to certain types of oceanic sediments, reduces gas production rates and leads to extremely high dissociation pressures at the hydrate dissociation front, in contrast to previous studies in permafrost sediments which found that the production rate is independent of permeability. The most important factors affecting the feasibility and the economic efficiency of thermal stimulation are the thermal efficiency (the ratio between the heat for hydrate dissociation and total input heat) and energy ratio (the ratio between the output energy due to the combustion of produced gas and total input energy) of natural gas hydrate production. Based on the derivation of the temperature distribution of hydrate bearing sediments under thermal stimulation, Tang [27] suggested that the thermal properties of hydrate-bearing sediments and hydrate saturations are key factors in deciding the energy ratio. For the production condition of steam injections, the energy ratio can reach 7.0 which fits well with the expectations of early thermal stimulation models built by Makogon [17].
Results of thermal stimulation models
Studies examining methane hydrate dissociation in porous media by thermal stimulation are conducted and the factors of thermal stimulation models are more complex than those of depressurization models. The thermal recovery process of natural gas hydrate can be divided into three periods [26]: the release of free gas,
4
Discussion and conclusion
Various models have been developed to simulate the process of natural gas production from hydrate dissociation and both laboratory and field scale experiments have been conducted to justify the models.
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The scientific basis for gas production from natural gas hydrate reservoirs has been established. Under suitable conditions, natural gas can be produced from hydrate reservoirs containing free natural gas by a depressurization well. In a natural gas reservoir with high hydrate saturation and no free water or gas, the methods of thermal stimulation and inhibitor injection are also available. However, the kinetic progress of hydrate dissociation is still not completely understood. Current studies including the kinetic reaction model almost depend on the work of Kim et al.[18], which was based on a relatively simple first-order rate law. The dissociation experiments conducted to develop this model were under conditions considerably far from the equilibrium state while some numerical models assume that the dissociation front is at equilibrium, which potentially brings possible biases. The interactions between natural gas, water produced from hydrates and hot water injected should be given more attention. Since the extensively different property parameters of phases, such as density and viscosity, and relative motion (slip viscosity) could be significant and a model using Darcy’s Law singly to determine phases’ velocities could lead to a wrong expectation of production rate of both water and natural gas. At present, there exist tremendous studies of natural gas hydrate as well as many models. It is hard to compare the results of different models because of their diverse initial pressures, temperature, boundary conditions, saturations, and media porosities. A standard setting condition of dissociation should be established to make it easier to compare different models. In addition, new solutions should be found to satisfy the long term and large scale numerical simulations because of the huge computational demand of the existing models. Further research may focus on calculations with a comprehensive numerical simulator to investigate the controlling methods of gas production from various hydrate-bearing reservoirs by using appropriate methods. In the thermal stimulation process, the increase in volume of reservoir fluids due to hydrate dissociation causes pressure increase and leads to the reformation of hydrate somewhere with particular temperature (hydrate recovery). The reformed hydrates increase the resistance of flows and continuously increase pressure partially, which may cause gas venting. Another problem is the reduction of the water produced from hydrate production, because it is both expensive and difficult to handle and dispose of large volumes of reservoir water in some conditions. Other new ideas to produce natural gas from hydrates should also be proposed and further research is needed. For example, the emitted carbon dioxide can help natural gas escape from the crystal structure and store itself in the form of hydrates instead of natural gas. Such approach can improve the economics of natural gas hydrate exploitation and the management of carbon emissions.
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