Estimating the upper limit of gas production from Class 2 hydrate accumulations in the permafrost: 1. Concepts, system description, and the production base case

Journal of Petroleum Science and Engineering 76 (2011) 194–204

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Estimating the upper limit of gas production from Class 2 hydrate accumulations in the permafrost: 1. Concepts, system description, and the production base case George J. Moridis ⁎, Matthew T. Reagan Lawrence Berkeley National Laboratory, 1 Cyclotron Rd., Berkeley, CA 94610, United States

a r t i c l e

i n f o

Article history: Received 12 September 2009 Accepted 29 November 2010 Available online 21 February 2011 Keywords: methane hydrates permafrost production

a b s t r a c t Gas hydrates are solid crystalline compounds in which gas molecules are lodged within the lattices of ice crystals. The amounts of hydrocarbon gases (mainly CH4) trapped in natural hydrate accumulations are enormous, leading to a recent interest in the evaluation of their potential as an energy source. Class 2 hydrate deposits are characterized by a Hydrate-Bearing Layer (HBL) underlain by a saturated water zone (WZ), and are encountered in the permafrost and in deep ocean sediments. In this numerical study of long-term gas production from permafrost-associated (PA) Class 2 deposits, we use fine grids to analyze a base case that involves a conventional vertical well with a 5 m-long production interval in the WZ that begins at the HBL base. The production process follows a cyclical pattern, with each cycle composed of two stages: a long stage (months to years) of increasing gas production and decreasing water production, followed by a reduction in the fluid withdrawal rate. We determine that the base case can yield large volumes of gas that are produced at high rates (reaching a maximum of over 6 MMSCFD, and an average of 3.11 MMSCFD over the entire production period) for long times, while the corresponding water production declines continuously. © 2010 Elsevier B.V. All rights reserved.

1. Introduction 1.1. Background Gas hydrates are solid crystalline compounds in which gas molecules (referred to as guests) occupy the lattices of ice crystal structures (called hosts). Natural hydrates in geological systems usually contain CH4 as their main gas ingredient, and occur in two distinctly different geologic settings where the necessary conditions of low T and high P exist for their formation and stability: in the permafrost and in deep ocean sediments. Although the range of current estimates of the size of the hydrocarbon resource trapped in hydrates is very wide (Klauda and Sandler, 2005; Milkov, 2004; Sloan and Koh, 2008), ranging between 1015 and 1018 ST m3, there is general agreement that it is vast and that it exceeds the total energy content of known conventional fossil fuel resources. Even if the most conservative estimate is considered, and if only a fraction of the resource is recoverable, the magnitude of the resource is sufficiently large to attract attention as a potential energy source (Dallimore and Collett, 2005; Makogon, 1987), given the ever increasing global energy demand, the dwindling conventional fossil hydrocarbon reserves, and the environmental desirability of CH4 as a fuel. To that end, there has been a proliferation of recent studies evaluating the technical and economic feasibility of gas production from natural hydrate accumulations (Dallimore and Collett, 2005; Hong and

⁎ Corresponding author. Tel.: +1 510 486 4746. E-mail address: [email protected] (G.J. Moridis). 0920-4105/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.petrol.2010.11.023

Pooladi-Darvish, 2005; Kurihara et al., 2005a,b; Moridis and Reagan, 2007a,b; Moridis and Sloan, 2007; Moridis et al., 2007). A thorough review of the current status of the effort to produce gas from hydrate accumulations in geologic systems can be found in Moridis et al. (2009). 1.2. Dissociation methods Gas can be produced from hydrates by inducing dissociation by one of the three main dissociation methods (Makogon, 1997) (or combinations thereof): (1) depressurization, involving lowering of the pressure P below the hydration pressure Pe as defined by the Lw– H–V and I–H–V three-phase lines in Fig. 1 at the temperature T, (2) thermal stimulation, based on raising T above the hydration temperature Te at the prevailing P, and (3) the use of inhibitors (such as salts and alcohols), which shifts the Pe–Te equilibrium through competition with the hydrate for guest and host molecules. 1.3. Classification of gas hydrate deposits Natural hydrate accumulations are divided into four main classes (Moridis and Reagan, 2007a,b; Moridis and Sloan, 2007; Moridis et al., 2007) that are defined by their geologic features and their initial conditions. Class 1 accumulations are composed of two layers: the Hydrate-Bearing Layer (hereafter referred to as HBL) and an underlying two-phase fluid layer containing gas and liquid water. In Class 1 deposits, the bottom of the HBL occurs under equilibrium conditions (i.e., the on Lw–H–V three-phase line of Fig. 1), and defines the bottom of stability zone (i.e., the Lw–H region, in which hydrates

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Fig. 1. Pressure–temperature equilibrium relationship in the phase diagram of the water–CH4–hydrate system (Moridis et al., 2008) (Lw: liquid water; H: hydrate; V: vapor (gas phase); I: ice; Q1: quadruple point = I + Lw + H + V).

are stable because of thermodynamically favorable P and T conditions). In Class 2 deposits, an HBL overlies a layer of mobile water. Class 3 accumulations are composed of a single zone, the hydrate interval (HBL), and are characterized by the absence of an underlying zone of mobile fluids. A fourth class (Class 4) involves exclusively oceanic systems, and involves disperse, low-saturation hydrate deposits that lack confining geologic strata (Moridis and Sloan, 2007). 1.4. Characteristics of Class 2 hydrate deposits in the permafrost Class 2 accumulations are bounded by confining strata (overburden and underburden), and are composed of two layers: the HBL and an underlying zone of mobile water (WZ). In this type of hydrate accumulation (as in Class 3), the bottom of the hydrate stability zone (i.e., the location above which hydrates are stable because of thermodynamically favorable P and T conditions, as indicated by the Lw–H–V and I–H–V lines in Fig. 1) may occur at or below the bottom of the hydrate interval. Thus, the entire HBL may be well within the hydrate stability zone, i.e., it can occur at any point within the Lw–H or I–H two-phase regions. Proximity of the base of the HBL to the bottom of the hydrate stability zone (which defines equilibrium and is characterized by the maximum possible temperature T = Te at the prevailing P) enhances the gas production potential of the deposit because of the larger “sensible heat reservoir” at the higher T (available to support the endothermic dissociation reaction), in addition to the ease of destabilizing the hydrate in the vicinity of thermodynamic equilibrium (Moridis and Reagan, 2007b). Class 2 deposits are quite common both in the permafrost (Dallimore and Collett, 2005) and in the oceans (Moridis and Reagan, 2007a), and there is geologic, geochemical and thermodynamic justification for the expectation that they are probably the most prevalent type among the hydrate deposits that are potential production targets. There are three differences between oceanic and Class 2 permafrost-associated (PA) accumulations. The first difference is obviously the relatively low concentrations of salt (an inhibitor) in the majority of PA deposits (Dallimore and Collett, 2005; Wright et al., 1999), which are generally insufficient to cause a substantial shift in the Pe–Te equilibrium. For example, at a temperature Te = 13 °C, the equilibrium hydration pressure Pe = 12.24 MPa in a typical marine deposit with a water salinity of XS = 3.5%, but is only Pe = 10.26 MPa in

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a PA deposit with XS = 0.35%, and Pe = 10.07 MPa for XS = 0. Consequently, depressurization-induced gas production is more difficult in PA deposits because it is deprived of the beneficiary effect of salt. This means lower and delayed gas production because larger pressure drops ΔP (requiring larger fluid withdrawal rates and/or longer production periods) are needed to effect the same gas production. The second difference involves the initial P and T in Class 2 deposits, as determined by their location in the subsurface. Barring very large abnormalities in the geothermal gradient, the deepest interface in Class 2 PA deposits occurs at a depth of about 1150– 1200 m, with corresponding P and T not exceeding 11.3–11.8 MPa (=1640–1700 psi) and about 14 °C, respectively. Conversely, oceanic Class 2 deposits can be encountered at practically any depth below a minimum threshold, and very deep such deposits have been reported (Boswell et al., 2009). Deeper deposits are characterized by larger P and T (as they generally follow the hydrostatic and the geothermal gradients), making them more desirable targets because of (a) a larger depressurization ΔP potential, and (b) a larger sensible heat reservoir to support the endothermic dissociation reaction. Given the fixed maximum depth of hydrate deposits in the permafrost and the general desirability of deeper, warmer deposits as production targets, the deepest PA accumulations appear to be less promising than the deepest oceanic ones because of lower P and T (reflecting the combined effect of the shallower depth and the influence of permafrost). Note that this evaluation is based on the production potential of these two deposit types, and does not account for the considerable technical and economic challenges of offshore operations. A practical implication of the generally lower P and T in Class 2 PA deposits is a limitation on the mass rate of fluid withdrawal from the well (QM) to effect depressurization, and, consequently, on the rate of gas production (QP). This limitation is not imposed by permeability restrictions but by concerns about the possible early emergence of ice, which can have an adverse impact on the effective permeability keff. Thus, given the fact that the heat of hydrate dissociation ΔH is practically unaffected by T (Gupta et al., 2009) and the sensible heat reservoir is smaller in the colder PA deposits, a relatively low QM is necessary to maintain T above the freezing point. For a given hydrate saturation SH, the low QM limits the rate of cooling brought about by dissociation and the Joule–Thompson effect, while allowing heat inflows through the boundaries to replenish the heat losses. A much higher QM is possible in deeper, warmer Class 2 oceanic deposits with the same geometry, SH, and intrinsic permeability k. The third difference between oceanic and PA hydrate deposits is the level of hydrate saturation SH. In general, because of the manner of their formation from pre-existing gas reservoirs, permafrost-associated hydrate deposits are characterized by SH levels that are usually higher than those in oceanic deposits (which are formed from CH4supersaturated solutions, and have routinely much lower SH). It is important, however, to realize that this is not an absolute rule, as oceanic hydrate deposits with high SH have been reported in the literature (Boswell et al., 2009; Moridis et al., 2010). Production from oceanic Class 2 deposits was discussed in detail by Moridis and Reagan (2007a). Although there have been earlier studies of gas production from Class 2 PA deposits (Kurihara et al., 2005a,b; Moridis, 2003; Moridis et al., 2004), these were exploratory in nature because they did not have the benefit of recent advances in our understanding of the thermal and hydraulic behavior of hydratebearing geologic media, e.g., the phase-dependent thermal conductivity, compressibility, relative permeability and capillary pressure of hydrate-bearing media (Moridis et al., 2005; Moridis et al., 2008). Thus, the results of the earlier studies provided important insights into the system behavior through the sensitivity analysis of the factors affecting gas production from Class 2 deposits, but they had mainly qualitative value (in the sense of providing indications of the relative

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importance of different factors on performance, rather than reliable estimates of gas production). 1.5. Objectives The main objective of both parts of this study (as reported in this paper, and in Part II, also in this issue) is to evaluate by means of numerical simulation the maximum production potential of Class 2 PA accumulations, and to determine the factors and conditions affecting it. Additionally, we investigate the performance of different well configurations. Note that, because the focus is on developing an estimate of the upper limit of production, our study hews close to standard current production practices as long as possible in the earlier stages of the production period, but deviates from them (i.e., by operating the well at the highest – but time-variable – production rates that could be sustained by the system, even after the well pressure reaches a level sufficiently low to warrant switching to production at a constant well pressure under standard field operating conditions) in the later stages of production. Moreover, we do not address other considerations (i.e., geomechanical stability issues) that can limit production from such PA hydrate deposits. 2. Geological system description The geologic system in this study is similar to that in the Mallik deposit (Dallimore and Collett, 2005; Moridis, 2003) (Mackenzie Delta, Northwest Territories, Canada), and is analogous to that discussed by Moridis et al. (2007) in their analysis of production from a Class 1 deposit. The Class 2 PA deposit we investigate is confined by an impermeable overburden and underburden, and involves a 15 m-thick HBL (with a base at z = −1150 m), underlain by a 15 m-thick WZ. The geometry and configuration of the system are shown in Fig. 2. The thickness of both the overburden and the underburden (i.e., the no-flow, but heat-exchanging boundaries) is 30 m, which earlier calculations (Moridis and Kowalsky, 2007; Moridis and Reagan, 2007a) had indicated to be sufficient to allow accurate heat exchange with the hydrate deposit during a 30-yr long production period (i.e.,

the standard life cycle of a well). The well at the center of this cylindrical hydrate deposit (Fig. 2) had a radius rw = 0.1 m. A no-flow (of fluids and heat) boundary was applied at the reservoir radius rmax = 567.5 m. This corresponded to a well spacing of about 100 ha (=250 acres), with the no-flow boundary provided by the presence of other wells on the same spacing pattern. 3. Methods 3.1. Production techniques As discussed in detail by Moridis and Reagan (2007a,b), depressurization appears to be the production method of choice for the following reasons: its simplicity, its technical and economic effectiveness, the fast response of hydrates to the rapidly propagating pressure wave, the near-incompressibility of water (which expands the reservoir volume over which depressurization is sensed by the HBL), and the large heat capacity of water. The latter plays a significant role in providing part of the heat needed to support the strongly endothermic dissociation reaction as warmer water flows from the outer reaches of the formation toward the well. Pure thermal stimulation does not appear to be an effective dissociation method (Moridis and Reagan, 2007a,b), but it can be effectively used in conjunction with depressurization for localized applications involving the destruction of secondary hydrate and/or ice that often develop in the vicinity of the well and have the potential to inhibit flow and production. Similarly, the use of inhibitors is not recommended because of serious practical limitations (Moridis and Reagan, 2007a,b) that include (a) rapid reduction in effectiveness because of inhibitor dilution by the H2O released from dissociation, (b) the high cost (and limited recovery potential) of chemical inhibitors, and (c) the potential permeability reduction by halite precipitation in salt-based applications. Note that the present study focuses on gas production from ideal Class 2 accumulations that are confined between an effectively impermeable overburden and underburden. Class 2 accumulations without such strata can have a disappointingly low gas production because flow through the boundaries limits the effectiveness of depressurization and leads to large production volumes of undesirable water (Kurihara et al. 2005a). While a confining underburden is highly desirable, a near-impermeable overburden is critically important to the feasibility of gas production from a Class 2 deposit because of the development of an upper dissociation interface at the top of the hydrate body (a feature typical of depressurization-induced gas production from hydrates), leading to gas accumulation that is augmented by buoyancydriven gas ascent to the top of the formation (Moridis and Reagan, 2007a). Lack of a confining overburden could lead to gas loss though the overburden and release at the ground surface, with potentially serious environmental, health, safety and economic consequences. 3.2. Properties and initial conditions

Fig. 2. A schematic of the Class 2 PA hydrate deposit simulated in this study.

The hydraulic and thermal properties of the various geological media (the HBL, WZ, and the confining layers), as well as the initial conditions, are listed in Table 1. We determined the initial conditions in the reservoir by following the initialization process described by Moridis and Reagan (2007a). The initial P distribution followed the hydrostatic pressure gradient, and the initial T distribution follows a geothermal gradient of about dT/dz = 0.03 K/m and that was consistent with observations at the Mallik site. Slight variations of dT/dz along z were caused by the effects of the permafrost, and of the thermal conductivities of the geologic media and the phases in the pores. Because the bottom of the hydrate stability zone was assumed to occur slightly below the elevation of the HBL base (which corresponded to a known hydrostatic pressure), the hydrate base temperature TB was determined as slightly lower than the equilibrium

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Table 1 Hydrate deposit properties. Parameter

Value

Water zone thickness Hydrate zone thickness Initial pressure PB (at base of HBL) Initial temperature TB (at base of HBL) Gas composition Initial saturations in the HBL Intrinsic permeability kr = kz (HBL and water zone) Intrinsic permeability kr = kz (U and L strata—overburden and underburden) Porous media grain density ρR (all formations) Initial mass production rate QM0 Dry thermal conductivity kΘRD (all formations) Wet thermal conductivity kΘRW (all formations) Composite thermal conductivity model (Moridis et al., 2005) Capillary pressure model (van Genuchten, 1980) SmxA λ P0 Relative permeability model (Moridis et al., 2008)

15 m 15 m 1.067 × 107 Pa 286.45 K (13.3 °C)

n (Moridis et al., 2007) SirG SirA

100% CH4 SH = 0.7, SA = 0.3 10−12 m2 (= 1 D) 0 m2 (= 0 D)

2750 kg/m3 9.2 kg/s (= 5000 BPD) 0.5 W/m/K 3.1 W/m/K 1/2 kΘC = kΘRD + (S1/2 A + SH )(kΘRW − kΘRD) + ϕ SI kΘI h i−λ A −SirA Þ Pcap = −P0 ðS
Þ−1 = λ −1 ; S
= ðSðSmxA −SirA Þ

1 0.45 2 × 103 Pa OPM model, krA = (SA*)n, krG = (SG*)n SA* = (SA − SirA) / (1 − SirA), SG* = (SG − SirG) / (1 − SirA) 3.572 0.02 0.20

hydration temperature Te at that location (see Table 1 and Fig. 1). The initial P- and T-profiles in the simulated domain are shown in Fig. 3. Both the HBL and the WZ were assumed to have the same homogeneous and isotropic properties (flow and thermal), with a porosity ϕ = 0.35 and an intrinsic permeability k = 10 −12 m 2 (= 1 Darcy). Similarly, the overburden and underburden were assumed to have the same properties and to be impermeable. The initial hydrate saturation and aqueous saturation were SH = 0.7 and SA = 0.3, respectively, were consistent with saturation levels encountered in PA deposits (Dallimore et al., 1999; Kurihara, et al., 2005b), and were assumed to be uniformly distributed in the HBL. The aqueous and gas relative permeabilities (krA and krG), and the capillary pressure (Pcap) relationships, as well as the corresponding parameters, are based on data from the first field test of gas production from hydrates at the Mallik site, while the capillary pressure relationships and parameters are consistent with the ϕ and k of the HBL formation. Because of its simplicity, the “Original Porous Medium” (OPM) model (Moridis et al., 2008) was used in the estimation of krA, krG and Pcap in this study. The OPM model is based on the principle that (a) the medium porosity is unaffected by the emergence of hydrates and/or ice (although subject to change due to changes in pressure and temperature), (b) the intrinsic permeability of the porous media does not change during the evolution of the solid phases, and (c) the fluid flow as a relative permeability issue is controlled by the saturations of the various phases in the pores. 3.3. The numerical simulation code The numerical studies in this paper were conducted using the TOUGH + HYDRATE simulator (Moridis et al., 2008). This code can model the non-isothermal hydration reaction, phase behavior, and flow of fluids and heat under conditions typical of natural CH4hydrate deposits in complex geologic media. It accounts for all the known physics involved in hydrate-bearing systems, and does not

Fig. 3. Initial P- and T-profiles in the simulated domain. Note that the elevation z = 0 m corresponds to the top of the HBL.

allow non-physical approximations (e.g., ignoring CH4 dissolution into H2O, assigning arbitrary thermophysical properties, or disregarding any heat-transfer mechanism). The TOUGH + HYDRATE code includes both an equilibrium and a kinetic model (Clarke and Bishnoi, 2000; Kim et al., 1987) of hydrate formation and dissociation. The model accounts for heat and up to four mass components (i.e., water, CH4, hydrate, and water-soluble inhibitors such as salts or alcohols) that are partitioned among four possible phases: gas, aqueous liquid, ice, and hydrate. A total of 15 states (phase combinations) can be described by the code, which can handle any combination of hydrate dissociation mechanisms and can describe the phase changes and steep solution surfaces that are typical of hydrate problems.

3.4. Domain discretization The cylindrical domain was discretized into 100 × 100 = 10,000 gridblocks in (r,z), of which 9700 were active (the remaining being boundary cells). The uppermost and lowermost layers corresponded to constant T, no-flow boundaries, while the layers corresponding to the top and bottom confining layers (denoted as U and L strata, see Table 1) were impermeable but allowed heat exchange with the HBL and the WZ. To describe accurately the processes and phenomena occurring in the vicinity of the wellbore (which has been shown to be critically important to production because of maximum cooling and the potential for secondary hydrate formation, see Section 5.2.1 and Moridis and Reagan, 2007a), we used a very fine discretization along the r direction (especially in the r b 20 m zone). The 100 radial increments were logarithmically distributed according to Δri = Δr0 ki, 100

with Δr0 = 0.1 m and ∑ Δri = r max . i=0

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The HBL was subdivided into segments of uniform Δz = 0.25 m each along the z-direction. Such a fine discretization of the HBL is critically important for accurate predictions (Moridis and Reagan 2007b; Moridis et al., 2007), but a coarser discretization along the zaxis is possible within the WZ, and within the U and L strata. The vertical discretization in the WZ, and in the U and L strata, had been determined from earlier scoping studies as the coarsest grid that could accurately describe the curvature of the water and heat flow lines (by providing solutions that were practically identical to ones corresponding to any finer vertical discretization). This high definition provided the level of detail needed near the wellbore and in the entire hydrate-bearing zone. Because there appears to be no kinetic limitation in long-term gas production from hydrates (Kowalsky and Moridis, 2007), there is practically no difference between the results from a kinetic and an equilibrium model of the dissociation reaction. Thus, the equilibrium model was used, resulting in 29,100 coupled equations that represented a reduction in the order of the matrix-to-be-solved by 25%. The numerical simulations involved a physical representation of the wellbore that was based on the approximation of wellbore flow by a process of Darcian flow through a pseudo-porous medium describing the interior of the well (Moridis and Reagan, 2007a). This pseudo-porous medium had a ϕ = 1, a very high k = 10−9–10−8 m2 (= 1000–10,000 Darcies), a capillary pressure Pc = 0, a relative permeability that was a linear function of the phase saturations in the wellbore, and a low (but non-zero) irreducible gas saturation SirG = 0.005 (necessary to allow the emergence of a free gas phase in the well). Our analysis confirmed earlier results (Moridis and Reagan, 2007a) that had shown this approximation to result in a solution that deviates by less than 5% from the more accurate solution of the Navier–Stokes equation of wellbore flow or a conventional Peaceman model, while reducing the execution time by a factor of at least 2. 3.5. Simulation process and outputs The maximum simulation period was the typical 30-year life span of the well, but the deposit was invariably exhausted much earlier. In the course of the simulation, the following conditions and parameters were monitored: spatial distributions of P, T, and gas and hydrate phase saturations (SG and SH); volumetric rate of CH4 released from dissociation and of CH4 production at the well (QR and QP, respectively); cumulative volume of CH4 released from dissociation and of CH4 produced at the well (VR and VP, respectively); water mass production rate at the well (QW) and cumulative mass of produced water (MW). 4. Well design and system behavior during depressurizationinduced production 4.1. Case A: short production interval (base case) The well design in the base case (Case A) involves a production (perforated) interval that begins at the HBL base and extends 5 m into the WZ. The decision to locate the perforated interval into the WZ below the hydrate zone is based on the very low effective permeability keff in the HBL (caused by the high SH = 0.70, see Table 1) and the need to ensure a sufficiently high QM at the well. This is the simplest possible design, involves conventional technology, and poses no particular technical challenges. The initial mass rate of fluid production from the well was QM0 = 9.2 kg/s (=5000 BPD of water). This was half the QM0 applied to the wells in an earlier investigation of production from deeper, warmer oceanic Class 2 deposits (Moridis and Reagan, 2007a). Note that the present study seeks to determine the upper limits of production from PA hydrates, and, as such, fluid production continues throughout the simulated period; other techniques (such as constant

bottomhole-Pw production) are not employed, and we do not attempt to replicate the production schedule of a commercial well. 4.2. Dissociation- and production-related issues The initial stages of production invariably involve fluid removal (practically 100% water) almost exclusively from the WZ because of the very low keff of the HBL. Continuous fluid withdrawal from the WZ leads to the evolution of a dissociation interface along the HBL base because of the very low compressibility of water (which allows the depressurization disturbance to be sensed over a large area along the HBL base) and the low keff of the hydrate interval (which promotes horizontal flow along the HBL base). As dissociation proceeds and the hydrate recedes along the HBL base, the hydrate interface advances upward. A unique feature of gas production from hydrates (universal to all hydrate deposits) is the formation of another horizontal dissociation interface that develops at the top of the hydrate interval and advances downward during depressurization-induced dissociation (Moridis and Reagan, 2007a; Moridis et al., 2007). This is caused by the combination of depressurization (which leads to dissociationinduced cooling) and the resulting early reversal of the geothermal gradient at the upper reaches of the HBL (leading to heat flow from the overburden into the HBL, i.e., reversing the initial direction of heat flow). As in the case of an oceanic Class 2 deposit of Moridis and Reagan (2007a), a mass production rate QM is imposed at the well, and the production rates of the aqueous and gas phases are monitored. As was indicated earlier, because the focus is on developing an estimate of the upper limit of production, the well is operated at the maximum possible (but time-variable) QM that can be sustained by the system, even after the well pressure has reached a level sufficiently low to warrant switching to production at a constant well pressure under standard field operating conditions. Gas emerges at the well after SG in the reservoir exceeds the irreducible level SirG. An important feature of depressurization-based gas production from hydrates is that the total mass rate QM of produced fluids (gas and aqueous phases) cannot be maintained constant, but needs to decrease as time advances (Moridis and Reagan, 2007a,b). This is a consequence of three factors. The first is the competition between depressurization (which tends to increase gas release and production as it advances) and the correspondingly increasing difficulty of gas release as the deposit temperature declines. The cooling is caused by the endothermic nature of dissociation (which absorbs heat from its environment to fuel the reaction), in addition to the Joule–Thompson effect, and is in competition with the continuing pressure drop in the deposit. While initially the pressure drop (which enhances dissociation) outweighs the adverse effects of lower T (which slows dissociation), eventually the rate of QR slows significantly, resulting in a decline in QP. The second factor is hydrate depletion, which reaches a point that cannot sustain the initial rate. The third factor is the continuously increasing contribution of gas to the production stream for any given QM, with a corresponding decrease in the water production. As more low-density gas replaces the denser water in the production stream, a point is reached where the system effective permeability is incapable of supplying the well with the prescribed QM, resulting in cavitation at the well (characterized by rapid pressure drops, which, if left unchecked, can reach levels below the atmospheric). This necessitates a reduction in QM if production is to continue. Cavitation can also occur if secondary hydrates formed in the vicinity of the well block flow. Note that, per our observations, the pressure at the well (not including cavitations, which are very-short term phenomena on the order of seconds to minutes, and the effects of which can be easily reversed by reducing QM) falls below the levels that would normally trigger switching to constant bottomhole-Pw production after about 50% of the hydrate has dissociated.

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Note that a reduction in QM does not necessarily lead to a decline in the rate of CH4 production QP. While such a decline is expected immediately after the QM reduction, QP can match (and routinely exceed) its earlier level as the increasing gas contribution compensates for the reduction in total mass production. However, an eventual decline in QP is inevitable because of the reasons discussed earlier. Secondary hydrate can often form next to the wellbore after the destruction of the primary (original) hydrate at that location. This is possible if P at that location remains relatively high (above the quadruple point, see Fig. 1), while T drops below the hydration temperature Te. In addition to the unavoidable dissociation-induced cooling, the Joule–Thompson effect is at its maximum in the immediate vicinity of the well where the highest gas flow velocities occur. If dissociation is very rapid or gas velocities are very high, ice can also form, especially when SH is high and/or T is already low. Secondary hydrate and ice can accumulate next to the well at saturations sufficiently high to severely restrict (“choke”) flow to the well, leading to cavitation. In this case, hot water injection can be used to destroy these solid phases and restore production. 5. System response during production in case a (production base case) 5.1. Gas and water production Fig. 4 shows the evolution of QR, QP, and of the average production rate Qavg = VP/t in the base Case A. Fig. 5 shows the corresponding QW and MW, in addition to the QM imposed at the well. QR increases rapidly as the depressurization disturbance propagates along the lower interface and induces dissociation (because of the near-incompressibility of water). A local maximum of QR = 1.15 ST m3/s (about 3.5 MMSCFD) is reached very early, before a mild decline begins. This is attributed to the combination of a locally higher P (caused by gas accumulation in the deposit because the released gas cannot yet be produced at the well when SA b SirA) and the resulting lower T, both of which slow dissociation until more heat

Fig. 4. Rates of (a) hydrate-originating CH4 release in the reservoir (QR) and (b) CH4 production at the well (QP) during production from the Class 2 PA hydrate deposit in the base Case A. The evolution of the average gas production rate (Qavg) over the simulation period is also shown.

Fig. 5. (a) Mass rate of total fluid production, QM, (b) mass rate of H2O production, QW and (b) cumulative mass of produced H2O (MW) during production from the Class 2 PA hydrate deposit in Case A.

arrives from the boundaries and gas production begins in earnest. When this occurs at about t = 200 days, QR increases again rapidly, as gas production enhances depressurization and further dissociation. The increase is monotonic, and continues until the first cavitation event (which defines the first production cycle) occurs at t = 1020 days. At that time, QR = 1.78 ST m3/s (=5.43 MMSCFD) and QP = 1.50 ST m3/s (=4.78 MMSCFD). The gas production rate (as described by QP) is initially (for t b 200 days) very low, but then it begins to increase rapidly and monotonically. During the same period, QW declines continuously (Fig. 5). In the second production cycle (defined as the interval between the 1st and the 2nd cavitation events), QM is reduced (Fig. 5) for the reasons discussed earlier, and production resumes. As discussed in detail by Moridis and Reagan (2007a), the decrease in QM results in an initial reduction in QR, QP and Qw (Figs. 3 and 4). After the resumption of production, both QR and QP increase rapidly and monotonically, and reach levels that exceed their respective values at the end of the first production cycle when the second cavitation event (marking the end of the second production cycle) occurs at t = 1550 days. At that time, the maximum QR (=1.98 ST m3/s = 6.04 MMSCFD) and QP (=1.95 ST m3/s = 5.95 MMSCFD) levels are observed. The third and fourth production cycles follow the same pattern: (a) the reduction in QM produces a corresponding initial reduction in reduction in QR, QP and Qw, but (b) QR and QP continuously increase during each cycle, while (c) Qw decreases (Figs. 3 and 4). What is different from the first two cycles is that the maximum QR and QP at the end of each cycle (after the 2nd one) follow a declining trend for the reasons discussed earlier. Additionally, gas production begins to exceed gas release, i.e., QP N QR, with gas accumulated earlier in the reservoir supplying the balance. The fifth production cycle is the longest, lasting from t = 2400 days until t = 5860 days. The most interesting feature of the cycle is a spike in gas production (QP) at about t = 4300 days. It is caused by a drop in P below the quadruple point near the well, leading to the dissociation of a thin layer of secondary hydrate that had formed near the well. The elimination of this blockage and the uninhibited gas access to the well

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(without any further secondary hydrate formation) are the reasons for this surge in QP. QR is practically constant during this cycle, exhibits only a mild increase after the QP spike, and drops to zero (indicating hydrate exhaustion) at t = 5640 days. Subsequent production cycles exhibit precipitous reductions in QR because the only gas source is the CH4 stored in the reservoir during earlier dissociation. Production can stop at any point deemed uneconomical. A criterion for the determination of this point (in addition to the QP magnitude) may be the Qavg magnitude and trend. Fig. 4 indicates that Qavg remains practically constant at 1.02 ST m3/s (=3.11 MMSCFD) from about t = 2400 days until t = 5860 days, and then begins to decline slowly. QW is initially almost equal to QM, but represents a progressively diminishing portion of QM as time advances because of the increasing contribution of gas to the production stream until the depletion of the hydrate (Fig. 5). Past that point, the water contribution to QM increases again. Compared to production from oceanic Class 2 hydrate deposits (Moridis and Reagan, 2007a), there is a significant difference in the early QP response. Thus, the stage of monotonic and rapidly increasing gas production begins earlier (i.e., at about t = 60 days) in PA deposits, as opposed to the several hundred days needed in oceanic accumulations. The difference is due to the insignificant contribution of dissolved gas to production from PA deposits. Because of the lower P, the amount of dissolved gas is small, and gas release originates almost exclusively from gas dissociation. Conversely, the higher P in oceanic accumulations lead to large initial releases of dissolved gas that help maintain a high pressure, prevent effective dissociation, and result in low gas production for long times. Fig. 6 shows the VR and VP in the base Case A. At the end of the simulation (t = 6480 days), the hydrate has long been exhausted (as indicated by the flat portion of the VR curve after t = 5630 days). Thus, if the well is operated at the variable QM regime described earlier, and if geomechanical stability is not a consideration, a very high recovery (VP N 0.95 VR, i.e., the upper limit of production) can be attained.

Fig. 6. Cumulative volumes of (a) hydrate-originating CH4 released in the reservoir (VR) and (b) produced CH4 at the well (VP) during production from the Class 2 PA hydrate deposit in Case A.

During the 6480 days of the simulation, a total of VP = 5.44 × 108 ST m3 (=1.92 × 1010 ST ft3) of CH4 were produced. 5.2. Spatial distributions of important variables in Case A The white lines in all of the figures that describe the spatial distribution of reservoir properties and conditions in Cases A (Figs. 6 through 8) denote the initial position of the base of the HBL, while the top of the HBL coincides with the z = −30 m datum. 5.2.1. Spatial distributions of SH and SG Figs. 6 and 7 show the evolution of the SH and SG distributions over time in the deposit near the wellbore (r b 20 m). Comparison of the SH to its initial distribution in the HBL provides a measure of the magnitude of dissociation of the hydrate. As will be shown, the process of gas production from hydrate deposits is controlled by the phenomena that occur within a narrow radius near the well, hence the focus on this zone. Review of Figs. 6 and 7 indicates that hydrate dissociation in Case A proceeds initially along the lower hydrate interface, and is more pronounced (as expected) close to the well. A cylindrical dissociation interface around the well is also evident. The entire hydrate zone appears to be dissociating even at an early stage (Fig. 6b and beyond). Secondary hydrates at saturations exceeding the original level (i.e., SH N 0.7) are formed near the top of the perforated interval (Fig. 6a to e), but their extent is limited and do not lead to structures that bock flow. The largest extent of the secondary hydrate occurrence is observed in Fig. 7d, in which it reaches r = 9 m. Generally, such secondary hydrate formation is typical in production from vertical wells (it is rarely an issue in horizontal wells), and is confined within a critical radius rc that rarely (if ever) exceeds 15 m (Moridis and Reagan, 2007a). This is because the conditions within the cylindrical zone for r ≤ rc are favorable for secondary hydrate formation because of (a) the availability of gas and water, and (b) maximum cooling (caused by the low temperatures of the dissociation-originating fluids and the Joule–Thompson cooling, which is most pronounced when gas velocities are at their maximum) around the well. In the base Case A, continuing depressurization and contact with warmer fluids arriving from the boundaries lead to the destruction of this secondary hydrate, which practically disappears after t = 1620 days. Elimination of the flow obstruction caused by the very thin secondary hydrate “skin” near the wellbore (Fig. 7f) is responsible for the QP spike at about t = 4300 days in Fig. 4. Fig. 7 shows the evolution of the upper horizontal interface at the top of the HBL. As indicated earlier, this is a result of continuing depressurization and heat flows from the upper boundary. The upper dissociation interface is clearly shown in Fig. 6b and beyond. The corresponding SG distributions in Fig. 8 indicate gas accumulation in the hydrate-free zone between the base of the overburden and the receding hydrate interface, leading to the highest SG observed in the deposit. The reason for this accumulation is the continuing dissociation along the upper interface, in addition to the rising of the gas released elsewhere in the deposit due to buoyancy. The emergence of the upper dissociation interface and the gas accumulation at the top of the HBL have important implications for gas recovery, highlighting the necessity for overburden permeability barriers if gas production from hydrates is to become possible. Absence of such barriers will inevitably lead to gas escaping through the permeable overburden toward the ground surface. Advancing dissociation and gas release along the HBL base result in increasing SG levels at that location (Fig. 7b and beyond). However, SG does not reach the levels at the top of the HBL because continuous flow to the well prevents gas accumulation. Continuous production leads to the gradual dissociation of the entire hydrate body (Fig. 6g and h), until the hydrate is exhausted (Fig. 4). Of particular interest is the uniformity of the dissociation

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Fig. 7. Evolution of spatial distribution of SH during gas production from the Class 2 PA hydrate deposit in the base Case A.

pattern of the hydrate along the reservoir radius (practically the same as that shown for r N 10 m in Fig. 7f to h). Conversely, very different SH and SG distributions have been observed in gas production from oceanic Class 2 hydrates (Moridis and Reagan, 2007a) when using the well configuration of Case A. These are characterized by isolation of the upper dissociation interface and impaired production. The differences are attributed to the faster dissociation and larger gas availability in the warmer oceanic hydrates, which lead to the early (and substantial) formation of large secondary hydrates structures that cut off access to the upper dissociation interface.

5.2.2. Spatial distribution of T The T distribution in Fig. 9 indicates continuous cooling as dissociation and production proceed, and is consistent with expectations. Actually, it is possible to identify from Fig. 9 regions of intense dissociation as the locations where significant T drops occur. This is more evident in Fig. 9f to h, in which the outline of the low-T region mirrors the SH distribution at the same times. Note the higher temperatures of the deeper water below the HBL at early times

(Fig. 9a), and the final temperature of less than 2 °C within the remaining body of the hydrate in Fig. 9h. 6. Summary (1) We investigate gas production from a permafrost-associated (PA) Class 2 hydrate deposit. Gas production from such deposits is generally more difficult than from marine ones because of the lack of the beneficial effect of salt, and because of their generally lower P and T (which limits depressurization and the sensible heat available to support hydrate dissociation). The well design in the base case analyzed here (Case A) entails conventional technology, and involves a production interval 5 m long within the WZ (beginning at the base of the HBL). (2) In Case A, we applied an initial mass withdrawal rate from the well QM0 = 9.2 kg/s (=5000 BPD). Gas from dissociation is released rapidly into the hydrate deposit. Gas production is characterized by a relatively short (b100 days) lead period of low gas production, followed by a period of rapid QP rise fueled

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Fig. 8. Evolution of spatial distribution of SG during gas production from the Class 2 PA hydrate deposit in Case A.

by hydrate dissociation, and begins in earnest when SG exceeds the SirG level. (3) QR and QP continue to increase until cavitation (characterized by rapid pressure drop at the well) occurs. The main reason for its occurrence in Case A is the replacement of the denser water by the lighter gas in the production stream at levels that cannot satisfy the imposed QM. Cavitation is easily corrected by reducing QM. A reduction in QM does not necessarily translate into a reduction of QP. (4) Production proceeds in cycles between cavitation events. The first stage of each cycle involves continuous gas production and is several hundred days long. The second stage can be very short (a few minutes at worst) because only a reduction in QM is needed to overcome cavitation. QP continuously increases during the production stage of each cycle, with a corresponding reduction in QW. (5) Processes and phenomena that occur within a narrow zone around the well control gas production from the entire hydrate deposit. This critical zone has a radius rc ≤ 10–15 m, and fine

discretization must be used in its simulations if these near-well phenomena are to be accurately described. Dissociation and flow patterns are uniform and smooth along the entire area of the horizontal interfaces for r N rc. (6) In the base Case A, the CH4 production rate QP reaches a maximum level of 1.98 ST m3/s (=6.04 MMSCFD). During the 5860 days of the simulation, a total of VP = 5.44 × 108 ST m3 (=1.92 × 1010 ST ft3) of CH4 were produced at an average rate Qavg = 1.02 ST m3/s (= 3.11 MMSCFD). In general, such production rates are well within commercial viability limits for onshore production. (7) The results indicate that gas can be produced from hydrates at high rates using the conventional well design and technology employed in the base Case A when the HBL is bound by confining boundaries. Dissociation is characterized by features that are common to all deposits: (a) the evolution of an upper dissociation interface at the top of the hydrate layer (caused by heat flows from the upper boundary) in addition to the lower dissociation interface at the bottom of the HBL, and (b) gas accumulation below the base of the

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Fig. 9. Evolution of spatial distribution of T during gas production from the Class 2 PA hydrate deposit in Case A.

overburden because of continuing dissociation and buoyancydriven gas rise to the top of the formation. Nomenclature Δr Radial increment (m) Δt Timestep size (s) Δz Vertical discretization, i.e., in the z-direction (m) C specific heat (J/kg/K) k intrinsic permeability (m2) keff effective permeability (m2) kΘ thermal conductivity (W/m/K) kΘRD thermal conductivity of dry porous medium (W/m/K) kΘRW thermal conductivity of fully saturated porous medium (W/ m/K) MW cumulative mass of water released into the ocean through the annular gravel pack (kg) NH hydration number P pressure (Pa) QΘ rate of heat injection into the formation next to the well (W/ m of wellbore)

QI QM QP QR QW QR r,z rc rw rmax RWGC S t T VP VR

mass rate of injected warm water at the well (kg/s) mass rate of fluid withdrawal at the well (kg/s) volumetric rate of CH4 production at the well (ST m3/s) volumetric rate of CH4 release from hydrate dissociation into the reservoir (ST m3/s) mass rate of water release into the ocean through the annular gravel pack (kg/s) rate of CH4 release from hydrate dissociation (ST m3/s) coordinates (m) critical radius of maximum activity around the wellbore (m) well radius (m) maximum radius of the simulation domain (m) cumulative water-to-gas ratio (kg/ST m3) phase saturation time (days) temperature (K or °C) cumulative volume of CH4 released into the ocean through the annular gravel pack (ST m3) cumulative volume of CH4 released from hydrate dissociation (ST m3)

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Greek symbols λ van Genuchten exponent—Table 1 ϕ porosity

Subscripts and superscripts 0 denotes initial state A aqueous phase e equilibrium conditions cap capillary G gas phase initial gas phase G0 H solid hydrate phase H0 initial solid hydrate phase irG irreducible gas irA irreducible aqueous phase n permeability reduction exponent—Table 1 P production stream ref reference Case C R rock R rock w well

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