Effect of Hydrates on Sustaining Reservoir Pressure in a ... · PDF fileEffect of Hydrates on Sustaining Reservoir Pressure in a Hydrate ... Natural gas hydrates are solid ... of the

October 2007, Volume 46, No. 10 39

Effect of Hydrates on Sustaining Reservoir Pressure in a Hydrate-Capped Gas Reservoir

S. Gerami, m. POOladi-darViSh University of Calgary

Peer reviewed PaPer (“review and Publication Process” can be found on our web site)

IntroductionNatural gas hydrates are solid molecular compounds of water

with natural gas that are formed under certain thermodynamic conditions. There is evidence that enormous amounts of natural gas exist in the form of hydrate deposits in many regions of the world(1). These deposits occur in sub-oceanic sediments as well as in arctic regions. Every unit volume of gas hydrate has the poten-tial to contain 170 to 180 volumes of gas at standard conditions,

AbstractA hydrate-capped gas reservoir is defined here as a reservoir

that consists of a hydrate-bearing layer underlain by a two-phase zone involving mobile gas. In such a reservoir, hydrates at the top contribute to the produced gas stream once the reservoir pressure is reduced by gas production from the free-gas zone. Large gas reservoirs of this type are known to exist in Alaska and Siberia and are expected to exist in the Mackenzie Delta of the North-west Territories in Canada.

Gas production from a hydrate-capped gas reservoir is a pro-cess governed by a combination of mechanisms of heat transfer, fluid flow, thermodynamics and kinetics of hydrate decomposi-tion. Using a comprehensive numerical simulator, an extensive simulation study indicates that some of the non-linear processes involved in gas production from hydrate reservoirs (i.e. the con-vective heat transfer and the kinetics of hydrate decomposition) have a negligible effect on the overall physics of the process. This significantly reduces the complexity of the heat and fluid flow equations and legitimizes the construction and use of sim-plified models.

In this work, we invoke the above approximations and develop a generalized gas material balance equation. This equation has two significant differences from the material-balance equation for conventional gas reservoirs, including the incorporation of: i) the effect of cooling due to endothermic decomposition of the hydrate; and ii) the effect of generated gas and water from the hydrate decomposition. In this model, it is assumed that a mo-bile phase exists in the hydrate zone; thus, no sharp hydrate dis-sociation interface is assumed. Considering the sensible heat of the hydrate zone and heat transfer from cap and base rocks, the gas and water generation rates are determined on the basis of the equilibrium rate of the decomposition process. Verification of the solution is obtained by comparing results with those of a compre-hensive hydrate reservoir numerical simulator.

The model developed here can be used as an approximate en-gineering tool for evaluating the role of hydrates in improving the productivity and extending the life of hydrate-capped gas reservoirs.

making the energy content of one cubic metre of a hydrate reser-voir more than other types of unconventional gas reservoirs(2).

In view of the large untapped resources of natural gas hydrates, extensive research and development work is underway to deter-mine what fraction of this resource is recoverable. A number of recovery processes have been suggested for producing gas from hydrates in sediments. Sloan(3) and Makogan(4) have presented an extensive review of the suggested methods including depressuriza-tion, thermal stimulation and inhibitor injection.

A typical form of depressurization technique is illustrated in Figure 1. A hydrate-capped gas reservoir is defined here as a gas reservoir capped with a partially saturated hydrate interval. The in-tercept of the hydrate-water-gas equilibrium curve and the depth-temperature curve shows the base of the hydrate stability zone. Above this baseline, hydrates are expected to be stable. A well is drilled through the hydrate layer and is completed in the free gas zone. Gas production from the well causes pressure reduction, which propagates into the reservoir and provides the driving force for the decomposition of the hydrate at the fluid/hydrate inter-face. The endothermic decomposition of hydrate has two effects: i) cooling of the decomposed zone; and ii) generation of gas and water according to Equation (1). The cooling effect creates a tem-perature gradient in the reservoir system. This leads to the initia-tion of conductive heat flow towards the cooled zone that provides part of the necessary energy for further decomposition. Another part of the heat of decomposition is provided from the sensible heat of the hydrate cap itself. The second effect (the generation of gas and water) causes the two-phase fluid flow and convective heat transfer in the reservoir.

FIGURE 1: Conceptual model for methane recovery from hydrates using depressurization.

40 Journal of Canadian Petroleum Technology

Hydrate Energy CH N H OH+ → + ⋅4 2 ................................................... (1)

The only field case of gas production from a hydrate reservoir took place in the Messoyakha Field and was primarily based on the depressurization technique(4). It is foreseen by many that the next commercial project for gas production from hydrate reser-voirs will use this technique(5), partially because it relies on con-ventional technology, and because it is estimated to be by far more economic than the other two methods of thermal stimulation and inhibitor injection(2).

The numerical modelling(6, 7) of gas production from hydrate reservoirs involves simultaneously solving the coupled equations of mass and energy balances along with the equilibrium and ki-netics relations of hydrate decomposition. However, in analytical models, the consideration of all processes is essentially impos-sible. As a result, such models usually are developed on the basis of some simplifying assumptions that ideally do not materially af-fect the overall behaviour of the process. A number of analytical models for predicting gas production from hydrates have been re-ported by Selim and Sloan(8), Makogon(4), Goel et al.(9), Ji et al.(10), Hong(11) and Hong et al.(12) All of these analytical models assume that decomposition happens at a sharp interface dividing the res-ervoir into two regions: the hydrate zone and the dissociated zone. However, the thermodynamic equilibrium conditions of hydrates specify that, in general, hydrates coexist with a second phase, making the presence of an aqueous or gaseous phase most prob-able at temperatures above 0˚C. The presence of this second phase, if mobile, allows pressure reduction deep within the hydrate zone, leading to deep decomposition of the hydrate. Departing from the previous sharp-interface models, Gerami and Pooladi-Darvish(13) accordingly developed an analytical model that allowed for hy-drate decomposition deep within the hydrate-bearing formation. Similar to the previous analytical models of depressurization, this model assumed that the pressure was suddenly reduced to a constant lower pressure level and was kept constant thereafter. Comparison of the results between the sharp-interface and deep-decomposition models showed that the former provides a much more pessimistic prediction. In this work, the previous decomposi-tion model is extended by continuous pressure reduction due to the production from a free gas zone in communication with the over-laying hydrates.

In comparison with a conventional gas reservoir, one major dif-ference for an engineering evaluation of a hydrate-capped gas res-ervoir is accounting for the replenishment of gas generated over the life of the project. This work is undertaken to develop an ana-lytical model to incorporate the dynamic effect of hydrate decom-position on reservoir pressure as a result of gas production from a hydrate-capped gas reservoir. For this purpose, a generalized material balance equation is developed. This is followed by the

development of solutions for the temperature of the hydrate cap, the rate of gas generation and the reservoir pressure during the pe-riod of constant rate production from a hydrate-capped gas reser-voir. Next, the analytical model developed here is validated against a comprehensive numerical hydrate reservoir simulator and used to perform sensitivity studies to investigate the effect of different res-ervoir parameters on reservoir performance.

Physical ModelReferring to Figure 2, we consider a gas reservoir capped with a

partially saturated hydrate layer in contact with cap and base rocks. The pressure and temperature (pi and Ti) conditions at the base of the hydrate layer are related as determined by the prevailing equi-librium relation. A well is drilled through the hydrate layer and is completed in the free-gas zone. At time t = 0, gas is produced from the reservoir, causing the pressure in the free-gas zone to be re-duced to some pressure p below the equilibrium pressure pi at Ti.

Figure 3 shows a schematic of the depressurization process on a hydrate three-phase equilibrium curve. Since the decomposition of hydrate is an endothermic process, the temperature of the hydrate will decrease to Tse, corresponding to the new prevailing pressure there. The heat of decomposition is provided by the sensible heat within the hydrate layer and adjacent base and cap rocks.

The material balance equation for conventional gas reservoirs relates average reservoir pressure, p, to the cumulative gas pro-duced, Gp. For a hydrate-capped gas reservoir, such as that de-scribed above, there are additional factors that need to be accounted for, i.e., the gas and water generated from the hydrates, the changes in temperature and pore volume related to decomposition. These factors are taken into account in the generalized form of the mate-rial balance equation that is described in the next section.

Generalized Material Balance EquationThe material balance equation is the basis of a fundamental cal-

culation in reservoir engineering, and is considered to yield one of the more reliable estimates of hydrocarbons-in-place, particu-larly for gas reservoirs. The standard material balance model used to represent oil and gas reservoirs is derived by assuming uniform or average fluid properties across the reservoir. At any time, the remaining hydrocarbon pore volume of the reservoir is related to the initial hydrocarbon pore volume, water influx and pore volume change due to connate water and rock expansion, while the mass of fluid remaining is equated to the initial mass minus any net pro-duction from the reservoir.

For hydrate-capped gas reservoirs, the same approach is used, except that the gas and water generated from hydrate

FIGURE 2: Gas production model of a hypothetical hydrate-capped gas reservoir. FIGURE 3: Equilibrium model for decomposition of hydrate(17).


decomposition during the production period cannot be neglected. The material balance equation in terms of a p/Z formulation can be written as Equation (2), with the following assumptions:

1. The reservoir is comprised of, at most, three components in-cluding hydrate, water and methane gas.

2. One mole of hydrate decomposes to one mole of methane and NH moles of water (~6), where NH is the hydration number [see Equation (1)].

3. The expansion of water and rock can be modelled using av-erage compressibilities of cw and c f , respectively.

4. The reservoir can be modelled with an average pressure and temperature.

5. The porosity and initial saturations are uniform throughout the reservoir.

pZT

p

Z T

G G

G

c p p

S

i

i i

p g

f

f i

wi

=

−−

−−( )

−−

1

11

cc S p p

S

w w B

G

NM B

M

w wi i

wi

e p w

f

HW w H

H w

−( )−

−−

+ −

1

1ρ

ρ

G

E Gg

H f............................. (2)

In Equation (2) Gp and Gg are cumulative gas production and gas generation, respectively, and Gf is the initial free gas-in-place.

Equation (2) differs from the standard gas material balance equation in several ways.

1. Produced gas is related to p /(ZT ) instead of p /Z, since tem-perature may change due to endothermic hydrate decomposi-tion. The choice of temperature is discussed later.

2. In the numerator, the term containing the produced gas volume also contains the generated gas volume, such that the numerator represents the net gas produced, Gp – Gg.

3. The last term in the denominator contains the effect of volume change due to hydrate decomposition and generated water volume.

For the specific case of a conventional gas reservoir, where Gg = 0 and T = Ti, the material balance Equation (2) simplifies to the conventional material balance equation. Similar to the equa-tion for conventional gas reservoirs, Equation (2) relates average reservoir pressure, p , to the cumulative gas produced, Gp. How-ever, there are two other unknowns in Equation (2): the cumula-tive gas generation, Gg, and temperature, T . Generally, these are functions of many factors like fluid flow, heat transfer,and the ther-modynamics of hydrate decomposition. In the following sections, we will formulate the problem for the case of constant production from a volumetric reservoir, and we will then develop two addi-tional equations which will be solved to obtain the two extra un-knowns of T and Gg in Equation (2).

Analytical ModelAs described above, gas production from hydrates involves a

combination of different mechanisms of fluid flow, heat transfer and thermodynamics of hydrate decomposition. Under some sim-plifying assumptions described in the Appendix, the material bal-ance equation for a volumetric hydrate-capped gas reservoir, Equation (2) is simplified to Equation (3):

p t

Z t

p

Z

G t G t

Gi

i

p g

f

( )( ) = − ( ) − ( )

1

................................................................. (3)

As shown in the Appendix, the reservoir pressure for constant rate gas production from a hydrate-capped gas reservoir can be ob-tained analytically by using Equations (4), (5) and (6):

p Tse= −( )exp λ β ................................................................................. (4)

T t T b t t T Hse i se( ) = − ( ) ≥ >, . ,273 15 0K.......................................... (5)

b t qp Z p Z

T TG

E AH c

Hwoe i i oe

i oef

H p

H( ) =

− ( ) ( )−

+1 ρ

ρ ∆88

31

1

H ck c t

p

cr r prρ π

ρ +

−

(6)

where Tse is hydrate cap temperature and b(t) is the rate of hydrate cap temperature drop. Other parameters are given in the Nomen-clature. Parameter b is an important quantity, and is a function of production rate, reservoir volume, thermo-physical properties of the hydrate cap and production time. Once this parameter is cal-culated from Equation (6), temperature is found from Equation (5) and the corresponding pressure is obtained from Equation (4). It turns out that, for constant rate production, parameter b is almost constant, resulting in a constant rate of temperature drop with time (for temperatures above the freezing point of water).

Equation (3) shows that the cumulative gas generation, Gg, has a significant role in sustaining reservoir pressure. The expression Gg can be calculated by integrating the gas generation rate, Equation (7), over the production period:

q tE AH c

Hb t

c

c Htg

H p

H

r pr

p

r( ) = ( ) +

ρ

ρ

ρ

πρ

α∆

41

........................................ (7)

This completes the development of the material balance Equa-tion (3) that relates reservoir pressure to cumulative gas produced and generated. As shown in this paper, this model can be used in a forward mode to predict rate of gas generation (and contribution of hydrates to production) as well as the change in average reservoir pressure with production for a reservoir with known properties. The use of this model in a backward mode for reserve estimation is given elsewhere(14).

Verification of the ModelIn this section, the validity of the material balance equation de-

veloped in the previous section is examined. Due to the lack of long-term production data for hydrate-capped gas reservoirs, we are unable to compare the developed model against any actual field data. However, the model presented above has been compared against Hydrsim(7), which is a comprehensive numerical model for simulating hydrate-bearing geologic media.

Hydrsim(7) is a two-phase, gas-water numerical simulator that accounts for viscous, capillary and gravity forces. The permea-bility of the hydrate is assumed to be a function of hydrate satu-ration. Heat transfer by conduction and convection is considered. This includes the consideration of heat transfer from the surround-ings by conduction, as well as sensible heat of the hydrate cap. The Kim-Bishnoi(15) equation is used to determine the dissocia-tion rate.

A hypothetical cylindrical hydrate reservoir of 100 m radius with a hydrate cap of 16 m thickness on top of a 4 m thick free-gas zone is considered as a basecase for this study (Figure 2). The ini-tial gas trapped in hydrate form and initial free gas-in-place are 19.2 × 106 (0.7 Bcf) and 4.6 × 106 std m3 (0.16 Bcf), respectively. The initial reservoir temperature is 11.85˚C and the initial pressure is 8.4 MPa. Reservoir porosity is 30% and initial hydrate satura-tion is 70%. We consider a well completed in the free-gas zone of the reservoir and produced at a constant flow rate of 50,000 std m3/day (1.8 MMSCF/day). Other relevant physical properties of the reservoir are given in Tables 1 and 2. The predicted hydrate cap temperature and reservoir pressure from the analytical model are compared with Hydrsim(7). The latter does not make any of the simplifying assumptions considered in the analytical model.


Average temperature and pressure of the reservoir are obtained from the temperature and pressure of each grid block at every time step. Obviously, in the hydrate zone above the hydrate-gas inter-face, only two phases exist. However, to avoid numerical instabili-ties during the course of the simulation study, a third phase was included by arbitrarily assigning gas saturation in the hydrate zone of 10%. To maintain immobility of this additional gas, the residual gas saturation was also set to 10%. To have a consistent compar-ison between the analytical and numerical results, the effect of the additional gas saturation in the hydrate layer was also considered in the parameters of the analytical model.

Figures 4(a) and 4(b) show a comparison between the predicted hydrate cap temperature and reservoir pressure of the new model versus those of the numerical simulator. Figure 4(a) shows that, as production continues, the hydrate cap temperature declines al-most linearly. This is because, when gas is produced from the well, the reservoir pressure declines, as can be seen from Figure 4(b). As a result, the hydrate decomposes into water and gas. However, decomposition is an endothermic process, resulting in the tem-perature decline of the hydrate cap. It must also be noted that de-composition is assumed to be an equilibrium process in this model. Therefore, the hydrate cap temperature always remains at the equi-librium temperature at the prevailing reservoir pressure. In Figure 4(b), a good match is obtained for average reservoir pressure. Fur-ther validation of the analytical model is demonstrated in the next

section, where the effect of different parameters on the solution be-haviour is investigated.

Results and Sensitivity StudyThe model developed herein can be used in a forward calcula-

tion mode to estimate the contribution of the hydrate in extending the lifetime of the underlying gas reservoir by sustaining the res-ervoir pressure [see Equation (3)]. In addition, the model can be used for estimating gas generation arising from the decomposi-tion process in the reservoir [see Equation (7)]. For this purpose, Equation (4) together with Equations (5) and (6) can be easily pro-grammed in spreadsheet form to obtain reservoir pressure. The in-puts to the model are related to initial pressure, porosity, net pay, drainage area, thermo-physical properties of reservoir components and production rate.

In this section, we study the effects of those important param-eters on hydrate reservoir behaviour. For this purpose, the results of five cases listed in Table 3 are presented in Figures 5(a) through 8(b). In addition, the contribution of hydrates on sustaining the res-ervoir pressure is presented in Figure 9. Results of additional cases are given elsewhere(16).

Figures 5(a) and 5(b) show the effects of reducing the basecase porosity from 30% to 20%. This comparison reveals that the res-ervoir pressure in the low porosity system is slightly lower than that of the basecase. This is because, when porosity is reduced, the amount of initial free gas-in-place is also reduced and therefore provides less pressure support to the reservoir. However, the reser-voir with lower porosity has more sensible heat and leads to more hydrate recovery (see Table 3). This partially (but not completely)

TABlE 3: list of cases studied.

Parameter Gg/Gp Hydrate Case ID Studied Value (%) Recovery (%)

1 Basecase * 61 22 2 φ 0.2 71 33 3 kcr(W/mK) 3 64 24 4 h(m) 8 50 23 5 re(m) 300 67 21

0 50 100 1500

2

4

6

8

10

12

(a)

Time (days)

T (˚

C)

Analytical modelHydrsim

0 50 100 1503,000

3,500

4,000

4,500

5,000

5,500

6,000

6,500

7,000

7,500

8,000

8,500

Time (days)

Pre

ssur

e (K

Pa)

(b)


FIGURE 4: Comparison between the analytical and numerical results – Case 1 (basecase).

TABlE 1: Reservoir geometry and properties for basecase.

reservoir radius (m) 100Thickness of hydrate zone (m) 16Thickness of gas zone (m) 4Porosity 0.3Permeability (md) 20Swi 0.2SHi (hydrate zone) 0.7Sgi (hydrate zone) 0.1SHi (gas zone) 0.0Sgi (gas zone) 0.8initial pressure (kPa) 8,407Temperature (˚C) 11.85initial free gas (std m3) 4.62 × 106

initial gas in hydrate (std m3) 19.2 × 106

eh (std m3/m3) 181λ (dimensionless) 38.98β (K) 8,533.80

TABlE 2: Values of other parameters(7).

density (kg/m3): rock 2,650 hydrate 919.7 Water 1,000

heat capacity (J/kg·K): rock 800 hydrate 1,600 Water 4,180

Thermal conductivity (W/m·K): rock 1.5 hydrate 0.393 Water 0.6

heat of decomposition (J/kg) 477,000


compensates for the effect of lower initial gas-in-place. The lower temperature is related to the temperature of the hydrate cap drop-ping faster through the equilibrium relation.

Figures 6(a) and 6(b) show the effect of doubling rock thermal conductivity. The comparison with the basecase shows that, at least for the case studied in this range, thermal conductivity has an in-significant effect on reservoir performance. The effect of thermal conductivity becomes more pronounced for hydrate layers that are thinner and when the production time is much longer (results are not shown here).

Figures 7(a) and 7(b) show the effect of reducing hydrate cap thickness from the basecase value of 16 m down to 8 m. The de-crease of the hydrate cap thickness results in a decrease in hydrate content, which causes a significant decrease in the gas generation rate. Therefore, reservoir pressure and corresponding equilibrium temperature decline faster [Figures 7(b) and 7(a), respectively]. Mathematically, decreasing hydrate thickness decreases H in the denominator of Equation (6) and increases the temperature parameter b.

Effects of reservoir radius are presented in Figures 8(a) and 8(b), covering the 1,000 days production period studied in this compar-ison. As reservoir radius increases, the amount of initial gas-in-place increases, leading to a reduction in the rate of pressure drop. Also, as reservoir radius increases, the hydrate cap surface area subject to heat transfer from cap and base rocks increases. There-fore, the time duration of sustaining a constant production rate is extended. While the amount of heat transfer from cap and base rocks increases due to greater surface area, the rate of tempera-ture drop decreases significantly as a result of higher (equilibrium)

reservoir pressure, sustained by the greater amount of initial res-ervoir volume.

Figure 9 shows the contribution of hydrates on sustaining the reservoir pressure. Figure 9(a) shows the familiar p/z – Gp plot for a hydrate-capped gas reservoir and its corresponding conventional gas reservoir (both have the same initial conditions and initial free gas-in-place). Obviously, for a conventional volumetric gas reser-voir, this plot is always a straight line and intercepts the cumula-tive gas production axis at initial free gas-in-place. However, in the case of a hydrate-capped gas reservoir, the plot deviates from a straight line due to the contribution of hydrates. This is similar to the behaviour of a conventional gas reservoir subjected to some sort of pressure support. Figure 9(b) shows the contribution of hy-drates in cumulative gas produced from the reservoir. As can be seen from the figure, during the production period, the generated gas in the reservoir is more than 60% of total produced gas.

Figures 4 to 8 show that there is reasonable agreement between the results of the analytical model and that of Hydrsim(7). More im-portantly, the analytical model captures the effects of all important parameters. In addition, the study shows that hydrates contribute significantly to the overall gas production from the reservoir. As demonstrated in Table 3, in most cases, the contribution of gen-erated gas over the period studied is more than 50% of the pro-duced gas.

Discussion In this paper, and in our other studies(14, 16), we have found that

the simple model developed here correctly represents the effects of

0 50 100 1500

2

4

6

8

10

12

(a)

Time (days)

T (˚

C)


= 20%

Basecase

Increasing

0 50 100 1503,000

3,500

4,000

4,500

5,000

5,500

6,000

6,500

7,000

7,500

8,000

8,500

Time (days)

pav

g (K

Pa)

(b)


= 20%

Basecase

Increasing

FIGURE 5: Comparison between the analytical and numerical results – Case 2 (φ = 20%).

0 50 100 1500

2

4

6

8

10

12

(a)

Time (days)

T(˚C

)


kcr = 3 W/mK

Basecase

Increasing kcr

0 50 100 1503,000

3,500

4,000

4,500

5,000

5,500

6,000

6,500

7,000

7,500

8,000

8,500

Time (days)

pav

g (K

Pa)

(b)


Basecase

kcr = 3 W/mK

Increasing kcr

FIGURE 6: Comparison between the analytical and numerical results – Case 3 (kcr = 3).


important rock and fluid properties over a wide range. However, to avoid using this model beyond its range of applicability, some of the subtle features and limiting assumptions of this model are dis-cussed below.

A material balance equation for a volumetric conventional gas reservoir is a function of cumulative gas produced, and does not depend on how fast the gas is produced. This is not the case in a hydrate reservoir, because rate of heat flow to the reservoir (and

therefore the rate of gas generated from hydrates) depends on the production history. For example, consider a case of production for some time from a hydrate-capped gas reservoir, followed by a pe-riod of no production. During this latter period, while cumulative gas produced remains constant, hydrate decomposition continues as a result of continued heat flow from the cap and base rocks to-wards the cooled hydrate cap. This generated gas will increase the reservoir pressure. For an analogous conventional reservoir, the

0 50 100 1500

2

4

6

8

10

12(a)

Time (days)

T (˚

C)


H = 8 m Basecase

Increasing H

0 50 100 1502,000

3,000

4,000

5,000

6,000

7,000

8,000

9,000

Time (days)

pav

g (K

Pa)

(b)


H = 8 m Basecase

Increasing H

FIGURE 7: Comparison between the analytical and numerical results – Case 4 (H = 8).

0 200 400 600 800 1,0000

2

4

6

8

10

12

(a)

Time (days)

T (˚

C)


re = 300 m

Basecase

Increasing re

0 200 400 600 800 1,0002,000

3,000

4,000

5,000

6,000

7,000

8,000

9,000

Time (days)

pav

g (K

Pa)

(b)


re = 300 m

Basecase

Increasing re

FIGURE 8: Comparison between the analytical and numerical results – Case 5 (re = 300).

0 1 2 3 4 5 6 7 8x106

0

1,000

2,000

3,000

4,000

5,000

6,000

7,000

8,000

9,000

10,000

Gp(std. m3)

p/z

(KP

a)

(1) Hydrate-capped gas reservoir(2) Conventional gas reservoir

(2)

(1)

(a)

0 20 40 60 80 100 120 1400

1

2

3

4

5

6

7

8x 106

(b)

Time (days)

Cum

ulat

ive

pro

duc

tio

n (s

td.m

3 ) (1) Total production(2) Hydrate contribution-Analytical(3) Hydrate contribution-Hydrsim

(3)

(2)

(1)

FIGURE 9: Contribution of hydrates on sustaining the reservoir pressure (Case 1).


pressure would have remained constant when there was no pro-duction. Therefore, while the material balance Equation (3) does not depend on the history of production, the gas generated from hy-drates Gg does depend on production history. In this paper, we have developed an analytical solution for a volumetric hydrate-capped gas reservoir that is produced at a constant rate.

In this study, a tank-type approach is used to predict reservoir pressure decline in response to constant rate gas production. The assumption of a tank-type model is reasonable when a free-gas layer is in thermo-physical contact with a hydrate cap and a mo-bile phase is present to transmit the pressure decline into the hy-drate zone. In addition, the transient flow regime period must not be of long duration because the assumption of tank-type behaviour will be violated during the transient period. On this basis, it is ex-pected that this model would not be suitable for low permeability reservoirs at early times when pressure gradients are sharp. How-ever, a fairly good match is obtained within the range of param-eters studied.

In deriving the rate of heat transfer from cap rock, the hydrate cap acts as a time-dependent boundary condition for the semi-infi-nite cap rock medium. It was assumed that the temperature at the boundary is the same everywhere within the hydrate cap. This as-sumption is violated if a significant temperature gradient exists in the hydrate cap. For example, as hydrate cap thickness increases or permeability in the hydrate cap decreases, a pressure gra-dient arises within the hydrate cap, leading to a temperature gra-dient and violating the assumption of uniformity of pressure and temperature.

Furthermore, it was assumed that the temperature of the free-gas layer remains constant. It is expected that, as time increases, the effect of cooling of the hydrate zone would, in fact, lower the temperature in the free-gas zone, making the temperature of the hydrate zone a better approximation for the average temperature used in Equation (3). For the cases studied in this work, and for the durations considered, we did not find consideration of a variable temperature in the free-gas zone necessary.

This study assumes the change of reservoir volume due to hy-drate dissociation to be negligible. Results show that, in most cases, less than 25% of the hydrate dissociates during the constant pro-duction period (Table 3). In addition, the volume change from hy-drate to water is very small and, because of capillary forces, most of the generated water from hydrate decomposition could remain in the reservoir. Other simulation results(7) also show that water production at the surface is small when the initial water saturation in the free-gas zone is at irreducible saturation. The simulator used in this study accounted for water flow and production and the re-sults agreed with the analytical ones.

One of the assumptions used in the Appendix for the develop-ment of the analytical solution is the linearization of the three-phase temperature-pressure equilibrium curve. If the temperature of the hydrate cap noticeably changes during the production pe-riod, linearization of the equilibrium curve by use of a cord line from initial conditions may lead to larger errors. Therefore, in such cases it would be better to linearize the curve over a more represen-tative range. In the present study, the equilibrium curve is linear-ized within the range of 0 – 14˚C.

Equation (7) indicates that the gas generation rate increases with time; a seeming contradiction. Equation (7) consists of two terms: gas generation rate due to heat transfer from cap and base rocks, and gas generation rate due to sensible heat of the hydrate zone. The rate of heat becoming available from sensible heat decreases with time (as b decreases slightly with time), while the rate of heat transfer from cap and base rocks increases as production continues and more than offsets the sensible heat decrease. The time-depen-dent term in this equation is related to heat transfer from cap and base rocks. Over time, system pressure and corresponding equilib-rium temperature decrease. As a result, the driving force for heat transfer from cap and base rocks increases, causing more hydrate to decompose. However, the constant rate production period is limited by system deliverability, wellbore temperature (and its ap-proach to freezing point of water) and the amount of hydrate. This means that eventually gas cannot be produced at a constant rate

(i.e. the rate ultimately declines). Therefore, the time-dependent term remains bounded.

Summary and ConclusionsThe generalized material balance equation for hydrate-capped

gas reservoirs was developed. For the special case of a volumetric reservoir produced at constant pressure, the contribution of gas hy-drates in sustaining reservoir pressure and its effect on the material balance equation was evaluated. This was achieved through the de-velopment of a new zero-dimensional (tank-type) analytical model incorporating 1D heat transfer and an equilibrium rate of dissocia-tion of the hydrate cap in a gas reservoir. The new model was val-idated against a comprehensive numerical model over a range of reservoir parameters.

For constant rate gas production from a hydrate-capped gas reservoir, the solution is very simple and can be easily used for approximate engineering calculations to estimate contribution of hydrates and reservoir pressure as functions of time. As a result of this study, we can draw the following conclusions:

1. At constant rate production, hydrate zone temperature drops in a close-to-linear manner and the rate of temperature de-cline is a function of production rate, reservoir volume, ther-mo-physical properties of hydrate cap and a weak function of production time.

2. The decomposition of hydrates due to depressurization can contribute significantly to the total production of a gas reservoir.

3. The dissociation of a major portion of the hydrates is sup-ported by the sensible heat of the hydrate cap itself. It is shown that a decrease in porosity could lead to an increase in hydrate recovery, through an increase in the sensible heat of the hydrate cap.

4. The rate of hydrate decomposition depends strongly on the degree of pressure reduction.

AcknowledgementsFunding for this research on gas hydrates has been provided

by Imperial Oil Resources and the Geological Survey of Canada (GSC), and the support of each is gratefully acknowledged. The study program of Mr. Gerami, a Ph.D. candidate at the University of Calgary, was also supported by a grant from the National Iranian Oil Company (NIOC).

NOmeNClaTUreA = hydrate block surface area in contact with cap and base

rocks, m2

b = hydrate cap temperature parameter, K/sBw = water formation volume factor, m3/std m3

c f = average formation compressibility, 1/kPa cpr = heat capacity of cap and base rocks, J/kgKcp = average hydrate cap heat capacity including rock, hy-

drate, water and gas, J/kgKcw = average connate water compressibility, 1/kPa EH = gas hydrate expansion factor, std m3/m3

Gf = initial free gas-in-place at standard conditions, std m3

Gg = cumulative gas generation at standard conditions, std m3

GH = initial gas in the form of hydrate at standard conditions, std m3

Gp = cumulative gas production at standard conditions, std m3

H = hydrate zone thickness, m∆H = heat of dissociation of hydrate, J/kg hydratek = reservoir permeability, m2

kcr = thermal conductivity of cap and base rocks, w/mKMH = molecular weight of hydrate, kg/kg-moleMW = molecular weight of water, kg/kg-moleNH = hydration number, dimensionless


p = reservoir pressure, kPap = average reservoir pressure, kPapi = initial reservoir pressure , kPapoe = equilibrium pressure at reference temperature Toe,

p Toe oe= −( )exp /λ β , 2,293 kPapse = equilibrium pressure, kPaqg = gas generation rate at standard conditions, std m3/sqw = gas production rate at standard conditions, std m3/s,re = reservoir radius, mSH = initial hydrate saturation, fractionSwi = initial water saturation, fractiont = time, sT = temperature in cap and base rocks, KT = average temperature in cap and base rocks, KTi = initial reservoir temperature, KToe = reference temperature, 273.15 KTse = hydrate cap temperature, KVb = hydrate cap volume, m3

we = cumulative water influx, m3

wp = cumulative water production, m3

z = spatial position in caprock, mZ = compressibility factor, fractionZi = compressibility factor at initial pressure and tempera-

ture, fractionZoe = compressibility factor at reference temperature and its

corresponding equilibrium pressure

Greek letters

α = thermal diffusivity, α = kc/ρ cp, m2/s

β = hydrate equilibrium curve constant (= 8,533.80 K)(16)

λ = hydrate equilibrium curve constant (= 38.98)(16)

φ = porosity, fractionρ = average hydrate cap density including rock, hydrate,

water and gas, kg/m3

ρH = hydrate density, kg/m3

ρr = caprock density, kg/m3

ρw = water density, kg/m3

refereNCeS 1. KVENVOLDEN, K.A. and LORENSON, T.D., The Global Occur-

rence of Natural Gas Hydrates; in Natural Gas Hydrates: Occurrence, Distribution, and Dynamics, Paull, C.K. and Dillon, W.P. (eds.), AGU Monograph, 2000.

2. COLLETT, T.S. and KUUSKRAS, V.A., Hydrates Contain Vast Store of World Gas Resources; Oil and Gas Journal, Vol. 96, No. 19, pp. 90-95, 11 May 1998.

3. SLOAN, JR., E.D., Clathrate Hydrates of Natural Gases; Second Edi-tion, Marcel Dekker, Inc., New York, NY, 1998.

4. MAKOGON, Y.F., Hydrates of Natural Gas; PennWell Publishing Company, Tulsa, OK, 1981.

5. KAMATH, V.A., A Perspective on Gas Production From Hydrates; paper presented at the JNOC’s Methane Hydrate International Sym-posium, Chiba City, Japan, 20-22 October 1998.

6. MORIDIS, G. J., Numerical Studies of Gas Production From Methane Hydrates; SPE Journal, Vol. 8, No. 4, pp. 359-370, December 2003.

7. HONG, H. and POOLADI-DARVISH, M., Simulation of Depres-surization for Gas Production from Gas Hydrate Reservoirs; Journal of Canadian Petroleum Technology, Vol. 44, No. 11, pp. 39-46, No-vember 2005.

8. SELIM, M.S. and SLOAN, E.D., Hydrate Dissociation in Sediment; SPE Reservoir Engineering, Vol. 3, No. 3, pp. 245-251, May 1990.

9. GOEL, N., WIGGINS, M. and SHAH S., Analytical Modelling of Gas Recovery From In Situ Hydrates Dissociation; Journal of Pe-troleum Science and Engineering, Vol. 29, No. 2, pp. 115-127, April 2001.

10. JI, C., AHMADI, G. and SMITH, D.H., Natural Gas Production from Hydrate Decomposition by Depressurization; Chemical Engineering Science, Vol. 56, No. 20, pp. 5801-5814, October 2001.

11. HONG, H., Modelling of Gas Production From Hydrates in Porous Media; M.Sc. Thesis, University of Calgary, 2003.

12. HONG, H., POOLADI-DARVISH, M. and BISHNOI, P.R., Analyt-ical Modelling of Gas Production from Hydrates in Porous Media; Journal of Canadian Petroleum Technology, Vol. 42, No. 11, pp. 45-56, November 2003.

13. GERAMI, S. and POOLADI-DARVISH, M., Predicting Gas Gen-eration by Depressurization of Hydrates Where the Sharp-Interface Assumption is Not Valid; Journal of Petroleum Science and Engi-neering, Vol. 56, Nos. 1-3, pp. 146-164, March 2007.

14. GERAMI, S. and POOLADI-DARVISH, M., Material Balance and Boundary-Dominated Flow Models for Hydrate-Capped Gas Res-ervoirs; paper SPE 102234 presented at the SPE Annual Technical Conference and Exhibition, San Antonio, TX, 24-27 September 2006.

15. KIM, H.C., BISHNOI, P.R., HEIDEMANN, R.A. and RIZVI, S.S.H., Kinetics of Methane Hydrate Decomposition; Chemical Engineering Science, Vol. 42, No. 7, pp. 1645-1653, April 1987.

16. GERAMI, S., Predictive and Production Analysis Models for the Un-conventional Gas Reservoirs; Ph.D. Thesis, University of Calgary, 2007.

17. KAMATH, V.A. and HOLDER, G.D., Dissociation Heat Transfer Characteristics of Methane Hydrates; AIChE Journal, Vol. 33, No. 2, pp. 347-350, February 1987.

Appendix: Mathematical ModelThe development of the analytical model for prediction of res-

ervoir pressure under constant production from a hydrate-capped gas reservoir must consider three important elements including: (i) material balance equation incorporating the gas generated from hydrate decomposition; (ii) energy balance equation considering endothermic heat of hydrate decomposition and heat transfer from cap and base rocks; and (iii) the equilibrium hydrate decomposi-tion model which relates the hydrate decomposition pressure to system temperature. In this section, the details of development will be described on the basis of the following assumptions:

1. Convective heat flow is ignored.2. Kinetics of hydrate decomposition is neglected, i.e., hydrate

decomposition follows the three-phase hydrate equilibrium relation.

3. The change in formation pore volume is negligible, and there is no water influx.

4. The free-gas zone temperature remains at the initial reservoir temperature.

5. The thermo-physical properties of hydrate, the reservoir and surrounding formations (cap and base rocks) remain constant during the production period.

The appropriateness of most of the above assumptions has been provided in the text of this paper.

(i) Simplified material Balance equation A tank-type model is used to predict average reservoir pressure.

This implies that the temperature and pressure within the reservoir are instantaneously uniform (i.e. no spatial dependence) and are therefore only functions of time. Furthermore, we assume that the geothermal gradient and the hydrostatic pressure can be ignored. Considering the assumptions described, a simple form of Equation (2) is obtained:

p t

Z t

p

Z

G t G t

Gi

i

p g

f

( )( ) = − ( ) − ( )

1

............................................................. (A-1)

In Equation (A-1), the average reservoir pressure is related to the difference between cumulative gas production and gas genera-tion due to hydrate decomposition, Gp(t) – Gg(t), which is the net gas production from the reservoir. In the depressurization tech-nique, the gas generated from hydrates Gg is limited by the avail-able heat. This relation is explored next.

(ii) energy Balance Calculations We account for two sources of heat available for hydrate decom-

position: the sensible heat of the rock and fluids surrounding hy-drates in the porous medium and the heat conducted from the cap and base rocks.


To solve for the latter, we consider the caprock as a semi-infi-nite medium (z = 0 to ∞) with a variable temperature, Tse(t), at the boundary, where temperature is reduced because of the cooling ef-fect of hydrate decomposition. The governing equation for heat transfer from the caprock is determined by conservation of energy using Fourier’s law of heat conduction.

∂∂

= ∂∂

Tt

T

zcrα

2

2 ..................................................................................... (A-2)

The initial and boundary conditions for the system are:

T T at t zi= = ≥ 0 0 ................................................................ (A-3)

T T t at z tse= = >( ) 0 0................................................................... (A-4)

T T at z ti= → ∞ > 0................................................. (A-5)

where T = T(z,t) is the temperature distribution in the caprock, and Tse(t) is the time-dependent temperature at the reservoir-caprock interface. In this model, we assume that temperature everywhere within the decomposing hydrate zone is the same (note assump-tion 4 in the main text). Justifications for this assumption are given elsewhere(7) and its implications are given within the Discussion section above.

The unknown boundary temperature, Tse(t), is related to the rate of hydrate decomposition and to the rate of heat flow from the caprock into the reservoir. As mentioned earlier, the conservation of energy for the hydrate block relates the rate of change in in-ternal energy within the hydrate zone to the rate of heat input from the caprock and the rate of heat consumed as a result of the en-dothermic process of hydrate decomposition. Applying an energy balance to the hydrate block, we obtain:

dTdz

H

k AE

dG

dt

c H

kz

H

cr H

g p

cr=

=

+

0 2 2

∆ ρ ρ

dT

dtse

........................................ (A-6)

(iii) hydrate decomposition modelIn the present study, the intrinsic kinetics of hydrate decomposi-

tion is ignored, and it is assumed that the pressure and temperature at the hydrate cap are the equilibrium pressure, p(t), and equilib-rium temperature, Tse(t), respectively, which vary slowly with time. The main factors affecting the pressure-temperature equilibrium relation of gas hydrates are the composition of natural gas and the salinity of water present in the system. Often, the equilibrium rela-tion is approximated by an exponential function. In this study, the equilibrium conditions (p,T) of the methane gas, methane hydrate and water are calculated using the following correlation(8, 17):

p Tse= −( )exp λ β.................................................................... (A-7)

where λ and β are the hydrate equilibrium curve constants. Typical values are given in Table 1.

SolutionEquations (A-1), (A-2), (A-6) and (A-7) comprise a system

of four equations for the four unknowns of p(t), Tse(t), Gg(t) and T(z,t). Equation (A-6) can be thought of as an equation for Tse(t) in boundary condition Equation (A-4), where the gas generation rate, dGg/dt, is related to Tse(t) via Equation (A-1) and the three-phase equilibrium curve Equation (A-7).

Our efforts to solve the system of four equations analytically were not successful. However, in an attempt to see the behav-iour of hydrate cap temperature, Tse(t), during the production pe-riod, a numerical solution to Equations (A-1) – (A-7) is presented elsewhere(17). According to the numerical solution, we assume a general equation for the hydrate block temperature which may be written as:

T t T b t t Tse i se( ) = − ( ) ≥ .273 15K .............................................. (A-8)

As can be seen, the chosen functional form of Equation (A-8) contains the initial reservoir temperature, the production time and a free parameter b(t) (the hydrate cap temperature parameter) which is a positive value to be determined later. Now, a new unknown, b(t), with a new equation, Equation (A-8), is added to the system of equations. Equations (A-2) – (A-5) along with Equation (A-8) specify the boundary temperature Tse(t), giving the complete for-mulation of the problem. The prior assumption for the form of how hydrate temperature Tse varies with time allows an analytical so-lution by application of the Laplace transform, while the slope of change in hydrate temperature with time b is found as part of the solution. Under some simplifying assumptions, including linear-ization of the equilibrium curve, Equations (A-1) to (A-7) can be solved analytically to obtain the temperature gradient at the hy-drate cap interface as(16):

∂∂

= ( )=

Tz

b tt

z r0

2πα

................................................................ (A-9)

Introducing Equations (A-8) and (A-9) into Equation (A-6), one may obtain the gas generation rate as a function of time:

q tE AH c

Hb t

c

c Htg

H p

H

r pr

p

r( ) = ( ) +

ρ

ρ

ρ

πρ

α∆

41

............................. (A-10)

where EH is the gas hydrate expansion factor and is defined as the ratio of a standard volume of gas trapped in a unit reservoir volume of hydrate.

In Equations (A-8), (A-9), and (A-10), the parameter b(t) is still unknown. To determine b(t), the material balance equation, Equa-tion (A-1), together with an energy balance around the hydrate cap, Equation (A-6), and the three-phase equilibrium curve are used(16). In this way, the hydrate-water-gas equilibrium data in the form of p/Z are correlated as a linear function of temperature, Tse(t), in the range of interest, Ti – Toe. This therefore provides the temperature parameter, b(t), which is the rate of decrease in hydrate cap tem-perature with time and is given by:

b t q

p Z p Z

T TG

E AH c

H

w

oe i i oe

i oef

H p

H

( ) =

− ( ) ( )−

+1

ρ

ρ ∆88

31

H ck c t

p

cr r prρ π

ρ +

−−1

...................... (A-11)

Once b(t) is known from Equation (A-11), the gas generation rate may be found from Equation (A-10). Average reservoir tem-perature and pressure are found from Equations (A-8) and (A-7), respectively. This completes the solution.

Provenance—Original Petroleum Society manuscript, Effect of Hydrates on Sustaining Reservoir Pressure in a Hydrate-Capped Gas Reservoir (2006-018), first presented at the 7th Canadian International Petroleum Conference the 57th Annual Technical Meeting of the Petroleum Society), June 13-15, 2006, in Calgary, Alberta. Abstract submitted for review No-vember 17, 2005; editorial comments sent to the author(s) January 12, 2007; revised manuscript received February 10, 2007; paper approved for pre-press February 21, 2007; final approval September 10, 2007.


Authors’ BiographiesShahab Gerami is presently working

for the R&D group at the National Iranian Oil Company. He received his Ph.D. degree in petroleum engineering from the Univer-sity of Calgary in 2007, where he conducted research on mathematical modelling of un-conventional gas reservoirs. Shahab holds a B.Sc. degree in gas engineering from the Petroleum University of Technology (1991) and an M.Sc. degree in hydrocarbon res-ervoir engineering from the University of

Tehran (2001), both in Iran. His experience has been obtained through working with the NIOC for about eight years. His areas of interest include mathematical modelling of conventional and un-conventional gas reservoirs, well testing and production decline curve analysis and phase behaviour of hydrocarbon fluids. He is a member of SPE and the Petroleum Society of CIM.

Mehran Pooladi-Darvish is an Asso-ciate Professor of petroleum engineering at the University of Calgary and a Senior Technical Advisor at Fekete Associates Inc. His research focuses on examining re-covery mechanisms of hydrocarbons from petroleum reservoirs and modelling these processes by developing appropriate math-ematical models. His current research activ-ities are on modelling gas production from hydrate reservoirs, CO2 sequestration in

geological formations, experimental and modelling studies of cold production of heavy oil and immiscible displacement in naturally fractured reservoirs. He is the winner of the “Best Paper Published in the JCPT Award” in 2000 and 2005, and was invited to appear in the “Distinguished Author Series” in SPE’s Journal of Petro-leum Technology (JPT) in 2004. He is also the winner of a number of teaching awards at the University of Calgary. Mehran has previ-ously worked at the Reservoir Engineering Research Institute, Palo Alto, California and the National Iranian Oil Company (NIOC) in Ahwaz, Iran. He appeared as an expert witness at the Alberta En-ergy and Utilities Board hearing dealing with Gas over Bitumen. Mehran received his B.Sc. and M.Sc. degrees in chemical and pe-troleum engineering from Amir Kabir University of Technology in Tehran, Iran and the University of Petroleum Technology in Ahwaz, Iran, respectively. He graduated with a Ph.D. in petroleum engineering from the University of Alberta. He is a member of the Petroleum Society of CIM, SPE and APEGGA.

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