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Naturally occurring gas hydrates are regarded as an important future source of energy and considerable efforts are currently being invested to develop methods for an economically viable recovery of this resource. The recovery of natural gas from gas hydrate deposits has been studied by a number of researchers. Depressurization of the reservoir is seen as a favorable method because of its relatively low energy requirements. While lowering the pressure in the production well seems to be a straight forward approach to destabilize methane hydrates, the intrinsic kinetics of CH_{4}hydrate decomposition and fluid flow lead to complex processes of mass and heat transfer within the deposit. In order to develop a better understanding of the processes and conditions governing the production of methane from methane hydrates it is necessary to study the sensitivity of gas production to the effects of factors such as pressure, temperature, thermal conductivity, permeability, porosity on methane recovery from naturally occurring gas hydrates. A simplified model is the base for an ensemble of reservoir simulations to study which parameters govern productivity and how these factors might interact.
Naturally occurring gas hydrates are regarded as an important future source of energy and considerable efforts are currently being invested to develop methods for an economically viable recovery of this resource. The recovery of natural gas from gas hydrate deposits has been studied by a number of researchers [
With the development of new computational techniques and robust numerical calculations in the last decades, reservoir simulation has evolved into a costeffective tool for industries, not only for testing new production designs but also for maximizing the production by optimizing the process variables. It is in this context that sensitivity analysis can contribute to phenomenological understanding, key factor determination, and assessing interactions between factors, process optimization and production forecasting [
OFAT his is one of the most common methods to carry out sensitivity analysis by selecting a baseline for each factor and then sequentially varying each factor over its range with the other factors fixed at the initial (baseline) level [
In factorial design, all factors are varied together taking all possible combinations in the different levels of each factor. The analysis of the results is usually carried out using analysis of variance (ANOVA); which is a collection of statistical models in which the observed variance in a particular variable is partitioned into components attributable to different sources of variation [
To study the characteristics of CH_{4}hydrate decomposition in porous media we developed a model based on the following considerations:
Reservoir is an unsteadystate open system;
Phases involved are: gas, aqueous, hydrate;
Components: CH_{4}, H_{2}O, CH_{4}hydrate;
Darcy's law will be used to describe the fluid flow in porous media;
Reservoir is a homogeneous and isotropic medium;
Gas hydrate molecule is assumed to be CH_{4}•5.75H_{2}O.
Gas hydrate decomposition can be represented by the following kinetic reaction:
CMG STARS™ [
In the simulation of gas hydrate several parameters are considered as being important for the production of methane from CH_{4}hydrate deposits. The most important are: geometry of the reservoir (dimensions and shape), reservoir properties (porosity, permeability,
As in the case for reservoir properties, a literature review was conducted for gas hydrate physical properties and it is summarized in
The model was designed as a radially symmetrical model of a gas hydrate deposit. It includes all three ratecontrolling mechanisms (multiphase fluid flow in porous media, kinetics of decomposition and heat transfer) that govern CH_{4} production from naturally occurring gas hydrates [
Mass balance for CH_{4}:
Fluid flow velocities are described by the following equations:
The velocity of gas along
The velocity of gas along
The velocity of water along
The velocity of water along
The rates of gas and water production and the rate of hydrate decomposition are represented by
The energy balance is described by the following equations:
As mentioned before, the kinetics of methane hydrate decomposition follows the KimBishnoi model [
Kinetic parameters (
The equilibrium pressure equation is determined by regression from experimental data compiled by Sloan and Koh [
Gas hydrate decomposition affects reservoir properties such as permeability and porosity since solid gas hydrate partially blocks the reservoir pore space, thus decreasing its permeability. During the decomposition process the pore space is freed from solid gas hydrate, thus increasing its permeability, which favors fluid transport though the reservoir. To take into account the effect of hydrate saturation in the pore space, STARS™ offers the option to determine the reservoir absolute permeability,
Gas and aqueous relative permeability are thus described by the following equations:
Capillary pressure between gaseous and aqueous phases is expressed as:
Following the simulation carried out by Hong [
A trial and error method was used to determine the time of the simulation in order to ensure the development of the decomposition profile that makes best use of the available hydrates. Three periods of time were evaluated: 8, 12 and 20 years. The results of these simulations are shown in
Before starting analyzing the different results, it is important to highlight that the purpose of this paper is to carry out a systematic sensitivity analysis of variables, thus, the selection of parameter's values is not done based on a single type of formation encountered on Earth, but rather, a collection of multiple combinations that although might create “nonpossible” hydrate reservoirs will also contain all the hydrate reservoirs found in the different regions, allowing the authors to unveil the what the most important variables are and its different interactions among each other.
The literature review presented in previous sections provided the parameter values that were selected to create the base case for a sensitivity study to investigate the influence of the chosen parameters on gas recovery from methane hydrates (
To ensure that the results of the models are comparable through all modifications of the reservoir parameters we kept the total molar amount of gas hydrate in the reservoir constant. Two parametersporosity and thickness of the hydrate layerdeserve special attention since any modification in these values causes a change in the formation pore volume and volume of the reservoir. In these two cases, it was necessary to modify the geometry of the system to keep the total volume of the reservoir constant.
Variables such as thermal conductivity of the rock, initial pressure and well radius had a smaller effect on the response variable (cumulative gas production) indicating that their significances are low in comparison to absolute permeability and
As noted above, changes in porosity and thickness of the hydrate layer affect the formation pore volume and the volume of the reservoir, respectively. In the case of a decreased porosity it was necessary to increase the thickness of the hydrate layer by a factor of 2.5 to compensate the change in porosity from 0.5 to 0.2. In the case of a reduced thickness of the gas hydrate it was necessary to increase the radius of the reservoir by a factor of 2.5 to compensate the change in thickness from 14 m to 7 m.
In the case of reducing the thickness of the hydrate layer, the radius of the reservoir was increased in order to keep the same initial volume. The result of this change was less cumulative methane production and is shown in
For our full factorial design we chose six parameters:
Six factors and two levels; this design constitutes a total of 64 simulations (2^{6});
Response variable: cumulative production of CH_{4};
Level of significance (α): 0.05;
Replicates: one (number of results per run).
For instance, for Runs #9, 20 and 37; it is established that shown in
The chosen parameter values were
As mentioned before, this system is an unreplicated 2^{6} factorial design. With only one replicate there is no internal estimate of error, which causes ANOVA analysis to fail. To overcome this problem, it is assumed that high order interactions are negligible (sparsity of effects principle) and combine their mean squares to estimate the error [
To carry out this type of ANOVA it is necessary to calculate its main components: Sum of squares (
From
It is important now to rule out higher order interactions. Montgomery [
In general to estimate the contrast for effect the
Considering this,
In addition,
An additional interpretation of the effects is possible; since the effects of initial pressure, irreducible water saturation and well radius and all their interactions are negligible it is possible to discard these variables so that the design becomes 23 with 8 replicates, this method is known in the literature as hidden replication. The ANOVA using this simplification is presented in
The OFAT sensitivity study and the full factorial design analyzed using ANOVA showed that reservoir absolute permeability (κ),
Considering the levels, by which these factors contribute to productivity, the most significant factors, by far, are those controlling the transport of gas to the well (κ and
The design of this study will help to estimate the upper limits of productivity in natural gas hydrate deposits. In the field, further limitations will apply, such as trapped gas bubbles, inhomogeneous hydrate distribution or anisotropic permeability.
This research was funded by the German Federal Ministry of Economics and Technology as part of the project “Submarine Gas Hydrates” (SUGAR).
The authors would like to thank the reviewers for their helpful comments. The German Federal Ministry for Economic Affairs and Energy (BMWi) provided funding for this work through Research Grant 03SX250E.
The authors declare no conflict of interest.
Constant in the phase equilibrium equation
Hydrate surface area per unit volume (m^{2}m^{3})
Specific area of hydrate particles (m^{2}m^{3})
Constant in the phase equilibrium equation (K)
Bottom hole pressure (kPa)
Gas heat capacity (J/(gmol·K))
Degrees of freedom
Activation energy (J/mol)
Equilibrium fugacity (kPa)
Fugacity of the hydrate former in the vapor phase (kPa)
Fugacity (kPa)
Mass generation rate (kg/m^{3}·s)
Specific enthalpy (J/kg)
Irreducible water saturation
Thermal conductivity (W(m^{2}·s))
Decomposition rate constant (mol/(m^{2}·Pa·s))
Intrinsic decomposition rate constant (mol/(m^{2}·Pa·s))
Molecular mass (kg/mol)
Number of moles of component
Capillary pressure (kPa)
Pressure (kPa)
Aspect ratio
Heat of hydrate decomposition unit bulk volume (J/m^{3}·s)
Direct heat input bulk volume (J/m^{3}·s)
Radius (m)
Well radius (m)
Universal gas constant, 8.314 J/(mol·s)
Saturation of phase
Irreducible water saturation
Residual gas saturation
Temperature (K)
Time (s)
Specific internal energy (J/kg)
Volume (m^{3})
Axial axis in the reservoir (m)
Level of significance
Heat of reaction (kJ/mol)
Fluid gravity (kPa/m)
Absolute permeability (mD)
Relative permeability
Viscosity (Pa·s)
Density (kg/m^{3})
Porosity
Velocity of the phase
Data from Sloan and Koh [
Schematic representation of the hydrate reservoir in Computer Modelling GroupAdvanced Processes & Thermal Reservoir Simulator (CMG STARS).
Concentration of solid methane hydrate in a model reservoir after eight years of production. Most methane hydrates still remain in the reservoir.
Concentration of solid methane hydrate in a model reservoir after twelve years of production. Significant amounts of methane hydrate remain in the reservoir.
Concentration of solid methane hydrate in a model reservoir after twenty years of production. Significant amounts of methane hydrate have been removed from the reservoir.
Cumulative gas production in the base case scenario.
Temperature distribution in the reservoir base case at the end of the operation.
CH_{4}hydrate concentration distribution in the reservoir base case at the end of the operation.
Influence of thermal conductivity of the rock on gas production.
The influence of absolute permeability on gas production.
Influence of initial pressure on gas production.
Influence of bottomhole pressure (
Influence of porosity on gas production.
Influence of thickness of the hydrate layer on gas production.
Influence of well radius on gas production.
Normal probability plot2^{6} factorial design.
Main effect plot2^{6} factorial design.
Interaction effect plot2^{6} factorial design.
Literature review for gas hydrate reservoirs (1).
Porosity  0.5  0.35  0.2  0.2  0.28  0.3  0.35  0.3  0.3  0.36  0.2 
Permeability (mD)  0.1  1,000  4.2  1  20  140  1,000  1,000    300  10–100 
Thermal conductivity of the rock (W/m·K)  1  0.5  2.73–5.57  1.5  1.5–8  2.7  2  0.5  1.5  1.7   
Thickness (m)    60      10  semiinfinite  12.5  30  16  15  15 
Volumetric heat capacity (J/m^{3}·K)      1.76 × 10^{6}  2.12 × 10^{6}  2.12 × 10^{6}    2.60 × 10^{6}    2.12 × 10^{6}  2.35 × 10^{6}   
Radius (m)    900  100    200    450  567  100     
Initial pressure (kPa)  20,370  10,900    11,510  6,913    6800  10,670  8,540    5,514 
Initial temperature (°C)  3.1  12.45  12–16  15  10    2.8  13.5  12  11  4.75 
    3,000–4,000  2,000  4,300  (2)    4,000    2,068  3,446  
Gas saturation          0.1    0    0  0.1  0.4 
Water saturation          0.3    0.35    0.25  0.2  0.3 
Hydrate saturation    0.4  0.19  0.4  0.6    0.65    0.75  0.7   
(1) To improve readability, the explanation of the symbols used in the formulae has been moved to an appendix at the end of this article; and (2) Thermal stimulation method.
Literature review of gas hydrate properties.
Heat capacity (J/kg·K)  3,300    2,200  2,031  1,600  1,600.5 
Thermal conductivity (W/m·K)  0.5    0.49  0.57  0.4  0.4 
Density (kg/m^{3})  912  920  910  929  919.7  919.7 
Heat of reaction (kJ/mol)      54.7    57  51.9 
Molecular weight (kg/kmol)          119.5  119.5 
Physical properties of the compounds involved in the formation of methane hydrates.
Thermal conductivity (W/m·K)  0.5  0.6  0.04  Gabitto 
Molecular weight (g/mol)  119.5  18  16  Uddin 
Density (kg/m^{3})  912  1,000  (1)  Gabitto 
Heat capacity (J/kg·K)  2,200  (2)  (3)  Liu 
(1) Calculated by Advanced Processes & Thermal Reservoir Simulator (STARS) using an equation of state;
(2) From STARS database; and (3)
Data for gas hydrate reservoir base case.
System  Nonadiabatic  More realistic than adiabatic case 
Hydrate layer radius (m)  500  [ 
Well radius (m)  0.086  Default value from STARS™ 
Hydrate layer thickness (m)  14  [ 
Porosity  0.5  [ 
Absolute permeability (mD)  10  [ 
Thermal conductivity of rock (W/(m·K))  3  [ 
Temperature (°C)  8  [ 
3,000  [  
Pressure (kPa)  6,000  [ 
Rock heat capacity (J/(m^{3}·K))  2.6 × 10^{6}  [ 
Initial gas saturation  0.08  [ 
Initial hydrate saturation  0.4  [ 
Initial water saturation  0.62  Determined by difference 
Results of the one factor at a time (OFAT) analysis.
Base case  1.78 
Thermal conductivity of rock (8 W/(m·K))  1.88 
Absolute permeability (100 mD)  3.12 
Initial pressure (7,000 kPa)  1.78 
1.16  
Porosity (0.2). 
2.54 
Thickness of the hydrate layer (7 m). 
1.38 
Well radius (0.3 m)  2.2 
Factors and levels of the factorial design.
a  3,000–4,000  
Initial pressure 
b  6,000–6,500 
Thermal conductivity of rock 
c  0.5–8 
Absolute permeabilityκ (mD)  d  0.1–300 
Irreducible water saturation 
e  0.2–0.35 
Well radius 
f  0.086–0.3 
Simulation results.

 

1  1  1  −1  −1  −1  −1  a  8.43 × 10^{−1} 
2  −1  −1  −1  −1  −1  −1  b  1.66 
3  −1  −1  1  −1  −1  −1  c  1.98 
4  −1  −1  −1  1  −1  −1  d  2.75 × 10^{2} 
5  −1  1  −1  −1  1  −1  e  2.04 
6  −1  −1  −1  −1  −1  1  f  2.41 
7  1  −1  −1  −1  −1  −1  ab  8.83 × 10^{−1} 
8  1  1  1  −1  −1  −1  ac  1.15 
9  1  −1  −1  1  −1  −1  ad  1.82 × 10^{2} 
10  −1  1  1  −1  −1  −1  bc  2.04 
11  1  −1  −1  −1  1  −1  ae  1.07 
12  −1  1  −1  −1  −1  −1  bd  2.76 × 10^{2} 
13  1  −1  1  −1  −1  1  af  1.19 
14  −1  1  −1  −1  1  −1  be  2.09 
15  −1  −1  −1  1  −1  −1  cd  3.56 × 10^{2} 
16  −1  −1  −1  −1  −1  1  bf  2.52 
17  −1  −1  1  −1  1  −1  ce  2.47 
18  −1  −1  1  −1  −1  1  cf  2.88 
19  −1  −1  −1  1  1  −1  de  2.80 × 10^{2} 
20  −1  1  −1  1  −1  1  df  2.77 × 10^{2} 
21  −1  1  −1  −1  1  1  ef  3.01 
22  1  1  1  −1  −1  −1  abc  9.14 × 10^{−1} 
23  1  −1  −1  1  −1  −1  abd  1.83 × 10^{2} 
24  1  1  −1  −1  1  −1  abe  1.11 
25  1  −1  1  1  −1  −1  acd  2.15 × 10^{2} 
26  1  1  −1  −1  −1  1  abf  1.27 
27  1  −1  1  −1  1  −1  ace  1.16 
28  −1  −1  1  1  −1  −1  bcd  3.57 × 10^{2} 
29  1  1  1  −1  −1  1  acf  1.64 
30  1  −1  −1  1  1  −1  ade  1.86 × 10^{2} 
31  −1  1  1  −1  1  −1  bce  2.52 
32  1  1  −1  1  −1  1  adf  1.84 × 10^{2} 
33  −1  −1  1  −1  −1  1  bcf  3.03 
34  −1  1  −1  1  1  −1  bde  2.81 × 10^{2} 
35  1  −1  −1  −1  1  1  aef  1.51 
36  −1  1  −1  1  −1  1  bdf  2.79 × 10^{2} 
37  −1  −1  1  1  1  −1  cde  3.61 × 10^{2} 
38  −1  −1  −1  −1  1  1  bef  3.13 
39  −1  −1  1  1  −1  1  cdf  3.60 × 10^{2} 
40  −1  1  1  −1  1  1  cef  3.56 
41  −1  1  −1  1  1  1  def  2.82 × 10^{2} 
42  1  1  1  1  −1  −1  abcd  2.16 × 10^{2} 
43  1  1  1  −1  1  −1  abce  1.34 
44  1  1  1  −1  −1  1  abcf  1.68 
45  1  −1  −1  1  1  −1  abde  1.87 × 10^{2} 
46  1  1  −1  1  −1  1  abdf  2.79 × 10^{2} 
47  1  −1  1  1  1  −1  acde  2.19 × 10^{2} 
48  1  1  −1  −1  1  1  abef  1.59 
49  1  −1  1  1  −1  1  acdf  2.17 × 10^{2} 
50  −1  1  1  1  1  −1  bcde  3.63 × 10^{2} 
51  1  −1  1  −1  1  1  acef  2.04 
52  −1  1  1  1  −1  1  bcdf  3.61 × 10^{2} 
53  1  1  −1  1  1  1  adef  1.87 × 10^{2} 
54  −1  −1  1  −1  1  1  bcef  3.78 
55  −1  1  −1  1  1  1  bdef  2.83 × 10^{2} 
56  −1  1  1  1  1  1  cdef  3.65 × 10^{2} 
57  1  1  1  1  1  −1  abcde  2.05 × 10^{2} 
58  1  1  1  1  −1  1  abcdf  2.18 × 10^{2} 
59  1  −1  1  −1  1  1  abcef  2.10 
60  1  1  −1  1  1  1  abdef  1.87 × 10^{2} 
61  1  −1  1  1  1  1  acdef  2.21 × 10^{2} 
62  −1  1  1  1  1  1  bcdef  3.67 × 10^{2} 
63  1  1  1  1  1  1  abcdef  2.22 × 10^{2} 
64  −1  −1  −1  −1  −1  −1  (1)  1.60 
(1) All factors are at low level.
Label structure for simulation runs.
1  −1  −1  1  −1  −1  ad 
−1  −1  −1  1  −1  1  df 
−1  −1  1  1  1  −1  cde 
Analysis of variance (ANOVA) results 2^{6} factorial design.
52,574  1  52,574  230.26  0.00  
149  1  149  0.65  0.42  
10,590  1  10,590  46.38  0.00  
1,094,245  1  1,094,245  4,792.61  0.00  
16  1  16  0.07  0.79  
390  1  390  1.71  0.20  
89  1  89  0.39  0.54  
3,896  1  3,896  17.06  0.00  
50,394  1  50,394  220.72  0.00  
236  1  236  1.03  0.32  
134  1  134  0.59  0.45  
183  1  183  0.80  0.38  
142  1  142  0.62  0.43  
180  1  180  0.79  0.38  
187  1  187  0.82  0.37  
10,265  1  10,265  44.96  0.00  
109  1  109  0.48  0.49  
64  1  64  0.28  0.60  
κ 
32  1  32  0.14  0.71 
κ 
276  1  276  1.21  0.28 
106  1  106  0.46  0.50  
Error  9,589  42  228     
 
Total  1,233,846  63       
ANOVA results23 factorial design “hidden replication”.
52,574  1  52,574  366.86  0.00  
10,590  1  10,590  73.90  0.00  
κ  1,094,245  1  1,094,245  7,635.68  0.00 
3,896  1  3896  27.19  0.00  
50,394  1  50,394  351.65  0.00  
10,265  1  10,265  71.63  0.00  
3,857  1  3,857  26.92  0.00  
Error  8,025  56  143     
 
Total  1,233,846  63       