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Non-isothermal, multi-phase, multi-component flows through deformable methane hydrate reservoirs

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Abstract

We present a hydro-geomechanical model for subsurface methane hydrate systems. Our model considers kinetic hydrate phase change and non-isothermal, multi-phase, multi-component flow in elastically deforming soils. The model accounts for the effects of hydrate phase change and pore pressure changes on the mechanical properties of the soil. It also accounts for the effect of soil deformation on the fluid-solid interaction properties relevant to reaction and transport processes (e.g., permeability, capillary pressure, and reaction surface area). We discuss a ’cause-effect’ based decoupling strategy for the model and present our numerical discretization and solution scheme. We then proceed to identify the important model components and couplings which are most vital for a hydro-geomechanical hydrate simulator, namely, (1) dissociation kinetics, (2) hydrate phase change coupled with non-isothermal two phase two component flow, (3) two phase flow coupled with linear elasticity (poroelasticity coupling), and finally (4) hydrate phase change coupled with poroelasticity (kinetics-poroelasticity coupling). To show the versatility of our hydrate model, we numerically simulate test problems where, for each problem, we methodically isolate one out of the four aforementioned model components or couplings. A special emphasis is laid on the kinetics-poroelasticity coupling for which we present a test problem where an axially loaded hydrate bearing sand sample experiences a spontaneous shift in the hydrate stability curve causing the hydrate to melt. For this problem, we present an analytical solution for pore-pressure, which we subsequently use to test the accuracy of the numerical scheme. Finally, we present a more complex 3D example where all the major model components are put together to give an idea of the model capabilities. The setting is based on a subsurface hydrate reservoir which is destabilized through depressurization using a low pressure gas well. In this example, we simulate the melting of hydrate, methane gas generation, and the resulting ground subsidence and stress build-up in the vicinity of the well.

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Abbreviations

\(\chi ^{\kappa }_{\alpha }\) :

Mole fraction of component κ = C H 4,H 2 O in phase α=g,w

\(\dot g^{CH_{4}}\) :

C H 4 generation rate

\(\dot g^{H_{2}O}\) :

H 2 O generation rate

\(-\dot g^{Hyd}\), \(-\dot g^{h}\) :

Hydrate consumption rate

\(\dot Q_{h}\) :

Heat of hydrate phase change

\(\dot q_{m_{\alpha }}^{\kappa }\) :

Volumetricinjection rate for phase α = g,w

𝜖 :

Volumetric or isotropic strain

g :

Gravity vector

\(\mathbf {J}_{\alpha }^{\kappa }\) :

Diffusion flux of component κ = C H 4,H 2 O in phase α=g,w

u :

Sediment displacement vector

v s :

Sediment displacement velocity

v β,t :

Total phase velocity

v β :

Phase velocity relative to the sediment

μ α :

Dynamic viscocity of phase α=g,w

ν s h :

Poisson ratio for composite solid

ϕ :

Actual or total porosity

ϕ e f f :

Apparent or effective porosity

ρ γ :

Density of phase γ=g,w,h,s

ρ s h :

Density of composite solid

\(\sigma , \sigma ^{\prime }\) :

Isotropic total and effective stresses

τ :

Tortuosity

\(\tilde \epsilon \) :

strain tensor

\(\tilde {\sigma },\tilde {\sigma }^{\prime }\) :

Total and effective stress tensors

A r s :

Specific reaction area

A s :

Specific surface area of hydrate-bearing sediment

B γ :

Bulk modulus of phases γ=g,w,h,s

B m :

Bulk modulus of bulk REV

B s h :

Bulk modulus of composite matrix

C p α :

Specific heat capacity at constant pressure of phase α=g,w

C v γ :

Specific heat capacity at constant volume of phase γ=g,w,h,s

D α :

Binary diffusion constant in phase α=g,w

E h ,E s :

Young’s modulus for hydrate and soil

E s h :

Young’s modulus for composite solid

f g :

Gas phase fugacity

G s h ,λ s h :

Lame’s parameters

h α :

Flow enthalpy of phase α=g,w

H :

Henry’s constant for methane

K :

Intrinsic permeability of hydrate bearing sediment

\(k^{c}_{\gamma }\) :

Thermal conductivity of phase γ=g,w,h,s

\(k^{c}_{eff}\) :

Lumped thermal conductivity of the REV

k d :

Hydrate dissociation rate constant

k r α :

Relative permeability of phase α=g,w

k r e a c :

Rate constant for kinetic phase change of hydrate

M κ :

Molar mass of component κ = H 2 O ,C H 4 ,H y d

N H y d , N h :

Hydration number

\(P^{sat}_{H_{2}O}\) :

Saturated water vapor pressure

P α :

Pressure of phase α=g,w

P c :

Capillary pressure

P e , P e q b :

Equilibrium pressure for hydrate phase

P e f f :

Effective fluid pressure

R u :

Universal gas constant

S α r :

Effective aqueous phase saturation

S β :

Saturation of phase β=g,w,h

T :

Temperature

u γ :

Internal energy of phase γ=g,w,h,s

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Authors and Affiliations

  1. Chair for Numerical Mathematics, Technical University Munich, Boltzmannstraße 3, 85748, Garching bei München, Germany

    Shubhangi Gupta & Barbara Wohlmuth

  2. Department of Hydromechanics and Modelling of Hydrosystems, University of Stuttgart, Pfaffenwaldring 61, 70569, Stuttgart, Germany

    Rainer Helmig

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  1. Shubhangi Gupta
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Correspondence to Shubhangi Gupta.

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Gupta, S., Helmig, R. & Wohlmuth, B. Non-isothermal, multi-phase, multi-component flows through deformable methane hydrate reservoirs. Comput Geosci 19, 1063–1088 (2015). https://doi.org/10.1007/s10596-015-9520-9

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