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Analysis of Pore Pressure Distribution in Shale Formations under Hydraulic, Chemical, Thermal and Electrical Interactions

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Abstract

Change in pore pressure in chemically active rocks such as shale is caused by several mechanisms and numerous studies have been carried out to investigate these mechanisms. However, some important coupling terms or driving forces have been neglected in these studies due to simplifying assumptions. In this study, a hydro-chemo-thermo-electrical model based on finite element method is presented to investigate the change in pore pressure in shale formations resulted from thermal, hydraulic, chemical and electric potential gradients. The change in pore pressure is induced by hydraulic conduction, chemical, electrical and thermal osmotic flow. In order to solve the problem of ion transfer under the influence of an electrical field, the Nernst–Planck equation is used. In addition, ion advection is considered to investigate its possible effect on ion transfer for the range of shale permeability. All equations are derived based on the thermodynamics of irreversible processes in a discontinuous system. The numerical results are compared against existing and derived uncoupled analytical solutions and good agreement is observed. The numerical results showed that the ion transfer and pore pressure are considerably affected by the electric field in the vicinity of the wellbore. It was also found that advection can play a remarkable role in ion transfer in shale formations. It was further shown that the change in pore pressure in shale formation is characterized by the combined effect of hydraulic, chemical, thermal and electro osmotic flow.

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Abbreviations

\({\mathop{C^{S}}\limits^-}\) :

Average solute mass fraction in formation

\({\mathop{C^{D}}\limits^-}\) :

Average diluent mass fraction in formation

C a :

Anions mass fractions

C c :

Cations mass fractions

C j :

Solute mass fraction of n chemical species

c T :

Thermal conductivity

C :

Specific heat capacity

C m :

Average solute mass fraction in drilling fluid

C f :

Average solute mass fraction in pore fluid

D j :

Solute diffusion coefficient of each chemical species

\({D_{j}^{T}}\) :

Coefficient of thermal diffusion of each chemical species

E :

Electric potential

E m :

Average electric potential of drilling fluid

E f :

Average electric potential of pore fluid

F :

Faraday’s constant (96,485 C/mol electrons)

k :

Permeability

K T :

Thermal osmosis coefficient

K E :

Electrical osmosis coefficient

K f :

Fluid bulk module

M S :

Molar mass of the solute

M j :

Molar mass of j chemical species

n :

Number of nodes

N P :

Pressure shape functions

N E :

Electric potential shape functions

N T :

Temperature shape functions

\({N_{\rm C}^{S}}\) :

Mass fraction shape functions

p :

Pressure

R :

Universal gas constant

t :

Time

T :

Temperature

T a :

Absolute temperature

T m :

Average temperature of drilling fluid

T f :

Average temperature of pore fluid

z j :

Charge of j chemical species

η :

Coefficient of solute retardation

μ :

Viscosity

\({\mathop {\rho _{\rm f}}\limits^- }\) :

Average fluid density

ρ :

Fluid density

\({\phi}\) :

Porosity

\({\mathfrak{R}}\) :

Standard solute reflection coefficient

σ ee :

The effective electric conductivity of porous media

C IP :

The electrical capacitance per unit volume

σ et :

The coefficient of thermo-electricity (Seebeck effect)

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Authors and Affiliations

  1. School of Petroleum Engineering, University of New South Wales, Sydney, Australia

    Hamid Roshan

  2. Department of Mining and Petroleum Engineering, IK International University, Qazvin, Iran

    M. A. Aghighi

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  1. Hamid Roshan
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  2. M. A. Aghighi
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Correspondence to Hamid Roshan.

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Roshan, H., Aghighi, M.A. Analysis of Pore Pressure Distribution in Shale Formations under Hydraulic, Chemical, Thermal and Electrical Interactions. Transp Porous Med 92, 61–81 (2012). https://doi.org/10.1007/s11242-011-9891-x

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  • DOI: https://doi.org/10.1007/s11242-011-9891-x

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