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Transport in Porous Media

, Volume 92, Issue 1, pp 61–81 | Cite as

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

  • Hamid RoshanEmail author
  • M. A. Aghighi
Article

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.

Keywords

Thermodynamics of irreversible processes Shale formation Pore pressure 

List of Symbols

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

Average solute mass fraction in formation

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

Average diluent mass fraction in formation

Ca

Anions mass fractions

Cc

Cations mass fractions

Cj

Solute mass fraction of n chemical species

cT

Thermal conductivity

C

Specific heat capacity

Cm

Average solute mass fraction in drilling fluid

Cf

Average solute mass fraction in pore fluid

Dj

Solute diffusion coefficient of each chemical species

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

Coefficient of thermal diffusion of each chemical species

E

Electric potential

Em

Average electric potential of drilling fluid

Ef

Average electric potential of pore fluid

F

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

k

Permeability

KT

Thermal osmosis coefficient

KE

Electrical osmosis coefficient

Kf

Fluid bulk module

MS

Molar mass of the solute

Mj

Molar mass of j chemical species

n

Number of nodes

NP

Pressure shape functions

NE

Electric potential shape functions

NT

Temperature shape functions

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

Mass fraction shape functions

p

Pressure

R

Universal gas constant

t

Time

T

Temperature

Ta

Absolute temperature

Tm

Average temperature of drilling fluid

Tf

Average temperature of pore fluid

zj

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

σee

The effective electric conductivity of porous media

CIP

The electrical capacitance per unit volume

σet

The coefficient of thermo-electricity (Seebeck effect)

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Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.School of Petroleum EngineeringUniversity of New South WalesSydneyAustralia
  2. 2.Department of Mining and Petroleum EngineeringIK International UniversityQazvinIran

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