Incorporating electrokinetic effects in the porochemoelastic inclined wellbore formulation and solution

Abstract

The porochemoelectroelastic analytical models and solutions have been used to describe the response of chemically active and electrically charged saturated porous media such as clays, shales, and biological tissues. However, these attempts have been restricted to one-dimensional consolidation problems, which are very limited in practice and not general enough to serve as benchmark solutions for numerical validation. This work summarizes the general linear porochemoelectroelastic formulation and presents the solution of an inclined wellbore drilled in a fluid-saturated chemically active and ionized formation, such as shale, and subjected to a three-dimensional in-situ state of stress. The analytical solution to this geometry incorporates the coupled solid deformation and simultaneous fluid/ion flows induced by the combined influences of pore pressure, chemical potential, and electrical potential gradients under isothermal conditions. The formation pore fluid is modeled as an electrolyte solution comprised of a solvent and one type of dissolved cation and anion. The analytical approach also integrates into the solution the quantitative use of the cation exchange capacity (CEC) commonly obtained from laboratory measurements on shale samples. The results for stresses and pore pressure distributions due to the coupled electrochemical effects are illustrated and plotted in the vicinity of the inclined wellbore and compared with the classical porochemoelastic and poroelastic solutions.

Anisotropic Porochemoelectroelastic Solution for an Inclined Wellbore Drilled in Shale

“…(10) with Eq. (9b) yields the familiar constitutive relation for the total fluid content variation ti-f (11) in which M is the Biot's modulus [21]. The constitutive relation for the variation of individual fiuid components can be obtained as follows [11]: +j^dpj+ ( 12) where n,-= m,-/mf is the mole fraction of the ";•" component in the solution.…”

“…NaCl, KCl), i.e. x = y=l, applying the electro neutrality condition for the salt, i.e., xzc +yza = 0 gives the native mole fraction of each ion species in a shale formation as follows [11] 1 with 10-^CEC-…”

“…(13)) into the mass and electrical charge balance equations (Eq. (16)) while assuming electrostatic condition (dp^jdt = 0), and ignoring the ion transport by advection terms gives [11] d_ dt …”

“…Simultaneously, the effective stress and strain distributions in the formation are also modified which could lead to detrimental effects on the formation integrity. With increasing shale drilling and fracturing activities for oil and gas production, these coupled chemical-mechanical processes in shale have become lately a topic of extensive research [9][10][11][12]. For example, the isotropic solution of a plane strain wellbore was given in Ref.…”

“…Recently, the porochemoelectroelastic analytical solution of inclined wellbore in isotropic formations was derived and presented by Ref. [11].…”