Application of Electrokinetics for Enhanced Oil Recovery - Electrokinetics for Petroleum and Environmental Engineers - page 117

the coupled flow coefficient, L 1,3 , includes junction potential
and the coupled flow coefficient, L 1.5 , includes Streaming
Potential and Membrane Potential.
• If J 2 is heat flow and Ø 2 is temperature, then L 22 is thermal
conductivity tensor, K , while the coupled flow coefficient,
L 2,1, includes Joule Heating.
• If J 3 is ionic flux and Ø 3 is ionic concentration, L 3,3 is (ionic)
diffusion coefficient, D i, then the coupled flow coefficient,
L 3,1 , includes electro-migration.
• If J 4 is charged particle flux and Ø 4 is charged-particle sus-
pension density, L 4,4 is the (charged particle) diffusion coef-
icient, D p , and the coupled flow coefficient, L 4,1 , includes
electro-phoresis.
• If J 5 is fluid flux and Ø 5 is pressure, then L 5,5 is k/μ, k is the
absolute permeability tensor, μ is the fluid viscosity, and the
coupled flow coefficient, L 51 , includes electro-osmosis.
• If J 6 is chemical reaction product flux and Ø 6 is the chemi-
cal reactant concentration, then L 6,6 is the chemical reaction
rate constant, and the coupled flow coefficient, L 6,1 , includes
electro-chemically enhanced reactions.

If the units of the left hand side (LHS) fluxes J i and the right hand side
gradients, ∇ Ø j , of equations 3.2a & 3.2b are such that their products, J i • ∇ Ø j ,

represent free energy dissipation, then, by Onsager's Principle :

LL
ij

=

. (3.3)

ji

Onsager's Principle (equation 3) is extremely useful because it is often
easier to measure one of the pair of coupled coefficients than the other.
The five DCEOR (electrokinetic) mechanisms listed above, as well as
Streaming and Membrane Potentials, are all (equations 3.2a & 3.2b) off
diagonal and, as such, are coupled mechanisms. Lorenz (1952) discusses the
relationship between two coupled flows: Electro-Osmosis and Streaming
Potential. The Primary DCEOR mechanisms are described below.

3.7.2 Joule Heating

The formation is heated by the passage of the electrical current through
conducting fluids and solids within the reservoir. Electrical heating ele-
ments, such as stovetop burners and space heaters, are based on Joule heat-
ing. Joule heating of the reservoir matrix and fluids raises the reservoir