Mathematical modeling of shale swelling in water based muds

Abstract

A method of servicing a wellbore comprises determining a cation exchange capacity of a sample of a shale, determining a swelling characteristic of the shale using the cation exchange capacity in an equation comprising a term of the form:(cation exchange capacity)where Ais a final swelling volume of the shale in the presence of an aqueous fluid having a salt concentration of z %, and x and y are empirical constants, determining a composition of a wellbore servicing fluid based on the determined swelling characteristic, and drilling the wellbore using the wellbore servicing fluid. The swelling characteristic of the shale can be determined using the cation exchange capacity of the shale and a salt concentration in an equation comprising a term of the form:()*()(cation exchange capacity)where Ais a final swelling volume of the shale in contact with an aqueous fluid having a salt concentration of m %, f(m,z) is a function based on the salt concentration of m % relative to salt concentration of z % in the aqueous fluid in contact with the shale, and x and y are empirical constants defining the relation A=x (cation exchange capacity).