Experimental determination of the matrix-to-fracture transfer functions for oil recovery by water imbibition

Abstract

Unique determination of the parameters of the triple-exponential matrix-to-fracture transfer functions is of profound importance to accurately simulate waterflooding and determine sweep efficiency in naturally fractured reservoirs. To accomplish this task, two novel approaches are investigated. Firstly, to our knowledge, the first attempt is made to facilitate not only the function values and their derivative, but also the integral to uniquely determine the transfer function parameters from a suite of in-house imbibition data. Secondly, a random number-based algorithm is applied to uniquely compute the parameters, and its results are compared to those generated through a conventional, nonlinear optimization method using spreadsheet software. The inclusion of the random component helps alleviate the inherent tendency of parametric optimization type algorithms to converge to that possible solution, predefined through the guessed values assigned to the parameters as starting values. Through precisely and more importantly uniquely determining the parameters of the matrix-to-fracture transfer function, experimental imbibition data can be correctly matched and better transposed to field applications. The presented approach of simultaneous correlation of the function and its derivative and integral provides an effective method to scale from laboratory experiments to field applications. Comparative studies presented in this paper delineate the outstanding advantages of the presented approach over the previous and frequently utilized function correlation approaches, which do not generally yield unique determination of transfer function parameters. With the help of a mathematically sound, uniquely defined model, a variety of issues pertaining to spontaneous imbibition can be addressed and resulting problems remedied. One such area of application is underbalanced drilling, where precise and advance knowledge of a formation's imbibition behavior would allow for optimized design and minimized formation damage. Another area is exploitation from naturally fractured reservoirs, in the presence of a strong water drive or a waterflood. Detailed understanding of the mechanisms governing matrix, fracture, and fluid interactions will result in optimized development and exploitation strategies.