Matrix-to-fracture transfer functions derived from the data of oil recovery, and itʹs derivative and integral

It is demonstrated that using integrals, derivatives, and inflection points of the oil recovery data measured by imbibition tests on cores improves the accuracy of correlations of the matrix-to-fracture oil transfer data. The tri-exponential transfer functions with the present numerical approach yield a reliable technique to represent the experimental imbibition data. Accurately estimated function parameters allow the laboratory results to be scaled to field applications. Several issues pertaining to spontaneous imbibition as a recovery mechanism while waterflooding naturally fractured reservoirs are addressed. The contribution of the wettability and dead-end pores is also determined. The triple-exponential function for double-porosity systems is able to adjust to actual spontaneous imbibition trends observed in experiments conducted in naturally fractured cores. The analysis and interpretation of the results verify the considerations of the proposed mechanisms for fluid transfer from matrix to fracture.