The effect of a distributed block length function on double porosity transitions during linear flow

Double porosity reservoirs may be described by a multitude of blocks of low permeability and fractures of high permeability. The present work is based on the assumption that the characteristic length of the blocks are distributed according to a continuous probability density function. The behavior of the resulting model is compared against the conventional model. The latter is based on the assumption that all low permeability regions may be described by an average characteristic length. It was found that the two models behave differently only during the transition period. The model with the distributed length function may lead to a transition period of linear appearance. This can easily be misinterpreted as equivalent homogeneous behavior. The main difference between the transitional linear and the homogeneous reservoir linear flow period is that the former will have a higher intercept on a square-root of time plot. This behavior is attributed to the simultaneous occurrence of two or more primary flow periods. The theoretical result is compared to a field example of the same behavior.