The Pressure Transient Behavior for Naturally Fractured Reservoirs With Multiple Block Size

Abstract

ABSTRACT A new analytical model is presented to study the pressure-transient behavior of a naturally fractured reservoir composed of a fracture network and matrix blocks of multiple size. Matrix blocks are considered to be uniformly distributed--through a reservoir of infinite extent. A general model for fluid transfer between matrix and fractures is established; this model justifies the use of both the Warren and Root model and the transient matrix flow model for double porosity systems. The multiple block size situation is handled through the use of a distribution function f(hma) that represents the fraction of matrix pore volume contained in blocks of size hma. It is demonstrated that classical parallel semilog straight lines can be present under these circumstances and the transitior zone may exhibit the characteristic half slope straight line when there is no flow restriction between matrix and fractures; --however, the transition between the end of the second and the third semilog straight line appears to be longer. It is found that the behavior of this type of systems is dominated by matrix of smaller size and the matrix blocks size computed from well testing by using the semilog straigt line intersection method corresponds to the weighted harmonic average; that is, in discrete form 1/h¯ma = Σi=1NB f i/hmai where NB is the number of block sizes. On the other hand, the λ value from well test analysis corresponds to the arithmetic weighted average, that is λ = Σi=1NB f iλ i. These findings are important wher applying the transient pressure result to waterflooding project design.