Pseudosteady-State Analysis of Finite Conductivity Vertical Fractures

Abstract A new solution methodology for pseudosteady-state behavior of a well with a finite-conductivity vertical fracture is formulated using a reservoir/fracture domain resistivity concept. The formulation encompasses a transformed resistivity domain based on an equivalent or effective wellbore radius. The resulting pseudosteady solution is presented in the form of the dimensionless productivity index (JD). Some of the major advantages of this pseudosteady solution for finite-conductivity vertical fractures are 1) the methodology is based on fundamental principles, 2) the solution is analytical and easily implemented, 3) the equations are formulated for rectangular reservoirs, 4) the model includes wellbore flow (i.e., wellbore radius effect) which is important for low-conductivity fractures, and 5) the formulation accounts for a piece-wise continuous linearly varying fracture conductivity including: proppant tail-ins, over-flushing, pinch zones, choked flow (internal), and external skin mechanisms. The stimulation ratios for finite-conductivity fractures with an undamaged well are compared with those of McGuire and Sikora1 (1960), and Holditch2 (1974). The accuracy and validity of the pseudosteady model is also illustrated by comparison with the works of Prats3,4 (1961,1962), Gringarten et al.5,6 (1974), Cinco-Ley et al.7–10 (1978,1981), Barker and Ramey11 (1978), and Valko and Economides12 (1998). A summary of the fundamental building blocks, effective wellbore radius concept, pseudo-skin functions and fracture skin are discussed. An improvement to Gringarten's dimensionless productivity solution for infinite-conductivity vertical fractures in rectangular closed reservoirs is also presented.