Analysis of Vertical Fracture Length and Non-Darcy Flow Coefficient Using Variable Rate Tests

Abstract

ABSTRACT In this investigation, a new method is presented for predicting both the non-Darcy flow coefficient and vertical fracture length based upon single-point, variable flow drawdown tests of shallow, low permeability gas reservoirs. The mathematical model simultaneously incorporates the effects of non-Darcy flow and variable rate expressed as a continuous function of time, thus providing a corrected pressure-drawdown versus time relationship. Pascal and Quillian1 described a method of analyzing variable flow tests where rate variation, usually declining during the test, is considered a continuous function of time. Solutions proposed in the foregoing article offered credible values for permeability and skin when matched with well production histories. Pascal, Quillian and Kingston have now expanded upon the basic concepts presented under reference 1 to provide solutions for vertical fracture length and the non-Darcy flow coefficient, using single-point variable flow data, resulting in a comprehensive model for analyzing transient pressure behavior. A correlation between the non-Darcy flow coefficient and permeability is also proposed. In low permeability gas reservoirs, the effects of variable (declining) rate become less apparent as flow time is extended. Conversely, the influence of non-Darcy flow becomes more dominant with increasing flow time. The model is illustrated using several field from hydraulically fractured gas wells in a low permeability reservoir.