Effect of Stress-Sensitive Fracture Conductivity on Transient Pressure Behavior for a Horizontal Well With Multistage Fractures

Abstract

Summary In this study, theoretical models have been formulated, validated, and applied to evaluate the transient pressure behavior of a horizontal well with multiple fractures in a tight formation by taking stress-sensitive fracture conductivity into account. On the basis of the superposition principle in the Laplace domain, we propose a coupled matrix/fracture-flow model with consideration of the stress-sensitivity effect in fractures, which strengthens the nonlinearity of the governing equations. More specifically, a new slab-source function in the Laplace domain was developed to describe the transient pressure responses caused by fluid flow from the matrix to the fracture, and a new solution was derived to describe the fluid flow in the fracture under the stress-sensitivity effect. Subsequently, a semianalytical method was applied by discretizing each hydraulic fracture into small segments, and a linearization scheme and an iteration method are adopted to deal with the nonlinear problem in the Laplace domain. Meanwhile, a modified superposition principle was proposed and applied to generate the pressure distributions for buildup tests with consideration of stress-sensitive fracture conductivity. Furthermore, pressure responses and their corresponding derivative type curves were generated to examine the effect of stress-sensitive conductivity. For pressure-drawdown tests, it is found that gradual increases in both pressure drop and pressure derivative occur over time because of the partial closure of the fractures. The stress-sensitivity effect in fractures becomes more evident with a smaller fracture conductivity and a larger fracture-permeability modulus. From the pressure-buildup curves, a one-fourth-slope line characteristic of the bilinear-flow period and constant derivatives of 0.5 representing a pseudoradial-flow regime can be clearly observed. Only fracture conductivity near the wellbore at the shut-in time can be estimated from the buildup pressures obtained in this work, whereas pressure-buildup analysis derived from the traditional superposition principle will result in an erroneous evaluation of the stress-sensitive fracture conductivity. It is also found that the effect of permeability hysteresis in the fractures has a negligible impact on the pressure-buildup responses.