Elliptical-Flow-Based Pressure-Transient Interpretation Technique
Authors: Bybee Karen 
Published: February 2015

This article, written by Assistant Technology Editor Karen Bybee, contains highlights of paper SPE 105767, "A New Approach for Reliable Estimation of Hydraulic-Fracture Properties in Tight Gas Wells," by Y. Cheng, SPE, W.J. Lee, SPE, and D.A. McVay, SPE, Texas A&M U., prepared for the 2007 SPE Hydraulic Fracturing Technology Conference, College Station, Texas, 29–31 January.
Pressure-transient analysis in hydraulically fractured tight gas wells commonly is based on analysis of three flow regimes: bilinear, linear, and pseudoradial. With current well-test-analysis techniques, a reliable estimation of hydraulic-fracture and reservoir properties relies on occurrence of all three flow regimes. Because pseudoradial flow often is absent, the estimation of reservoir permeability, k, and fracture half-length, xf, is uncertain and unreliable. Elliptical flow, which exists between linear flow and pseudoradial flow, is of long duration (typically months to years). Much rate and pressure data can be acquired during this flow regime, but no practical well-test-analysis technique is available currently to interpret these data.

Introduction
Hydraulic fracturing is used widely to complete wells in tight gas reservoirs. Fracturing increases well productivity significantly so the well can achieve economic production rates. To evaluate stimulation effectiveness, reservoir and hydraulic-fracture properties, such as k, xf, and fracture conductivity, CfD, need to be estimated. Knowledge of these parameters not only is important for predicting future production performance of fractured wells, but also has significant influence in determining development strategies in exploitation of tight gas resources. Reservoir and fracture properties determine the drainage pattern of tight gas wells. With different estimates of reservoir and fracture properties, different well patterns and effective drainage areas can be expected.
Post-fracture pressure-transient testing is the technique most commonly used to estimate reservoir and fracture parameters for evaluating the stimulation effectiveness in hydraulically fractured gas wells. Current pressure-transient-test analysis in hydraulically fractured wells typically consists of conventional graphical-interpretation techniques and type-curve matching methods. The conventional graphical-interpretation techniques are based on analysis of three flow regimes: bilinear, linear, and pseudoradial. With test data during the bilinear-flow period, CfD can be estimated, and with test data during the linear-flow period, xf can be estimated. However, these estimates depend on the permeability estimate. Without independent knowledge of k, none of these estimates can be obtained reliably. The presence of pseudoradial flow is a prerequisite to determine k uniquely. However, impractically long times are required to reach pseudoradial flow in a tight gas reservoir. For example, for a typical tight gas well intersected by a hydraulic fracture with an xf of 100 ft in a reservoir with 0.01-md k, 0.15 porosity, and 0.03-cp gas viscosity, it takes 213 days to reach pseudoradial flow. If xf is 1,000 ft and other conditions are the same, 58 years are required to reach pseudoradial flow. Thus, it is very common in practice that pseudoradial flow is absent in post-fracture pressure-transient tests. As a result, the reservoir and fracture parameters usually are not determined independently from post-fracture pressure-transient analysis.