Analysis of Well Tests From Naturally Fractured Reservoirs by Automated Type-Curve Matching

Abstract

ABSTRACT Due to the diversity of existing idealized naturally fractured reservoir models, e.g. double porosity models with transient or pseudo-steady interporosity flow, etc., and the large number of parameters needed to be estimated in these models, the analysis of well test data from naturally fractured reservoirs by the well-known conventional graphical techniques is often difficult if not impossible. In recent years, the computer-aided automated type curve matching techniques based on nonlinear regression methods (e.g. least-squares, least absolute value, etc.) have been increasingly popular in estimating well/reservoir parameters from transient well test data. In this work, we explore in detail the applicability of nonlinear regression techniques to obtain the parameter estimates from well-test pressure data from naturally fractured reservoirs. We implement both the nonlinear regression technique based on L2 norm (least-squares) minimization and the nonlinear regression technique known as "robust" regression based on L1 norm (least absolute value) minimization. Important characteristics of these nonlinear regression methods are discussed. In modeling the pressure data, we consider the most commonly used double porosity models such as Warren and Root’s pseudo steady state interporosity flow model as well as transient interporosity flow models with slab and spherical matrix blocks (with or without interporosity skin effects) including wellbore and storage effects. The analysis of multi-rate tests by nonlinear regression techniques is also given. As model functions, pressure (or pressure change), conventional pressure derivative, pressure plus pressure derivative, pressure/pressure derivative ratio and integral pressure functions are considered in regression. The advantages and disadvantages associated with use of each function in the analysis are discussed. It is shown that the pressure/pressure derivative ratio increases the chances of obtaining a unique fit, that is, that it is not very sensitive to different initial guesses for parameter values unlike the other model functions. In addition, we show that the regression method using the integral functions yields more accurate estimates (with narrower confidence intervals) than the methods based on pressure derivative in cases where the pressure data is very noisy. Guidelines for the effective use of nonlinear regression techniques when analyzing well tests from dual porosity reservoirs are also provided. The applicability of the proposed methods is demonstrated by analyzing several sets of synthetic and field data.