Explicit Deconvolution of Well Test Data Distorted by Wellbore Storage

Abstract

Abstract The analysis/interpretation of wellbore storage distorted pressure transient test data remains one of the most significant challenges in well test analysis. Deconvolution (i.e., the "conversion" of a variable-rate distorted pressure profile into the pressure profile for an equivalent constant rate production sequence) has been in limited use as a "conversion" mechanism for the last 25 years. Unfortunately, standard deconvolution techniques require accu-rate measurements of flowrate and pressure --- at downhole (or sandface) conditions. While accurate pressure measurements are commonplace, the measurement of sandface flowrates is rare, essentially non-existent in practice. As such, the "deconvolution" of wellbore storage distorted pressure test data is problematic --- in theory, this process is possible, but in practice, without accurate measurements of flowrates, this process can not be employed. In this work we provide explicit (direct) deconvolution of wellbore storage distorted pressure test data using only those pressure data. The value of this work is that we provide explicit tools for the analysis of wellbore storage distorted pressure data --- specifically, we utilize the following techniques: --- Russell method (1965) (very approximate approach). --- "Beta" deconvolution (1950s and 1980s). --- "Material Balance" deconvolution (1990s). Each method has been validated using both synthetic data and literature field cases and each method should be considered valid for practical applications (the Russell method was not used). Our primary technical contribution in this work is the adaptation of various deconvolution methods for the explicit analysis of an arbitrary set of pressure transient test data which are distorted by wellbore storage --- without the requirement of having measured sandface flowrates. Objectives The objective of this work is to provide a comprehensive study of the analytic techniques that can be used to explicitly deconvolve wellbore storage distorted well test data using only the given pressure data and the well/reservoir information. Introduction Previous Work: For the elimination of wellbore storage effects in pressure transient test data, a variety of methods using different techniques have been proposed. An approximate "direct" method by Russell (1966) "corrects" the pressure transient data distorted by wellbore storage into the equivalent pressure function for the constant rate case. Despite its simplicity, it has several shortcomings such as limited accuracy and erroneous skin factor estimation. In short, the Russell (1966) method should not be used. Rate normalization techniques [Gladfelter et. al., (1955), Fetko-vich and Vienot (1984)] have also been employed to correct for wellbore storage effects and these rate normalization methods were successful in some cases. The most appropriate appli-cation of rate normalization is its use for pressure transient data influenced by continuously varying flowrates. The application of rate normalization requires the sandface rate measurements and generally yields a shifted results trend that has the correct slope, but incorrect intercept in a semilog plot (incorrect skin factor). Johnston (1992) showed that "material balance deconvolution" is a practical approach for the analysis of pressure transient data distorted by wellbore storage effects. In particular, this approach remedies the issue of a poor skin factor estimate that is typically obtained using rate normalization. Material balance deconvolution is also though to require continuously varying sandface flowrate measurements. We will show that sandface flowrates can be approximated from the observed pressure data. Essentially, rate normalization techniques are restricted when the lack of rate measurement exists. van Everdingen (1953) and Hurst (1953) demonstrated empirically that the sandface rate profile can be modeled approximately using an exponential rela-tion for the duration of wellbore storage distortion during a pres-sure transient test. The van Everdingen/Hurst exponential rate model is given in dimensionless form as: (during wellbore storage distortion)..... (1)