Explicit deconvolution of wellbore storage distorted well test data

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 accurate measurements of flow-rate 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 underlying equations associated with each deconvolution scheme are derived in the Appendices and implemented via a computational module. 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 (1966) (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. 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.