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.

This dissertation is composed of three parts of major contributions. In Chapter II, we discuss analytical study of contaminant transport from a finite source in a finite-thickness aquifer. This chapter provides analytical solutions of contaminant transport from one-, two-, and three-dimensional finite sources in a finite-thickness aquifer using Green's function method. A library of unpublished analytical solutions with different finite source geometry is provided. A graphically integrated software CTINT is developed to calculate the temporal integrations in the analytical solutions and obtain the final solutions of concentration. In Chapter III, we obtained solutions of groundwater flow to a finite-diameter horizontal well including wellbore storage and skin effect in a three-dimensionally anisotropic leaky aquifer. These solutions improve previous line source solutions by considering realistic well geometry and offer better description of drawdown near the horizontal well. These solutions are derived on the basis of the separation of the source and the geometric functions. The graphically integrated computer program FINHOW is written to generate type curves of groundwater flow to a finite-diameter horizontal well. The influence of the finite-diameter of the well, the wellbore storage, the skin effect, the leakage parameter, and the aquifer anisotropy is thoroughly analyzed. In Chapter IV, a general theory of groundwater flow to a fractured or non-fractured aquifer considering wellbore storage and skin effect is provided. Solutions for both leaky confined and water table aquifers are provided. The fracture model used in this study is the standard double-porosity model. The storage of the aquitard (the leaky confining layer) is included in the formula. A program denoted FINHOW2 is written to facilitate the calculation. Sensitivity of the solution to the confined versus unconfined conditions, fractured versus non-fractured conditions, and wellbore storage and skin effects is analyzed.