A review of applications to constrain pumping test responses to improve on geological description and uncertainty

TLDR: In this paper, the authors present a review of the classical approaches to handle the issue of heterogeneity in well test analysis and explore procedures to evaluate pumping test or pressure-response curves.

Abstract: [1] This review examines the single-phase flow of fluids to wells in heterogeneous porous media and explores procedures to evaluate pumping test or pressure-response curves. This paper examines how these curves may be used to improve descriptions of reservoir properties obtained from geology, geophysics, core analysis, outcrop measurements, and rock physics. We begin our discussion with a summary of the classical attempts to handle the issue of heterogeneity in well test analysis. We then review more recent advances concerning the evaluation of conductivity or permeability in terms of statistical variables and touch on perturbation techniques. Our current view to address the issue of heterogeneity by pumping tests may be simply summarized as follows. We assume a three-dimensional array (ordered set) of values for the properties of the porous medium as a function of the coordinates that is obtained as a result of measurements and interpretations. We presume that this array of values contains all relevant information available from prior geological and geophysical interpretations, core and outcrop measurements, and rock physics. These arrays consist of several million values of properties, and the information available is usually on a very fine scale (often <0.5 m in the vertical direction); for convenience, we refer to these as cell values. The properties are assumed to be constant over the volume of each of these cells; that is, the support volume is the cell volume, and the cell volumes define the geologic scale. In this view it is implicit that small-scale permeability affects the movement of fluids. Although more information than porosity is available, we refer to this system as a “porosity cube.” Because it is not economically possible to carry out computations on a fine-scale model with modern resources on a routine basis, we discuss matters relating to the aggregation and scale-up of the fine-scale model from the perspective of testing and show that specific details need to be addressed. The focus is on single-phase flow. Addressing the issue of scale-up also permits us to comment on the application of the classical or analytical solutions to heterogeneous systems. The final part of the discussion outlines the inversion process and the adjustment of cell values to match observed performance. Because the computational scale and the scale of the porosity cube are different, we recommend that the inversion process incorporate adjustments at the fine scale. In this view the scale-up process becomes a part of the inversion algorithm.