This paper presents a semi-analytical model to investigate the effect of Forchheimer's non-Darcy flow on the transient pressure behavior of vertical well in an infinite homogeneous reservoir. This model uses the Forchheimer number, defined as the product of the reservoir non-Darcy flow coefficient and a reference rate, to quantify the non-Darcy flow in reservoirs accurately. The traditional non-Darcy skin factor, generally applied to model the non-Darcy flow in reservoirs, is employed to describe the non-Darcy flow across completions only. This study shows that the non-Darcy flow effect may influence the local flow rate profile over a reservoir region of several hundred times the wellbore radius. Therefore, it is not satisfactory to merely use the traditional non-Darcy skin factor to model non-Darcy flow in reservoirs.

Type curves are documented for both drawdown and buildup tests for the first time using the semi-analytical model proposed. It is observed that, when non-Darcy flow in reservoirs and/or across completions are considered, the dimensionless pressure derivative curves of drawdown tests have a wider-transition region with gentler slopes, while those of buildup tests exhibit a shorter transition region with steeper slopes. In the radial flow period, compared to the cases with only non-Darcy flow across completions, the cases with non-Darcy flow in reservoirs for drawdown and buildup tests possess dimensionless pressure derivatives that are moving downwards to approach 0.5 at decreasing rates more gradually and smoothly. In general, the pressure derivatives of drawdown tests are larger than those of buildup tests before they converge to 0.5.

With this model, the skin factor for non-Darcy flow across completions and the dimensionless Forchheimer number for non-Darcy flow in reservoirs can be estimated from a common drawdown or buildup test. Guidelines for interpreting field test data are presented. Several typical cases from the literature are analyzed, and better type curve matches and more reliable results are obtained.

Keywords:
drillstem/well testing, flow rate, flow in porous media, Fluid Dynamics, completion, Drillstem Testing, drawdown, pressure drop, derivative curve, reservoir
Subjects:
Reservoir Fluid Dynamics, Formation Evaluation & Management, Flow in porous media, Drillstem/well testing
Copyright 2006, Society of Petroleum Engineers
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