The aim of this work is to examine the wellbore pressure behavior in reservoirs with single phase non-Darcy flow conditions produced at a constant sandface rate.
The transient flow period is analyzed by means of results generated with a finite difference model.
Analytical expressions of pressure drop and its semi-logarithmic slope are presented for the first time. These equations contain the laminar flow solution as a particular case and they provide means to evaluate the total skin factor. Another use of the analytical solution to the non-Darcy flow problem is to be able of identifying the presence of inertial effects by using a diagnostic plot which consists of graphing the derivative of the pressure data. versus the inverse of the square root of time on a cartesian paper. In this way, an analyst can easily predict the magnitude of the skin due to non-laminar flow under any condition of mechanical skin and rate. Furthermore, better stimulation jobs can be designed if non-Darcy flow conditions during a transient test are properly identified through the methodology presented in this study.
The use of the methodology obtained in this work is illustrated with synthetic examples for homogeneous and naturally fractured reservoirs. Also, a field example of an undersaturated reservoir and a dry gas case (taken from the literature) show the application of this technique. For the case of naturally fractured reservoirs new insights are provided.
Some of the techniques for pressure analysis that are available in the literature use the assumption of laminar flow which not always can be justified. Most of the work about the effect of non-Darcy flow on the wellbore response consider dry gas systems. Recently, Ref. 10 and 11 studied the presence of inertial effects in slightly compressible liquid flow systems, and Ref. 12 in both liquid and solution gas-drive systems with production at a constant wellbore pressure.
Currently, there is a debate in the literature about the presence of a semi-logarithmic straight line of the pressure drop under non-Darcy flow conditions. Carter et. al. showed a disagreement among the permeability values obtained from tests carried out at different flow rates. In this work it is investigated the possible presence of a semilog straight line and new insights are provided about the dependence of the semi-logarithmic slope with the production rates.
The existing methodology uses at least two tests in order to obtain the two components of the total skin factor, the mechanical skin and the skin due to inertial effects. In this work, an equation is presented to obtain the total skin in terms of physical properties.
Currently there are few analytical solutions to the non-laminar flow problem during the transient period. These solutions use the assumption that pressure and/or velocity are unique functions of the Boltzmann variable.