This work investigates the possibility of characterizing the permeability distribution in areally heterogeneous reservoirs through the interpretation of pressure response to cyclic flow-rate variations.
We formulated a mathematical model for the pressure behavior caused by sinusoidal flow rates in reservoirs with continuously and smoothly varying radial-permeability distributions. The solution is obtained by the application of a regular perturbation analysis, and a correlation between the radius of cyclic influence and the frequency of a sinusoidal flow rate is developed. The analytical perturbation solution allows a qualitative assessment of the effects of areal reservoir heterogeneities on the pressure response either at the active well or at an observation well.
Because the perturbation method results in only an approximate solution, we propose a quantitative method to describe the permeability distribution based on the fully correct multicomposite radial reservoir model. The permeability in each zone of the equivalent reservoir is estimated by using a nonlinear regression procedure.
The frequency correlation may be used to design pulse-test flowrate schedules so that an optimum result can be achieved in terms of parameter estimation. We investigated several factors affecting the quality and the uncertainty in the estimated permeability distribution, along with examples including a variety of geometric and permeability distribution configurations. These factors include the type of test (constant-rate drawdown or pulse test) and reservoir configuration. In particular, we found the frequency of flow-rate changes and the point in the system at which to measure and interpret the pressure data to be important.