Pressure-rate convolution and deconvolution response for fractured conventional and unconventional reservoirs using new decline rate model
Salam Al-Rbeawi , Jalal Farhan Owayed
Petroleum ›› 2019, Vol. 5 ›› Issue (3) : 243 -251.
This paper introduces new approach for pressure-rate convolution and deconvolution analysis of multi-stages hydraulically fractured conventional and unconventional reservoirs. This approach demonstrates the impact of variable Sand face flow rate on reservoir performance. A new model for P/R deconvolution is used to convert pressure pulse from variable flow rate to single and constant rate response. The target of this study is fractal reservoirs with and without stimulated and unstimulated reservoir volume.
Multi-linear flow regimes approach is used to describe pressure behavior in the reservoirs while decline flow rate behavior is described by newly proposed model in this study. This model depicts, instead of van Everdingen model, indirectly the declining rate with time by using pressure responses with production time. Decline flow rate behavior simulated by linear and bi-linear flow models are also studied and compared with the one obtained by the new model. Several analytical models are used in this study by applying P/R convolution and deconvolution technique and solved for constant and variable flow rate considering different reservoir configurations and operating conditions. The results are interpreted and analyzed for better understanding pressure behaviors, flow regime types, and productivity index trends for continuously changing flow rate especially at early production time. Estimating stimulated reservoir volume (Vsrv) is considered one of the applications of convolved pressure since it is calculated from pseudo-steady state flow when late time boundary dominated flow regime is reached.
The outcomes of this study can be summarized as: 1) Introducing new approach for pressure-rate convolution and deconvolution technique for multi-stages hydraulically fractured reservoirs by applying new decline flow rate model that indirectly simulates variable flow rate with time. 2) Generating analytical models for dimensionless pressure and flow rate for constant and variable flow rate using the concept of P/R convolution and deconvolution. 3) Comparing the result of newly proposed models with the results obtained by applying van Everdingen model for decline rate behavior. 4) Studying the applicability of linear and bi-linear flow models in converting variable flow rate pressure response to single and constant flow rate pressure response. 5) Applying the deconvolution technique to simulate pressure response at late production time to estimate stimulated reservoir volume.
The most interesting points are: 1) The main difference in wellbore pressure behavior between variable and constant flow rate can be seen at early production time, however intermediate production time could also show very limited changes for the case of variable rate wellbore pressure. 2) A unit slope line flow regime could be developed for varied flow rate pressure response at very early production time similar to the wellbore storage dominated flow regime. 3) Productivity index calculated by the proposed models for variable flow rate is greater than the index for constant flow rate. 4) The impact of petrophysical properties of porous media and hydraulic fracture characteristics on pressure response are similar in the two cases of variable and constant flow rate. 5) The decline rate models for linear and bi-linear flow are not applicable in pressure deconvolution technique.
Convolution and convolution technique / Rate transient analysis / Pressure transient analysis / Fractured reservoirs / Reservoir performance
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