Direct Spatiotemporal Interpolation of Reservoir Flow Responses

The traditional reservoir modeling workflow consists of first developing a reservoir model, performing flow simulation on that model, validating the model by performing history matching and finally using the history matched model to make predictions of future performance. In contrast, this paper presents two approaches to directly analyze the spatio-temporal variations of dynamic responses such as pressure and well flowrates and perform interpolation. Both these techniques are anchored to the data at the wells. Therefore, the resultant spatio-temporal predictions of dynamic response are history matched by construction. Interpolation or extrapolation of dynamic response to locations away from wells is possible using both the approaches. Therefore, the proposed approaches can be used to quickly determine optimal location to drill additional wells and to gauge the influence of reservoir management decisions. <br><br>In the first approach, dynamic responses such as pressure transients are treated as time series data. They are analyzed using wavelets that facilitate multiscale decomposition of pressure signals. Using a wavelet-lifting scheme, the transient signal is decomposed into averages and residuals. The corresponding filter coefficients defining the wavelets are treated as spatial random variables and estimated using geostatistics at locations away from wells. Pressure response is reconstructed at unsampled locations by employing the inverse wavelet transform. <br><br>In the alternate approach, direct spatiotemporal extrapolation of pressure is performed. The transient pressure data at the wells are first analyzed using correlation measures such as semi-variograms. For simplicity, time is taken as another spatial dimension and variogram values corresponding to the resultant lag-vectors are inferred and subsequently modeled. Spatiotemporal extrapolation is then performed to obtain the response at any location in space and at any instant in time. The robustness of both these approaches is verified on a number of case examples.<br><br>