Horizontal wells with hydraulic fractures enable economical hydrocarbon extraction from unconventional reservoirs, and the associated transient production data is a reliable source for reservoir characterization. However, the complicated convolution of rate-pressure-time history leads to a less informative analysis of true reservoir characteristics. This paper presents a novel data-driven deconvolution approach using physics-based superposition to reconstruct constant-rate-drawdown pressure response, which are further translated into diagnostic plots for efficient production analysis.

Traditional deconvolution in pressure transient analysis is usually an ill-conditioned "inverse" process that requires systematic curve-fitting, and the deconvolution response is highly sensitive to noise. Our proposed approach uses superposition equations as training features to honor the transient physics, and further projects them into higher dimensional ‘reservoir’ space (kernel-space) for the purpose of rigorous regression. Additionally, by implementing Laplacian eigenmaps, our algorithm is relatively insensitive to noise owing to its locality-preserving character. After training, the constant-rate-drawdown pressure response is reconstructed and a diagnostic plot is generated to identify key reservoir characteristics such as flow regimes.

We first validated our approach with two synthetic cases, a horizontal well with single and multiple transverse fractures (MTFW), and the drawdown pressure response was obtained through simulation using a highly variable flow rate history. Additionally, we added artificial white Gaussian noise to the simulation output to mimic measured signals collected in the field, and we input this data into our model for deconvolution. The model-reconstructed constant-rate-drawdown pressure response was used to determine flow regimes and reservoir properties such as permeability and stimulated reservoir volume (SRV) using traditional transient testing diagnostic tools and specialized plots. The deconvolved response for each case were in alignment with the fractured-basement reservoir model proposed by Kuchuk et al. (2012), and the flow regimes identified during MTFW production followed the theory proposed by Song et al. (2011). All deconvolved responses were further validated through comparison with both simulation results and analytical solutions. Through the inherent locality-preserving character, our proposed algorithm was able to handle a moderate level of noise in addition to the variation of pressure-rate signals. We then applied the methodology to a field case, and the outcomes were satisfactory.

This study showed that our proposed methodology is a reliable diagnostic tool to interpret pressure-rate data using traditional pressure transient analysis for unconventional reservoirs. Rapid and accurate deconvolved pressure response greatly enhances the analysis of data with moderate noise and highly variable production histories, enabling engineers to recognize flow patterns and estimate reservoir properties. We demonstrated the versatility and applicability of our proposed approach with synthetic and field cases.

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