This paper introduces an efficient surrogate model with the aim of accelerating joint estimation of subsurface geological properties and relative permeability parameters for high-dimensional inversion problems. We fully replace the high-fidelity model with a set of subdomain linear models through integrating model linearization with smooth local parameterization where the Gaussian geological parameters and non-Gaussian facies indicators are locally parameterized. These subdomain linear models with smooth local parameterization, referred to as SLM-SLP, are constructed in each subdomain individually using only a few high-fidelity model simulations. An adaptive scheme, that is, weighting smooth local parameterization (WSLP), is introduced as well to mitigate the negative effects of inappropriate domain decomposition schemes by adaptively optimizing the domain decomposition strategy. The computational advantages of the proposed algorithm are demonstrated on a synthetic non-Gaussian facies model and a real-world high-dimensional Gaussian model. The amount of computational cost has been drastically reduced while reasonable accuracy remains. Specifically, SLM-SLP only needs 220 fidelity simulations to optimize 302 parameters. Compared to ensemble smoother with multiple data assimilation (ES-MDA), SLM-SLP effectively and efficiently mitigates the ensemble collapse problem in the course of uncertain quantification.@en

Shale gas resources (SGR), as a representative of natural gas hydrate reservoirs, have been the main energy supply for the energy consumption currently. The multi-scale pore structure of shale, complicated seepage mechanisms, including Knudsen diffusion, matrix deformation, stress sensitivity, non-Darcy flow and spatial fracture network stimulated by hydraulic fracturing technology have posed huge challenges to an accurate prediction and assessment of shale gas recovery. A full understanding of gas seepage mechanism of shale gas is the critical and scientific issue to develop carbon hydrogen energy resources effectively. It is very urgent to establish a comprehensive mathematical model to analyze the productivity capacity through simultaneously considering various flow mechanisms and fractures network system. To fill this gap, this paper presents a comprehensive numerical model of hydraulic fracturing horizontal well with discrete fracture network where embedded discrete fracture model (EDFM) is employed to characterize the coupled phenomenon between discrete fracture network and fractured SGR. And then two numerical discretization methods, e.g., finite difference and finite-volume, are used to numerically discretize the equations, subsequently, the Newton-Raphson iterative method is adopted to obtain the final solutions. Finally, the sensitivity analysis experiments are employed to investigate the effects of the key parameters. The results can provide some certain guidance for the optimization of stimulated treatment in natural gas hydrate reservoirs.

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Five-spot well pattern (FSWP) scheme has shown appealing potentialities to enhance the recovery of coal-bed methane (CBM) from methane hydrocarbon reservoirs (MHR). In this paper, a new framework aimed at systematically investigating productivity performance of FSWP scheme with inter-well pressure interference (IWPI) is presented. First, mathematical models which are used to characterize the fluid flow within MHR and hydraulic fractures (HFs) are separately derived. Second, Laplace transformation and Stehfest numerical algorithm are utilized to couple those two flow systems and obtain the pressure-transient solutions of FSWP scheme. Finally, pressure characteristics are discerned and sensitivity analysis of key parameters is implemented as well. This semi-analytical approach outperforms numerical simulation from the point of computational efficiency. Several common flow regimes, e.g., linear and bi-linear flow regimes, are essentially deformed induced by IWPI. Several significant parameters, including gas rate, fracture half-length, and well spacing on the occurrence of IWPI are systematically analyzed. This work gains some new knowledge about the productivity performance of FSWP scheme with the existence of IWPI when extracting CBM from methane hydrate reservoirs (MHR), which provides energy engineers considerable instructions on optimizing the development of methane hydrate reservoirs.

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Based on fractal theory (FT) and fractional calculus (FC), a new fractally fractional diffusion model (FFDM) of composite dual-porosity has been developed to evaluate performance of multiple fractured horizontal wells (MFHWs) with stimulated reservoir volume (SRV) in tight gas reservoirs (TGRs). More specifically, FT is used to characterize the complex and heterogeneous fracture network (FN) both inside and outside of SRV, while anomalous behavior of diffusion processes both inside and outside of SRV is quantified by applying the temporal fractional derivatives. The FFDM is then solved by the Laplace transformation, line source function, the numerical discrete method, and superposition principle. The transient pressure responses are then inversely converted from Laplace domain into real time domain with the Stehfest algorithm, and the FFDM is also validated, and type curves are generated as well. Flow stages are subsequently identified together with analysis on characteristics of the type curves, especially the anomalous features different with those generated from the conventional Euclidean model. Sensitivity analyses of some related parameters have also been discussed as well. And the FFDM is then also matched with the real field well-testing data of a MFHW with SRV in a TGR. The proposed FFDM provides a new understanding of the performance of MFHWs with SRV in TGRs, which can be used to interpret the field pressure data more accurately and appropriately.

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Recently, a multiwell-pad-production (MWPP) scheme has been the center of attention as a promising technology to improve shale-gas (SG) recovery. However, the increasing possibility of multiwell pressure interference (MWPI) in the MWPP scheme severely distorts flow regimes, which strongly challenges the traditional pressure-transient analysis methods that focus on single multifractured horizontal wells (SMFHWs) without MWPI. Therefore, a methodology to identify pressure-transient response of the MWPP scheme with and without MWPI is urgent. To fill this gap, a new semianalytical pressure-transient model of the MWPP scheme is established by use of superposition theory, Gauss elimination, and the Stehfest numerical algorithm. Type curves are generated, and flow regimes are identified by considering MWPI. Finally, a sensitivity analysis is conducted. Our results show that there are good agreements between our proposed model and numerical simulation; moreover, our semianalytical approach also demonstrates a promising calculation speed compared with numerical simulation. Some expected flow regimes are significantly distorted by MWPI. In addition, well rate determines the distortion of pressure curves, whereas fracture length, well spacing, and fracture spacing determine when the MWPI occurs. The smaller the gas rate, the more severely flow regimes are distorted. As the well spacing increases, fracture length decreases, fracture spacing decreases, and the occurrence of MWPI occurs later. The stress-sensitivity coefficient has little to no influence on the occurrence of MWPI. Similar to the concept of the dual-porosity model, three new flow regimes—the single-well flow regime, MWPI flow regime, and MWPP flow regime—are artificially defined to systematically characterize the flow regimes of the MWPP scheme. This work offers some additional insights on pressure-transient response for the MWPP scheme in the SG reservoir, which can provide considerable guidance for fracture-properties estimation and well-pattern optimization for the MWPP scheme.

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