We present an efficient adjoint model based on the deep-learning surrogate to address high-dimensional inverse modeling with an application to subsurface transport. The proposed method provides a completely code nonintrusive and computationally feasible way to approximate the model derivatives, which subsequently can be used to derive gradients for inverse modeling. This conceptual deep-learning framework, that is, an architecture of deep convolutional neural network through combining autoencoder and autoregressive structure, efficiently produces an analogously analytical adjoint with the help of auto-differentiation module in the popular deep-learning packages. We intentionally retain training data at the specific time instances where the measurements are taken, the storage of the intermediate states and computation of their adjoint, therefore, are completely avoided. This proposed adjoint state method is tested on a synthetic two-dimensional model for parameter estimations. The preliminary results reveal the feasibility of the proposed adjoint state method in term of computational efficiency and programming flexibility.

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.