-Fractured nanoporous reservoirs include multi-scale and discontinuous fractures coupled with a complex nanoporous matrix. Such systems cannot be described by the conventional dual-porosity (or multi-porosity) idealizations due to the presence of different flow mechanisms at multiple scales. More detailed modeling approaches, such as Discrete Fracture Network (DFN) models, similarly suffer from the extensive data requirements dictated by the intricacy of the flow scales, which eventually deter the utility of these models. This paper discusses the utility and construction of 1D analytical and numerical anomalous diffusion models for heterogeneous, nanoporous media, which is commonly encountered in oil and gas production from tight, unconventional reservoirs with fractured horizontal wells. A fractional form of Darcy's law, which incorporates the non-local and hereditary nature of flow, is coupled with the classical mass conservation equation to derive a fractional diffusion equation in space and time. Results show excellent agreement with established solutions under asymptotic conditions and are consistent with the physical intuitions.Résumé -Modélisation de la diffusion anormale en 1D dans des milieux nanoporeux fracturés -Des réservoirs nanoporeux fracturés comprennent des fractures à échelles multiples et discontinues couplées à une matrice nanoporeuse complexe. Ces systèmes ne peuvent pas être décrits par les modélisations conventionnelles à double porosité (ou multi-porosité) du fait de la présence de différents mécanismes de flux à multiples échelles. Des approches de modélisation plus détaillées, telles que les modèles de Réseau de Fracture Discret (DFN, Discrete Fracture Network) souffrent de même des exigences extensives en matière de données, dictées par la complexité des échelles de flux, qui nuisent éventuellement à l'utilité de ces modèles. Le présent article traite de l'utilité et de la construction de modèles analytiques et numériques de diffusion anormaux en 1D pour des milieux hétérogènes nanoporeux, qui se rencontrent communément dans la production de pétrole et de gaz, pour les réservoirs étanches, non conventionnels avec des puits horizontaux fracturés. Une forme fractionnée de la loi de Darcy, qui comprend la nature non-locale et héréditaire du flux, est reliée à l'équation de conservation de la masse classique afin d'obtenir une équation de diffusion fractionnée dans l'espace et le temps. Les résultats montrent une parfaite concordance avec des solutions établies dans des conditions asymptotiques et ils sont conformes aux intuitions physiques.

A new approach for production data analysis in unconventional reservoirs is presented. Unlike the existing decline-curve analysis methods, this approach is not empirical and it is theoretically rigorous. The basis of the approach is an anomalous diffusion model for the performance of fractured horizontal wells surrounded by a stimulated reservoir volume. In the anomalous diffusion model, instead of Darcy's Law, a more general constitutional relation is used to incorporate the non-local and hereditary nature of flow in highly heterogeneous nanoporous media. The sub-or super-diffusive state of flow can be deduced from the slope of the straight line on the log-log plot of rate vs. time. Nonnecessity of a detailed description of the intrinsic properties and spatial distribution of matrix and fracture constitutes the practical advantage of the model. The reduced number of parameters can be conveniently estimated from production data and used in the anomalous diffusion model to predict future production. In this paper, a one-dimensional numerical model is implemented and applied to two Barnett shale gas wells and compared to common empirical models. It is shown that, even with limited completion, reservoir, and production data, the anomalous diffusion model has the potential to capture the production characteristics. Moreover, the model can be used to run sensitivities on actual system variables such as hydraulic fracture length, height and spacing, as well as to account for changing operating conditions. Current approaches for analyzing well performances in tight-oil and shale-gas plays mostly use the dual-porosity idealization for the stimulated (naturally fractured) reservoir volume (SRV) between hydraulic fractures. In these approaches, fluid flow is described at two distinct scales: the low permeability, high storativity matrix, and the high permeability but low storativity fracture network. The matrix acts as a source term to the continuum-forming fracture network, which transports the fluids to the well. Average properties are assigned to both matrix and fractures and uniform spatial distributions are assumed. The flux equation describing flow in both media is the well-known Darcy's law, which relates the flux to an instantaneous and local pressure gradient and assumes that the fluid-particle displacement during flow can be modeled as Brownian motion with a Gaussian (normal) distribution. This approach is well suited for conventional naturally fractured reservoirs where the matrix permeabilities are reasonably high and both, matrix and fracture network, can be treated as relatively homogeneous.Tight, unconventional reservoirs, on the other hand, exhibit a multitude of different scales including nano-and micro-pores, microfractures within the matrix, disconnected natural fractures, and induced fractures. The absence of a clear scale separation in the petrophysical heterogeneity makes definitions of locally averaged flow properties inappropriate and dual-or multi-porosity idealizations inapplicable. Anomalous diff...

This paper presents an anomalous diffusion based approach for modeling two-phase oil/water flow in fractured nanoporous media, such as that encountered in unconventional oil and gas reservoirs. Production is assumed to be from a multiply fractured horizontal well and the focus of the discussions is 1D linear flow in the region between hydraulic fractures. To account for the complexity and heterogeneity of the fractured medium, anomalous diffusion is considered in the flow domain between hydraulic fractures. To do so, the conventional Darcy phase fluxes are replaced by more general fractional flux laws which incorporate the non-local and hereditary nature of flow by means of fractional space-time phase and capillary pressure gradients. A modified IMPES scheme is derived for linear oil/water flow under specified terminal pressure production, and the impact of sub- and super-diffusion on phase rates, as well as pressure and saturation distributions across the system is studied.

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Operators face many challenges when selecting well-intervention candidates and evaluating a field’s potential because the process is highly time consuming, labor intensive, and susceptible to cognitive biases. An operator can lose up to USD 10 million/year because of ineffective well-intervention strategies in a single field. The objective of this study is to reduce such losses and standardize the well-intervention process by intelligently using the domain knowledge with artificial-intelligence (AI) and machine-learning (ML) techniques. The workflow developed in this study can automatically and autonomously analyze the surface-subsurface data to expeditiously recommend the top intervention candidates. The workflow leverages proven petroleum-engineering methods and customizable business logic to identify underperforming wells and then recommend workover techniques, post-workover production, success probability, and profitability. It uses production, petrophysics, reservoir, and economics data to run a series of AI/ML techniques. The data-analytics engine runs k-nearest neighbors to predict post-workover rates, followed by a decision tree to identify the remedies. Artificial neural network, random forest, and Monte-Carlo simulation are adapted to identify new perforation opportunities in existing wells. Analytic hierarchy process ranks the top intervention candidates based on post-workover rate, permeability, remaining reserves, and reservoir-production trends. Finally, Bayesian belief network calculates the probability of success. With this implementation, the manual benchmarking process of opportunity identification, which usually takes weeks to months, can now be completed within minutes. Once the opportunity is identified and reviewed, it gets registered in the opportunity tracker list for the final evaluation by the asset team. The results are displayed on web-based applications with customizable dashboards and can be integrated with any existing online/offline systems. Because the whole process is now automated and takes very little execution time, petroleum engineers can review the field’s performance on a daily basis. With more than 80% predictive accuracy and 90% time saving compared to the manual process, this workflow presents a step-change in the operator’s well-intervention management capacity. In this paper, the authors discuss the adaptations to the industry-standard AI/ML algorithms and the best practices to provide a faster, more accurate, and efficient well-intervention advisory system.