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Navratil, Jiri (IBM T.J. Watson Research Center) | De Paola, Giorgio (Repsol) | Kollias, Georgos (IBM T.J. Watson Research Center) | Nadukandi, Prashanth (Repsol) | Codas, Andres (IBM's Brazil Research Laboratory) | Ibanez-Llano, Cristina (Repsol)
Despite considerable progress in the development of rapid evaluation methods for physics-based reservoir model simulators there still exists a significant gap in acceleration and accuracy needed to enable complex optimization methods, including Monte Carlo and Reinforcement Learning. The latter techniques bear a great potential to improve existing workflows and create new ones for a variety of applications, including field development planning. Building on latest developments in modern deep learning technology, this paper describes an end-to-end deep surrogate model capable of modeling field and individual-well production rates given arbitrary sequences of actions (schedules) including varying well lo-cations, controls and completions. We focus on generalization properties of the surrogate model which is trained given a certain number of simulations. We study its spatial and time interpolation and extrapolation properties using the SPE9 case, followed by a validation on a large-scale real field. Our results indicate that the surrogate model achieves acceleration rates of about 15000x and 40000x for the SPE9 and the real field, respectively, incurring relative error ranging between 2% and 4% in the interpolation case, and between 5% and 12% in the various spacial and time extrapolation cases. These results provide concrete measures of the efficacy of the deep surrogate model as an enabling technology for the development of optimization techniques previously out of reach due to computational complexity.
Challenges remain in the upscaling and flow simulation of reservoir models from strong heterogeneity that may arise when representing complex patterns of connectivity and barriers. This is especially true in high contrast systems, e.g. for carbonate reservoirs, where statistical upgridding and upscaling approaches developed for clastic reservoirs perform less well. This has led to the development of a novel "Distance Based" upgridding technique which we combine with "Diffuse Source" upscaling to successfully simulate such models.
We replace previously developed variance-based statistical sequential layer grouping reservoir coarsening analyses, with a novel distance-based calculation. It relies on the local errors in the interstitial velocity and the time-of-flight introduced when layers are grouped, as a measure of distance between reservoir models. The use of a distance measure allows for the inclusion of flow capacity in this calculation, and avoids the strong biases that arise from the previous variance-based approaches, especially with high contrast systems.
We utilize the "Diffuse Source" (DS) upscaling approach to obtain the intercell transmissibility and well indices for the upscaled reservoir model. The DS approach is an extension of pseudo-steady-state (PSS) flow-based upscaling that utilizes the diffusive time of flight to identify well-connected sub-volumes in each adjacent pair of coarsened reservoir grid cells. DS upscaling retains the same localization advantage as the PSS approach. Unlike steady state upscaling, there is no coupling to a global flow field and local-global iterations are not required. DS upscaling was previously developed for more general reservoir coarsening, but the description now includes an extremely simple implementation for 1×1×N layer coarsening that naturally avoids the issues that arise in the use of the harmonic average for the vertical transmissibility.
Starting from a high-resolution fine scale 3D geologic model, sequential layer grouping provides us with a series of increasingly coarsened reservoir models. Each model in turn minimizes the integrated distance between the fine and coarsened models, which is used as a measure of heterogeneity lost during coarsening. From these layer designs we apply a combined cost and heterogeneity objective function to determine an optimal layer design, which is then used for upscaling and flow simulation.
We show that this distance-based optimal layer design does not experience the over-grouping of layers that arose from the previous variance-based approach. The new approach has been able to integrate the flow capacity similar to a Lorenz plot into the calculation of distance between reservoir models to include the impact of reservoir quality. This replaces the simple use of a net-to-gross cutoff utilized in previous work. The distance calculation uses a hyper-volume Lebesgue measure which provides a consistent means of combining different physical attributes: in this case interstitial velocity and the time-of-flight. The generalization of the hyper-volume to multiple properties, e.g., anisotropic permeability, is straight-forward.
1×1xN layer grouping is examined specifically to show the improvement in the optimal layer design compared to the previous statistical analyses. Areal coarsening is increased beyond 1×1 to show the general applicability of the DS upscaling approach.
The combination of distance-based upgridding and DS upscaling is tested and performs extremely well on a series of sector, outcrop and full-field 3D reservoir models using a research simulation code and a commercial finite difference simulator. These models include the SPE10 reference model, the Amellago carbonate model, and additional full field examples.
A novel distance-based measure of reservoir heterogeneity has been developed and applied to the design of an optimal reservoir simulation layering scheme, given a prior 3D geologic model. The distance measure combines elements of the Lorenz plot and previous variance-based analyses to avoid the strong biases and collapse of layering seen in the earlier approaches. Flow simulation based on Diffuse Source upscaled properties are shown to perform extremely well compared to the fine scale model.
Viscous fingering is a common phenomenon in viscous oil waterflooding, gas flooding and carbon sequestration processes. Wettability has been shown to have a significant effect on viscous fingering. The objective of this research is to model viscous fingering during drainage displacements, i.e., a non-wetting phase displacing a viscous wetting phase. We modified a previously proposed effective-fingering model for imbibition processes. Laboratory unstable coreflood experiments were history matched. Power-law correlations were developed between history matched model parameters and physical parameters such as the velocity and viscosity ratio. Fine-grid intermediate scale simulations were conducted with the effective-fingering model for domains with different degrees of heterogeneity. Coarse-grid simulations were run to determine the shape factor (one of the effective-fingering model parameters) needed to match the result of fine-grid simulations. The shape factor is a function of the correlation length, Dykstra-Parsons coefficient and viscosity ratio. This correlation can be used to upscale the interaction between viscous fingering and channeling in large scale simulations.
SPE, through its Energy4me programme, will present a free one-day energy education workshop for science teachers (grades 8–12). A variety of free instructional materials will be available to take back to the classroom. Educators will receive comprehensive, objective information about the scientific concepts of energy and its importance while discovering the world of oil and natural gas exploration and production. Energy4me is an energy educational public outreach programme that highlights how energy works in our everyday lives and promote information about career opportunities in petroleum engineering and the upstream professions. SPE’s Energy4me programme values the role teachers and energy professionals play in educating young people about the importance of energy.