Stein Krogstad

This work considers a coupled system of the MATLAB Reservoir Simulation Toolbox, a multi-phase network simulator and topside processing facilities, with the intent to provide a research tool for studying integrated planning and optimization. To this end, a collection of open-source tools are presented that can be combined with MATLAB Reservoir Simulation Toolbox to model, evaluate and optimize the economy of integrated systems, including reservoir and network under different market (costs and revenue) scenarios. The tools are organized in four repositories containing code for cost/price scenario modelling, derivative-free trust region optimization, pipe/network simulation and reservoir-network coupling and examples. A brief background on each of these tools is given, followed by the presentation of a fully implicit approach for the reservoir-network coupling. Moreover, a description is given on how to set up coupled simulation models, and finally, a presentation of numerical examples, including an optimization example that utilizes the full set of above-mentioned tools. Document Type: Original article Cited as: Leinan, P. R., Ustad, T. S., Krogstad, S., Silva, T. L., Ortiz, M. M., Hellemo, L., Smith, I. E. Simulation and optimization of a coupled reservoir and multi-phase flow network model. Advances in Geo-Energy Research, 2025, 15(3): 203-215. https://doi.org/10.46690/ager.2025.03.04

Summary: Fractured reservoir simulation plays a crucial role in understanding various subsurface geo-energy recovery and storage processes, including shale gas/oil extraction, enhanced geothermal systems, and CO2 sequestration in basaltic rocks. However, such simulations often entail significant computational expenses due to the high contrast in permeability and pore volume (PV) between matrix and fractures. To address this challenge, we introduce a reduced-order model (ROM) tailored for fractured reservoir simulation that offers flexible fracture representations by generating coarse matrix nodes based on reservoir outlines and adding extra diagonal connections between unconnected matrix nodes, whose corresponding volumes are intersected by fractures. This approach avoids the need for additional fracture nodes, effectively reducing computational costs. Dimensionality reduction methods, such as principal component analysis (PCA), are used to give quality priors for sampling matrix transmissibility and PV arrays. Tuning to well observation data, such as flow rates and bottomhole pressures (BHPs), is achieved through a gradient-based optimization method within a general automatic-differentiable simulator framework. Our results demonstrate robust calibration using synthetic well observation data from a fine-scale reference simulation model. Incorporating dominant flow physics, such as water breakthrough, from observation data improves history-matching (HM) convergence and prediction accuracy. Additionally, PCA for parameterization enhances the convergence rate of model calibration compared with random initialization. Calibrated transmissibilities align with high-connectivity regions from the fine-scale reference model, rendering the model interpretable in terms of reservoir connectivity or geology. This feature enables our method to be used effectively for reservoir HM and optimization using field observation data.

This paper presents a scenario-based optimization framework applied to Daily Production Optimization (DPO) for an Electric Submersible Pump lifted oil field under parametric uncertainty. The study also develops a simplified combined well-reservoir model, which is used solely to assess the performance of the methods in a more realistic setting. The combined model consists of the steady-state model of wells combined with the reservoir model through bottom hole pressure and well flow. Moreover, it successfully represents the change in uncertain parameters based on reservoir dynamics rather than random variations. The superiority of scenario-based DPO and the importance of considering uncertainty are demonstrated through extensive comparisons between deterministic and robust methods. The comparisons show that the deterministic DPO fails to satisfy output constraints, leading to violations, particularly in wellhead pressure. Conversely, the scenario-based DPO exhibits significant potential for real oil field application, effectively respecting all input and output constraints. Nevertheless, this safety comes at the cost of sacrificing net profit to some extent. The research emphasizes the importance of considering uncertainty in DPO for oil field operations, providing valuable insights for achieving robustness and operational safety.

We propose to use a conventional simulator, formulated on the topology of a coarse volumetric 3D grid, as a data-driven network model that seeks to reproduce observed and predict future well responses. The conceptual difference from standard history matching is that the tunable network parameters are calibrated freely without regard to the physical interpretation of their calibrated values. The simplest version uses a minimal rectilinear mesh covering the assumed map outline and base/top surface of the reservoir. The resulting CGNet models fit immediately in any standard simulator and are very fast to evaluate because of the low cell count. We show that surprisingly accurate network models can be developed using grids with a few tens or hundreds of cells. Compared with similar interwell network models (e.g., Ren et al., 2019, 10.2118/193855-MS), a typical CGNet model has fewer computational cells but a richer connection graph and more tunable parameters. In our experience, CGNet models therefore calibrate better and are simpler to set up to reflect known fluid contacts, etc. For cases with poor vertical connection or internal fluid contacts, it is advantageous if the model has several horizontal layers in the network topology. We also show that starting with a good ballpark estimate of the reservoir volume is a precursor to a good calibration.

Shallow geothermal reservoirs are excellent candidates for low-enthalpy energy storage, and can serve as heat batteries providing constant discharge of base heat, as well as rapid discharge of heat in periods of high demand. Recharging can be done by pumping down hot water, heated using excess heat from e.g. waste incinerators. In addition to having a very low carbon footprint, such systems also require limited surface infrastructure, and can easily be placed near or under the end-user, such as below residential buildings. The geological setting is typically complex, with horizons, faults, and intertwined patterns of natural fractures, and the nearwell region is often hydraulically fractured to enhance inter-well communication. Therefore, in order to fully utilize the potential of shallow geothermal heat storage, numerical simulations are imperative. In this work, we show how to practically model such systems, including generation of computational grids with a large number of wells and fractures, numerical discretizations with discrete fractures, and complex storage strategies with multiple wells working together under common group targets. We also discuss how adjoint-based methods can be used to tune model parameters (e.g. well injectivities, rock properties, and hydraulic fracture conductivities) so that the model fits observed data, and to find well controls (e.g. rates and temperatures) that optimize storage operations. The methodology is demonstrated using one artificial and two real underground thermal energy storage projects currently under development, and we highlight important challenges and our suggested solutions related to each of them. Thematic collection: This article is part of the Earth as a thermal battery: future directions in subsurface thermal energy storage systems collection available at: https://www.lyellcollection.org/topic/collections/thermal-energy

Model-based optimization of placement and trajectories of wells in petroleum reservoirs by the means of reservoir simulation forecasts is computationally demanding due to the high number of simulations typically required to achieve a local optimum. In this work, we develop an efficient flow-diagnostics proxy for net-present-value (NPV) with adjoint capabilities for efficient computation of well control gradients and approximate sensitivities with respect to placement/trajectory parameters. The suggested flow-diagnostic proxy consists of numerically solving a single pressure equation for the given scenario and the solution of a few inter-well time-of-flight and steady-state tracer equations, typically achieved in a few seconds for a reservoir model of medium size. Although the proxy may not be a particularly good approximation for the full reservoir simulation response, we find that for the cases considered, the correlation is very good and hence the proxy is suitable for use in an optimization loop. The adjoint simulation for the proxy model which provides control gradients and placement sensitivities is of similar computational complexity as the forward proxy model (a few seconds). We employ a version of the generalized reduced gradient for handling individual well constraints (e.g., bottom-hole-pressures and rates). As a result, the individual well constraints are enforced within the flow-diagnostics computations, and hence every parameter update becomes feasible without sacrificing gradient information. We present two numerical experiments illustrating the efficiency and performance of the approach for well placement problems involving trajectories and simulation models of realistic complexity. The suggested placements are evaluated using full simulations. We conclude by discussing limitations and possible enhancements of the methodology.