Application of Fast Marching Methods for Rapid Reservoir Forecast and Uncertainty Quantification

Rapid economic evaluations of investment alternatives in the oil and gas industry are typically contingent on fast and credible evaluations of reservoir models to make future forecasts. It is often important to also quantify inherent risks and uncertainties in these evaluations. These ideally require several full-scale numerical simulations which is time consuming, impractical, if not impossible to do with conventional (Finite Difference) simulators in real life situations. In this research, the aim will be to improve on the efficiencies associated with these tasks. This involved exploring the applications of Fast Marching Methods (FMM) in both conventional and unconventional reservoir characterization problems. In this work, we first applied the FMM for rapidly ranking multiple equi-probable geologic models. We demonstrated the suitability of drainage volume, efficiently calculated using FMM, as a surrogate parameter for field-wide cumulative oil production (FOPT). The probability distribution function (PDF) of the surrogate parameter was point-discretized to obtain 3 representative models for full simulations. Using the results from the simulations, the PDF of the reservoir performance parameter was constructed. Also, we investigated the applicability of a higher-order-moment-preserving approach which resulted in better uncertainty quantification over the traditional model selection methods. Next we applied the FMM for a hydraulically fractured tight oil reservoir model calibration problem. We specifically applied the FMM geometric pressure approximation as a proxy for rapidly evaluating model proposals in a two-stage Markov Chain Monte Carlo (MCMC) algorithm. Here, we demonstrated the FMM-based proxy as a suitable proxy for evaluating model proposals. We obtained results showing a significant improvement in the efficiency compared to conventional single stage MCMC algorithm. Also in this work, we investigated the possibility of enhancing the computational efficiency for calculating the pressure field for both conventional and unconventional reservoirs using FMM. Good approximations of the steady state pressure distributions were obtained for homogeneous conventional waterflood systems. In unconventional system, we also recorded slight improvement in computational efficiency using FMM pressure approximations as initial guess in pressure solvers

Effective Reservoir Management for Carbon Utilization and Storage Applications

It is believed that the observed rapid rise in global temperatures is caused by high atmospheric concentration of CO2, due to emissions from fossil fuel combustion. While global efforts are currently in place to mitigate the effect, it is expected that hydrocarbons will remain the main source of energy supply for the planet in the foreseeable future. Harmonizing these seemingly conflicting objectives has given rise to the concept of Carbon Capture Utilization and Storage (CCUS). A prominent form of CCUS involves the capture and injection of anthropogenic CO2 for Enhanced Oil Recovery (EOR). During CO2 EOR, substantial amount of injected CO2 is retained and permanently stored in the subsurface. However, due to inherent geological and thermodynamic complexities in subsurface environments, most CCUS projects are plagued with poor sweep efficiencies. For successful CCUS implementation, advanced reservoir management strategies which appropriately capture relevant physics are therefore required. In this regard, effective techniques in three fundamental areas of reservoir management including forward modeling, inverse modeling and field development optimization methods are presented herein. In each area, we demonstrate the validity and utility of our methodologies for CCUS applications with field examples. First, a comprehensive streamline-based simulation of CO2 in saline aquifers is proposed. Here, the unique strength of streamlines at resolving sub-grid resolution which enables a high-resolution representation of CO2 transport during injection is exploited. Relevant physics such as compressibility and formation dry-out effects which were ignored in previously proposed streamline models are accounted for. The methodology is illustrated with a series of synthetic models and applied to the Johansen field in North Sea. All streamline-based models are benchmarked with commercial compositional simulation response with good agreement. Second, a Multiresolution Grid Connectivity-based Transform (M-GCT) for effective subsurface model calibration is proposed. M-GCT allows the representation and update of grid property fields with improved spatial resolutions. This enables improved characterization of the subsurface, especially for CCUS systems in which CO2 transport is highly sensitive to contrasts in hydraulic conductivity. The approach is illustrated with a synthetic and a field scale problem. To demonstrate its utility, the proposed method is applied to a field actively supporting a post-combustion CCUS project. Finally, a streamline-based rate optimization of intelligent wells used in CCUS projects is proposed. Based on a previously developed method, a combination of the incremental oil recovery, CO2 storage efficiency and CO2 utilization factor are optimized through an optimal rate schedules of the installed ICVs. The approach is particularly efficient since required objective function gradients and hessians are computed analytically from streamline-derived sensitivities obtained from a single simulation run. This significantly reduces the computational expense required to obtain solutions at level of optimality comparable to existing methods. The approach is illustrated with a synthetic case and applied to the Norne field to demonstrate the robustness of the approach

A General Spatio-Temporal Clustering-Based Non-local Formulation for Multiscale Modeling of Compartmentalized Reservoirs

Representing the reservoir as a network of discrete compartments with neighbor and non-neighbor connections is a fast, yet accurate method for analyzing oil and gas reservoirs. Automatic and rapid detection of coarse-scale compartments with distinct static and dynamic properties is an integral part of such high-level reservoir analysis. In this work, we present a hybrid framework specific to reservoir analysis for an automatic detection of clusters in space using spatial and temporal field data, coupled with a physics-based multiscale modeling approach. In this work a novel hybrid approach is presented in which we couple a physics-based non-local modeling framework with data-driven clustering techniques to provide a fast and accurate multiscale modeling of compartmentalized reservoirs. This research also adds to the literature by presenting a comprehensive work on spatio-temporal clustering for reservoir studies applications that well considers the clustering complexities, the intrinsic sparse and noisy nature of the data, and the interpretability of the outcome. Keywords: Artificial Intelligence; Machine Learning; Spatio-Temporal Clustering; Physics-Based Data-Driven Formulation; Multiscale Modelin

Application of Fast Marching Methods for Rapid Reservoir Forecast and Uncertainty Quantification

Rapid economic evaluations of investment alternatives in the oil and gas industry are typically contingent on fast and credible evaluations of reservoir models to make future forecasts. It is often important to also quantify inherent risks and uncertainties in these evaluations. These ideally require several full-scale numerical simulations which is time consuming, impractical, if not impossible to do with conventional (Finite Difference) simulators in real life situations. In this research, the aim will be to improve on the efficiencies associated with these tasks. This involved exploring the applications of Fast Marching Methods (FMM) in both conventional and unconventional reservoir characterization problems. In this work, we first applied the FMM for rapidly ranking multiple equi-probable geologic models. We demonstrated the suitability of drainage volume, efficiently calculated using FMM, as a surrogate parameter for field-wide cumulative oil production (FOPT). The probability distribution function (PDF) of the surrogate parameter was point-discretized to obtain 3 representative models for full simulations. Using the results from the simulations, the PDF of the reservoir performance parameter was constructed. Also, we investigated the applicability of a higher-order-moment-preserving approach which resulted in better uncertainty quantification over the traditional model selection methods. Next we applied the FMM for a hydraulically fractured tight oil reservoir model calibration problem. We specifically applied the FMM geometric pressure approximation as a proxy for rapidly evaluating model proposals in a two-stage Markov Chain Monte Carlo (MCMC) algorithm. Here, we demonstrated the FMM-based proxy as a suitable proxy for evaluating model proposals. We obtained results showing a significant improvement in the efficiency compared to conventional single stage MCMC algorithm. Also in this work, we investigated the possibility of enhancing the computational efficiency for calculating the pressure field for both conventional and unconventional reservoirs using FMM. Good approximations of the steady state pressure distributions were obtained for homogeneous conventional waterflood systems. In unconventional system, we also recorded slight improvement in computational efficiency using FMM pressure approximations as initial guess in pressure solvers

Effective Reservoir Management for Carbon Utilization and Storage Applications

It is believed that the observed rapid rise in global temperatures is caused by high atmospheric concentration of CO2, due to emissions from fossil fuel combustion. While global efforts are currently in place to mitigate the effect, it is expected that hydrocarbons will remain the main source of energy supply for the planet in the foreseeable future. Harmonizing these seemingly conflicting objectives has given rise to the concept of Carbon Capture Utilization and Storage (CCUS). A prominent form of CCUS involves the capture and injection of anthropogenic CO2 for Enhanced Oil Recovery (EOR). During CO2 EOR, substantial amount of injected CO2 is retained and permanently stored in the subsurface. However, due to inherent geological and thermodynamic complexities in subsurface environments, most CCUS projects are plagued with poor sweep efficiencies. For successful CCUS implementation, advanced reservoir management strategies which appropriately capture relevant physics are therefore required. In this regard, effective techniques in three fundamental areas of reservoir management including forward modeling, inverse modeling and field development optimization methods are presented herein. In each area, we demonstrate the validity and utility of our methodologies for CCUS applications with field examples. First, a comprehensive streamline-based simulation of CO2 in saline aquifers is proposed. Here, the unique strength of streamlines at resolving sub-grid resolution which enables a high-resolution representation of CO2 transport during injection is exploited. Relevant physics such as compressibility and formation dry-out effects which were ignored in previously proposed streamline models are accounted for. The methodology is illustrated with a series of synthetic models and applied to the Johansen field in North Sea. All streamline-based models are benchmarked with commercial compositional simulation response with good agreement. Second, a Multiresolution Grid Connectivity-based Transform (M-GCT) for effective subsurface model calibration is proposed. M-GCT allows the representation and update of grid property fields with improved spatial resolutions. This enables improved characterization of the subsurface, especially for CCUS systems in which CO2 transport is highly sensitive to contrasts in hydraulic conductivity. The approach is illustrated with a synthetic and a field scale problem. To demonstrate its utility, the proposed method is applied to a field actively supporting a post-combustion CCUS project. Finally, a streamline-based rate optimization of intelligent wells used in CCUS projects is proposed. Based on a previously developed method, a combination of the incremental oil recovery, CO2 storage efficiency and CO2 utilization factor are optimized through an optimal rate schedules of the installed ICVs. The approach is particularly efficient since required objective function gradients and hessians are computed analytically from streamline-derived sensitivities obtained from a single simulation run. This significantly reduces the computational expense required to obtain solutions at level of optimality comparable to existing methods. The approach is illustrated with a synthetic case and applied to the Norne field to demonstrate the robustness of the approach