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WellPINN: Accurate Well Representation for Transient Fluid Pressure Diffusion in Subsurface Reservoirs With Physics‐Informed Neural Networks
Accurate representation of pumping wells is essential for reliable reservoir characterization and simulation of operational scenarios in subsurface flow models. Physics-informed neural networks (PINNs) are emerging as a promising alternative to numerical models for reservoir modeling, offering seamless integration of monitoring data and governing physical equations. However, existing PINN-based studies face major challenges in capturing fluid pressure near wells when using a source/sink term, particularly during the early stages after pumping begins. We address this problem by introducing WellPINN, a workflow in which an initially trained PINN infers fluid pressure across the entire reservoir domain using a large equivalent well radius. This initial PINN solution is then locally refined around the well by a set of subdomain PINNs that are trained for smaller equivalent well radii. Continuity across these subdomain interfaces as well as at the initial condition is ensured by hard-constraining each PINN on its subdomain boundary. Our results demonstrate WellPINN as the first workflow of its kind to focus on accurate inference of fluid pressure from pumping rates throughout the entire injection period, significantly advancing the potential of PINNs for inverse modeling and operational scenario simulations. All data and code for this paper are openly available at https://doi.org/10.20350/DIGITALCSIC/17260.
Sequentially coupled flow and geomechanical simulation with a discrete fracture model for analyzing fracturing fluid recovery and distribution in fractured ultra-low permeability gas reservoirs
More accurate characterization and prediction of the in-situ distribution of fracturing fluid in fractured reservoirs are needed for enhancing well productivity. In this study, an implicit-sequentially coupled flow/geomechanics simulator incorporating an efficient discrete fracture model is developed to model fluid distribution and recovery performance of ultra-low permeability gas reservoirs. The finite-volume and finite-element methods are used for space discretization of the flow and geomechanics equations, respectively, while the backward Euler method is employed for time discretization. The flow and geomechanics equations are solved sequentially based on fixed-stress splitting. An efficient discrete-fracture model is used to explicitly model the fractured system. Flexible unstructured gridding is employed to model arbitrarily-oriented fractures. The interrelations among pore volume, permeability and geomechanical conditions are considered dynamically using two-way coupled flow and geomechanics computations. The geometry of fracture (networks) due to hydraulic fracturing has significant impacts on the fracturing fluid recovery efficiency and ensuing fluid distribution. Under the same injection volume, the fracturing fluid recovery is higher when the fracture geometry is planar. Fluid recovery is relatively lower whenever natural fractures are activated during fracturing treatments; flowback time is also shortened when complex fracture network with enlarged fracture interface is present. Fracturing fluid in hydraulic fractures may leak off into the natural fractures and subsequently imbibes into the surrounding matrix due to capillarity effects. The fracturing fluid recovery and in-situ fluid distribution are sensitive to the shut-in duration and fracture closure behavior. This study analyzes the coupled flow-geomechanical responses of fractured gas reservoirs during the post-fracturing periods. Understanding the fate of the fracturing fluid can provide insights on, to some extent, the stimulated fracture volume, size of the water invasion zone, and efficiency of the fracturing design. The simulation predictions can also provide more accurate initial reservoir conditions (e.g. distributions of different phases and pressure) for long-term well performance estimation.
Influence of extreme fracture flow channels on the thermal performance of open-loop geothermal systems at commercial scale
Abstract Adequate stewardship of geothermal resources requires accurate forecasting of long-term thermal performance. In enhanced geothermal systems and other fracture-dominated reservoirs, predictive models commonly assume constant-aperture fractures, although spatial variations in aperture can greatly affect reservoir permeability, fluid flow distribution, and heat transport. Whereas previous authors have investigated the effects of theoretical random aperture distributions on thermal performance, here we further explore the influence of permeability heterogeneity considering field-constrained aperture distributions from a meso-scale field site in northern New York, USA. Using numerical models of coupled fluid flow and heat transport, we conduct thermal–hydraulic simulations for a hypothetical reservoir consisting of a relatively impervious porous matrix and a single, horizontal fracture. Our results indicate that in highly channelized fields, most well design configurations and operating conditions result in extreme rates of thermal drawdown (e.g., 50% drop in production well temperatures in under 2 years). However, some other scenarios that account for the risks of short-circuiting can potentially enhance heat extraction when mass flow rate is not excessively high, and the direction of geothermal extraction is not aligned with the most permeable features in the reservoir. Through a parametric approach, we illustrate that well separation distance and relative positioning play a major role in the long-term performance of highly channelized fields, and both can be used to help mitigate premature thermal breakthrough.
Operation of Natural Gas Pipeline Networks With Storage Under Transient Flow Conditions
Here, we formulate a nonlinear optimal control problem for intraday operation of a natural gas pipeline network that includes storage reservoirs. The dynamics of compressible gas flow through pipes, compressors, reservoirs, and wells are considered. In particular, a reservoir is modeled as a rigid, hollow container that stores gas under isothermal conditions and uniform density, and a well is modeled as a vertical pipe. For each pipe, flow dynamics are described by a coupled partial differential equation (PDE) system in density and mass flux variables, with momentum dissipation modeled using the Darcy–Wiesbach friction approximation. Compressors are modeled as scaling up the pressure of gas between the inlet and outlet. The governing equations for all network components are spatially discretized and assembled into a nonlinear differential-algebraic equation (DAE) system, which synthesizes above-ground pipeline and subsurface reservoir dynamics into a single reduced-order model. We seek to maximize an objective function that quantifies economic profit and network efficiency subject to the flow equations and inequalities that represent operating limitations. The problem is solved using a primal–dual interior point solver, and the solutions are validated in computational experiments and simulations on several pipeline test networks to demonstrate the effectiveness of the proposed methodology.
Predicting Fluid Flow Regime, Permeability, and Diffusivity in Mudrocks from Multiscale Pore Characterisation
In geoenergy applications, mudrocks prevent fluids to leak from temporary (H 2 , CH 4 ) or permanent (CO 2 , radioactive waste) storage/disposal sites and serve as a source and reservoir for unconventional oil and gas. Understanding transport properties integrated with dominant fluid flow mechanisms in mudrocks is essential to better predict the performance of mudrocks within these applications. In this study, small-angle neutron scattering (SANS) experiments were conducted on 71 samples from 13 different sets of mudrocks across the globe to capture the pore structure of nearly the full pore size spectrum (2 nm–5 μm). We develop fractal models to predict transport properties (permeability and diffusivity) based on the SANS-derived pore size distributions. The results indicate that transport phenomena in mudrocks are intrinsically pore size-dependent. Depending on hydrostatic pore pressures, transition flow develops in micropores, slip flow in meso- and macropores, and continuum flow in larger macropores. Fluid flow regimes progress towards larger pore sizes during reservoir depletion or smaller pore sizes during fluid storage, so when pressure is decreased or increased, respectively. Capturing the heterogeneity of mudrocks by considering fractal dimension and tortuosity fractal dimension for defined pore size ranges, fractal models integrate apparent permeability with slip flow, Darcy permeability with continuum flow, and gas diffusivity with diffusion flow in the matrix. This new model of pore size-dependent transport and integrated transport properties using fractal models yields a systematic approach that can also inform multiscale multi-physics models to better understand fluid flow and transport phenomena in mudrocks on the reservoir and basin scale.
Rapid Simulation of Unconventional Reservoirs by Multidomain Multiresolution Modeling Based on the Diffusive Time of Flight
Summary The fast marching method (FMM)-based rapid flow simulation has been shown to accelerate simulation efficiency by orders of magnitude by transforming 3D simulation to equivalent 1D simulation using the concept of the “diffusive time of flight” (DTOF). However, the 1D transformation does not directly apply to multiwell problems. In this paper, we propose a novel DTOF-based multidomain multiresolution discretization scheme to accelerate multiwell simulation of unconventional reservoirs. Our method formulates multiwell simulation problems based on the DTOF which displays the pressure front propagation in unconventional reservoirs. The DTOF contours are used to partition the reservoir into local and shared domains. A local domain is where the flow is dominated by a single well, and the shared domain is where the fluid flow is influenced by multiple wells. The DTOF contours expand independently in local domains and interfere in the shared domain. After the partitioning, each domain is discretized using a multiresolution scheme whereby the original 3D fine mesh is preserved near the wells to account for detailed physics including gravity, and the rest of the domain is discretized into 1D mesh based on the DTOF contours to alleviate the simulation workload. The power and efficacy of our approach are demonstrated using synthetic and field-scale simulation models with different degrees of geologic and well-completion complexity. The simulation results, number of active cells, and computation time for the proposed discretization scheme are compared with the original high-fidelity 3D model for each case. The results show that the proposed method is suitable for multiwell simulation problems in unconventional reservoirs and can accelerate flow simulations by orders of magnitude with minimal loss of accuracy. The novelty of this work is the creation of DTOF-derived multiresolution discretization with local and shared domains to simplify and accelerate the calculation of subsurface flow problems, especially in unconventional reservoirs. Our workflow can be easily interfaced with commercial simulators, making it suitable for large-scale field applications.
Modeling Subsurface Performance of a Geothermal Reservoir Using Machine Learning
Geothermal power plants typically show decreasing heat and power production rates over time. Mitigation strategies include optimizing the management of existing wells—increasing or decreasing the fluid flow rates across the wells—and drilling new wells at appropriate locations. The latter is expensive, time-consuming, and subject to many engineering constraints, but the former is a viable mechanism for periodic adjustment of the available fluid allocations. In this study, we describe a new approach combining reservoir modeling and machine learning to produce models that enable such a strategy. Our computational approach allows us, first, to translate sets of potential flow rates for the active wells into reservoir-wide estimates of produced energy, and second, to find optimal flow allocations among the studied sets. In our computational experiments, we utilize collections of simulations for a specific reservoir (which capture subsurface characterization and realize history matching) along with machine learning models that predict temperature and pressure timeseries for production wells. We evaluate this approach using an “open-source” reservoir we have constructed that captures many of the characteristics of Brady Hot Springs, a commercially operational geothermal field in Nevada, USA. Selected results from a reservoir model of Brady Hot Springs itself are presented to show successful application to an existing system. In both cases, energy predictions prove to be highly accurate: all observed prediction errors do not exceed 3.68% for temperatures and 4.75% for pressures. In a cumulative energy estimation, we observe prediction errors that are less than 4.04%. A typical reservoir simulation for Brady Hot Springs completes in approximately 4 h, whereas our machine learning models yield accurate 20-year predictions for temperatures, pressures, and produced energy in 0.9 s. This paper aims to demonstrate how the models and techniques from our study can be applied to achieve rapid exploration of controlled parameters and optimization of other geothermal reservoirs.
1D Modeling for the Development of a Digital Twin for Hydropower Systems with Applications for a Testing Rig
Modeling and simulation constitute two important parts in constructing a sensible digital twin to mimic the dynamics of hydropower systems. Because of the physical nature of a hydropower system, the basic modeling should cover the water flow systems from the reservoir to the penstock (inlet water pipes), penstock to hydro turbine, and hydro turbine to generator and from the linkage of the hydropower systems to the grid. This report describes initial attempts to model these dynamic components, including the formulation of the linearized state space model for hydro turbine systems using the well-known six-coefficients linearization method and the formulation of the voltage and power dynamical models of a synchronous generator. To validate the accuracy of the proposed model, data collected from Norwegian University of Science and Technology were used to obtain relevant parameters for the model, and the desired simulation results were obtained. Additionally, neural network modeling and learning were also developed and applied to model the generation torque and water flow rate subsystems to demonstrate a potential learning scheme, which can be used in the development of a digital twin.
A Novel Relative Permeability Model for Gas and Water Flow in Hydrate-Bearing Sediments With Laboratory and Field-Scale Application
In a producing gas hydrate reservoir the effective porosity available for fluid flow constantly changes with dissociation of gas hydrate. Therefore, accurate prediction of relative permeability using legacy models (e.g. Brooks-Corey (B-C), van Genuchten, etc.) that were developed for conventional oil and gas reservoirs would require empirical parameters to be calibrated at various S h over its range of variation, but such calibrations are precluded because of lack of experimental relative permeability data. This study proposes a new relative permeability model for gas hydrate-bearing media that is a function of maximum capillary pressure, capillary entry pressure, pore size distribution index, residual saturations, hydrate saturation, and four other constants. The three novel features of the proposed model are: (i) requires fitting its six empirical parameters only once using experimental data from any single S h , and the same set of empirical parameters predict relative permeability at all S h , (ii) includes the effect of capillarity, and (iii) includes the effect of pore-size distribution. From practical standpoint, the model can be used to simulate multiphase flow in gas hydrate-bearing sediments where the proposed relative permeability can account for the evolving hydrate saturation. The proposed model is implemented in a numerical simulator and the wall time required to perform simulations using the proposed model is shown to be similar to the time it takes to run same simulations with the B-C model. The proposed model is a step forward towards achieving the goal of physically accurate modeling of multiphase flow for gas hydrate-bearing sediments that accounts for the effect of gas hydrate saturation change on relative permeability.
Technical and Economic Evaluation of the First Ever Polymer Flood Field Pilot to Enhance the Recovery of Heavy Oils on Alaska's North Slope via Machine Assisted History Matching
Polymer flooding has become globally established as a potential enhanced oil recovery method for heavy oils. To determine whether this technology may be useful in developing the substantial heavy oil resources on the Alaska North Slope, a polymer flood field pilot commenced at the Milne Point Unit in August 2018. This study seeks to evaluate the results of the field pilot on a technical and economic basis. A reservoir simulation model is constructed and calibrated to predict the oil recovery performance of the pilot through machine-assisted reservoir simulation techniques. To replicate the early water breakthrough observed during waterflooding, transmissibility contrasts are introduced into the simulation model, forcing viscous fingering effects. In the ensuing polymer flood, these transmissibility contrasts are reduced to replicate the restoration of injection conformance during polymer flooding. Transmissibility contrasts are later reinstated to replicate fracture overextension interpreted in one of the producing wells. The calibrated simulation models produced at each stage of the history matching process are used to forecast oil recovery. These forecasts are used as input for economic analysis, incremental to waterflooding expectations. The simulation forecasts indicate that polymer flooding significantly increases the heavy oil production for this field pilot compared to waterflooding alone, yielding attractive project economics. However, meaningful variations between simulation scenarios demonstrate that a simulation model is only valid for prediction if flow behavior in the reservoir remains consistent with that observed during the history matched period. Critically, this means that a simulation model calibrated for waterflooding may not fully capture the technical and economic benefits of an enhanced oil recovery process such as polymer flooding. Subsequently, the simulation model and economic model are used in conjunction to conduct a sensitivity analysis for polymer flood design parameters, from which recommendations are provided for both the continued operation of the current field pilot and future polymer flood designs. The results demonstrate that a higher polymer concentration can be injected due to the development of fractures in the reservoir. The throughput rate should remain high without exceeding operating constraints. A calculated point-forward polymer utilization parameter demonstrates the decreasing efficiency of the polymer flood at later times in the pattern life. Future projects will benefit from starting polymer injection earlier in the pattern life. A pattern with tighter horizontal well spacing will observe a greater incremental benefit from polymer flooding.
Oil Recovery Prediction for Polymer Flood Field Test of Heavy Oil on Alaska North Slope Via Machine Assisted Reservoir Simulation
The first ever polymer flood field pilot to enhance the recovery of heavy oils on the Alaska North Slope is ongoing. This study constructs and calibrates a reservoir simulation model to predict the oil recovery performance of the pilot through machine-assisted reservoir simulation techniques. To replicate the early water breakthrough observed during waterflooding, transmissibility contrasts are introduced into the simulation model, forcing viscous fingering effects. In the ensuing polymer flood, these transmissibility contrasts are reduced to replicate the restoration of injection conformance during polymer flooding, as indicated by a significant decrease in water cut. Later, transmissibility contrasts are reinstated to replicate a water surge event observed in one of the producing wells during polymer flooding. This event may represent decreased injection conformance from fracture overextension; its anticipated occurrence in the other production well is included in the final forecast. The definition of polymer retention in the simulator incorporates the tailing effect reported in laboratory studies; this tailing effect is useful to the simultaneous history match of producing water cut and produced polymer concentration. The top 24 best-matched simulation models produced at each stage of the history matching process are used to forecast oil recovery. The final forecast clearly demonstrates that polymer flooding significantly increases the heavy oil production for this field pilot compared to waterflooding alone. This exercise displays that a simulation model is only valid for prediction if flow behavior in the reservoir remains consistent with that observed during the history matched period. Critically, this means that a simulation model calibrated for waterflooding may not fully capture the benefits of an enhanced oil recovery process such as polymer flooding. Therefore, caution is recommended in using basic waterflood simulation models to scope potential enhanced oil recovery projects.
Improving deep learning performance for predicting large-scale geological ${{CO}_{2}}$ sequestration modeling through feature coarsening
Physics-based reservoir simulation for fluid flow in porous media is a numerical simulation method to predict the temporal-spatial patterns of state variables (e.g. pressure p) in porous media, and usually requires prohibitively high computational expense due to its non-linearity and the large number of degrees of freedom (DoF). This work describes a deep learning (DL) workflow to predict the pressure evolution as fluid flows in large-scale 3-dimensional(3D) heterogeneous porous media. In particular, we develop an efficient feature coarsening technique to extract the most representative information and perform the training and prediction of DL at the coarse scale, and further recover the resolution at the fine scale by spatial interpolation. We validate the DL approach to predict pressure field against physics-based simulation data for a field-scale 3D geologic CO 2 sequestration reservoir model. We evaluate the impact of feature coarsening on DL performance, and observe that the feature coarsening not only decreases the training time by >74% and reduces the memory consumption by >75%, but also maintains temporal error 0.63% on average. Besides, the DL workflow provides predictive efficiency with 1406 times speedup compared to physics-based numerical simulation. The key findings from this research significantly improve the training and prediction efficiency of deep learning model to deal with large-scale heterogeneous reservoir models, and thus it can also be further applied to accelerate workflows of history matching and reservoir optimization for close-loop reservoir management.
Subsurface Characterization and Machine Learning Predictions at Brady Hot Springs Results
Geothermal power plants typically show decreasing heat and power production rates over time. Mitigation strategies include optimizing the management of existing wells - increasing or decreasing the fluid flow rates across the wells - and drilling new wells at appropriate locations. The latter is expensive, time-consuming, and subject to many engineering constraints, but the former is a viable mechanism for periodic adjustment of the available fluid allocations. Data and supporting literature from a study describing a new approach combining reservoir modeling and machine learning to produce models that enable strategies for the mitigation of decreased heat and power production rates over time for geothermal power plants. The computational approach used enables translation of sets of potential flow rates for the active wells into reservoir-wide estimates of produced energy and discovery of optimal flow allocations among the studied sets. In our computational experiments, we utilize collections of simulations for a specific reservoir (which capture subsurface characterization and realize history matching) along with machine learning models that predict temperature and pressure timeseries for production wells. We evaluate this approach using an "open-source" reservoir we have constructed that captures many of the characteristics of Brady Hot Springs, a commercially operational geothermal field in Nevada, USA. Selected results from a reservoir model of Brady Hot Springs itself are presented to show successful application to an existing system. In both cases, energy predictions prove to be highly accurate: all observed prediction errors do not exceed 3.68% for temperatures and 4.75% for pressures. In a cumulative energy estimation, we observe prediction errors that are less than 4.04%. A typical reservoir simulation for Brady Hot Springs completes in approximately 4 hours, whereas our machine learning models yield accurate 20-year predictions for temperatures, pressures, and produced energy in 0.9 seconds. This paper aims to demonstrate how the models and techniques from our study can be applied to achieve rapid exploration of controlled parameters and optimization of other geothermal reservoirs. Includes a synthetic, yet realistic, model of a geothermal reservoir, referred to as open-source reservoir (OSR). OSR is a 10-well (4 injection wells and 6 production wells) system that resembles Brady Hot Springs (a commercially operational geothermal field in Nevada, USA) at a high level but has a number of sufficiently modified characteristics (which renders any possible similarity between specific characteristics like temperatures and pressures as purely random). We study OSR through CMG simulations with a wide range of flow allocation scenarios. Includes a dataset with 101 simulated scenarios that cover the period of time between 2020 and 2040 and a link to the published paper about this project, where we focus on the Machine Learning work for predicting OSR's energy production based on the simulation data, as well as a link to the GitHub repository where we have published the code we have developed (please refer to the repository's readme file to see instructions on how to run the code). Additional links are included to associated work led by the USGS to identify geologic factors associated with well productivity in geothermal fields. Below are the high-level steps for applying the same modeling + ML process to other geothermal reservoirs: 1. Develop a geologic model of the geothermal field. The location of faults, upflow zones, aquifers, etc. need to be accounted for as accurately as possible 2. The geologic model needs to be converted to a reservoir model that can be used in a reservoir simulator, such as, for instance, CMG STARS, TETRAD, or FALCON 3. Using native state modeling, the initial temperature and pressure distributions are evaluated, and they become the initial conditions for dynamic reservoir simulations 4....
Understanding How Reservoir Operations Influence Methane Emissions: A Conceptual Model
Because methane is a potent greenhouse gas (GHG), understanding controls on methane emissions from reservoirs is an important goal. Yet, reservoirs are complex ecosystems, and mechanisms by which reservoir operations influence methane emissions are poorly understood. In part, this is because emissions occur in ‘hot spots’ and ‘hot moments’. In this study, we address three research questions, ‘What are the causal pathways through which reservoir operations and resulting water level fluctuations (WLF) influence methane emissions?’; ‘How do influences from WLF differ for seasonal drawdown and diurnal hydropeaking operations?’; and ‘How does understanding causal pathways inform practical options for mitigation?’. A graphical conceptual model is presented that links WLF in reservoirs to methane emissions via four causal pathways: (1) water-column mixing (2) drying–rewetting cycles, (3) sediment delivery and redistribution, and (4) littoral vegetation. We review what is known about linkages for WLF at seasonal and diurnal resolutions generate research questions, and hypothesize strategies for moderating methane emissions by interrupting each causal pathway. Those related to flow management involve basin-scale management of tributary flows, seasonal timing of hydropeaking (pathway #1), timing and rates of drawdown (pathway #2). In addition, we describe how sediment (pathway #3) and vegetation management (pathway #4) could interrupt linkages between WLF and emissions. We demonstrate the strength of conceptual modeling as a tool for generating plausible hypotheses and suggesting mitigation strategies. Future research is needed to develop simpler models at appropriate timescales that can be validated and used to manage flow releases from reservoirs.
System and method for optimizing hydrocarbon production from subsurface reservoirs
A method is described for subsurface hydrocarbon reservoir characterization including receiving a time-lapse electromagnetic (EM) dataset and a flow dataset; inverting the time-lapse EM dataset using a parametric inversion that models steel well casings to determine a volume of fluid-changed reservoir; inverting the time-lapse EM dataset and the flow dataset using a joint inversion that honors the volume of the fluid-changed reservoir to determine relative permeability and capillary pressure; and characterizing flow characteristics in the volume of the fluid-changed reservoir. The method may be executed by a computer system.
Influence of Clay Wettability Alteration on Relative Permeability
Abstract Understanding the wettability of porous materials is important to model fluid flow in the subsurface. One of the critical factors that influences wetting in real reservoirs is the composition of geologic materials. The wetting properties for clay minerals can have a particularly strong impact on flow and transport. In this work, we analyze the chemical composition of a Mt. Simon sandstone core to resolve the microscopic structure of clay regions and assess how alterations to the local wetting properties influence multiphase transport based on core flooding experiments and relative permeability simulations. We show that whichever fluid has greater affinity toward clay minerals will tend to accumulate within these high surface area regions, leading to dramatic shifts in the relative permeability. This work establishes the essential importance of the mineral composition and associated wetting properties in the modeling of flow and transport in reservoir‐scale systems.