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The 11th Society of Petroleum Engineers Comparative Solution Project: Problem Definition
Nordbotten, Jan M. (Department of Mathematics, University of Bergen) | Ferno, Martin A. (Norwegian Research Center (NORCE) (Corresponding author)) | Flemisch, Bernd (Department of Physics and Technology, University of Bergen) | Kovscek, Anthony R. (Norwegian Research Center (NORCE)) | Lie, Knut-Andreas (Institute for Modelling Hydraulic and Environmental Systems, University of Stuttgart)
Summary This article contains the description of, and call for participation in, the 11th Society of Petroleum Engineers Comparative Solution Project (the 11th SPE CSP, ). It is motivated by the simulation challenges associated with CO2 storage operations in geological settings of realistic complexity. The 11th SPE CSP contains three versions: Version 11A is a 2D geometry at the laboratory scale, inspired by a recent CO2 storage forecasting and validation study. For Version 11B, the 2D geometry and operational conditions from 11A are rescaled to field conditions characteristic of the Norwegian Continental Shelf. Finally, for Version 11C, the geometry of Version 11B is extruded to a full 3D field model. The CSP has a two-year timeline, being launched at the 2023 SPE Reservoir Simulation Conference and culminating at the 2025 SPE Reservoir Simulation Conference. A community effort is run in parallel to develop utility scripts and input files for common simulators to lower the threshold of participation; see the link to supplementary material on the CSP website. At the time of writing, complete input decks for one simulator are already ready for all three versions.
- Reservoir Description and Dynamics > Storage Reservoir Engineering > CO2 capture and sequestration (1.00)
- Reservoir Description and Dynamics > Reservoir Simulation (1.00)
- Reservoir Description and Dynamics > Reservoir Fluid Dynamics > Flow in porous media (1.00)
- (9 more...)
Summary In this paper, we present a new approach for simulating reservoirs with tilted fluid contacts produced by hydrodynamics. The proposed method solves a nonlinear inverse problem to determine the aquifer flow field that best reproduces the observed contact tilt. The computational effort required to solve this inverse problem is reduced by choosing a pressure-based objective function and applying gradient-based optimization. This approach is entirely automated, in contrast to previous works that have used laborious trial-and-error methods to estimate the aquifer flow field. In addition, the proposed method introduces no additional physics beyond hydrodynamics to model reservoirs with tilted contacts. The proposed method is integrated into a parallel reservoir simulator. A synthetic reservoir is constructed by introducing an artificial tilt, and the new approach is applied to estimate the aquifer flow field. The estimate produced by the proposed method matches the true flow field well and is able to prevent large fluid motions near the contact surface when simulating production from the reservoir. The proposed method is compared with an existing approach that uses capillary pressure adjustments to hold the tilted contact in place. The proposed method is shown to outperform the existing approach without significantly impacting the simulation results.
- Europe (1.00)
- Asia > Middle East (1.00)
- North America > Canada (0.93)
- North America > United States > Texas > Dawson County (0.24)
- North America > United States > California > Ventura Basin (0.99)
- Europe > Norway > Norwegian Sea > Mรธre Basin > PL 442 > Block 6305/8 > Ormen Lange Field > Springar Formation (0.99)
- Europe > Norway > Norwegian Sea > Mรธre Basin > PL 442 > Block 6305/8 > Ormen Lange Field > Egga Formation (0.99)
- (30 more...)
- Reservoir Description and Dynamics > Reservoir Simulation (1.00)
- Reservoir Description and Dynamics > Reservoir Fluid Dynamics > Flow in porous media (1.00)
- Reservoir Description and Dynamics > Reservoir Characterization (1.00)
- Data Science & Engineering Analytics > Information Management and Systems (1.00)
Abstract This paper introduces two new approaches for modeling reservoirs with tilted fluid contacts. We first introduce a method based on local capillary pressure adjustments, which uses adjustments of the capillary pressure near the oil-water contact to ensure that the contact surface does not move during production. The second approach uses hydrodynamic aquifer flow to support the oil-water tilt. A non-linear inverse problem is solved to determine the parameters that control the aquifer flow. Both approaches are implemented in a parallel reservoir simulator and applied to a synthetic reservoir case.
- Europe (0.69)
- Asia > Middle East > Saudi Arabia (0.69)
- North America > United States (0.68)
- Europe > Norway > Norwegian Sea > Mรธre Basin > PL 442 > Block 6305/8 > Ormen Lange Field > Springar Formation (0.99)
- Europe > Norway > Norwegian Sea > Mรธre Basin > PL 442 > Block 6305/8 > Ormen Lange Field > Egga Formation (0.99)
- Europe > Norway > Norwegian Sea > Mรธre Basin > PL 442 > Block 6305/6 > Ormen Lange Field > Springar Formation (0.99)
- (29 more...)
- Reservoir Description and Dynamics > Reservoir Simulation (1.00)
- Reservoir Description and Dynamics > Reservoir Fluid Dynamics > Flow in porous media (1.00)
- Reservoir Description and Dynamics > Reservoir Characterization (1.00)
- Reservoir Description and Dynamics > Formation Evaluation & Management (1.00)
Abstract Stress-dependence of reservoir matrix and fractures can strongly affect the performance of multifractured horizontal wells (MFHWs) completed in unconventional hydrocarbon reservoirs. In order to model fluid flow in unconventional reservoirs exhibiting this stress-dependence, most traditional reservoir flow simulators, and many simulators described in published work, use conventional reservoir fluid flow model formulations. These formulations typically neglect the influence of the rate of change of volumetric strain of the reservoir matrix and fractures, even though reservoir stress and pressure change significantly during the course of production. As a result, the effect of matrix and fracture deformation on production is neglected, which can lead to errors in predicting production performance in most stress-sensitive reservoirs. To address this problem, some studies have proposed the use of porosity and transmissibility multipliers to model stress-sensitive reservoirs. However, in order to apply this approach, multipliers must be estimated from laboratory experiments, or used as a history-match parameter, possibly resulting in large errors in well performance predictions. Alternatively, fully-coupled, fully numerical geomechanical simulation can be performed, but these methods are computationally costly, and models are difficult to setup. This paper presents a new fully-coupled, two-way analytical modeling approach that can be used to simulate fluid flow in stress-sensitive unconventional reservoirs produced through MFHWs. The model couples poroelastic geomechanics theory with fluid flow formulations. The two-way coupled fluid flow-geomechanical analytical model is applied simultaneously to both the matrix and fracture regions. In the proposed algorithm, a porosity-compressibility coupling parameter for the two physical models is setup to update the stress- and pressure-dependent fracture/matrix properties iteratively, which are later used as input data for the fracture-matrix reservoir fluid flow model at each iteration step. The analytical approach developed for the fully-coupled, two-way analytical model, using the enhanced fracture region conceptual model, is validated by comparing the results with numerical simulation. Predictions using the fully-coupled enhanced fracture region model are then compared with the same enhanced fracture region model but with the conventional pressure-dependent modeling approach implemented. A sensitivity study performed by comparing the new fully-coupled model predictions with and without geomechanics effects accounted for reveals that, without geomechanics effects, production performance in stress-sensitive reservoirs might be overestimated. The study also demonstrates that use of the conventional stress-dependent modeling approach may cause production performance to be underestimated. Therefore, the proposed fully-coupled, two-way analytical model can be useful for practical engineering purposes.
- North America > Canada > Alberta (0.46)
- North America > United States > Texas (0.46)
- Geology > Geological Subdiscipline > Geomechanics (1.00)
- Geology > Geological Subdiscipline > Economic Geology > Petroleum Geology (0.48)
- North America > Canada > British Columbia > Western Canada Sedimentary Basin > Greater Peace River High Basin > Upper Montney Formation (0.99)
- North America > Canada > British Columbia > Western Canada Sedimentary Basin > Alberta Basin > Montney Formation (0.99)
- North America > Canada > Alberta > Western Canada Sedimentary Basin > Alberta Basin > Montney Formation (0.99)
- (2 more...)
- Well Completion > Hydraulic Fracturing (1.00)
- Reservoir Description and Dynamics > Reservoir Simulation (1.00)
- Reservoir Description and Dynamics > Reservoir Fluid Dynamics > Integration of geomechanics in models (1.00)
- (4 more...)
The Mixed Virtual Element Method for Grids with Curved Interfaces in Single-Phase Flow Problems
Dassi, Franco (Universitร degli Studi di Milano Bicocca - Member of INdAM-GNCS research group) | Fumagalli, Alessio (Politecnico di Milano - Member of INdAM-GNCS research group) | Losapio, Davide (Politecnico di Milano - Member of INdAM-GNCS research group) | Scialรฒ, Stefano (Politecnico di Milano - Member of INdAM-GNCS research group) | Scotti, Anna (Politecnico di Milano - Member of INdAM-GNCS research group) | Vacca, Giuseppe (Universitร degli Studi di Milano Bicocca - Member of INdAM-GNCS research group)
Abstract In many applications the accurate representation of the computational domain is a key factor to obtain reliable and effective numerical solutions. Curved interfaces, which might be internal, related to physical data, or portions of the physical boundary, are often met in real applications. However, they are often approximated leading to a geometrical error that might become dominant and deteriorate the quality of the results. Underground problems often involve the motion of fluids where the fundamental governing equation is the Darcy law. High quality velocity fields are of paramount importance for the successful subsequent coupling with other physical phenomena such as transport. The virtual element method, as solution scheme, is known to be applicable in problems whose discretizations requires cells of general shape, and the mixed formulation is here preferred to obtain accurate velocity fields. To overcome the issues associated to the complex geometries and, at the same time, retaining the quality of the solutions, we present here the virtual element method to solve the Darcy problem, in mixed form, in presence of curved interfaces in two and three dimensions. The numerical scheme is presented in detail explaining the discrete setting with a focus on the treatment of curved interfaces. Examples, inspired from industrial applications, are presented showing the validity of the proposed approach.
- Reservoir Description and Dynamics > Reservoir Simulation (1.00)
- Reservoir Description and Dynamics > Reservoir Fluid Dynamics > Flow in porous media (1.00)
- Reservoir Description and Dynamics > Reservoir Characterization (1.00)
- Data Science & Engineering Analytics > Information Management and Systems (1.00)
Abstract The dynamics of tracer particles in a viscous Newtonian fluid is studied analytically and numerically through channels of varying thickness for fluids undergoing creeping flow. Exact analytical solutions of mass conservation equations of tracer particles including consideration for pressure forces are obtained. Results of the analysis indicates that Stokes velocity is an indispensable parameter and is dependent on parameters such as channel thickness (height), viscosity of the fluid, pressure gradient driven the fluid and Reynolds number corresponding to the channel thickness. The accuracy of the solution obtained is verified by comparing its velocity profiles with those obtained from finite-element-based numerical simulation studies.
- Reservoir Description and Dynamics > Reservoir Simulation (1.00)
- Reservoir Description and Dynamics > Reservoir Fluid Dynamics > Flow in porous media (1.00)
- Reservoir Description and Dynamics > Reservoir Characterization (1.00)
- Reservoir Description and Dynamics > Formation Evaluation & Management (1.00)
ABSTRACT: Coupled hydro-mechanical simulations are by now a standard tool for reservoir modeling. However, challenges remain regarding the proper implementation of faults into such reservoir-scale numerical models which result mainly from the scale difference between the element size of the numerical grid and the internal heterogeneity of real fault zones. In this study, we present an AI-based upscaling approach from detailed fault zones to homogenized fault properties in finite element models. The detailed fault zone model contains a fault core with shear bands and host rock lenses as well as accompanying damage zones with a fracture density decreasing with distance from the fault core. This detailed fault zone model is automatically compared by using the Structural Similarity Index and difference images with a database of 432 models describing the fault zone as one uniform material homogenizing the different fault zone units. The goal is to introduce a new upscaling workflow of hydro-mechanical fault zone properties in reservoir-scale simulations through a database driven approach to represent the fault in a numerical simulation with an optimal grid size while maintaining the bulk effect of a detailed fault zone description on fluid flow, stress and deformation and thus, improving the predictive power of reservoir-scale simulations. 1. Introduction Faults are a common feature in the subsurface and often have a high impact on a variety of geotechnical engineering and engineering geology tasks like tunneling (Schubert and Riedmรผller, 1997; Schubert and Riedmรผller, 2000; Jeon et al., 2004; Schubert et al., 2006; Zhang et al., 2006; Schubert, 2009; Kun and Onargan, 2013; Paltrinieri et al., 2015), mining (Brady and Brown, 1993; Burtan et al., 2014; Sainoki and Mitri, 2015; Kushwaha et al., 2016; Wang et al., 2016), nuclear waste storage sites (Martin and Lanyon, 2003; Guglielmi et al., 2017; Jaeggi et al., 2017; Park et al., 2020) or reservoir related projects like hydrocarbon production (Wiprut and Zoback, 2002; Cuisiat et al., 2010), geothermal energy (Gan and Elsworth, 2014; Loveless et al., 2014; Duwiquet et al., 2019; Anyim and Gan, 2020) and more recently the storage of CO2 in the underground (Carbon Capture and Storage - CCS; (Nagelhout and Roest, 1997; Vidal-Gilbert et al., 2009; Vidal-Gilbert et al., 2010; Morris et al., 2011; Orlic et al., 2011; Rinaldi et al., 2014). Faults in the subsurface not only have a profound impact on fluid flow, but also effect the stress field in their vicinity. In addition, pore pressure changes due to injection or production can induce slippage and fault reactivation, respectively (Pereira et al., 2014; Rueda et al., 2014; Sanchez et al., 2015; Haug et al., 2018). This may cause induced seismicity, land subsidence and well collapse (Segall et al., 1994; Morton et al., 2006; Chan and Zoback, 2007; Vilarrasa et al., 2017). Fault reactivation may also breach the reservoir seal causing up-fault leakage and allowing fluid migration due to enhanced permeability inside the fault zone (Wiprut and Zoback, 2000; Cuisiat et al., 2010; Faulkner et al., 2010). In order to prevent these hazards numerical modelling is a well-established tool in the industry. Both fluid flow simulations (Manzocchi et al., 2008; Qu et al., 2015) and geomechanical modeling have turned out to be of tremendous help when trying to gain quantitative insights into the hydraulic behavior as well as spatial distribution of stress and strain on the reservoir-scale (Geertsma, 1973; Segall et al., 1994; Fisher and Jolley, 2007; Ferronato et al., 2008; Orlic and Wassing, 2012). Due to the interaction of fluid flow and mechanical behavior, fully-coupled hydro-mechanical simulations gain more and more importance (Cappa and Rutqvist, 2011; Fachri et al., 2016; Serajian et al., 2016; Schuite et al., 2017). Since faults are important features in the subsurface a proper incorporation of faults into such hydro-mechanical models is of crucial relevance for various reasons. However, challenges for the proper implementation of faults into reservoir-scale numerical models remain (Chan and Zoback, 2007; Fredman et al., 2007; Faulkner et al., 2010; Orlic and Wassing, 2012). The three main challenges arise from the need to incorporate faults into geomechanical FE models: (1) How can the small-scale (centimeters to meters) heterogeneity of faults and fault zones be adequately described regarding the typical cell size of FE reservoir models of tens to hundreds of meters and (2) how can the geometry of the FE grid properly honor the fault geometry? (3) How can reasonable, fault-specific material parameters be achieved or estimated from literature sources to populate the hydro-mechanical model?
- Oceania > Australia (0.68)
- Europe > Norway > North Sea (0.28)
- North America > United States > Texas (0.28)
- South America > Colombia > Risaralda Department > Pereira (0.24)
- Geology > Structural Geology > Fault (1.00)
- Geology > Rock Type > Sedimentary Rock > Clastic Rock (0.68)
- Oceania > Australia > Victoria > Otway Basin > Naylor Field (0.99)
- Oceania > Australia > South Australia > Otway Basin (0.99)
- Europe > United Kingdom > North Sea > Northern North Sea > East Shetland Basin > Block 211/25 > Statfjord Field > Statfjord Group (0.99)
- (35 more...)
- Reservoir Description and Dynamics > Storage Reservoir Engineering > CO2 capture and sequestration (1.00)
- Reservoir Description and Dynamics > Reservoir Simulation > Scaling methods (1.00)
- Reservoir Description and Dynamics > Reservoir Fluid Dynamics > Flow in porous media (1.00)
- (4 more...)
Summary Various unified gas flow (UGF) and apparent permeability models have been proposed to characterize the complex gas transport mechanisms in shale formations. However, such models are typically expressed as combinations of multiple gas flow mechanisms so that they cannot predict gas velocity profile. In this study, we develop a novel approach to predict the gas velocity profile in the entire Knudsen number (Kn) regime for circular and noncircular (i.e., square, rectangular, triangular and elliptical) nanochannels and investigate the effects of cross-sectional geometry on gas transport in nanochannels. To this end, a new UGF model is proposed to describe the gas flow behaviors in the entire Kn regime, considering the effects of gas slippage, bulk diffusion, Knudsen diffusion, surface diffusion, and cross-sectional geometry of flow channel. In addition, the boundary condition of the semianalytical second-order slip model applicable to various cross-sectional geometries is modified by adjusting the slip coefficients through the comparison between the proposed UGF model and the Navier-Stokes (N-S) equation with second-order slip boundary condition. As a result, the velocity profile of free gas in the entire Kn regime for the nanochannel with a specific cross section can be determined by solving the second-order slip model with adjusted slip coefficients via the finite element method. The results indicate that the geometry of the cross section has a significant influence on the mass flow rate and gas velocity profile in nanochannels. The predicted mass flow rates for the nanochannels with identical hydraulic diameter decrease with the cross-sectional geometry in the sequence as ellipseโ>โequilateral triangleโ>โrectangleโ>โsquareโ>โcircle. However, the ranking of velocity profiles for such nanochannels, which is governed by the cross-sectional geometry, also varies with Kn. These findings indicate that the developed approach can predict the synergetic gas transport (i.e., gas slippage, bulk diffusion, Knudsen diffusion, and surface diffusion) and gas velocity profile in nanochannels with different cross-sectional geometries for a wide range of Kn, which gives insight into the characterization of gas flow behaviors in nanoporous shale.
- Reservoir Description and Dynamics > Unconventional and Complex Reservoirs > Shale gas (1.00)
- Reservoir Description and Dynamics > Reservoir Simulation (1.00)
- Reservoir Description and Dynamics > Reservoir Fluid Dynamics > Flow in porous media (1.00)
- (4 more...)
A Novel Semi-Analytical Model for Highly Deviated Wells in Fractured-Vuggy Carbonate Gas Reservoirs
Wang, Kongjie (Changqing Downhole Technology Company, CNPC Chuanqing Drilling Engineering Co., Ltd.) | Li, Zhiping (School of Energy Resources, China University of Geosciences, Beijing, China) | Wang, Lian (School of Energy Resources, China University of Geosciences, Beijing, China) | Shi, Hua (State Engineering Laboratory of Low-permeability Oil and Gas Field Exploration and Development, Xi'an, Shanxi, China, Oil and Gas Technology Research Institution of Petrochina Changqing Company, Xi'an, Shanxi, China) | Adenutsi, Caspar Daniel (Council for Scientific and Industrial Research-Institute of Industrial Research, Ghana) | Wu, Junda (School of Energy Resources, China University of Geosciences, Beijing, China) | Wang, Chao (Schlumberger, Binhai New District, Tianjin, China)
Abstract The study of pressure transient behavior in fractured-vuggy reservoirs has recently received considerable attention because a number of such reservoirs have been found worldwide with significant oil and gas production and reserves. In recent years, the use of highly deviated wells (HDW) is considered an effective means for developing this type of gas reservoir. However, in many fractured-vuggy reservoirs unexpected high gas production have been observed which cannot be identified with pressure transient models of horizontal well with pseudo state triple-porosity interporosity flow. This paper presents a semi-analytical model that analyzed the pressure transient behavior of HDW in triple-porosity continuum medium which consist of fractures, vugs and matrix. Introducing pseudo-pressure, Laplace transformation and Fourier transformation were employed to establish a point source and line source pseudo-pressure solutions in Laplace space. Then the pseudo-pressure transient curve was got by numerical inversion. Furthermore, the flow characteristics were analyzed thoroughly by examining the curve which is mainly affected by inclination angle of HDW and interporosity flow coefficients between different pore media. Sensitivity analysis on the pressure transient behavior was performed by varying some important parameters such as the inclination angle, fracture storativity ratio and interporosity flow coefficients. Finally, a field case was successfully used to show the application of the presented semi-analytical model. With its high efficiency, this approach will serve as a reliable tool to evaluate the pressure behavior of HDW in fractured-vuggy carbonate gas reservoirs.
- Asia > China (1.00)
- Europe (0.68)
- North America > United States > Texas (0.28)
- Well Completion > Hydraulic Fracturing (1.00)
- Reservoir Description and Dynamics > Unconventional and Complex Reservoirs > Carbonate reservoirs (1.00)
- Reservoir Description and Dynamics > Reservoir Simulation (1.00)
- (7 more...)
Abstract Various unified gas flow (UGF) and apparent permeability models have been proposed to characterize the complex gas transport mechanisms in shale formations. However, such models are typically expressed as combinations of multiple gas flow mechanisms so that they cannot predict the gas velocity profile. In this study, we develop a novel approach to predict the gas velocity profile in the entire Knudsen number (Kn) regime for circular and noncircular (i.e., square, triangular and elliptical) nanochannels and investigate the effects of cross-sectional geometry on gas transport in nanoporous shale. A new UGF model is proposed to describe the gas flow behavior in the entire Kn regime, considering the effects of advection, gas slippage, bulk diffusion, Knudsen diffusion and cross-sectional geometry. To predict the velocity profile in high Kn flow regime, the boundary condition of second-order slip model is modified. Herein, the slip coefficients in a general second-order slip model applicable to various crosssectional geometries are obtained by comparing the Navier-Stokes (N-S) equation with second-order slip boundary condition with the proposed UGF model. As a result, the velocity profile of free gas in the entire Kn regime for the nanochannel with a specific cross-section can be determined by solving the second-order slip model with adjusted slip coefficients via the finite element method. The results indicate that the geometry of cross-section has a significant influence on the mass flow rate and velocity profile in nanochannels. The predicted mass flow rates for the nanochannels with identical hydraulic diameter decrease with the cross-sectional geometry in the sequence as ellipse > equilateral triangle > square > circle. However, the ranking of velocity profiles for such nanochannels, which is governed by the cross-sectional geometry (aspect ratio), also varies with Kn. The developed approach is able to predict gas velocity profile for the synergetic gas transport (i.e., advection, gas slippage, bulk diffusion and Knudsen diffusion) in nanochannels with different cross-sectional geometries. This study gives insight into the characterization of gas transport behaviors in nanoporous shale.
- North America > United States > South Dakota > Williston Basin > Bakken Shale Formation (0.99)
- North America > United States > North Dakota > Williston Basin > Bakken Shale Formation (0.99)
- North America > United States > Montana > Williston Basin > Bakken Shale Formation (0.99)
- Reservoir Description and Dynamics > Unconventional and Complex Reservoirs > Shale gas (1.00)
- Reservoir Description and Dynamics > Reservoir Simulation (1.00)
- Reservoir Description and Dynamics > Reservoir Fluid Dynamics > Flow in porous media (1.00)
- (3 more...)