A Mass-Conservative Sequential Implicit Multiscale Method for Isothermal Equation-of-State Compositional Problems

SPE Journal ◽  
2018 ◽  
Vol 23 (06) ◽  
pp. 2376-2393 ◽  
Author(s):  
Olav Møyner ◽  
Hamdi A. Tchelepi
Keyword(s):  
Oil Recovery ◽  
Reservoir Simulation ◽  
Equations Of State ◽  
Gas Injection ◽  
Computational Cost ◽  
Nonlinear Behavior ◽  
Multiscale Method ◽  
Compositional Simulation ◽  
Fine Grid ◽  
Miscible Gas Injection

Summary Compositional simulation is necessary for a wide variety of reservoir-simulation applications, and it is especially valuable for accurate modeling of near-miscible gas injection for enhanced oil recovery. Because the nonlinear behavior of gas injection is sensitive to the resolution of the simulation grid used, it is important to use a fine grid to accurately resolve the compositional and saturation gradients. Compositional simulation of highly detailed reservoir models entails the use of small timesteps and large, poorly conditioned linear systems. The high computational cost of solving such systems renders field-scale simulations practically unfeasible. The coupling of the flow and transport to the phase-equilibrium calculations adds to the challenge. This is especially the case for near-miscible gas injection, in which the phase state and the phase compositions are very strong functions of space and time. We present a multiscale solver for compositional displacements with three-phase fluid flow. The thermodynamic phase behavior is described by general nonlinear cubic equations of state (EOS). The fully implicit (FI) natural-variables formulation is used as the basis to derive a sequential implicit (SI) solution strategy, whereby the pressure field is decoupled from the multicomponent transport. The SI scheme is mass conservative without the need to iterate between the pressure and transport equations during the timestep. This conservation property allows the errors caused by fixing the total-velocity field between the pressure- and transport-updating steps to be represented as a volume error. The method computes approximate pressure solutions—within a prescribed residual tolerance—that yield conservative fluxes on the computational grid of interest (fine, coarse, or intermediate). We use basis functions computed using restricted smoothing to allow for generally unstructured grids. The new method is verified against existing research and commercial compositional simulators using a simple conceptual test case and also using more-complex cases represented on both unstructured and corner-point grids with strong heterogeneity, faults, and pinched-out and eroded cells. The SI method and the implementation described here represent the first demonstrated multiscale method applicable to general compositional problems with complexity relevant for industrial-reservoir simulation.

Improved Mappings for Streamline-Based Simulation

SPE Journal ◽  
2006 ◽  
Vol 11 (03) ◽  
pp. 294-302 ◽  
Author(s):  
Bradley T. Mallison ◽  
Margot G. Gerritsen ◽  
Sebastien F. Matringe
Keyword(s):  
Mass Balance ◽  
Adaptive Mesh Refinement ◽  
Piecewise Linear ◽  
Gas Injection ◽  
Computational Cost ◽  
Adaptive Mesh ◽  
Linear Representation ◽  
Compositional Simulation ◽  
Background Grid ◽  
Streamline Method

Summary Our interest lies in extending the streamline method to compositional simulation. In this paper, we develop improved mappings to and from streamlines that are necessary to obtain reliable predictions of gas injection processes. Our improved mapping to streamlines uses a piecewise linear representation of saturations on the background grid in order to minimize numerical smearing. Our strategy for mapping saturations from streamlines to the background grid is based on kriging. We test our improvements to the streamline method by use of a simple model for miscible flooding based on incompressible Darcy flow. Results indicate that our mappings offer improved resolution and reduce mass-balance errors relative to the commonly used mappings. Our mappings also require fewer streamlines to achieve a desired level of accuracy. In compositional cases where the computational cost of a streamline solve is high, we anticipate that this will lead to an improvement in the efficiency of streamline-based simulation. Introduction The overall goal of our research is to improve the accuracy and efficiency of the streamline method in simulating compositional problems such as those that occur in miscible or near-miscible gas injection processes. This is our second paper suggesting improvements to this end. In Mallison et al. (2005) we investigated a 1D compositional finite-difference solver based on a high-order upwind scheme and adaptive mesh refinement that is appropriate for use in a compositional streamline simulator. Here, we propose new mappings to and from streamlines that improve the accuracy of the streamline method for problems in which the flow pattern does not remain fixed for large time intervals. Such problems require that streamlines be periodically updated in order to account for changing flow directions and for the treatment of gravity terms (Thiele et al. 1996; Bratvedt et al. 1996). For each set of streamlines, fluids must be mapped from an underlying background grid, on which the pressure is solved (or, say, the flow), to the streamlines, moved forward in time, and then mapped from the streamlines back to the background grid. The mappings introduce numerical smearing and generally also mass-balance errors. When streamlines are updated frequently, the mapping errors limit the overall accuracy of the streamline method. Our improved mapping algorithms are aimed at minimizing this type of error.

A Graphics Processing Unit–Based, Industrial Grade Compositional Reservoir Simulator

SPE Journal ◽  
2021 ◽  
pp. 1-16
Author(s):  
K. Esler ◽  
R. Gandham ◽  
L. Patacchini ◽  
T. Garipov ◽  
A. Samardzic ◽  
...  
Keyword(s):  
Reservoir Simulation ◽  
Graphics Processing Units ◽  
Equations Of State ◽  
Detailed Examination ◽  
Processing Unit ◽  
Compositional Simulation ◽  
Implicit Methods ◽  
Industrial Grade ◽  
Black Oil ◽  
Graphics Processing

Summary Recently, graphics processing units (GPUs) have been demonstrated to provide a significant performance benefit for black-oil reservoir simulation, as well as flash calculations that serve an important role in compositional simulation. A comprehensive approach to compositional simulation based on GPUs has yet to emerge, and the question remains as to whether the benefits observed in black-oil simulation persist with a more complex fluid description. We present a positive answer to this question through the extension of a commercial GPU-basedblack-oil simulator to include a compositional description based on standard cubic equations of state (EOSs). We describe the motivations for the selected nonlinear formulation, including the choice of primary variables and iteration scheme, and support for both fully implicit methods (FIMs) and adaptive implicit methods (AIMs). We then present performance results on an example sector model and simplified synthetic case designed to allow a detailed examination of runtime and memory scaling with respect to the number of hydrocarbon components and model size, as well as the number of processors. We finally show results from two complex asset models (synthetic and real) and examine performance scaling with respect to GPU generation, demonstrating that performance correlates strongly with GPU memory bandwidth. NOTE: This paper is published as part of the 2021 SPE Reservoir Simulation Conference Special Issue.

Minimum Miscibility Pressure of CO2/Hydrocarbon Systems Within Nanopores

2021 ◽  
Author(s):  
Gang Yang ◽  
Xiaoli Li
Keyword(s):  
Oil Recovery ◽  
Gas Injection ◽  
Unconventional Reservoirs ◽  
Minimum Miscibility Pressure ◽  
Theoretical Approaches ◽  
Fluid Systems ◽  
Confined Fluid ◽  
Miscible Gas Injection ◽  
Fluid Characterization ◽  
The Impact

Abstract Minimum miscibility pressure (MMP), as a key parameter for the miscible gas injection enhanced oil recovery (EOR) in unconventional reservoirs, is affected by the dominance of nanoscale pores. The objective of this work is to investigate the impact of nanoscale confinement on MMP of CO2/hydrocarbon systems and to compare the accuracy of different theoretical approaches in calculating MMP of confined fluid systems. A modified PR EOS applicable for confined fluid characterization is applied to perform the EOS simulation of the vanishing interfacial tension (VIT) experiments. The MMP of multiple CO2/hydrocarbon systems at different pore sizes are obtained via the VIT simulations. Meanwhile, the multiple mixing cell (MMC) algorithm coupled with the same modified PR EOS is applied to compute the MMP for the same fluid systems. Comparison of these results to the experimental values recognize that the MMC approach has higher accuracy in determining the MMP of confined fluid systems. Moreover, nanoscale confinement results in the drastic suppression of MMP and the suppression rate increases with decreasing pore size. The drastic suppression of MMP is highly favorable for the miscible gas injection EOR in unconventional reservoirs.

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