Multi-physics modeling of non-isothermal compositional flow on adaptive grids

Faigle, Benjamin; Elfeel, Mohamed Ahmed; Helmig, Rainer; Becker, Beatrix; Flemisch, Bernd; Geiger, Sebastian

doi:10.1016/j.cma.2014.11.030

Cited by 14 publications

(14 citation statements)

References 32 publications

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“…This multiphysics model considers two‐phase multicomponent flow only where both phases are present and solves a simpler one‐phase model that is a degenerate version of the two‐phase model everywhere else. The approach was extended to nonisothermal flow by Faigle et al (), using a subdomain in which nonisothermal effects are accounted for and a subdomain where simpler, isothermal equations are solved. The method is shown to be accurate and significantly reduces computational cost.…”

Section: Introductionmentioning

confidence: 99%

An Adaptive Multiphysics Model Coupling Vertical Equilibrium and Full Multidimensions for Multiphase Flow in Porous Media

Becker

Guo

Bandilla

et al. 2018

Water Resources Research

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Efficient multiphysics (or hybrid) models that can adapt to the varying complexity of physical processes in space and time are desirable for modeling fluid migration in the subsurface. Vertical equilibrium (VE) models are simplified mathematical models that are computationally efficient but rely on the assumption of instant gravity segregation of the two phases, which may not be valid at all times or at all locations in the domain. Here we present a multiphysics model that couples a VE model to a full multidimensional model that has no reduction in dimensionality. We develop a criterion that determines subdomains where the VE assumption is valid during simulation. The VE model is then adaptively applied in those subdomains, reducing the number of computational cells due to the reduction in dimensionality, while the rest of the domain is solved by the full multidimensional model. We analyze how the threshold parameter of the criterion influences accuracy and computational cost of the new multiphysics model and give recommendations for the choice of optimal threshold parameters. Finally, we use a test case of gas injection to show that the adaptive multiphysics model is much more computationally efficient than using the full multidimensional model in the entire domain, while maintaining much of the accuracy.

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Section: Introductionmentioning

confidence: 99%

An Adaptive Multiphysics Model Coupling Vertical Equilibrium and Full Multidimensions for Multiphase Flow in Porous Media

Becker

Guo

Bandilla

et al. 2018

Water Resources Research

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“…However, it could be beneficial to employ a multi-physics approach, e.g., by coupling the near-well region with MICP to an outer far-field region where only the hydraulics are modeled with a flow model. Or one could apply an analytical solution, similar to the multi-physics approach of, e.g., [20,21] or the mortar-space upscaling by e.g. [57].…”

Section: The State Of the Micp Model So Farmentioning

confidence: 99%

Field-scale modeling of microbially induced calcite precipitation

Cunningham

Class

Ebigbo³

et al. 2018

Comput Geosci

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The biogeochemical process known as microbially induced calcite precipitation (MICP) is being investigated for engineering and material science applications. To model MICP process behavior in porous media, computational simulators must couple flow, transport, and relevant biogeochemical reactions. Changes in media porosity and permeability due to biomass growth and calcite precipitation, as well as their effects on one another must be considered. A comprehensive Darcy-scale model has been developed by Ebigbo et al. (Water Resour. Res. 48(7), W07519, 2012) and Hommel et al. (Water Resour. Res. 51, 3695-3715, 2015) and validated at different scales of observation using laboratory experimental systems at the Center for Biofilm Engineering (CBE), Montana State University (MSU). This investigation clearly demonstrates that a close synergy between laboratory experimentation at different scales and corresponding simulation model development is necessary to advance MICP application to the field scale. Ultimately, model predictions of MICP sealing of a fractured sandstone formation, located 340.8 m below ground surface, were made and compared with corresponding field observations. Modeling MICP at the field scale poses special challenges, including choosing a reasonable model-domain size, initial and boundary conditions, and determining the initial distribution of porosity and permeability. In the presented study, model predictions of deposited calcite volume agree favorably with corresponding field observations of increased injection pressure during the MICP fracture sealing test in the field. Results indicate that the current status of our MICP model now allows its use for further subsurface engineering applications, including well-bore cement sealing and certain fracture-related applications in unconventional oil and gas production.

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“…The first class uses variables that represent the full fluid content. This is the case for Acs et al [1], Watts [33], Trangenstein & Bell [30,31], Dicks [8], Pau et al [26], Faigle et al [10] and Doster et al [9]. The variables used are: the total number of moles (mass) of each component, or the total number of mole (mass) of each component divided by the pore volume.…”

Section: Compositional Systemmentioning

confidence: 99%

“…Equation (21) is used to get the derivatives of the saturations with respect to P . Sequential formulations for compositional flows where derived in a semi-implicit context by Acs et al [1], Watts [33], Trangenstein & Bell [30,31], Dicks [8], Pau et al [26], Faigle et al [10] and Doster et al [9]. In these previous methods, the pressure equation is derived by linearizing the difference between the sum of the thermodynamic volumes of each phase and the pore volume.…”

Section: Comparison With Other Compositional Pressure Equationsmentioning

confidence: 99%

“…Their algorithm is convergent; however, in cases with strong coupling, the scheme needs large numbers of outer iterations. Acs et al [1], Watts [33], Trangenstein & Bell [30,31], Dicks [8], Pau et al [26], Faigle et al [10] and Doster et al [9] developed Sequential Implicit (SI) formulations for compositional multi-component displacements. In these SI formulations, extensive degrees-of-freedom (variables), such as the overall number of moles, or mass, of a component divided by the pore volume, are used.…”

Section: Introductionmentioning

confidence: 99%

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Sequential fully implicit formulation for compositional simulation using natural variables

Moncorgé

Tchelepi

Jenny

2018

Journal of Computational Physics

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The Sequential Fully Implicit (SFI) method was proposed (Jenny et al., JCP 2006), in the context of a Multiscale Finite Volume (MSFV) formulation, to simulate coupled immiscible multiphase fluid flow in porous media. Later, Lee et al. (Comp. Geosci. 2008) extended the SFI formulation to the black-oil model, whereby the gas component is allowed to dissolve in the oil phase. Most recently, the SFI approach was extended to fully compositional isothermal displacements by Moncorgé et al., (JCP 2017). SFI schemes solve the fully coupled system in two steps: (1) Construct and solve the pressure equation (flow problem). (2) Solve the coupled species transport equations for the phase saturations and phase compositions. In SFI, each outer iteration involves this two-step sequence. Experience indicates that complex interphase mass transfer behaviors often lead to large numbers of SFI outer iterations compared with the Fully Implicit (FI) method. Here, we demonstrate that the convergence difficulties are directly related to the treatment of the coupling between the flow and transport problems, and we propose a new SFI variant based on a nonlinear overall-volume balance equation. The first step consists of forming and solving a nonlinear pressure equation, which is a weighted sum of all the component mass conservation equations. A Newton-based scheme is used to iterate out all the pressure dependent nonlinearities in both the accumulation and flux terms of the overall-volume balance equation. The resulting pressure field is used to compute the Darcy phase velocities and the total-velocity. The second step of the new SFI scheme entails introducing the overall-mass density as a degree-of- freedom, and solving the full set of component conservation equations cast in the natural-variables form (i.e., saturations and phase compositions). During the second step, the pressure and the total-velocity fields are fixed. The SFI scheme with a nonlinear pressure extends the SFI approach of Jenny et al. (JCP 2006) to multi-component compositional processes with interphase mass transfer. The proposed compositional SFI approach employs an overall balance for the pressure equation; however, unlike existing volume-balance Sequential Implicit (SI) schemes (Acs et al.and Doster et al., CRC 2014), which use overall compositions, this SFI formulation is well suited for the natural variables (saturations and phase compositions). We analyze the 'splitting errors' associated with the compositional SFI scheme, and we show how to control these errors in order to converge to the same solution as the Fully Implicit (FI) method. We then demonstrate that the compositional SFI has convergence properties that are very comparable to those of the FI approach. This robust sequential-implicit solution scheme allows for designing numerical methods and linear solvers that are optimized for the sub-problems of flow and transport. The SFI scheme with a nonlinear pressure formulation is well suited for multiscale formulations, and it promises to replace the widely...

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Multi-physics modeling of non-isothermal compositional flow on adaptive grids

Cited by 14 publications

References 32 publications

An Adaptive Multiphysics Model Coupling Vertical Equilibrium and Full Multidimensions for Multiphase Flow in Porous Media

An Adaptive Multiphysics Model Coupling Vertical Equilibrium and Full Multidimensions for Multiphase Flow in Porous Media

Field-scale modeling of microbially induced calcite precipitation

Sequential fully implicit formulation for compositional simulation using natural variables

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