A Lagrangian, stochastic modeling framework for multi-phase flow in porous media

Tyagi, Manav; Jenny, Patrick; Lunati, Ivan

doi:10.1016/j.jcp.2008.03.030

Cited by 14 publications

(25 citation statements)

References 28 publications

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“…By analogy to probabilistic model concepts developed in hydrology for single-phase flow, the quantitative insights from pore-scale studies can also be used to develop probabilistic models for multiphase flow that link the variability in porescale physics to the Darcy scale. This approach provides a novel simulation approach that accounts for the pore-scale physics directly by reformulating the ADRE as a stochastic partial differential equation rather than using (incorrectly) averaged multiphase flow physics (Tyagi et al 2008;Tyagi & Jenny 2011). …”

Section: Selected Advancesmentioning

confidence: 99%

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Fundamental controls on fluid flow in carbonates: current workflows to emerging technologies

Agar

Geiger

2014

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The introduction reviews topics relevant to the fundamental controls on fluid flow in carbonate reservoirs and to the prediction of reservoir performance. The review provides research and industry contexts for papers in this volume only. A discussion of global context and frameworks emphasizes the value yet to be captured from compare and contrast studies. Multidisciplinary efforts highlight the importance of greater integration of sedimentology, diagenesis and structural geology. Developments in analytical and experimental methods, stimulated by advances in the materials sciences, support new insights into fundamental (pore-scale) processes in carbonate rocks. Subsurface imaging methods relevant to the delineation of heterogeneities in carbonates highlight techniques that serve to decrease the gap between seismically resolvable features and well-scale measurements. Methods to fuse geological information across scales are advancing through multiscale integration and proxies. A surge in computational power over the last two decades has been accompanied by developments in computational methods and algorithms. Developments related to visualization and data interaction support stronger geoscience-engineering collaborations. High-resolution and real-time monitoring of the subsurface are driving novel sensing capabilities and growing interest in data mining and analytics. Together, these offer an exciting opportunity to learn more about the fundamental fluid-flow processes in carbonate reservoirs at the interwell scale.

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Section: Selected Advancesmentioning

confidence: 99%

“…An alternative could be to augment the ADRE with a stochastic forcing term so that fluidfluid (Tyagi et al 2008;Tyagi & Jenny 2011) and fluid -rock interactions below the grid block scale are modelled in a probabilistic way rather than using volume-averaged parameters.…”

Section: ; Moog 2013)mentioning

confidence: 99%

Fundamental controls on fluid flow in carbonates: current workflows to emerging technologies

Agar

Geiger

2014

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“…Note that numerically the particle ensemble in a grid cell represents the JPDF at that location. Tyagi et al (2008) developed the stochastic particle method (SPM) for simulating multi-phase flow in porous media, which is an extension of the particle method for single-phase flows (Ahlstrom et al 1977;Prickett, Naymik & Longquist 1981;Kinzelbach 1992), and demonstrated its consistency and convergence. The following list outlines some important properties of the SPM that distinguish it from other particle methods for multi-phase flow such as the ones based on the method of characteristics (Dahle et al 1990;Dahle, Ewing & Russell 1995;Hewett & Yamada 1997).…”

Section: Modelling Of Multi-phase Flow With Ganglia In Porous Mediamentioning

confidence: 99%

“…Particles can carry other variables, which evolve in their corresponding sample spaces as the particles move. For example, in Tyagi et al (2008) we chose mobility as a particle property, and modelled its Lagrangian evolution by a Langevin equation. The presence of finite correlation time in the mobility model gives rise to non-equilibrium fluxes that relax towards the equilibrium values at a rate equal to the inverse of the correlation time.…”

Section: Modelling Of Multi-phase Flow With Ganglia In Porous Mediamentioning

confidence: 99%

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Probability density function approach for modelling multi-phase flow with ganglia in porous media

Tyagi

Jenny

2011

J. Fluid Mech.

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A probabilistic approach to model macroscopic behaviour of non-wetting-phase ganglia or blobs in multi-phase flow through porous media is proposed. The key idea is to consider a set of stochastic Markov processes that can mimic the microscopic multi-phase dynamics. These processes are characterized by equilibrium probability density functions (PDFs) and correlation times, which can be obtained from microscale simulation studies or experiments. A Lagrangian viewpoint is adopted, where stochastic particles represent infinitesimal fluid elements and evolve in the physical and probability space. Ganglion mobilization and trapping are modelled by a twostate jump process with transition probabilities given as functions of ganglion size. Coalescence and breakup of ganglia influence the ganglion size distribution, which is modelled by a Langevin type equation. The joint probability density function (JPDF) of the chosen stochastic variables is governed by a high-dimensional Chapman-Kolmogorov equation. This equation can be used to derive moment (e.g. saturation, mean mobility etc.) transport equations, which in general do not form a closed system. However, in some special cases, which arise in the limit of one time scale being smaller or larger than the others, a closed set of moment transport equations can be obtained. For slowly varying and quasi-uniform flows, the saturation transport equation appears in closed form with the mean mobility fully determined, if the equilibrium PDFs are known. Furthermore, it is shown how statistical parameters such as mobilization and trapping rates and equilibrium PDFs can be obtained from the birth-death type approach, in which ganglia breakup and coalescence are explicitly considered. A two-equation transport model (one equation for the total saturation and one for the trapped saturation) is obtained in the limit of very fast coalescence and breakup processes. This model is employed to mimic hysteresis in relative permeability-saturation curves; a well known phenomenon observed in the successive processes of imbibition and drainage. For the general case, the JPDFequation is solved using the stochastic particle method, which was proposed in our previous paper (Tyagi et al. J. Comput. Phys. 227, 2008, 6696-6714). Several one-and two-dimensional numerical simulation results are presented to show the influence of correlation times on the averaged macroscopic flow behaviour.

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Stochastic modeling of non‐equilibrium multiphase flow in porous media

Tyagi

Jenny

2007

Proc Appl Math and Mech

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Non-equilibrium phenomena arising from the pore scale dynamics can have considerable effect on the large scale dynamics of multiphase flow in porous media. In such cases, the relative permeabilities and capillary pressure curves are not just simple functions of phase saturations, rather are dynamic functions of space and time. The present work proposes a stochastic approach in which particle mobility can be modelled based on the actual conductance of fluid volume inside a pore space.

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A Lagrangian, stochastic modeling framework for multi-phase flow in porous media

Cited by 14 publications

References 28 publications

Fundamental controls on fluid flow in carbonates: current workflows to emerging technologies

Fundamental controls on fluid flow in carbonates: current workflows to emerging technologies

Probability density function approach for modelling multi-phase flow with ganglia in porous media

Stochastic modeling of non‐equilibrium multiphase flow in porous media

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