A Generalized Streamline Method to Predict Reservoir Flow

Blunt, Martin J.; Liu, K.; Thiele, Marco R.

doi:10.3997/2214-4609.201406938

Cited by 13 publications

(20 citation statements)

References 8 publications

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“…However, the development of numerical models requires verification and validation as to which new analytical solutions contribute an important part. Also, analytical solutions allow a deeper insight into the structure of a problem and, thus, as to which parameters control processes and often act as a building block for numerical methods [e.g., Lie and Juanes, 2005;Blunt et al, 1996]. Finally, constitutive relationships, such as relative permeabilities, are normally gained from core flood experiments where numerical simulations are matched with flow rates.…”

Section: Introductionmentioning

confidence: 99%

Semianalytical solutions for cocurrent and countercurrent imbibition and dispersion of solutes in immiscible two‐phase flow

Schmid

Geiger

Sorbie

2011

Water Resources Research

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[1] We derive a set of semianalytical solutions for the movement of solutes in immiscible two-phase flow. Our solutions are new in two ways: First, we fully account for the effects of capillary and viscous forces on the transport for arbitrary capillary-hydraulic properties. Second, we fully take hydrodynamic dispersion for the variable two-phase flow field into account. The understanding of immiscible two-phase flow and the simultaneous miscible displacement and mixing of components within a phase is important for many applications, including the location of nonaqueous phase liquids in the subsurface, the design of contaminant cleanup procedures, the sequestration of carbon dioxide, and enhanced oilrecovery techniques. For purely advective transport we combine a known exact solution for the description of immiscible two-phase flow with the method of characteristics for the advective transport equations to obtain solutions that describe cocurrent flow and countercurrent spontaneous imbibition and advective transport in one dimension. We show that for both cases the solute front can be located graphically by a modified Welge tangent. For the advective-dispersive solute transport, we derive approximate analytical solutions by the method of singular perturbation expansion. On the basis of this, we obtain analytical expressions for the growth of the dispersive zone for the case with and without the influence of capillary pressure. We show that for the case of spontaneous countercurrent imbibition the order of magnitude of the growth rate is far smaller than that for the viscous limit. We give some illustrative examples and compare the analytical expressions with numerical reference solutions.Citation: Schmid, K. S., S. Geiger, and K. S. Sorbie (2011), Semianalytical solutions for cocurrent and countercurrent imbibition and dispersion of solutes in immiscible two-phase flow, Water Resour.

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Section: Introductionmentioning

confidence: 99%

Semianalytical solutions for cocurrent and countercurrent imbibition and dispersion of solutes in immiscible two‐phase flow

Schmid

Geiger

Sorbie

2011

Water Resources Research

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“…Steady-state conditions are considered in this work, but the SFP method is applicable in the case of transient flow as well. Other techniques based on the idea of studying multiphase flow along flowpaths (or streamlines) have also been recently introduced in petroleum engineering [23], [24]. These techniques, however, address the solution of the simpler fractional flow model often used in oil recovery.…”

Section: Discussionmentioning

confidence: 99%

“…While our method bears some resemblance to the streamtube [22] and streamline [23], [24] approaches for solving multiphase flow equations, it differs from them in certain important ways. These approaches, which are very efficient computationally, provide numerical solutions for the multiphase system assuming fractional flow conditions.…”

Section: Introductionmentioning

confidence: 99%

Stochastic Flowpath Analysis of Multiphase Flow in Random Porous Media

Christakos¹,

Hristopulos²,

Kolovos³

2000

SIAM J. Appl. Math.

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Multiphase flow in random porous media is studied by means of a stochastic flowpath approach, which is built upon concepts of differential geometry. This approach replaces the partial differential equations of flow by a set of ordinary differential equations along the flowpaths. Geometrical characterization of multiphase flow involves space transformations. The stochastic flowpath approach accounts for heterogeneity and allows for random initial or boundary conditions. It does not require perturbative approximations, and it does not involve Green's functions. The differential geometric formulation involves tracking the flowpath trajectories of the different phases within the flow domain. We discuss the solution of the two-phase flow equation within a random permeability medium by numerical simulation. ). Steady-state two-phase flow.We study multiphase flow of two immiscible and incompressible fluids within a heterogeneous porous medium, the physical

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“…Streamline simulation is a semianalytic technique that is valid in three-dimensional heterogeneous porous media [Datta-Gupta and King, 1995;Blunt et al, 1996;Bratvedt et al, 1996;Cirpka et al, 1999a]. Streamline methods have increased in sophistication and are used in high-resolution reservoir models [Datta-Gupta and King, 2007].…”

Section: Introductionmentioning

confidence: 99%

Trajectory‐based modeling of fluid transport in a medium with smoothly varying heterogeneity

Vasco

Pride

Commer

2016

Water Resources Research

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Using an asymptotic methodology, valid in the presence of smoothly varying heterogeneity and prescribed boundaries, we derive a trajectory-based solution for tracer transport. The analysis produces a Hamilton-Jacobi partial differential equation for the phase of the propagating tracer front. The trajectories follow from the characteristic equations that are equivalent to the Hamilton-Jacobi equation. The paths are determined by the fluid velocity field, the total porosity, and the dispersion tensor. Due to their dependence upon the local hydrodynamic dispersion, they differ from conventional streamlines. This difference is borne out in numerical calculations for both uniform and dipole flow fields. In an application to the computational X-ray imaging of a saline tracer test, we illustrate that the trajectories may serve as the basis for a form of tracer tomography. In particular, we use the onset time of a change in attenuation for each volume element of the X-ray image as a measure of the arrival time of the saline tracer. The arrival times are used to image the spatial variation of the effective hydraulic conductivity within the laboratory sample.

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A Generalized Streamline Method to Predict Reservoir Flow

Cited by 13 publications

References 8 publications

Semianalytical solutions for cocurrent and countercurrent imbibition and dispersion of solutes in immiscible two‐phase flow

Semianalytical solutions for cocurrent and countercurrent imbibition and dispersion of solutes in immiscible two‐phase flow

Stochastic Flowpath Analysis of Multiphase Flow in Random Porous Media

Trajectory‐based modeling of fluid transport in a medium with smoothly varying heterogeneity

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