Analytical Solutions to Multiphase First-Contact Miscible Models with Viscous Fingering

Juanes, Ruben; Blunt, Martin J.

doi:10.1007/s11242-005-5049-z

Cited by 28 publications

(21 citation statements)

References 45 publications

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“…This leads to a system of hyperbolic conservation laws, and the method of characteristics or the method of chromatography can be used to derive analytical solutions (e.g. [32,33,36,53,54,57]). As explained in the introduction, our primary interest is the mixing of the adsorbing but otherwise inert components (Fig.…”

Section: Mathematical Modelmentioning

confidence: 99%

Analytical solutions for co- and counter-current imbibition of sorbing, dispersive solutes in immiscible two-phase flow

2012

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We derive a set of analytical solutions for the transport of adsorbing solutes in an immiscible, incompressible two-phase system. This work extends recent results for the analytical description for the movement of inert tracers due to capillary and viscous forces and dispersion to the case of adsorbing solutes. We thereby obtain the first known analytical expression for the description of the effect of adsorption, dispersion, capillary forces and viscous forces on solute movement in two-phase flow. For the purely advective transport, we combine a known exact solution for the description of flow with the method of characteristics for the advective transport equations to obtain solutions that describe both co-and spontaneous counter-current 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 dispersion, we derive approximate analytical solutions by the method of singular perturbation expansion. The solutions reveal that the amount of spreading depends on the flow regime and that adsorption diminishes the spreading behavior of the solute. We give some illustrative examples and compare the analytical solutions with numerical results.

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Section: Mathematical Modelmentioning

confidence: 99%

Analytical solutions for co- and counter-current imbibition of sorbing, dispersive solutes in immiscible two-phase flow

2012

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“…This is relevant because solvent injection often leads to an unstable displacement process, in which the solvent fingers through, leading to a lower displacement efficiency. A rather extensive mathematical analysis of the effects of viscous fingering has recently presented in (Juanes and Blunt 2006) using the empirical viscous fingering model proposed by Blunt and Christie (Blunt and Christie 1993; …”

Section: Discussionmentioning

confidence: 99%

“…Eclipse results are shown with solid lines; streamline/front-tracking results are shown with dashed lines Christie 1994). The new analytical solutions presented in (Juanes and Blunt 2006) constitute the first step towards a complete Riemann solver for first-contact miscible flow in the presence of viscous fingering.…”

Section: Fig 19mentioning

confidence: 99%

Numerical modeling of multiphase first-contact miscible flows. Part 2. Front-tracking/streamline simulation

Juanes

Lie

2007

Transp Porous Med

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In this paper we complete the description and application of a computational framework for the numerical simulation of first-contact miscible gas injection processes. The method is based on the front-tracking algorithm, in which numerical solutions to onedimensional problems are constructed in the form of traveling discontinuities. The efficiency of the front-tracking method relies on the availability of the analytical Riemann solver described in Part 1 and a strategy for simplifying the wave structure for Riemann problems of small amplitude. Several representative examples are used to illustrate the excellent behavior of the front-tracking method. The front-tracking method is extended to simulate higher-dimensional processes through the use of streamlines. The paper presents a validation exercise for a quarter five-spot homogeneous problem, and an application of this computational framework for the simulation of miscible flooding in three-dimensional, highly heterogeneous formations. In this case, we demonstrate that a miscible water-alternating-gas injection scheme is more effective than waterflooding or gas injection alone.

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“…MGF increases to 34% when the endpoint relative permeability of the gas phase is lowered to k o rg = 0.2, while it decreases to 16% when the endpoint relative permeability of the water phase is decreased to k o r w = 0.2. In (Juanes and Blunt 2006) it is shown that in WAG flooding with first-contact-miscible gas the optimal WAG ratio (equivalent to the MGF) is altered by viscous instability when a low viscosity gas pushes a higher viscosity oil out of the reservoir. A similar result could be obtained in fully compositional flow.…”

Section: Effect Of Relative Mobility On Mgfmentioning

confidence: 99%

Four-Component Gas/Water/Oil Displacements in One Dimension: Part III, Development of Miscibility

LaForce

Orr

2008

Transp Porous Med

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The structure of the system of conservation laws in fully compositional three-phase, four-component flow is examined for the first time. Two of the eigenvalues can be found analytically for this flow regime, regardless of the equation of state used to model the phase behavior. A cubic equation of state is used to calculate the gas/oil phase behavior and Henry's law is used to represent the partitioning of hydrocarbons between the hydrocarbon and water phases. Sample analytical solutions are found for Riemann problems modeling the injection of carbon-dioxide and water into an oil reservoir. Finally, the structure of the solutions at the minimum miscibility pressure (MMP) for the hydrocarbon system is studied. We show that when water is injected simultaneously with gas at the MMP, multicontact miscible displacement of the oil by the injected gas develops only if the fraction of water in the injected fluid is below a critical value. For water fractions above the critical value, water flowing at a high velocity forces the composition path of the solution to remain in the three-phase region in which two hydrocarbon phases are present. We study both condensing and vaporizing gas drives to demonstrate that this result is general.

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Analytical Solutions to Multiphase First-Contact Miscible Models with Viscous Fingering

Cited by 28 publications

References 45 publications

Analytical solutions for co- and counter-current imbibition of sorbing, dispersive solutes in immiscible two-phase flow

Analytical solutions for co- and counter-current imbibition of sorbing, dispersive solutes in immiscible two-phase flow

Numerical modeling of multiphase first-contact miscible flows. Part 2. Front-tracking/streamline simulation

Four-Component Gas/Water/Oil Displacements in One Dimension: Part III, Development of Miscibility

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