Three-phase immiscible displacement in heterogeneous petroleum reservoirs

Abreu, Eduardo; Douglas, Jim; Furtado, Frederico; Marchesin, D.; Pereira, Felipe

doi:10.1016/j.matcom.2006.06.018

Cited by 34 publications

(56 citation statements)

References 34 publications

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“…The states S = (s w , s g ) that are left states for shocks to the pure oil state O = (0, 0) satisfy the RH conditions (4), which reduce to f w (S) = σ s w , f g (S) = σ s g , obtained by taking into account that for pure oil, the saturations and corresponding relative permeabilities of water and gas are zero (from hypothesis (C1)). For the same reason, the saturation triangle edges s w = 0 and s g = 0 are part of the Hugoniot The arrows indicate the direction of increasing characteristic speed; notice the maximum speed at the dots, which are inflection points.…”

Section: Basic Structures In the Saturation Trianglementioning

confidence: 99%

On a universal structure for immiscible three-phase flow in virgin reservoirs

et al. 2016

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We discuss the solution for commonly used models of the flow resulting from the injection of any proportion of three immiscible fluids such as water, oil, and gas in a reservoir initially containing oil and residual water. The solutions supported in the universal structure generically belong to two classes, characterized by the location of the injection state in the saturation triangle. Each class of solutions occurs for injection states in one of the two regions, separated by a curve of states for most of which the interstitial speeds of water and gas are equal. This is a separatrix curve because on one side water appears at breakthrough, while gas appears for injection states on the other side. In other words, the behavior near breakthrough is flow of oil and of the dominant phase, either water or gas; the nondominant phase is left behind. Our arguments are rigorous for the class of Corey models with convex relative permeability functions. They also hold for Stone's interpolation I model [5]. This description of the universal structure of solutions for the injection problems is valid for any values of phase viscosities. The inevitable presence of an umbilic point (or of an elliptic region for the Stone model) seems to be the cause of this universal solution structure. This universal structure was perceived recently in the particular case of quadratic Corey relative permeability models and with the injected state consisting of a mixture of water and gas but no oil [5]. However, the results of the present paper are more general in two ways. First, they are valid for a set of permeability functions that is stable under perturbations, the set of convex permeabilities. Second, they are valid for the injection of any proportion of three rather than only two phases that were the scope of [5].

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Section: Basic Structures In the Saturation Trianglementioning

confidence: 99%

On a universal structure for immiscible three-phase flow in virgin reservoirs

et al. 2016

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“…The permeability for water assumes a slightly different form, k w = φ w 3 w 2 (1 − m 2 )/C where w = φ w /(φ m + φ w ). The relations just outlined here describe a simplified formulation borrowed from reservoir modeling which typically involves several phases like oil, gas and water (Corey et al, 1956;Stone, 1970;Peaceman, 1977;Dria et al, 1993;Abreu et al, 2006).…”

Section: Description Of the Multiphase Dynamic Modelmentioning

confidence: 99%

Petrological Geodynamics of Mantle Melting I. AlphaMELTS + Multiphase Flow: Dynamic Equilibrium Melting, Method and Results

Tirone

Sessing

2017

Front. Earth Sci.

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The complex process of melting in the Earth's interior is studied by combining a multiphase numerical flow model with the program AlphaMELTS which provides a petrological description based on thermodynamic principles. The objective is to address the fundamental question of the effect of the mantle and melt dynamics on the composition and abundance of the melt and the residual solid. The conceptual idea is based on a 1-D description of the melting process that develops along an ideal vertical column where local chemical equilibrium is assumed to apply at some level in space and time. By coupling together the transport model and the chemical thermodynamic model, the evolution of the melting process can be described in terms of melt distribution, temperature, pressure and solid and melt velocities but also variation of melt and residual solid composition and mineralogical abundance at any depth over time. In this first installment of a series of three contributions, a two-phase flow model (melt and solid assemblage) is developed under the assumption of complete local equilibrium between melt and a peridotitic mantle (dynamic equilibrium melting, DEM). The solid mantle is also assumed to be completely dry. The present study addresses some but not all the potential factors affecting the melting process. The influence of permeability and viscosity of the solid matrix are considered in some detail. The essential features of the dynamic model and how it is interfaced with AlphaMELTS are clearly outlined. A detailed and explicit description of the numerical procedure should make this type of numerical models less obscure. The general observation that can be made from the outcome of several simulations carried out for this work is that the melt composition varies with depth, however the melt abundance not necessarily always increases moving upwards. When a quasi-steady state condition is achieved, that is when melt abundance does not varies significantly with time, the melt and solid composition approach the composition that is found from a dynamic batch melting model which assumes the velocities of melt and residual solid to be the same. Time dependent melt fluctuations can be observed under certain conditions. In this case the composition of the melt that reaches the top side of the model (exit point) may vary to some extent. A consistent result of the model under various conditions is that the volume of the first melt that arrives at the exit point is substantially larger than any later melt output. The analogy with large magma emplacements associated to continental break-up or formation of oceanic plateaus seems to suggest that these events are the direct consequence of a dynamic two-phase flow process. Even though chemical equilibrium between melt and the residual solid is imposed locally in space, bulk composition of the whole system (solid+melt) varies with depth and may also vary with time, mainly as the result of the changes of the melt abundance. Potential factors that can influence the melting process such as b...

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“…Operator-splitting schemes have recently been developed for the approximation of multiphase flows in porous media (Abreu et al, 2006). These schemes are aimed at decomposing the underlying physical processes and treating each such component appropriately.…”

Section: Operator Splittingmentioning

confidence: 99%

“…These properly chosen time steps lead to a significant reduction in overall computing times. This set of ideas has been successfully applied to several multiphase flow problems: multicomponent gas flow (Douglas et al, 2003), two-phase flows in unfractured and fractured porous formations (Douglas, 1997a;Douglas, 1997b;Douglas et al, 2000), and three-phase flows (Abreu et al, 2006;Abreu et al, 2008;Abreu et al, 2009).…”

Section: Operator Splittingmentioning

confidence: 99%

Carbon Sequestration Monitoring Activities

Frost¹

2010

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Three-phase immiscible displacement in heterogeneous petroleum reservoirs

Cited by 34 publications

References 34 publications

On a universal structure for immiscible three-phase flow in virgin reservoirs

On a universal structure for immiscible three-phase flow in virgin reservoirs

Petrological Geodynamics of Mantle Melting I. AlphaMELTS + Multiphase Flow: Dynamic Equilibrium Melting, Method and Results

Carbon Sequestration Monitoring Activities

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