Sara Borazjani

Splitting in systems of PDEs for two-phase multicomponent flow in porous media

Abstract The paper investigates the system of PDEs for two-phase n -component flow in porous media consisting of hyperbolic terms for advective transport, parabolic terms of dissipative effects and relaxation non-equilibrium equations. We found that for several dissipative and non-equilibrium systems, using the stream-function as a free variable instead of time separates the general ( n + 1 ) × ( n + 1 ) system into an n × n auxiliary system and one scalar lifting equation. In numerous cases, where the auxiliary system allows for exact solution, the general flow problem is reduced to numerical or semi-analytical solution of one lifting equation.

Skin Due to Fines Mobilization, Migration, and Straining During Steady-State Oil Production

Abstract Permeability decline during core floods with high rates has been widely reported in the literature. It has often been explained by the lifting, migration, and subsequent plugging of pores by fine particles, which has been observed in numerous core flood tests. The phenomena have been connected to well productivity impairment during fines production that also has been widely observed in oilfields. The authors derive a formula for skin factor based on the modified particle detachment model with maximum retention function. The mobilized fines capture by the rock is assumed to be instant at the large reservoir scale, so skin factor drops at the beginning of production and remains constant. The fines migration induced skin is shown to increase with increase of rate and initial attached fines concentration.

Effects of Fines Migration on Low-Salinity Waterflooding: Analytical Modelling

We discuss the governing system for oil–water flow with varying water composition. The model accounts for wettability alteration, which affects the relative permeability, and for salinity-variation-induced fines migration, which reduces the relative permeability of water. The overall ionic strength represents the aqueous phase composition in the model. One-dimensional displacement of oil by high-salinity water followed by low-salinity-slug injection and high-salinity water chase drive allows for exact analytical solution. The solution is derived using the splitting method. The analytical model obtained analyses the effects of wettability alteration and fines migration on oil recovery as two distinct physical mechanisms. For typical reservoir conditions, the significant effects of both mechanisms are observed.

Exact Solution for Non-Self-Similar Wave-Interaction Problem during Two-Phase Four-Component Flow in Porous Media

Analytical solutions for one-dimensional two-phase multicomponent flows in porous media describe processes of enhanced oil recovery, environmental flows of waste disposal, and contaminant propagation in subterranean reservoirs and water management in aquifers. We derive the exact solution for 3x3 hyperbolic system of conservation laws that corresponds to two-phase four-component flow in porous media where sorption of the third component depends on its own concentration in water and also on the fourth component concentration. Using the potential function as an independent variable instead of time allows splitting the initial system to 2x2 system for concentrations and one scalar hyperbolic equation for phase saturation, which allows for full integration of non-self-similar problem with wave interactions.

Well Productivity Decline due to Fines Migration and Production: (Analytical model for the regime of strained particles accumulation)

Well index decline has been widely observed for oil, gas and artesian wells producing the reservoir fines. It has often been explained by the lifting, migration and subsequent plugging of pores by fine particles, which have been observed in numerous core flood tests. In this work, the basic equations for the detachment of fine particles, their migration and size exclusion, causing the rock permeability decline, have been derived. The analytical model, developed for the regime of steady state production with gradual accumulation of strained particles, show the linear skin factor growth vs time and vs the amount of produced reservoir fines. Introduction Well productivity decline under fines production is well known phenomenon in low consolidated and high clay contents reservoirs, and also in heavy oil and high rate gas fields (Mungan, N. 1965, Bernard, 1967, Lever and Dawe, 1984, Tiab and Donaldson, 1996, Civan, 2007). It is explained by detachment of the attached particles and clay fines by the drag and lifting forces, exerting the fine particles from the moving fluid; the mobilised fines strain thin pores causing the permeability decline. The reliable prediction of productivity index decline is based on the mathematical modelling. Kinetics of particle capture by the rock from the flowing suspension is described by the filtration equation (Herzig et al., 1970)

Low-Salinity Fines-Assisted Waterflooding: Multiscale Analytical and Numerical Modelling

The aim of this work is the development of mathematical models for oil–water flow with varying injected water compositions in oil reservoirs. The model accounts for two main mechanisms of low salinity waterflooding (LSW): Wettability alteration and salinity-variation-induced fines migration. Analytical and numerical models are developed and applied to low salinity fines-assisted core flood tests. In large reservoir scale, the general system of equations permits for an analytical solution. The solution is obtained by recently developed splitting technique, where the stream function is used as a variable instead of time. Large-scale approximation assumes that six dimensionless groups for dissipative and non-equilibrium effects are negligibly small. Numerical results are obtained for the general system, which accounts for dissipative and non-equilibrium effects. The effects of fines migration and wettability variation on oil recovery are discovered as two separate mechanisms in LSW. The significant EOR-effects of both mechanisms are observed under the typical oil reservoir conditions.

Formation Damage by Fines Migration: Mathematical and Laboratory Modeling, Field Cases

Abstract One of the widely spread causes of reservoir formation damage is fines migration. Migration of natural reservoir fines occurs during commingled production of oil or gas with low-salinity water, during high-rate production or injection, with low-salinity waterflooding and its combinations with enhancd oil recovery (EOR). At least 10% of

Analytical Modelling of Low-salinity Waterflooding with Fines Migration

100 billion annual worldwide expenditure on prevention, mitigation, and removal of formation damage is attributed to fines migration. The current chapter derives basic fundamental equations for fines detachment, migration, and size exclusion in single-phase and two-phase environments. The mathematical model for fines detachment derived in this chapter significantly differs from the classical approach: the maximum attached concentration as a function of velocity, salinity, and pH captures fines lifting due to change of the abovementioned variables. Exact analytical solutions are obtained for 1D linear flows with fines migration during rate increase and salinity decrease. Laboratory coreflood data are matched by the analytical models, providing the tuned parameter values. The laboratory-based parameters are used for field-scale predictions of behavior of injection and production wells during fines migration.

Effects of fines migration on well productivity during steady state production

Low-salinity waterflood is presently one of the most cost-effective EOR methods. The governing system of equations for oil and water flow with changing water salinity is derived. So-called mechanistic model is developed. This model accounts for two EOR factors: a) fines migration, which is induced by salinity variation and reduces the relative permeability of water, and b) wettability alteration, which affects the relative permeability and capillary pressure. The “lump-salt” description is used, i.e. the ionic water composition is represented by the total ionic concentration. The basic equations are simplified for three basic asymptotic cases: 1) large length scales, 2) low-velocities, 3) high-velocities. An exact analytical solution is derived for 1d displacement large-scale-approximation problem of oil using high-salinity water followed by the injection of low-salinity-slug and high-salinity water chase drive. The solution is obtained by so-called splitting method, where the Lagrangian coordinate is used as a free variable instead of time. The effects of wettability alteration and fines migration on oil recovery as two distinct physical mechanisms are analyses using the analytical model. The significant EOR-effects of both mechanisms are observed for the typical oil-reservoir conditions.