A stochastic model for particulate suspension flow in porous media

A population balance model for a particulate suspension transport with size exclusion capture of particles by porous rock is derived. The model accounts for particle flux reduction and pore space accessibility due to restriction for large particles to move through smaller pores – a particle is captured by a smaller pore and passes through a larger pore. Analytical solutions are obtained for a uniform pore size medium, and also for a medium with small pore size variation. For both cases, the equations for averaged concentrations significantly differ from the classical deep bed filtration model.A. Santos, P. Bedrikovetsk

Exact solution for long-term size exclusion suspension-colloidal transport in porous media

Long-term deep bed filtration in porous media with size exclusion particle capture mechanism is studied. For monodispersed suspension and transport in porous media with distributed pore sizes, the microstochastic model allows for upscaling and the exact solution is derived for the obtained macroscale equation system. Results show that transient pore size distribution and nonlinear relation between the filtration coefficient and captured particle concentration during suspension filtration and retention are the main features of long-term deep bed filtration, which generalises the classical deep bed filtration model and its latter modifications. Furthermore, the exact solution demonstrates earlier breakthrough and lower breakthrough concentration for larger particles. Among all the pores with different sizes, the ones with intermediate sizes (between the minimum pore size and the particle size) vanish first. Total concentration of all the pores smaller than the particles turns to zero asymptotically when time tends to infinity, which corresponds to complete plugging of smaller pores.Z. You, P. Bedrikovetsky and L. Kuzmin

Laboratory-Based Prediction of Sulphate Scaling Damage

SPE paper 100611The BaSO4 scaling is a chronicle disaster in water-flood projects with incompatible injected and formation waters. This is usually due to precipitation of barium sulphate from the mixture of both waters and consequent permeability reduction resulting in well productivity decrease. The sulphate scaling damage system contains two governing parameters: the kinetics coefficient characterising the velocity of chemical reaction and the formation damage coefficient reflecting permeability decrease due to salt precipitation. Previous work has derived analytical-model-based method for determination of kinetics coefficient from laboratory coreflood on quasi steady state commingled flow of injected and formation waters. The current study extends the method and derives formulae for calculation of formation damage coefficient from pressure drop measurements during coreflood. The proposed method can be extended for axi-symmetric flow around the well allowing calculation of both sulphate scaling damage coefficients from field data on barium concentration in produced water and well productivity decline. We treat several laboratory test data and field data, and obtain values of two sulphate scaling damage parameters. The values of kinetics and formation damage coefficients as obtained from either laboratory or field data vary in the same range intervals. It validates the proposed mathematical model for sulphate scaling damage and the analytical-model-based method "from lab to wells". Copyright 2006, Society of Petroleum Engineers.Bedrikovetski, P.G., Mackay, E., Monteiro, R., Glanstone, P. M., Rosario, F.http://www.proceedings.com/00192.htm

WAG displacements of oil-condensates accounting for hydrocarbon ganglia

The original publication can be found at www.springerlink.com © SpringerDuring two-phase flow in porous media, non-wetting phase is present simultaneously in states of mobile connected continuum and of trapped isolated ganglia. Mass exchange between these two parts of non-wetting phase is going on by dissolution and diffusion of component in the wetting phase, so, compositions of non-wetting phase in both parts are different. Nevertheless, the traditional mathematical model for two-phase multicomponent transport in porous media assumes the homogeneous distribution of each component in the overall non-wetting phase. New governing equations honouring ganglia of non-wetting phase are derived. They are successfully verified by a number of laboratory tests. Analytical model is developed for miscible water-alternate-gas (WAG) displacement of oil-condensates. The modelling shows that the significant amount of oil-condensate is left in porous media after miscible WAG, while the traditional model predicts that the miscible displacement results in the total sweep.Bedrikovetski, P. G

Suspension Flow in Petroleum Reservoirs: Fractional Flow Theory

SPE paper 110929P. Bedrikovetsky and P. Monteirohttp://www.proceedings.com/02266.htm

Elliptic random-walk equation for suspension and tracer transport in porous media

We propose a new approach to transport of the suspensions and tracers in porous media. The approach is based on a modified version of the continuous time random walk (CTRW) theory. In the framework of this theory we derive an elliptic transport equation. The new equation contains the time and the mixed dispersion terms expressing the dispersion of the particle time steps. The properties of the new equation are studied and the fundamental analytical solutions are obtained. The solution of the pulse injection problem describing a common tracer injection experiment is studied in greater detail. The new theory predicts delay of the maximum of the tracer, compared to the velocity of the flow, while its forward “tail” contains much more particles than in the solution of the classical parabolic (advection-dispersion) equation. This is in agreement with the experimental observations and predictions of the CTRW theory.A.A. Shapiro and P.G. Bedrikovetsk

Erratum: Size exclusion during particle suspension transport in porous media: stochastic and averaged equations

A pore scale population balance model is formulated for deep bed filtration of stable particulate suspensions in porous media. The particle capture from the suspension by the rock occurs by the size exclusion mechanism. The equations for particle and pore size distributions have been derived from the stochastic Master equation. The model proposed is a generalization of stochastic Sharma-Yortsos equations – it accounts for particle flux reduction due to restriction for large particles to move via small pores. Analytical solution for low particle concentration is obtained for any particle and pore size distributions. The averaged macro scale equations, derived from the stochastic pore scale model, significantly differ from the traditional deep bed filtration model.A. Santos and P. Bedrikovetsk

Hyperbolic systems of quasilinear equations

Bedrikovetski, P.G., Puime, A.P.http://trove.nla.gov.au/work/1714834