Mathematical Modeling of Suspension Filtration on a Rapid Filter at an Unregulated Rate

Mathematical modeling of detachable filtration in the split filter flow mode was carried out using exact and approximate analytical methods. An engineering technique has been developed to determine the duration of filter cycles, based on quality, economic and technical criteria. Determination of rational filter medium height was considered for two materials differed significantly by economic indexes.

A Theoretical Analysis of Profile Conformance Improvement Due to Suspension Injection

This study is focused on a solution for the problem of suspension penetration in a porous formation. Such a solution forms the basis of injection profile diversion technology for oil reservoir sweep improvement. A conventional model of deep-bed suspension flow was used to describe the suspension injection process. The suspension slug was followed by water injection, and the inflow injection profile before and after treatment was investigated. For the first time, the criteria that determine the effectiveness of the inflow profile improvement process are introduced. The effect of the suspension filtration coefficient on the particle penetration depth was studied. A specific filtration coefficient value for the maximum penetration depth was achieved. The obtained analytical solution was generalized on multi-reservoir strata with poor interlayer crosslinking. The efficiency of profile conformance improvement was described by the differences in the root-mean-square deviations of the inflow velocities in interlayers from mean values before and after the treatment. It was shown that the complex criterion of suspension treatment efficiency should include a reduction in total injectivity. An increase in suspension slug volume improves the injectivity profile but decreases the total injectivity of an injector.

Bentonite Suspension Filtration and its Electro-Kinetics in the Presence of Additives

Invasion of fluids into porous media during drilling can lead to irreparable damage and reduced well productivity. Hence, minimizing the filtration loss of the drilling fluid into the formation is very important. The stability of colloidal suspensions plays a crucial role in controlling the interfacial forces and consequently on minimizing the filtration. The zeta potential is an indicator of the stability of colloids with respect to their electrostatic interactions. In this study, the rheological properties of bentonite suspensions are investigated with and without additives. The starch and CMC were used as additives to enhance the rheological properties of bentonite. The effects of these additives on the drilling fluid filtration were examined. Zeta-potential, viscosity, gel strength and yield point were measured to characterize the extent to which control of the filtration loss of the drilling fluids can be achieved. The zeta-potential and the amount of filtration loss of water-bentonite suspensions were correlated. Finally, the results showed that the addition of either starch or carboxymethyl cellulose (CMC) enhances the filtration properties of water-bentonite suspensions.

Numerical Study of Suspension Filtration Model in Porous Medium with Modified Deposition Kinetics

Filtration is one of the most used technologies in chemical engineering. Development of computer technology and computational mathematics made it possible to explore such processes by mathematical modeling and computational methods. The article deals with the study of suspension filtration in a porous medium with modified deposition kinetics. It is suggested that deposition is formed in two types, reversible and irreversible. The model of suspension filtration in porous media consists of the mass balance equation and kinetic equations for each type of deposition. The model includes dynamic factors and multi-stage deposition kinetics. By using the symmetricity of porous media, the higher dimensional cases are reduced to the one-dimensional case. To solve the problem, a stable, effective and simple numerical algorithm is proposed based on the finite difference method. Sufficient conditions for stability of schemes are found. Based on numerical results, influences of dynamic factors on solid particle transport and deposition characteristics are analyzed. It is shown that the dynamic factors mainly affect the profiles of changes in the concentration of deposition of the active zone.

A Deep Bed Filtration Model of Two-Component Suspension in Dual-Zone Porous Medium

In the paper, a mathematical model for the filtration of two-component suspensions in a dual-zone porous medium is considered. The model consists of the mass balance equations, the kinetic equations for active and passive zones of porous medium for each component of the suspension and Darcy’s law. To solve the problem, a numerical algorithm for computer experimentation is developed on the basis of finite difference method. Based on numerical results, the main characteristics of suspension filtration in a porous medium are established. Influences of model parameters on transport and deposition of suspended particles of two-component suspension in porous media are analysed. It is shown that the polydispersity of suspension and multistage nature of the deposition kinetics can lead to various effects that are not characteristic for the transport of one-component suspensions with one-stage particle deposition kinetics. In particular, in distribution of the concentration of suspended particles in a moving fluid non-monotonic dynamics are obtained at individual points in the medium. It is shown that at the points of the medium near to the input section, the concentration of deposited particles can reach partial capacities in the passive zone.