Cake Filtration With Particle Penetration at the Cake Surface

Abstract

Summary Particles in drilling muds build a filter cake on borehole walls and can migrate into the adjacent porous formation and cause formation damage. This study analyzes cake formation, including particle penetration at the cake surface. Mass-balance equations for captured and suspended particles and the fluid phase are averaged along the cake thickness, taking particles and the fluid phase are averaged along the cake thickness, taking into account conditions on the surface and the septum. Capture mechanisms, such as surface straining, and internal cake erosion and particle capture are included in the analysis. The results are ordinary differential equations in terms of thickness, average particle concentration, average porosity, and such operational parameters as slurry concentration, porosity, and such operational parameters as slurry concentration, injection rate, and volumetric solid fraction. Results show that during early stages of cake formation, penetrated-particle concentration peaks and then declines rapidly shortly thereafter. Comparison of predicted cake thickness with experimental data showed an excellent match. Introduction Filter-cake formation is important in groundwater and oil wells where drilling mud contains suspended particles. The accumulation of these particles on the borehole wall creates a pressure drop in the well. Furthermore, the migration of colloidal pressure drop in the well. Furthermore, the migration of colloidal particles into adjacent porous rock could damage the formation and particles into adjacent porous rock could damage the formation and cause productivity decline. Cake-filtration techniques are also used in wastewater treatment, sludge dewatering, and industrial processes to remove suspended solids. processes to remove suspended solids. Compressible filter cakes are formed when a liquid with suspended particles (a slurry) is forced through a previous surface that allows liquid transport but retains solid particles either completely or partially by straining and sedimentation mechanisms. During filtration, new solid particles are laid down on the cake surface, gradually increasing its thickness. When the cake is deposited at the surface, it has a high porosity and a large liquid content. As the filter cake builds, the previous cake surface passes into the cake interior and the liquid is squeezed out as the cake is compressed during filtration. The filtrate from cake filtration may contain small particles that have passed through the cake medium. Such a phenomenon is known as "cloth bleeding." Fig. 1 is a schematic of filter-cake formation. Because filter-cake formation occurs in various fields, studies on cake filtration can be found in many disciplines. Corapcioglu et al. gave a comprehensive review of the subject. In this study, we briefly outline the most pertinent literature. A more detailed review is available in Refs. 1 and 2. Hermans and Bredee obtained expressions to estimate the blocking of a filter septum by cloth bleeding. Later, Gonsalves introduced an alternative technique to Hermans and Bredee's separate physical mechanisms of pore plugging. Grace published an extensive study of clogging mechanisms for nine different filter media and investigated the applicability of Hermans and Bredee's filtration laws. Wrotnowski provided bleeding data for various types of felt. Tiller and Crump reviewed studies by Tiller and other researchers on filter-cake mechanisms that led to various analytical expressions to predict pressure variations to estimate cake porosity, permeability, and specific cake resistance. Binkley et al. porosity, permeability, and specific cake resistance. Binkley et al. and Collins introduced a volumetric balance of solid and fluid phases to obtain an expression to estimate cake thickness. Shirato phases to obtain an expression to estimate cake thickness. Shirato et al. reported cake thickness data obtained with Hong Kong pink kaolin. Later, Shirato et al. presented an analytical method to explain apparent velocity variations of solid and fluid phases. Joo obtained a numerical solution of the cake-filtration problem based on Shirato's work. Outmans described the flow in compressible cakes in the borehole by a nonlinear diffusion equation. Atsumi and Akiyama and Wakeman developed theoretical analyses describing the growing cake surface as a moving-boundary problem. Tiller et al. studied the filtration of liquefied coal and problem. Tiller et al. studied the filtration of liquefied coal and noted the increased resistance caused by colloidal deposition in cakes. Through a nondimensional analysis, Willis et al. showed gravitational, pressure, and drag forces to be dominant for the liquid phase. Similarly, for the solid phase, deformation and gravitational phase. Similarly, for the solid phase, deformation and gravitational forces were found to be prevalent. Corapcioglu developed a conceptual model to use the mass-balance equation for solid particles to model the cake-filtration process. Later, Corapcioglu obtained expressions for cake formation by averaging mass-balance equations for solid and liquid phases along the cake thickness. Resulting analytical solutions for cake thickness compared favorably with the experimental results of Shirato et al. From this literature review, we can see that the "cloth bleeding" phenomenon is a problem of practical importance in well drilling. As phenomenon is a problem of practical importance in well drilling. As noted earlier, if the slurry contains colloidal particles, these fines might migrate through the cake and produce a cloudy filtrate. The level of effluent turbidity is an operational concern in well drilling and liquefied-coal-filtration processes. Migrating particles would also change the internal structure of the filter cake. In this study, we introduce an analysis of the cake-filtration processes, including particle penetration at the cake surface and migration in the cake. All particle penetration at the cake surface and migration in the cake. All governing equations developed in this paper are at the macroscopic level. For a pore-scale treatment, microscopic-level equations should be stated. Microscopic-level equations can be transformed to macroscopic ones by volume averaging over the representative elementary volume.