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Cake Filtration: Mechanism, Parameters and Modeling 263

linear and radial filter cake formation models offer significant advantages
over the partial differential models for the analysis, design, and opti-
mization of the cake filtration processes involving the well-bore and
hydraulically created fracture surfaces. Simplified models considering
incompressible particles and carrier fluids and analytical solutions for
incompressible cakes without fines invasion are also presented. These
models provide insight into the mechanism of cake filtration and offer
practical means of interpreting experimental data, estimating the model
parameters, and simulating the linear and radial filtration processes.

Introduction

Cake filtration occurs inherently in many in-situ hydrocarbon reservoir
exploitation processes. For example, hydraulic fracturing of petroleum
bearing rock and overbalanced drilling of wells into petroleum reservoirs
usually cause a cross-flow filtration, which leads to a filter cake build-
up over the face of the porous rock and filtrate invasion into the reservoir
(Civan, 1994, 1996). When the slurry contains particles of different sizes,
the larger particles of the slurry form the skeleton of the filter cake and
the smaller particles can migrate into and deposit within the porous cake
formed by the large particles. Simultaneously, the cake may undergo a
compaction process under the effect of the fluid drag as the suspension
of smaller particles flow through the cake (Tien et al., 1997). Con-
sequently, the porosity, permeability, and thickness of the cake vary, which
in turn effect the performance of the filtration process. Static filtration
occurs when a slurry is applied to a filter without cross-flow. Therefore,
the particles are continuously deposited to form thicker filter cakes.
Dynamic filtration involves some cross-flow. Therefore, the filter cake
thickness varies until the particle deposition and erosion rates equal.
Model assisted analyses, interpretation of experimental data and optimi-
zation and simulation of the filtration processes are of continuing interest
for the industry. The majority of the previous modeling efforts has been
limited to linear filtration applications, in spite of the fact that many
industrial filtration processes facilitate radial filtration applications. Linear
filtration models can closely approximate radial filtration only when the
thicknesses of the filter and filter cake are sufficiently small relative to
the radius of the filter surface exposed to slurry. Otherwise, radial models
should be used for radial filtration.
Because of their simplicity, empirical correlations such as those reviewed
by Clark and Barbat (1989) are frequently used for static and dynamic
filtration. Xie and Charles (1997) have demonstrated that the use of a
set of properly selected dimensionless groups leads to improved empirical
correlations. Simple models, are preferred in many applications because