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TECHNICAL PAPERS

# Numerical Prediction Method for Growth and Deformation of Filter Cakes

[+] Author and Article Information
A. J. Parry

Schlumberger Riboud Product Center, 1 rue Henri Becquerel, 92140 Clamart, Franceaparry@clamart.oilfield.slb.com

J. Fluids Eng 128(6), 1259-1265 (May 09, 2006) (7 pages) doi:10.1115/1.2354526 History: Received September 19, 2005; Revised May 09, 2006

## Abstract

During filtration of a fluid-solid mixture, a filter cake composed of solids is formed on the upstream side of the permeable interface—the filtrate or clean fluid passes through but not the solids. This paper describes a multi-dimensional calculation framework to carry out numerical simulations of growth and deformation of a filter cake. Two examples of cake growth and deformation phenomena of interest to the oil industry are the sticking of drill string within a wellbore and the sealing of wellbore sections by expandable packers. The calculation algorithm is based on the algebraic slip mixture model, involving the solution of a non-linear transport equation for solids concentration and the mass- and momentum-conservation equations of the mixture for the velocity and pressure field. The matrix stress and flow permeability are expressed as functions of solids concentration. The viscosity in the momentum equations is modeled using the Bingham approach and proportionality between yield stress and solids matrix pressure. Velocity and pressure fields are split into filtration and deformation components, thus permitting a stable calculation scheme. The simulated results match reasonably experimental observations.

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Copyright © 2006 by American Society of Mechanical Engineers
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## Figures

Figure 1

Schematic of filter cake growth

Figure 2

Cake growth in a 30deg wedge space shown at 24,000s, 800psi(5,515,840N∕m2), and 10% upstream solids concentration

Figure 3

Variation of solids deposition rate factor with and without correction for the 30deg wedge space as a function of time

Figure 4

Schematic of sphere torque test cell

Figure 5

Torque required to turn the sphere about an axis normal to the permeable interface as a function of time, at 200, 600, and 800psi (1.379MN∕m2, 4.137MN∕m2, and 5.516MN∕m2, respectively), experimental data from Sherwood (5)

Figure 6

Profiles of solids concentration within the cake (far from the sphere contact region) as a function of the Lagrangian similarity variable yt−1∕2 at 200, 600, and 800psi (1.379MN∕m2, 4.137MN∕m2, and 5.516MN∕m2, respectively)

Figure 7

Solids concentration and filtration velocity vector plots at t=6000s with 800psi(5,515,840N∕m2)

Figure 8

Variation of solids deposition rate factor with and without correction, 800psi(5,515,840N∕m2)

Figure 9

Disk force versus separation h, homogeneous Bingham fluid

Figure 10

Disk force versus separation h, filter cake

Figure 11

(a) solids concentration and filtration velocity at h∕R=0.19, (b) deformation velocity [m/s] at h∕R=0.19, (c) solids concentration and filtration velocity at h∕R=0.02, (d) deformation velocity [m/s] at h∕R=0.02. Axial coordinate stretched by 10 for (c) and (d).

Figure 12

Variation of solids deposition rate factor with and without correction for squeeze flow test of filter cake

Figure 13

Ratio of solids accumulation rate to outflow rate for squeeze flow test of filter cake

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