Journal of Engineering Mathematics

, Volume 43, Issue 2–4, pp 229–253

Mud removal and cement placement during primary cementing of an oil well – Laminar non-Newtonian displacements in an eccentric annular Hele-Shaw cell


DOI: 10.1023/A:1020370417367

Cite this article as:
Bittleston, S., Ferguson, J. & Frigaard, I. Journal of Engineering Mathematics (2002) 43: 229. doi:10.1023/A:1020370417367


A two-dimensional model is derived of the displacement flows that occur during primary cementing of oil and gas wells. The displacement geometry is a long narrow eccentric annulus, between the casing and the rock formation. The model consists of a series of first-order convection equations for the fluid concentrations and a quasi-linear Poisson-type equation for the stream function. Coupling is through the velocity field and the concentration-dependent fluid properties.

A range of computed results from this model is presented. One simulation illustrates how a channel of mud can be left behind on the narrow side of the annulus. Another shows that stable steady-state displacements can occur, although conditions under which this occurs are not yet understood. A third simulation captures some of the complexity that occurs in realistic cementing operations.

displacement flows Hele-Shaw cell non-Newtonian fluids visco-plastic fluid flow 

Copyright information

© Kluwer Academic Publishers 2002

Authors and Affiliations

  1. 1.Schlumberger Cambridge ResearchCB3 0EL
  2. 2.Department of Mathematics and Department of Mechanical EngineeringUniversity of British ColumbiaVancouverCanada

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