Mechanics Of The Displacement Process Of Drilling Muds By Cement Slurries Using An Accurate Rheological Model
Authors: Beirute Robert M. , Flumerfelt Raymond W. 
Published: December 2007

Abstract
This paper deals with the development of a mathematical model to describe the miscible displacement of drilling muds by cement slurries under laminar flow conditions. The model accounts for the effects of differing properties, geometry, and displacement rates. The model assumes that "mixing" in the displacement zone by molecular diffusion is minimal, and uses the Robertson-Stiff model to describe the rheological properties of both the drilling fluid and the cement slurry.
The application of the model to a range of displacement conditions (densities, viscosities, yield stresses, displacement rates, etc.) indicates the conditions under which optimal or near optimal displacements are possible, and hence, provides a basis for designing efficient cementing operations from simple material property characterizations. Of special interest is the effect of the yield stress. These parameters are founded to strongly affect the displacement efficiency, particularly the formation of cement channels. Such results are described quantitatively in the paper as well as the effects of the other rheological properties, the densities, and the displacement rates. Field application cases are also included in this paper.

Introduction
Although many papers have been written on the subject of drilling mud displacement from wellbores during cementing operations, there are still many unresolved fundamental and practical questions. In particular, both laminar and turbulent flow conditions can produce good displacements; however, it is still not clear which represents the most effective displacement mechanism. Also, the displacement achieved under laminar conditions can vary greatly depending on the material properties of the fluids involved and the flow conditions. In some cases, very stable, high efficiency displacements are achieved, while in others, unstable fingering of the displacing phase occurs resulting in extremely low efficiency displacements. Even in the stable displacement cases, it has been only recently that efforts have been reported relating the displacement efficiency to the cement and mud material properties (densities and rheological properties) and the displacement rates. In the unstable cases, turbulent flow displacement would probably be dictated, but, as yet, there is no basis for estimating the displacement expected under different rates, nor the amount of the displacing phase which would be required. Further, the critical conditions separating stable and unstable displacement regimes have only been partially defined, and these relate only to Newtonian fluids, whereas drilling fluids and cements are highly non-Newtonian.
It is clear that our knowledge of the fundamentals of the displacement processes in cementing is still quite limited, and, as a result, it is doubtful that many cementing operations are as effective or efficient as they might be if this information were available. Under normal conditions, satisfactory cement jobs are possible with suboptimal displacements; however, under possible with suboptimal displacements; however, under more demanding operations, such as displacement in permafrost zones, high efficiency displacements of permafrost zones, high efficiency displacements of the water base fluids are required. Clearly, in these latter situations a more accurate description of the displacement process is necessary, and such descriptions must influence the selection of the mud and cement properties to be used. properties to be used. In the present paper, we cannot consider all of the questions just raised. Instead, we focus on those aspects relating to the dependence of laminar flow displacement efficiency on the densities and rheological properties and the displacement rates. The fluids are considered to be non-Newtonian, and the displacement zone is taken as the narrow gap annuli between concentric cylinders, or equivalently, the region between two parallel plates. The approach is analytical and similar to that used previously by Flumerfelt; however, the rheological descriptions are more complete.