Displacement Mechanics in Primary Cementing
Authors: McLean R.H. , Manry C.W. , Whitaker W.W. 
Published: December 2007

Abstract
In an eccentric annulus, cement may favor the widest side and bypass slower-moving mud in the narrowest side. Tendency of the cement to bypass mud is a function of the geometry of the annulus, the density and flow properties of the mud and cement and the rate of flow. Bypassing can be prevented if the pressure gradient produced from circulation of the cement and buoyant forces exceeds the pressure gradient necessary to drive the mud through the narrowest side of the annulus at the same velocity as the cement. In the absence of buoyant forces, one requirement for this balance is maintenance of the yield strength of the cement greater than the yield strength of the mud multiplied by the maximum distance from the casing to the wall of the borehole and divided by the minimum distance. If the yield strength of the cement is below this value, bypassing of mud cannot be prevented unless buoyant forces or motion of the caving significantly aid the displacement.

Introduction
Successful primary cementing leaves no continuous channels of mud capable of flow during well treatment and production. Prevention of channels requires care. Teplitz and Hassebroek provide evidence of channels of mud after primary cementing in the field. Channeling of cement through mud in laboratory experiments has also been reported. Recommendations for improving the displacement of mud includecentralizing the casing in the borehole,attaching centralizers and scratchers to the casing and moving it during displacement,thinning the mud,isolating the cement by plugs while it is circulated down the casing,establishing turbulence in the cement, andholding the cement slurry at least 2 lb /gal heavier than the mud and circulating the cement slurry at a very low rate of flow.
Although much has been written about the above parameters, the relative importance of each has not been well defined. In this investigation, the mechanics of mud displacement are described through results from analytical models and experiments. The model chosen-a single string of casing eccentric in a round, smooth-walled, impermeable borehole-is analagous to casing centralized in a borehole which is not round and to placing more than one string of casing in a borehole. In each, some paths for flow are more restricted than others. A fluid flowing in the borehole may seek the least restricted, or most open, path. This tendency for uneven flow can lead to channeling of cement through mud unless preventive measures are taken. The analytical models describe channeling and give means of balancing the flow. Experimental data test the analytical models and illustrate effects of motion of the casing, differences in density and mud's tendency to gel. Results are encouraging. Piston-like displacement of mud by an equal density cement slurry is possible through proper balance of the flow properties of the mud and cement slurries to the eccentricity of the annulus. The more eccentric the annulus, the thicker must be the cement relative to the mud. If proper balance is not achieved, bypassing of mud by cement cannot be prevented without assistance from motion of the casing or buoyant forces. Increasing the rate of flow can help to start all mud flowing but cannot prevent channeling of cement through slower moving mud in an eccentric annulus. Thinning the cement slurry tends to increase channeling although the extent of turbulence in the annulus may be increased. Description of flow in an eccentric annulus begins in the next section. It is assumed thatthe casing is eccentric and is stationary,the mud and cement slurries have the same density andthe gel structure of the mud has been broken and the mud and cement follow the Bingham flow model. Effects related to these restrictions will be discussed.

FLOW PATTERNS
SINGLE FLUID IN ANNULUSFlow of a single fluid through an eccentric annulus is illustrated in Fig. 1. Part A shows laminar flow of a Newtonian fluid. This distribution of flow was calculated by Piercy, Hooper and Winney. In fully developed turbulent flow, the velocity distribution around the annulus is less distorted, but the flow still favors the widest part of the annulus. Parts B, C and D of Fig. 1 are a qualitative representation of the flow of a Bingham fluid. The yield strength of the fluid increases the severity of bypassing compared to Newtonian flow. At a very low rate of flow, all flow is confined to that portion of the annulus which has the minimum perimeter-to-area ratio, The fluid shears on the perimeter of that area when the pressure gradient multiplied by the area just exceeds the yield stress of the fluid multiplied by the perimeter. Whether or not the minimum perimeter-to-area region encompasses all of the annulus or only a part (as shown in Part B) depends on the geometry of the annulus. If only a part begins to flow, increasing the rate of flow increases the area flowing until finally there is flow throughout the annulus.
JPT
P. 251ˆ