An Evaluation of the Robertson-Stiff Model Describing Rheological Properties of Drilling Fluids and Cement Slurries

Abstract

Abstract This paper evaluates the Robertson-Stiff rheological model for cement slurries and drilling muds. The model is compared with the Herschel-Bulkley model and is found to be an improved model for cement slurries. The Robertson-Stiff equations for volumetric flow rates in narrow annuli and tubes are shown to be limited to fluids with no yield stress. This paper develops more general equations that include the Robertson-Stiff results as special cases. Introduction In a recent paper, Robertson and Stiff presented a new model for describing the rheological behavior of drilling fluids and cement slurries. The principal advantages claimed for this model areit provides better fits of rheological data than other three-constant viscous models, andit gives explicit relations for the velocity fields, wall shear rates, and flow-rate/pressure-drop relations for flow in tubes and annuli. The latter advantage is not possible with comparable models such as the possible with comparable models such as the Herschel-Bulkley model. In this paper we provide an independent evaluation of the model with regard to these characteristics. First, we checked the accuracy of the model in fitting cement-slurry data and found that it does provide a good match to the experimental data. Fig. provide a good match to the experimental data. Fig. 1 shows the experimental data for a cement slurry along with fitting curves for the Robertson-Stiff and Herschel-Bulkley models. It can be seen that the Robertson-Stiff model is somewhat superior to the Herschel-Bulkley model in representing the data. This is also true in Fig. 2, which represents results for a different cement slurry of higher yield. Here again, the performance of the Robertson-Stiff model is somewhat better. Based on these observations, as well as others not presented here, we agree with the authors that their model is an improved model for cement slurries. With regard to the claim that the model provides explicit relations for the wall shear rate and pressure-drop/flow-rate relation, we have found pressure-drop/flow-rate relation, we have found certain errors in the Robertson-Stiff analysis that invalidate this claim and make their final equations applicable only in certain special cases. The basic error in their paper is that Robertson and Stiff overlooked the existence of a plug flow region in the center of the pipe or narrow annulus. Because of this, the equations derived are strictly valid only for the case of fluids with zero yield stress. Since most drilling fluids and cement slurries show some finite yield stress, the equations provided by Robertson and Stiff are of limited provided by Robertson and Stiff are of limited application. In the remainder of this paper we derive the correct relations for the model; the Robertson-Stiff relations appear as special cases. SPEJ P. 97