Modelling the flow of drilling muds requires the use of existing generic time-independent models with a number of parameters incorporated. While these parameters quantify the uncertainties surrounding the mud rheology, the tuning of each parameter for proper flow description can be challenging and time consuming. As such, the introduction of new parameters in describing additional reservoir conditions associated with drilling muds would only increase the complexity of the computational process. Therefore, the predictive capability of applied rheological models for the different flow regimes and reservoir conditions associated with drilling muds is still limited in scope. Existing procedure using generic rheological models would give a generalized approach to computing the performance of drilling muds when taking into account new factors such as temperature and electrolyte effects. Therefore, there is need to accurately model the rheology of drilling muds taking into account new conditions without necessarily introducing new fitting parameters to a particular model. In this work, a novel approach was employed where the time constant of the modified Vipulanandan model was related to reservoir conditions without introducing a new fitting constants or parameters. The selection of the Vipulanandan model among others was based on the conditions stated by Vipulanandan and Mohammed (2014) and the use of statistical validation tools based on best fit. Moreover, the Vipulanandan model represents the only model which can be modified to have a time constant in it. (C) 2019 The Society of Powder Technology Japan. Published by Elsevier B.V. and The Society of Powder Technology Japan. All rights reserved.