Thesis (M.Sc. (Applied Mathematics)) --University of Limpopo, 2007 / The thermodynamic irreversibility in any fluid flow process can be quantified through entropy analysis. The first law of thermodynamics is simply an expression of the conservation of energy principle. The second law of thermodynamics states that all real processes are irreversible. Entropy generation is a measure of the account of irreversibility associated with the real processes. As entropy generation takes place, the quality of energy (i.e. exergy) decreases. In order to preserve the quality of energy in a fluid flow process or at least to reduce the entropy generation, it is important to study the distribution of the entropy generation within the fluid volume. In this dissertation, the inherent irreversibility in the flow of a variable viscosity fluid in both a closed channel and an open channel is investigated. The channel is assumed to be narrow, so that the lubrication approximation may be applied and the fluid viscosity is assumed to vary linearly with temperature. Both the lower and the upper surfaces of the channel are maintained at different temperature. The simplified form of governing equations is obtained and solved analytically using a perturbation technique. Expressions for fluid velocity and temperature are derived which essentially expedite to obtain expressions for volumetric entropy generation numbers, irreversibility distribution ratio and the Bejan number in the flow field. In chapter 1, a historic background of the study is highlighted. Both closed and open channels problem are investigated in chapters 2 and 3. In chapter 4, generally discussion on the overall results obtained from the investigation is displayed together with possible areas of future research work.

Heavy oil production has drawn more and more attention in petroleum industry. The amount of heavy oil in the world is twice more than the conventional oil (low viscosity), which has been consumed rapidly from the past. The understanding of flow patterns and pressure losses in multiphase flow with high viscosity oil are vital to assist the design of transportation pipeline. This thesis involves experimental investigation of two phase and three phase flows under high oil viscosity conditions (up to 17000cP) in horizontal pipelines. The multiphase (oil/water/solid/gas) facility was designed and constructed at Cranfield University and consists of 6m long horizontal pipeline of 0.026m diameter along with instrumentations. The principal objectives of the work were to study the effect of viscosity, water cut, temperature variance, and flow conditions on flow patterns and pressure drops for (oil/gas and oil/water) two phase flows; to compare the measured flow parameters and phase distribution with those predicted from models found in the literature for two phase flows; and to conduct an experimental study of gas injection effect on pressure gradient in (oil/water/gas) three phase flow. Due to the nature of heavy oil reservoirs, sand is associated with oil/water mixture when extracted; therefore sand concentration effect on pressure drop in (oil/water/sand) three phase flow is also examined. For oil-air flow, a smooth oil coating was observed in the film region of slug flow, while a ripple structure of oil coating film was found at higher superficial air velocity for slug flow regime and annular flow regime. The ripple structure was believed to increase the effective roughness of the pipe wall, which resulted in higher pressure gradients. The pressure drop correlations from Beggs and Brill (1973) and Dukler et al. (1964) were used to compare with experimental pressure gradients for oil/air flow. It was found that these correlations failed to predict the pressure gradients for heavy oil/air flows in this work. Several new heavy oil/water flow patterns were named and categorized based on observations. Though the heavy oil viscosity is an essential parameter for oil continuous phase flow on pressure drop, it had no significant effect beyond Water Assist Flow (WAF) condition, as a threshold was found for water cut with fixed superficial oil velocity. The transition criterion by McKibben et al. (2000b) for WAF was found to be able to predict this threshold reasonably well. Core Annular Flow (CAF) models were found to greatly under predict the pressure gradients mainly due to the coating (oil fouling) effect associated with this study. A new coating coefficient was introduced to models presented by Bannwart (2001) and Rodriguez et al (2009). The addition of solid in the mixed flow led to minor increase in the pressure gradient when the particles were moving with the flow. However, higher sand concentration in the system led to higher pressure gradient values. The addition of gaseous phase to the oil/water flow was more complex. The gaseous injection was beneficial toward reducing the pressure gradient when introduced in oil continuous phase only at very low water cuts.