**IMPLICATION OF VOID PREDICTION IN THE DETERMINATION OF PRESSURE GRADIENT IN VERTICAL PIPES**

**ABSTRACT**

This research work mainly investigates the implication of void prediction in the estimation of total pressure gradient in vertical pipes for multiphase flow systems. Experimental data was collected for a multiphase flow system with silicone oil and air as the liquid and gas phases. The void fraction prediction was carried out using Microsoft Excel. Ten correlations were used for void estimation in chronological order to include statistical analysis of correlation performance. Nicklin et al. (1962) drift flux correlation gives the best void fraction for bubble flow. The prediction from this correlation shows a fairly constant average absolute error of about 20.98% for low gas rate flow (bubble). Greskovich and Cooper (1975) give the best prediction for void fraction in slug flow regime with about 4.84% average absolute error in void fraction prediction. Hassan and Kabir (1989), show progressively higher accuracy and stability in the direction of increasing gas rate with an average absolute error of 6.99% in the churn flow regime. Hence a good correlation for transitional flow region. Pressure gradient prediction was carried out using two separate approaches: the Homogeneous model and the Duns and Ros model (1963).The statistical parameters used in this study are percentage absolute average error, average absolute and relative error. The parameters calculated were compared to determine the performance of the different correlations evaluated. The realization of this work was used to develop a quality assurance flow scheme for vertical sections.

**CHAPTER ONE**

**INTRODUCTION**

**1.1 Background**

Any fluid flow with more than one phase or flow species is termed ‘multiphase flow’. Most real life flow streams are multiphase. Common examples are hydrocarbon movement either from the reservoir to the wellbore or in transportation lines, blood flow streams in living organisms, nuclear fluids in nuclear reactors, etc. Multiphase systems may be two-phase, three-phase or more in no particular combination of the states of matter (i.e. liquid-liquid such as in oil droplets in water, solid-liquid such as in suspensions or gas-liquid-water found in common hydrocarbon traps). Multiphase flow is characterized by the simultaneous flow of the components of the flow stream. Therefore the parameter to be accounted for in any multiphase system design includes, the volumetric flow rate (total and phase) [m3/s] , the mass flow rate [kg/s], the mass flux [kg/m2], phase fraction, distribution term, flow velocities [m/s], slip values, drift factor and variations of fluid properties as a result of changes in flow stream (flow patterns).

The summation of the volumetric fraction of all the species in any multiphase stream is unity and each phase moves with a superficial velocity as a result of interference by the other phase(s). The mixture velocity is obtained as the algebraic sum of the superficial velocities of all the species. A common subject of interest by investigators in the field of multiphase streams are the flow regimes: prediction, identification, and marching, liquid holdup (or void fraction), convective heat transfers (due to mixing effects), pressure drop prediction and estimation, waxing and hydrate formation. One of the most challenging factors in a multiphase investigation or monitoring is the high tendency for flow stream modifications (i.e. changes in flow regimes), this is because each of the flow patterns has its unique impact on the flow parameters. The flow pattern is also very sensitivity to flow line orientation. Another important factor that affects the flow regime is the fluid characteristics of the two phases. Most works in literature are reported for air-water flow map, kerosene-air flow map, air-glycerin, and air-oil flow map.

**1.1.1 Bubble flow**

This type of flow pattern is characterized by a small free-gas phase with the pipe almost completely filled with the liquid phase. Hence a liquid dominated flow. The gas phase is randomly distributed as small bubbles with varying diameters. The individual gas bubble moves with unique velocities as a function of its diameter8. In a riser, the liquid moves up the pipe at a fairly uniform velocity and, except for its density, the gas phase has little effect on the pressure-gradient.