Journal of Mathematics Research; Vol. 10, No. 5; October 2018 ISSN 1916-9795 E-ISSN 1916-9809 Published by Canadian Center of Science and Education 19 Simulation of the Effect of Oil Volume Fractions in an Oil-Water Flows Along a Circular Pipe: A Finite Element Approach Ferdusee Akter 1 , Md. Moniruzzaman Bhuyan 2 , Ujjwal Kumar Deb 3 1 Department of Physical and Mathematical Sciences, Chittagong Veterinary and Animal Sciences University, Bangladesh 2 Department of Electrical & Electronic Engineering, Southern University Bangladesh 3 Department of Mathematics, Chittagong University of Engineering & Technology, Bangladesh Correspondence: Ferdusee Akter, Department of Physical and Mathematical Sciences, Chittagong Veterinary and Animal Sciences University, Bangladesh. E-mail: ferdusee2008@gmail.com Received: May 28, 2018 Accepted: June 13, 2018 Online Published: July 9, 2018 doi:10.5539/jmr.v10n5p19 URL: https://doi.org/10.5539/jmr.v10n5p19 Abstract Two phase flows in pipelines are very common in industries for the oil transportations. The aim of our work is to observe the effect of oil volume fraction in the oil in water two phase flows. The study has been accomplished using a computational model which is based on a Finite Element Method (FEM) named Galerkin approximation. The velocity profiles and volume fractions are performed by numerical simulations and we have considered the COMSOL Multiphysics Software version 4.2a for our simulation. The computational domain is 8m in length and 0.05m in radius. The results show that the velocity of the mixture decreases as the oil volume fraction increases. It should be noted that if we gradually increase the volume fractions of oil, the fluid velocity also changes and the saturated level of the volume fraction is 22.3%. Keywords: two phase flow, volume fraction, FEM, CFD simulation 1. Introduction The oil-water two phase flows are very important phenomena for basic research and have many applications in the various field of process industries especially in the petroleum industries. Two phase flow is an extension of single phase flow and more difficult because of the complex behaviour (Drew, 1983). Pipelines are one of the cheapest and efficient way of transportation of fluids. Water is often used for transportation of fluids because it is cheap and relatively safe. Besides, water has a significant effect during the transportation of oil (Alias et al., 2015). The Oiler might be economical to operate with water volume fraction in the liquid phase as high as 90% (Xu, 2007). Many extensive researches on oil-water flows in pipes have been performed theoretically and experimentally till today. A method provided by the Electrical Resistance Tomography (ERT) system has been used for measuring the oil in water pipe flow where the volume fraction of oil is upto 23.1%. It was observed that the ERT method can be used to perform the low fraction oil-water flows. If the oil volume fraction is so high, large oil bubbles or slugs begin to form and also some electrodes lose contact with water (Hua et al., 2005). The velocity profiles and pressure distribution of oil was performed in the presence of gas and it was noted that an increase in the gas volume fraction reduces the pressure drop. However, a discrepant behaviour was found when the gas volume fraction is more than 25% (Silva & Marinho, 2014). In 2009, Yaqob and Abbas experimented the performance of a pump by using crude oil-water two phase flow in a centrifugal pump and found that pump head and discharge of two phase flow decreased as oil volume fraction increased. Moreover, the power of the pump increased with the increase of oil volume fraction. A simulation study for viscosity is explained that the viscosity of oil affected the pressure drop and oil volume fraction on a two phase oil-gas flow and found the pressure drop increased as oil viscosity increased. Moreover, Gas phase accumulates at the pipe outlet and decreased the liquid volume fraction along the pipe length (Silva & Marinho, 2016). From a series experiment of volume fractions shown that the velocity of the oil droplet was power law in shape in a vertical oil-water bubbly flows with the maximum velocity at the center of the pipe and the velocity decreasing to zero at the pipe wall. The oil volume fraction distribution is of power law shape if the mean oil volume fraction is less than 8%, essentially flat for 8% to 15% and intermediate peak shape for greater than 15%. The hydrodynamic force is relatively strong for mean oil volume fraction less than 8% and its direction is in the center of the pipe (Lucas & Panagiotopoulos, 2009).