There is more than half of the original oil of the reservoir which is entrapped and immobile after orthodox recovery methods (primary and secondary recovery methods). Enhanced Oil Recovery (EOR) is essential to further extract the unrecovered residual oils. There are many EOR methods available to improve oil production by injecting fluids into the reservoir. In this thesis, the EOR method used is chemical injection and the specific chemical used is surfactant. Surfactant flooding utilises surface active agents (or surfactants) to adsorb onto oil-water interface and reduce their interfacial tension (IFT) to an ultralow value of 10-2 mN/m and below. Due to the low IFT, oil is readier to be mobilised and its relative permeability with water is increased and this in turn alters the wettability of the reservoir to become more water-wet.Henceforth, more residual oil can be displaced yielding a greater oil recovery. The reservoir used in this research is an oil field located in Libya. A numerical approach simulation is done on this field using STARS which is a software package by Computer Modelling Group (CMG). From the simulations executed, primary recovery is done from 1987 till 1995 using natural depletion as the reservoir has a strong water drive. Water flooding method is simulated as the secondary recovery method from year 1995. The optimum results are obtained when water is flooded at a rate of 3000 bbl/day and for 5 years till year 2000. From year 2000 onwards, the reservoir undergoes surfactant flooding. Sensitivity analyses are done for different surfactant concentrations, flow rates and flooding periods. From the results, surfactant is flooded for 6 years (2000- 2006) with a flow rate of 3000 bbl/day and concentration of 0.8 % weight. It is proven that with optimum surfactant flooding conditions, an extra of 167,167 barrels of oil is recovered.