In the oil industry, there are many different tertiary EOR methods; however, polymer flooding is the leading chemical EOR methods used in clastic reservoirs. Polymers are long-chain molecules composed of many repeated subunits with high molecular weight. When added to water, they increase the viscosity of the water and enhance the sweep efficiency, so theoretically more oil would be pushed out and recovered from the reservoir compared to injecting water solely. This thesis investigates an ineffective nine-month's pilot-polymer injection test in the HRD sandstone reservoir (Karim Small Fields' Cluster, Sultanate of Oman). A three dimensional simulator (CMG) has been utilized to create a hydraulic fracturing model and run a sensitivity analysis, history matching, and optimization for the nine months period. Streamlines simulations have also been performed to verify the hydraulic fracturing model and the flow directions. The results have given a clear illustration of the flood behavior and direction within the pattern A-53 for both cases. The sensitivity analysis has shown that the starting polymer concentration and the hydraulic fracturing parameters are the most dominating parameters that are controlling the performance of the polymer injection at the A-field, pattern A-53. The history-matching exercise has been carried out with the aid of the sensitivity results to history match the oil rate, water rate, liquid rate, and cumulative oil for the wells of pattern A-53. Eventually, the Pareto Front Particle Swarm Optimization technique has been adopted to recommend a feasible polymer injection design that can be successfully carried out with the maximum possible cumulative oil and Net Present Value. The concept of polymer slug grading was employed to control the flood front and prevent the rapid polymer breakthrough caused by the propped fractures. The study has revealed that the optimized polymer injection would have increased the NPV by 430k USD; nevertheless, it yielded an insignificant increase in the cumulative oil.