A fully implicit, three-dimensional simulator with local grid refinement around the wellbore is developed to solve reservoir and horizontal well flow equations simultaneously, for single-phase liquid and gas cases. The model consists of conservation of mass and Darcy's law in the reservoir and mass and momentum conservation in the wellbore for isothermal conditions. Establishing the continuity of pressure and preserving mass balance at the sandface satisfy the coupling requirements. The proposed simulator is tested against and verified with the results obtained from a commercial code ECLIPSE-100(TM), and available public domain simulators and semi-analytical models. The proposed model can be used for multiple purposes such as well productivity prediction, transient analyses, well length optimization, completion design and optimization, and production logging interpretation. Different completion scenarios and reservoir anisotropy are simulated and their effects on the productivity of the horizontal wells are discussed. Completion cases include open-hole and partial completions. During the production logging of a horizontal well, the coil tubing reduces the wellbore cross sectional area and may cause substantial changes in the wellbore flow behavior. Depending on the well and coil tubing diameters, a significant difference between the actual production rates and the rates obtained from a production log can be observed.