Reservoir deliverability can be mathematically modeled onthe basis of flow regimes such as transient flow, steadystate flow, and pseudosteady state flow. An analyticalrelation between bottom-hole pressure and productionrate can be formulated for a given flow regime. Therelation is called inflow performance relationship(IPR). This chapter addresses the procedures used forestablishing IPR of different types of reservoirs and wellconfigurations3.2.2 Steady-State FlowSteady-state flow is defined as a flow regime where thepressure at any point in the reservoir remains constantover time. This flow condition prevails when the pressurefunnel shown in Fig. 3.1 has propagated to a constantpressureboundary. The constant-pressure boundary canbe an aquifer or a water injection well. A sketch of thereservoir model is shown in Fig. 3.2, where pe representsthe pressure at the constant-pressure boundary. Assumingsingle-phase flow, the following theoretical relation can bederived from Darcys law for an oil reservoir under thesteady-state flow condition due to a circular constantpressureboundary at distance re from wellbore: