Productivity-Index Behavior for Hydraulically Fractured Reservoirs Depleted by Constant Production Rate Considering Transient-State and Semisteady-State Conditions

This paper introduces a new approach for studying productivity-index (PI) behavior of fractured oil and gas reservoirs during transientand pseudosteady-state conditions. This approach focuses on the fact that PI derivative could vanish at a certain production time, indicating the beginning of pseudosteady state, wherein the PI demonstrates constant value. The reservoirs in this study are considered depleted by horizontal wells intersecting multiple hydraulic fractures where Darcy flow and non-Darcy flow may control flow patterns in the porous media. The PI is calculated assuming constant production rate and considering pressure profile for early- and intermediate-production time when transient condition dominates fluid flow and late-production time when pseudosteady state is reached. The outcomes of this study can be summarized as understanding PI behavior at early- and intermediate-production time when transient flow is dominant in the porous media and late-production time when pseudosteady-state condition is reached; indicating the effect of reservoir configuration on PI and the time when this index approaches constant value; and introducing a study for the influence of non-Darcy flow in the PI. The most-interesting points in this study are the following. First, that PI reaches constant value when the rates of change with time for the two pressure drops transient and pseudosteady state are equal. Second, the time for approaching constant PI in a small drainage area is faster than for a large area. Third, that PI is affected by non-Darcy flow at early- and intermediate-production time; however, the effect is not seen at late-production time. Last, that PI could exhibit constant behavior for severe non-Darcy flow at early- and intermediate-production times even though transient-state condition dominates fluid flow in the porous media.