Summary
The objective of this paper is to revisit currently used techniques for analyzing reservoir performance and characterizing the horizontal-well productivity index (PI) in finite-acting oil and gas reservoirs. This paper introduces a new practical and integrated approach for determining the starting time of pseudosteady-state flow and constant-behavior PI. The new approach focuses on the fact that the derivative of PI vanishes to zero when pseudosteady-state flow is developed. At this point, the derivative of transient-state pressure drop and that of pseudosteady-state pressure drop become mathematically identical. This point indicates the starting time of pseudosteady-state flow as well as the constant value of pseudosteady-state PI. The reservoirs of interest in this study are homogeneous and heterogamous, single and dual porous media, undergoing Darcy and non-Darcy flow in the drainage area, and finite-acting, depleted by horizontal wells. The flow in these reservoirs is either single-phase oil flow or single-phase gas flow.
Several analytical models are used in this study for describing pressure and pressure-derivative behavior considering different reservoir configurations and wellbore types. These models are developed for heterogeneous and homogeneous formations consisting of single and dual porous media (naturally fractured reservoirs) and experiencing Darcy and non-Darcy flow. Two pressure terms are assembled in these models; the first pressure term represents the time-dependent pressure drop caused by transient-state flow, and the second pressure term represents time-invariant pressure drop controlled by the reservoir boundary. Transient-state PI and pseudosteady-state PI are calculated using the difference between these two pressures assuming constant wellbore flow rate. The analytical models for the pressure derivatives of these two pressure terms are generated. Using the concept that the derivative of constant PI converges to zero, these two pressure derivatives become mathematically equal at a certain production time. This point indicates the starting time of pseudosteady-state flow and the constant behavior of PI.
The outcomes of this study are summarized as the following:
Understanding pressure, pressure derivative, and PI behavior of bounded reservoirs drained by horizontal wells during transient- and pseudosteady-state production Investigating the effects of different reservoir configurations, wellbore lengths, reservoir homogeneity or heterogeneity, reservoirs as single or dual porous media, and flow pattern in porous media whether it has undergone Darcy or non-Darcy flow Applying the concept of the PI derivative to determine the starting time of pseudosteady-state stabilized PI
The novel points in this study are the following:
The derivative of the PI can be used to precisely indicate the starting time of pseudosteady-state flow and the constant behavior of PI. The starting time of pseudosteady-state flow determined by the convergence of transient- and pseudosteady-state pressure derivative or by the PI curve is always less than that determined from the curves of total pressure drop and its derivative. Non-Darcy flow may significantly affect the transient-state PI, but pseudosteady-state PI is slightly affected by non-Darcy flow. The starting time of pseudosteady-state flow is not influenced by non-Darcy flow. The convergence of transient- and pseudosteady-state pressure derivatives is affected by reservoir configurations, wellbore lengths, and porous-media characteristics.
A Treatise on Non-Darcy Flow Correlations in Porous Media
