Production Systems Analysis of Vertically Fractured Wells

Abstract

A systematic approach is presented for generating transient inflow performance relationship curves for finite conductivity vertically fractured wells. A semi-analytical model was developed to simulate dimensionless wellbore pressure drop and dimensionless pressure loss through the fracture vs. dimensionless time at constant-rate of production for wells intercepted by a finite-conductivity vertical fracture. Flowing bottom hole pressure can be predicted at any time period using these dimensionless variables. System average pressure at any stage of production can be obtained through material balance calculations. A straight line reference curve was observed at all times provided that the real gas pseudo-pressure function is used to plot m(pwf(t))/m(p¯R(t)) vs. qg(t)/qgmax (t). The advantage of normalizing the dimensionless variable in termas of pseudo-pressure function is that only one straight line relationship is obtained throughout the entire production life of the reservoir. This provides a more simple means for performance prediction purposes. The major contribution of this paper is the provision of a valuable tocl to study the sensitivity of fracture design parameters on ultimate well performance. The economic benefits of this approach can be substantial.

Nodal Analysis for Unconventional Reservoirs—Principles and Application

“…Outflow simulation, as usual, is performed with a steady-state pipeline simulator with flow correlations. In this paper, outflow curves are simulated with Hagedorn and Brown (1965) correlation for vertical flow, Beggs and Brill (1973) revised correlation for horizontal flow, and Moody (1947) for single-phase flow. For a given WHP, it gives a relationship between production rate q and BHP p wf .…”

Prediction of Future Well Performance, Including Reservoir Depletion Effects

“…1, the magnitude of the dIfferences between the reciprocal of the rate transient solution and the pressure transient solution for low dimensionless conductivity fractures is smaller than the differences exhibited by high dimensionless conductivity fractures. Therefore, the analysis technique proposed by Meng et al 6 should only be considered as an approximate analysis technique for estimating the inflow performance of wells intersected by low dimensionless conductivity fractures in high-permeability reservoirs during the infiniteacting flow regime.…”

“…qg seT qi qOi = - (6) qn For the Dirichlet inner boundary condition solutions (constant sandface and wellhead pressure production cases), the definition of the dimensionless well rate is given by Eq. 7, and the dimensionless pressures of each of the discrete steps in a multipressure production history are defined as in Eq.…”

“…This fact can be analytically proved with the pres~ure and rate transient solutions for fully boundarydominated flow for vertical, vertically fractured· and horizontal wells. 6 reported an analysis technique for predicting the transient behavior of wells intersected by finite conductivity fractures using Neumann inner boundary condition type curve solutions. The analysis technique reported by Meng, et aL 6 suffers from two limitations.…”

“…6 reported an analysis technique for predicting the transient behavior of wells intersected by finite conductivity fractures using Neumann inner boundary condition type curve solutions. The analysis technique reported by Meng, et aL 6 suffers from two limitations. The first of these limitations pertains to that just described above concerning the evaluation of the Dirichlet inner boundary condition solution behavior of finite conductivity fractures from the Neumann inner boundary condition solution, including the boundary-dominated flow behavior.…”