Reservoir Limit Testing For Fractured Wells

Abstract

ABSTRACT The purpose of the paper is to extend reservoir limit test analysis techniques to fractured wells. By deriving the pseudo-steady state pressure functions for an unfractured and a fractured well at any position of a closed rectangle, it is shown that shape factors for fractured wells are not readily obtainable from the ones for unfractured wells. Exact analytical expressions of shape factors for fractured and unfractured wells in a closed rectangle are presented, along with graphs of these quantities versus appropriate parameters. Type curves for a fractured well at the center of a closed rectangle are also provided. Both uniform flux and infinite conductivity fractures are considered. The curves presented in this paper are then used with actual field data for estimating the drainage volume of a fractured well and the shape of the well drainage area. INTRODUCTION Reservoir limit tests, introduced by Jones1, are commonly used for evaluating the reservoir volume communicating with the well. The analysis is based on the fact that the well pressure during pseudo-steady state flow is a linear function of the production time:Equation 1 whereEquation 2 andEquation 3 A represents the drainage area (in sq.ft) and CA the drainage area shape factor. Eq. 1 may also written in dimensionless form as:Equation 4 withEquation 5 andEquation 6 A cartesian plot of bottom-hole flowing pressure versus production time will thus yield a straight line after pseudo-steady state conditions are reached. The slope of the straight line (Eq.2) may be used to estimate the connected reservoir drainage volume:Equation 7 and the drainage area, if Ï?h is known. The shape of the drainage area may be estimated from the pseudo-steady state cartesian plot if pressure data are also available from an infinite acting flow period2. These are used to determine the semi-log straight line slope:Equation 8 and p1hr. The system shape factor is then obtained from:Equation 9 By comparing the calculated CA with the ones published in the literature for various drainage area configuration3–5, it is possible to estimate the shape of the drainage area.