Determining the Average Reservoir Pressure from Vertical and Horizontal Well Test Analysis Using the Tiab's Direct Synthesis Technique

Abstract

Abstract Tiab's Direct Synthesis (TDS) technique is a direct method to interpret transient well pressure tests without type curve matching. This method uses log-log plots of the pressure and pressure derivative versus time to compute reservoir parameters such as permeability, wellbore storage, skin factor, half fracture length, drainage area, distance to the boundaries, storage coefficient and interporosity flow parameter among others. The TDS technique gives accurate results because it uses exact analytical solutions to compute the reservoir parameters. During the last three decades there has not been a significant advance in well test analysis to determine the average reservoir pressure, and only conventional semilog analysis has been used. As a new concept, this paper extends the TDS technique, which primarily uses the pressure derivative function, to determine the average reservoir pressure for three cases: vertical well in closed homogeneous reservoir, hydraulically fractured vertical well, and horizontal well in a closed anisotropic reservoir. As result, new analytical equations to determine the average reservoir pressure from the pseudosteady state flow regime have been developed. A new flow regime for horizontal wells has been observed and is referred to here as the elliptical or biradial flow regime. This flow regime has been numerically modeled and incorporated to the TDS technique. Its corresponding characteristic straight line in the pressure derivative plot has a slope of 0.36. It is observed only when the horizontal well penetration, i.e. the ratio of the well length (Lw) to the reservoir width (hz) or Lw/hz, is between 0.10 and 0.70. The elliptical flow regime is very useful to compute the geometric average horizontal permeability or the effective horizontal penetration length, when the pseudoradial flow regime (also called late radial) is not well defined or the test was not run long enough to observe it in the pressure derivative plot. Procedures to determine the reservoir properties and the average reservoir pressure for each case are presented in detail for field and simulated examples. Introduction This paper presents new methods, based on the TDS technique, for determining the average reservoir pressure from pressure buildup tests for several oil systems:a vertical well in a closed homogeneous reservoir,a vertical hydraulically fractured well in a closed reservoir, anda horizontal well in a closed homogeneous reservoir. The details of these new methods are explained, including equations and the procedures involved in obtaining the values of reservoir parameters. In 1993 Tiab1 introduces the TDS technique to determine permeability, skin and wellbore storage from pressure transient test analysis in a vertical well in an infinite homogeneous reservoir. In 1994 Tiab2 extended the technique to vertically fractured wells to compute permeability, skin, wellbore storage, half-fracture length and drainage area; and later on in 1996 Tiab and Engler3 extended it to horizontal wells in anisotropic media4 to compute permeability in the three main directions and/or effective horizontal well length of the well. In 2003 Djebrouni4 extended the TDS technique to compute the average reservoir pressure for two common systems:a vertical well in a homogeneous closed reservoir anda vertically fractured well in a homogeneous closed reservoir. That same year Chacon5 extended the technique for determining the average reservoir pressure from horizontal well testing in a closed anisotropic system.