DST Analysis With Pressure Dependent Rock And Fluid Properties
Authors: Stright Daniel H. 
Published: December 2007

Abstract
Analytical techniques are developed to provide reservoir parameters that can be used to estimate reserves for a fractured reservoir in which quantitative log analysis is not possible. Porosity and fracture volume compressibility are derived from estimates of permeability and apparent fracture healing pressure. permeability and apparent fracture healing pressure. Numerical modeling, type curve and semilog analysis techniques are all used to interpret drill stem test data to supply best estimates of the necessary parameters. A pressure-dependent diffusivity was included parameters. A pressure-dependent diffusivity was included in the numerical model to describe fracture deformation which may occur during drill stem tests.
Results of the study indicate that fracture deformation caused by changes in net confining pressure may be an important mechanism in some fractured reservoirs, particularly ones in which the matrix contribution is particularly ones in which the matrix contribution is negligible and the reservoir fluid compressibility is small.

Introduction
The Trap Spring Field, located in east-central Nevada (Figure 1), was discovered in November, 1976. Production is from a fractured, welded volcanic tuff Production is from a fractured, welded volcanic tuff or ignimbrite. Essentially all the oil is contained in fractures created by cooling joints which, in some cases, may have been altered by tectonic faulting. The effective matrix porosity is negligible.
The oil at reservoir conditions contains no solution gas. Oil viscosity is about 80 cp (.08 Pas) at stock tank conditions but increases to 120 cp (0.12 Pas) at initial reservoir conditions. The large increase results because of a zero bubble point pressure and relatively low reservoir temperature pressure and relatively low reservoir temperature (43 degrees C). Other reservoir data are shown on Table 1.
Well logs and cores, the usual source of reservoir information, are not very helpful in Trap Spring. Experience at the AEC Nevada Test Site has shown that quantitative log interpretation in the volcanics sequence is not possible. Cores do not provide much quantitative information about in situ fracture porosity. At this time, the borehole televiewer log porosity. At this time, the borehole televiewer log appears to be the best device for identifying fractured intervals; however, the resolution of this log is not adequate to calculate porosities for small fracture widths.
The problem, then, was to make reserve estimates early in the life of the Trap Spring Field without quantitative information usually available from borehole logs and cores. The approach used in this study was to make use of extensive drill stem test data and limited performance data to arrive at estimates of oil-in-place and recoverable oil.
Early material balance calculations, using conventional formation compressibility, gave unrealistically high estimates of oil-in-place. Review of the geohydrology literature reveals that fracture volume compressibilities may be much larger than intergranular pore volume compressibility. A numerical model with pressure dependent diffusivity was formulated to investigate the problem and to assist in arriving at reservoir parameters which could be used in estimating fracture porosity and future performance for the Trap Spring Field. performance for the Trap Spring Field.

NUMERICAL MODEL
Drill stem tests are the primary source of data for the Trap Spring Field. History matching this test data is one way to estimate reservoir parameters. A numerical model was formulated to simulate drill stem tests. A pressure transformation similar to real gas pseudopressure was incorporated into the model to allow for pressure dependent rock and fluid properties. The following equation proposed by Raghavan, properties. The following equation proposed by Raghavan, et al, was chosen as the basis for the model:
(1)
where:
(2)