Semilog Analysis of the Pulse-Decay Technique of Permeability Measurement

Abstract

Semilog Analysis of the Pulse-Decay Technique Pulse-Decay Technique of Permeability Measurement Abstract An alternative solution to the system of equations describing the pulse-decay technique of permeability measurement has been obtained. It is a solution in which the sample PV is not neglected. The experimental data are analyzed by using the slope of a semilog plot to evaluate permeability. permeability. Introduction The pulse-decay technique of permeability measurement has been used by workers interested in radioactive waste storage and low-permeability gas reservoirs. The basic idea of this method is to allow the pressure in two vessels, initially maintained at different pressures, equilibrate by flowing through a core sample. The permeability of the sample then can be determined from permeability of the sample then can be determined from the pressure-decay record. Brace et al. assumed that the compressibility of the rock matrix is negligible compared with that of the pore fluid and that the PV is negligible compared with the downstream volume. Subsequent attempts have been made to eliminate one or both of these assumptions by numerical 12.4 or analytical solutions. Of these solutions, the error-function solution of Bourbie and Walls is particularly well suited to experimental-data reduction. However the applicable range of their solution is limited to dimensionless time, tD, of less than unity and a ratio of PV to downstream volume, y, of less than 0.6. This paper presents an alternative solution that is not restricted paper presents an alternative solution that is not restricted by to or y. It reduces to an exponential-decay solution similar to Brace et al.'s solution when to is greater than 0. 3. Experimental Setup A schematic of the setup is shown in Fig. 1. A cylindrical core sample is mounted inside the coreholder and hydrostatic pressure is applied to the circumference and ends of the sample. With Valves 1 and 2 open, nitrogen is pumped into Vessel 1 to a pressure of p 0. When the pressure in the system has reached equilibrium, Valves pressure in the system has reached equilibrium, Valves 1 and 2 are closed and the pressure in Vessel 1 is raised slightly to pi. A few minutes are allowed for the temperature and pressure in Vessel 1 to equilibrate. The test begins at time t=O with the opening of Valve 1. The differential pressure transducer measures the pressure drop as the gas in the large Vessel 1 flows through the core into the small Vessel 2. The test continues until the pressure difference is 50 to 80% of the initial pressure pressure difference is 50 to 80% of the initial pressure difference. Theory The diffusion equation for flow across the core is .....................................(1) where p1-p(x, t) PD (xD, tD = ., ............(2) PD (xD, tD = ., ............(2) p1-p02 Xd=x/L,..............................(3) .....................................(4) p1 is the constant pressure of the upstream vessel, p02 p1 is the constant pressure of the upstream vessel, p02 is the initial pressure of Vessel 2, L is the length of the core, and the rest of the symbols are as defined in the nomenclature. The initial and boundary conditions are PD (xD,0)=1,.........................(5) PD (xD,0)=1,.........................(5) Pd (0, tD)=0,.........................(6) Pd (0, tD)=0,.........................(6) and .....................................(7) where .....................................(8) A is the cross-sectional area of the core sample, and V2, is the volume of Vessel 2. Therefore, is the ratio of the PV to the volume of Vessel 2. SPEJ P. 639