Chapter 8: Steady-State and Transient Solutions of Pressure Diffusion for Packer-Probe Tool Configurations

In this chapter, we present solutions for the governing partial-differential equations (PDEs) of pressure diffusion in porous media that are transient-pressure tested with different configurations of the dual-packer (referred to herein as packer) module and one or two probes. In Chapter 3, we defined homogeneous, inhomogeneous, and heterogeneous porous media, as well as anisotropic homogeneous media. The solutions presented here cover different well and formation types. We assume that formation and fluid parameters are time-invariant, and the permeability tensor is independent of fluid properties.

The dual-packer with a single-probe configuration (wireline-conveyed dual inflatable packer), as shown in Fig. 8.1, is very useful for obtaining a discrete permeability (horizontal and vertical permeabilities) distribution along the wellbore. This configuration basically provides 3D (spatially r and z and time) pressure transient data, which is called an interval pressure transient test (IPTT). The same setup is also useful to test to determine fracture/fault conductivities. Furthermore, the packer and one- or two-probe configuration (see Fig. 8.1 and see Fig. 1.5g in Chapter 1) can be set at each geologic flow unit (layer or sublayer) for characterization of its permeabilities. The number of vertically distributed pressure transient tests depends on the expected variation of the vertical permeability and existence of fractures and faults. If there are many layers (flow units) with contrasting permeabilities and/or many fractured or faulted zones, the number of tests should be increased. If there are several layers, the number of tests in each well should not be more than several; see Section 8.5.3. For instance, if there are three layers within the radius of investigation of the measurements, one interval test with a setup, as shown in Fig. 8.1, can be sufficient to provide pressure measurements for a well-defined inverse problem from which all layer horizontal and vertical permeabilities can be determined uniquely, provided that the other properties of the formation (e.g., layer porosity and thickness) near the wellbore are obtained from openhole logs. Furthermore, the faults and main geological characterizations of the formation can be delineated from 3D IPTT pressure data by use of pressure transient well tests and integrating them with other geoscience data (e.g., seismic and depositional environment).