In wells producing water, oil, gas or geothermal energy, or in access wells to hydrocarbon storages, it is critical to evaluate the permeability of the formation as a function of depth. Continuous permeability logs in these wells are typically derived using tools that measure electrical, nuclear, magnetic or acoustic signals, using empirical relations that are often formation dependent. The permeability logs derived using these empirical relations often show significant differences when compared to the permeabilities obtained from core samples or well tests.
A new technique is proposed in this paper in which the open hole is scanned with an interface between two fluids with a large viscosity contrast. The injection rate into the formation depends on interface location and well pressure history. An inverse problem is solved to estimate permeability as a function of depth from the evolution of flow rates with time. During the test, the well is equipped with a central tube, typically a drill string, and the scanning is done by injecting in the central tube a liquid that is different from the liquid in the annulus, at a constant wellhead pressure. Injection and withdrawal rates are measured at the tubing and the annulus wellheads, respectively; the difference between these two rates gives the formation injection rate. Interface location is also estimated from the flow rates and pressure at the wellhead and an injection profile in the open hole is derived.
A permeability log is derived from this injection log by considering a radial, monophasic flow in each layer and same skin value for all formation layers. Initial formation pressure and storativity, estimated from other logs, are also used as inputs. The sensitivity of the permeability log to these inputs is estimated using analytical expressions. The proposed methodology is applicable to oil or water bearing formations drilled using oil or water-based muds, respectively.
A continuous permeability log is estimated from the synthetic test data using the proposed interpretation workflow; it shows a correlation of 0.95 (on a scale of 0 to 1) when compared to the input permeability log. A laboratory model that mimics a multi-layered formation is used to study the repeatability of the technique and the validity of the uniform skin assumption by creating a mudcake at the inner radius. Four consecutive tests were performed on the same set of samples and the interpreted permeability logs are compared to the benchmark permeability log; correlations are greater than 0.94.