Permeability can be measured in the laboratory and indirectly determined in the field. In the laboratory, analysts flow a single-phase fluid through a rock core of known length and diameter. The fluid has known viscosity and flows at a set rate. When the flow reaches steady state, an analyst measures the pressure drop across the core length and uses Darcy's law to calculate permeability. For routine core analysis, the fluid may be air, but is more often an inert gas, such as nitrogen or helium.
In an alternative laboratory method, analysts apply gas pressure to the upstream side of a sample and monitor as the gas flows through the sample and the pressure equilibrates with the downstream pressure. During this unsteady-state, or pressure-decay, procedure, analysts use the time rate of change of pressure and effluent flow rate to solve for permeability. The pressure-decay method is particularly good for measuring the permeability of tight, or low-permeability, samples because steady-state flow through these samples takes a long time to achieve.
Analysts apply corrections to compensate for differences between laboratory and downhole conditions. They account for stress differences by applying confining stress to one or more representative plug, or core, samples. To determine stress-related effects on permeability, analysts often use several confining stresses on a few samples and then apply a correction factor for the reservoir confining stress to the other samples.
Gas flow in pores is faster than liquid flow because liquids experience greater flow resistance, or drag, at pore walls than do gases. This gas slippage, or higher flow rate of gases compared with liquids, is an effect that can be corrected by incrementally increasing the mean gas pressure in the plug, which compresses the gas and increases its drag at the pore wall. The Klinkenberg correction is an extrapolation of these measurements to infinite gas pressure, at which point gas is assumed to behave like a liquid.
In the field, permeability can be estimated in the near-wellbore region using well logging data. The primary logging data come from nuclear magnetic resonance (NMR) tools. Permeability estimates from NMR measurements require knowledge of the empirical relationship between the computed permeability, porosity and pore-size distribution; estimates are often calibrated to direct measurements on core samples from the well or from nearby wells. Permeability may also be determined from downhole pressure and sampling tool measurements.
Permeability on the reservoir scale is typically determined with drill-stem tests (DSTs). Pressure transient analysis from DSTs assesses the aver-age in situ permeability of the reservoir. To match the transient behavior to that predicted by a formation model, interpreters use several techniques. They can estimate an average effective permeability from the flow rate and pressure during steady-state production measured during specific tests at established flow rates. An average permeability can also be calculated from production-history data by adjusting permeability until the correct history of production is obtained.
Permeability in a porous medium that is 100% saturated with a single-phase fluid is the absolute permeability, or synonymously, the intrinsic permeability or specific permeability.
Multiphase flow is the simultaneous flow of multiple fluids in a porous material partially saturated with each fluid. Each fluid phase flows at its own rate and competes for flow paths with the other phase or phases. Its admittance through the porous space is determined by its effective permeability, or phase permeability. The fractional flow of each fluid is related to its relative permeability, which is the ratio of the fluid's effective permeability divided by a reference value, typically the absolute permeability.
Multiphase flow is also affected by wettability, which is the preference that solids have to be in contact with one fluid phase rather than another. Wetting affects the local distribution of phases, which has an impact on their relative abilities to flow.
Permeability is the simplest measure of the producibility and injectivity of subsurface formations. In formations of sufficient permeability, operations such as producing fluid hydrocarbons or water, conducting secondary and tertiary recovery and sequestering carbon dioxide can be accomplished.
Oilfield Review Autumn 2014: 26, no. 3.
Copyright © 2014 Schlumberger.
For help in preparation of this article, thanks to Mark Andersen and Denis Klemin, Houston.