Relative permeability is one of the most important petrophysical parameters assessed in special core analysis. Traditionally, relative permeability is measurement via one of two methods: steady state and unsteady state. In both measurements, relative permeability is calculated from measurements of fluid saturations, pressure differences and fluid flow rates. NMR can be used to determine relative permeability through measuring saturation directly in the rock during an unsteady state experiment.

For steady-state relative permeability measurement methods, two fluids are injected simultaneously into the porous medium at a fixed ratio until the inflows equal the outflows and a constant pressure drop have been reached. It may take 2 to 40 hours or even longer to reach the steady-state conditions.

The relative permeability corresponding to the saturation established during the experiment can be determined by a modified form of Darcy’s law:

(1)

where Q_{j}, P_{j}, m_{j}, and K_{rj} are volume flux, pressure, viscosity, and relative permeability of fluid phase j, respectively. A, K, and L are the cross-sectional area, absolute permeability and length of the porous medium, respectively.

The injection ratio is then changed, until a new steady flow is established to calculate the relative permeability corresponding to this saturation. Different approaches may be employed to eliminate the capillary end effects and try to ensure uniform saturation distribution in the whole sample. The steady-state measurements are very time consuming. In addition, the conditions of steady-state and uniform saturation distribution are very rarely reached, and errors are introduced therefrom.

Because the steady state method is so time consuming, the unsteady state method is often preferred for determining relative permeability. In the unsteady state measurement, the core plug is saturated with one immiscible fluid. The other fluid is then injected into the core and displaces the first fluid. The pressure drop across the core and the average saturation by material balance (via collection of effluent volumes at the outlet) in the core are monitored as a function of time. For example, if the core is initially saturated with oil and brine is used to displace it, the amount of oil ejected as a function of time would be recorded. The monitoring of the amount of oil ejected can either be done by eye or with the assistance of optical/acoustic instruments which monitor the position of the oil/water boundary as a function of time.

The biggest difference between the unsteady state relative permeability measurement and the steady state measurement is that that saturation equilibrium is not achieved during the measurement and therefore Darcy’s Law does not apply. Instead, the Buckley-Leverret equation for linear fluid flow is the basis of all calculations. Many other properties influence the unsteady-state relative permeability measurement including wetting properties and fluid distribution. Although used more often than the steady state measurement because it is much faster, it is even more prone to errors.

As mentioned earlier, typically fluid saturations are calculated by material balance via collection of effluent volumes at the outlet. NMR can be used to measure the average saturation in-situ and allows the calculation of relative permeability in a much more elegant way. NMR is can be added to the unsteady-state method of calculating relative permeability where the saturation of the core has been tracked as a function of time using NMR T_{2} volume measurements. This measurement adds a level of accuracy to the conventional unsteady state measurement because it directly measures the in-situ saturation profiles in the core rather than relying on the material balance method. Factors such as dead volume and instrument uncertainties are can lead to errors in estimating core saturations are removed from the measurement.

GIT’s proprietary NMR relative permeability measurement outperforms other NMR relative permeability measurements as it uses the conventional method of determining relative permeability and does not rely on less well-established methods involving the measurement of capillary pressure. Our method couples fluid saturation determination via NMR T_{2} distributions with measurement of pressure drop across the rock.

We can perform these NMR relative permeability measurements at our in-house lab for you. Contact our team for information on how these measurements can help you better understand your reservoir.

If you want to perform these measurements in your own laboratory, any GeoSpec+ instrument (2 or 12 MHz) with a P5 Cell and GIT Systems Advanced software will allow you to measure relative permeability using NMR. Please contact our sales team to work together to find the best system set up for you.

Additional technical information can be found in this Application Note entitled “Measuring relative permeability with NMR”.