Measuring relative permeability with NMR

Application Note 8

Relative permeability is one of the most important petrophysical parameters assessed in special
core analysis experiments. Traditionally, relative permeability is measured via one of two
methods: steady state and unsteady state [1-5]. In both measurements, relative permeability
is calculated from measurements of fluid saturations, pressure differences and fluid flow rates.
In this work we propose using NMR to measure the saturation directly in the rock during an
unsteady state measurement.
Typically, the fluid saturations are calculated by materialbalance, via collection of effluent volumes at the outlet. In
this application note, we propose a more elegant technique
to measure relative permeability via Nuclear Magnetic
Resonance (NMR). NMR can be employed to measure theaverage saturation in-situ and hence derive the relative
permeability of a rock core sample. We have completed anunsteady state relative permeability measurement where
the saturation of the core has been tracked as a functionof time using NMR T2 volume measurements. This is a very
similar measurement to the conventional unsteady statemeasurement. However, we believe this measurement
should be more accurate than the conventional method

Experiments:
The overall experimental setup employed in this study isshown in Figure 1. The core was initially saturated withdodecane and then the sample was confined hydrostaticallyat a pressure of 4,500 psi in an Oxford Instruments P5
overburden NMR probe [9], using Fluorinert as confining fluid.
Fluorinert is chosen as the confining fluid as it produces noNMR signal and thus does not interfere with NMR signals fromthe core itself. The probe was then inserted into an
Oxford Instruments GeoSpec2/53 rock core analyser [10].
Once inside the analyser, the confining pressure was kept
constant using a Vindum Pump [11].

because it directly measures the in-situ saturation profiles

The success of the relative permeability experiment hinges onin the core rather than relying on the material balance

accurate measurement of pressure, specifically the pressure

method, where factors such as dead volumes and instrument

difference across the rock core. To ensure this is an accurate

uncertainties can lead to errors in estimating core saturations.

measurement, pressure transducers are placed on the inlet

In addition, we think that this measurement should

and outlet flow lines, as well as on the confining pressure line.

outperform other NMR relative permeability measurements

A data acquisition system was designed in which an Arduino[6-8] as it uses the conventional method for determining

microcontroller [12] continually logs the pressure from therelative permeability and doesn’t rely on less well-establishedtransducers. This log is crucial in ensuring that pressures canmethods involving the measurement of capillary pressure.

be accurately correlated to the NMR T2 measurements.

Measuring relative permeability with NMR

The relative permeability experiment began by flowing 2%

monitor the bulk saturation levels in the rock. Data acquisition

KCl in D2O brine through the rock at 0.1 ml/min using theand analysis of the NMR data were achieved via GreenHPLC pump [13]. The D2O brine was chosen as a surrogate

Imaging Technologies software [14]. The software includes afor H2O brine as D2O is NMR invisible. The invisibility of D2Oloop function that allows the NMR measurements to be run

is important to ensure that any NMR signal observed will onlycontinuously. The T2 measurement takes about 3 minutes

be from dodecane so that the relative saturation levels of D2O/

to complete. As mentioned above, pressure measurements

dodecane can easily be derived from the observed NMR signal

were continually recorded and their time stamps allowed

and the pore volume of the rock. The NMR measurements

the pressures to be correlated to the corresponding NMR

were begun simultaneously with the flow of D2O. T2 spectra

measurements (which also have independent time stamps).

were measured throughout the experiment and were used toFigure 1: Experimental setup employed to acquire
relative permeability via NMR.

Pressure
Transducer

Pressure
Transducer
Vindum Pump
D2O and Dodecane Waste

Fluorinert

GeoSpec 2-53
with OB cellPressure
Transducer

Server: Logs pressure every
minute to text file

NetworkCommunication

Internal Webpage

HPLC
Pump
D2O

Results
Figure 2 shows three T2 measurements taken at three

D2O from the outlet face of the core. The blue spectrum wasdifferent times throughout the experiment. The y-axis istaken towards the end of the experiment after breakthroughthe NMR signal in units of equivalent water volume. Theof D2O from the outlet face. The area under any of these

NMR spectrometer is calibrated in units of equivalent water

spectra is the amount of dodecane in the core at the time ofvolume. The black measurement was taken prior to thethe measurement. Plotting the area under these T2 spectra

initiation of D2O flow. This spectrum is from the 100%

as a function of time allows us to calculate the relative

dodecane saturated sample. The red spectrum was taken

permeability of the core.

after D2O had entered the core but prior to breakthrough ofBlack Trace - Prior to D2O flow entering rock.
Red Trace - After D2O flow enters rock but
before D2O breakthrough at outlet face.
Blue Trace - After D2O breakthroughat outlet face.

Figure 2: Typical T2 spectra recorded at various times during D2O flooding in the relative permeability experiment.

The upper panel of Figure 3 shows the NMR signal plotted as

the 80 minutes mark when a peak pressure of 1,400 PSI isa function of time, as well as the pressure difference acrossreached. This peak corresponds to breakthrough of D2O

the rock plotted as a function of time. This data was recorded

through the outlet face of the rock. The pressure slowly

as D2O was being injected through the core sample at 0.1 ml/

decreases after this as the rate of dodecane being evacuatedmin. Therefore, the NMR signal observed is proportional toby the D2O decreases. This is reflected in a reduction in thethe amount of dodecane in the rock as any D2O in the rockrate of change of the NMR signal observed. Eventually very

will be NMR invisible. During the first approximately 50 mins

little dodecane is produced from the core (Figure 3 – blue(Figure 3 - black lines) both the pressure across the core andlines) and only D2O is moving through the core (i.e. Sor isthe amount of dodecane in the core remain constant. This isreached).

because it takes about 50 minutes for the D2O to reach theTo derive relative permeability from this data, the NMR signal

core. After 50 minutes, the NMR signal observed from therock begins to decrease. This corresponds to D2O beginning
to replace dodecane in the plug (Figure 3 - red lines). The
decrease in the NMR signal is proportional to the amountof D2O entering the rock and dodecane leaving the rock.
During this same period, the pressure increases because thetwo immiscible fluids are being pushed through the rocksimultaneously. The pressure increases until approximately

observed as a function of time must be converted to oil
produced as a function of time. To do this, the NMR signal
in units of volume of water is converted to oil produced bysubtracting each measurement from the pore volume of therock. It should be noted that dodecane and water have asimilar hydrogen index so there is no need to convert NMR
signal in ml of water to ml of dodecane prior to doing thesubtractions.

Application Note 8Black Trace - Prior to D2O
flow entering rock.
Red Trace - After D2O flow entersrock but before D2O breakthroughat outlet face.
Blue Trace - After D2O breakthroughat outlet face.

Figure 3: NMR signal and pressure across the rock core as a function of time (Upper Panel).
Oil produced and pressure across the rock core as a function of time (Lower Panel).

The dodecane produced as a function of time is plottedin the lower panel of Figure 3.
To derive the relative permeability from theexperimental data, only those measurements taken
after D2O breakthrough at the outlet face occurs are tobe considered. Figure 4 shows both the oil produced(red plot) and pressure across the rock (blue plot) after
breakthrough. The figure also includes least-square fitsof the reduced data set to polynomial equations (blackplots) of time. Once the expressions for oil produced
and pressure difference as a function of time are
known, the derivation of relative permeability follows
the Johnson-Bossler-Naumann relative permeability
calculation [2-5]. Figure 5 shows the relativepermeability curves for oil (red plot) and water (blueplot) derived for this rock via the NMR measurement.

Measuring relative permeability with NMR

Figure 4: The pressure across the core (blue trace) and oil produced from the core (red trace) after breakthrough of D2O from the outlet face of core.

Figure 5: The relative permeability curves generated from NMR data. The relative permeability to water is shown in blue while the relative
permeability to dodecane is shown in red.

Measuring relative permeability with NMR

Conclusion:

Oxford Instruments Magnetic ResonanceThis application note summarises a conventional relative

For more information: magres@oxinst.com

permeability measurement done with NMR. This method

www.oxinst.com/geospec

couples fluid saturation determination via NMR T2 distributions

UKwith measurement of the pressure drop across the rock.
Using this method, we have successfully determined therelative permeability for a carbonate sample. This new relative
permeability measurement should be more accurate thanthe conventional method because it directly measures thein-situ saturation profiles in the core rather than relying on thematerial balance method, where factors such as dead volumes

Tel: +44 (0) 1865 393 200 Fax: +44 (0) 1865 393 333
USA300 Baker Avenue, Suite 150, Concord, MA, 01742, USA
Tel: +1 978 369 9933 Fax: +1 978 369 8287

and instrument uncertainties can lead to errors in estimating

Chinacore saturations.

Floor 1, Building 60, No.461, Hongcao Road,References

Shanghai, 200233, China

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and Analytical Techniques for Determination of Relative Permeability fromUnsteady State Flow Experiments, SPE 10th Technical Conference andExposition, Trinidad, 1991.

Tel: +86 21 6073 2925 Fax: +86 21 6360 8535

2.	McPhee, C., Reed, J. and Zubizarreta, I., Core Analysis: A Best Practice
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Green Imaging Technologies
For more information: info@greenimaging.com
www.greenimaging.com
Canada520 Brookside Drive, Suite B, Fredericton, NB, E3A 8V2,
Canada6.	Romanenko, K. and Balcom, B.J.,”An Assessment of Non-Wetting Phase
Relative Permeability in Water-Wet Sandstones Based On Quantitative MRIOf Capillary End Effects”, Journal of Petroleum Science and Engineering(2013), 110, 225-231.

Toll Free: +1 888 944 8462

7.	Zhao, Y. The Guide to Measurement and Estimation Of Oil-Water Relative
Permeability And Capillary Pressure From The Saturation Profile Of Capillary
End Effect (CEE), Fredericton, NB (2014).

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© Oxford Instruments plc, 2019. All rights reserved. Ref: MR/214/0719

8.	Liao, G., Romanenko, K. V., Marica, F., Balcom, B. J., Measuring Two-Phase
Relative Permeability from Unsteady-State Dynamic Flooding Experimentswith Magnetic Resonance Imaging, Fredericton, NB.
9.	P5 Overburden Probe User Manual, Version 1, Oxford Instruments, GreenImaging Technologies.
10. Geo-Spec 2-75 User Manual, Version 1.8, Oxford Instruments.
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12. Arduino Microcontroler, www.arduino.cc.
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A, Scientific Systems Inc.
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