Dr Adam K Moss – AKM Geoconsulting Ltd

How to Obtain Primary Drainage Capillary Pressure Curves and

Predict Transition Zone Water Saturation Using NMR

T2 Distributions

• The fully brine-saturated sample nuclear magnetic resonance (NMR) T2 distribution can be thought of as a ‘pseudo’ pore-size distribution. This property has been used by researchers to convert T2 distributions to capillary pressure curves.

• This talk details my work on the use of core calibrated variable scaling factors to derive capillary pressure curves from log NMR T2 distributions in sandstone and carbonate reservoir rocks.

• The resulting capillary pressure curves are used to predict ‘transition zone’ water saturation in a hydrocarbon column.

• Detailed discussions of this work are published in two Society of Core Analysts papers:

• Brandimarte, F., Eriksson, M. and Moss, A. - How to Obtain Primary Drainage Capillary Pressure Curves Using NMR T2 Distributions in a Heterogeneous Carbonate Reservoir, SCA2017-066

• Moss, A.K., Benson, T. and Barrow, T. - An Investigation into Different Correlation Methods between NMR T2 Distributions and Primary Drainage Capillary Pressure Curves Using an Extensive Sandstone Database, SCA2018-010

Introduction

Introduction to NMR in Porous Rocks

MagnetizationAmplitude

Time (ms)

INVERSION

T2 amplitude

Time (ms)

• NMR is unique. It measures total porosity and can be partitioned into pore-size and fluid component.

• The fully brine-saturated sample nuclear magnetic resonance (NMR) T2 distribution can be thought of as a ‘pseudo’ pore-size distribution.

B0

x

y

zHydrogen Nuclei

NMR Interpretation Data (T2 Distribution)

0.1 1.0 10.0 100.0 1000.0 10000.0

Rock Bulk Volume

RockMatrix

Clays

Micro-Porosityboundwater

Total Porosity

Effective Porosity

Capillary boundwater

Free water

Hydrocarbons

Minerals

T2 cutoff

• ‘Traditionally T2 Cut-offs can be used to distinguish free from capillary bound water.

• The use of T2 Cut-offs assumes that bound fluid is only bound in the smallest pores andthe pore-space resembles a bundle of capillary tubes.

• T2 Cut-offs do not account for transitions zones in the reservoir.

The fully brine-saturated sample nuclear magnetic resonance (NMR) T2 distribution can be thought of as a ‘pseudo’ pore-size distribution.

Introduction

• This property has been used by researchers to convert T2 distributions to capillary pressure curves:

Marschall et al. Paper SCA1995-11,Klienberg, Magnetic Resonance Imaging, 1996, Vol 14, Nos. 7/8,Lowden and Porter, 1998, Paper SPE 50607,

• These models use a single conversion/scaling factor, Rho (microns/mS).

• Therefore they assume that the rocks pore space resembles a simple bundle of capillary tubes. They do not considerthe existence of multiple pore body connections and pore body restrictions/throats.

MagnetizationAmplitude

Time (ms)

INVERSION

T2 amplitude

Time (ms)

Use of a Single Scaling Factor to Convert the T2 Distribution to a Capillary Pressure Curve

Sandstone example, scaling factor = 0.8 microns/mS Vuggy limestone with ‘pore shielding’, single scaling factor not so appropriate

• Single conversion factor/scaling factors have been used, but this assumes that the pore space has a single surface relaxivity value and resembles a bundle of capillary tubes.

Figures from:Volokitin, Y., Looyestijn, W.J., Slijkerman, W.F.J., Hofman. J.P., “A Practical Approach to Obtain Primary Drainage CapillaryPressure Curves from NMR Core and Log Data”, Paper SCA1999-25, Proc. Int. Symposium of Society of Core Analysts, (1999).

The most successful models utilise variable scaling factors to convert T2 times to pore diameters and hence capillarypressure.

The variable scaling factor approach recognises the existence of variable surface relaxivity throughout the pore spacedue to variations in mineralogy and pore topography.

Introduction – Variable Scaling Factors

Brandimarte, F., Eriksson, M. and Moss, A. - How to Obtain Primary Drainage Capillary Pressure Curves Using NMR T2 Distributions in a Heterogeneous Carbonate Reservoir, SCA2017-066

Transition Zone Water Saturation from NMR – A Carbonate Reservoir Study

A Carbonate Reservoir Study

• This work investigates the use of core calibrated variable scaling factors to derive capillary pressure curves from log NMR T2 distributions in a heterogeneous carbonate reservoir.

• The resulting capillary pressure curves are used to predict water saturation in a hydrocarbon column hundreds of metres thick.

Variable Scaling Factors – A Carbonate reservoir Study

Moss, A.K., Benson, T. and Barrow, T. - An Investigation into Different Correlation Methods between NMR T2 Distributions and Primary Drainage Capillary Pressure Curves Using an Extensive Sandstone Database, SCA2018-010

Transition Zone Water Saturation from NMR – A Sandstone Reservoir Study

• The work of Volokitin and Brandimarte utilise one variable scaling factor function for all samples. Can we derivedifferent scaling factor functions for different rock types?

• This investigation uses SCAL data from the ART NMR Sandstone Rock Catalogue to obtain core calibrated variablescaling factors for 174 reservoir sandstone samples.

• Three different methods for obtaining the scaling factors are presented and the relative merits of each discussed.

• A ‘global’ model to predict capillary pressure from NMR T2 distributions in reservoir sandstones has been developedusing correlations between the variable scaling factors and permeability.

• The resulting capillary pressure curves are used to predict water saturation in an oil reservoir.

A Sandstone Study

Volokitin et al. (1999) Brandimarte et al. (2017)

Move T2 distribution ‘over’ MICP pore size distribution

Single Scaling factors to convert T2 distributions to Capillary Pressure

𝑆𝑐𝑎𝑙𝑖𝑛𝑔 𝐹𝑎𝑐𝑡𝑜𝑟, 𝑅ℎ𝑜 (𝑚𝑖𝑐𝑟𝑜𝑛𝑠/𝑚𝑠) =−𝐶 2𝜎𝑐𝑜𝑠𝜃

𝑃𝑐𝑀𝐼𝐶𝑃 × 𝑇2

A less subjective single scaling factor can be obtained by calculating the ratio of the median pore size (diameter at 50%mercury saturation) from the mercury injection curve and the log mean T2 value from the brine saturated T2

distribution.

We refer to this type of scaling factor as Rhosimple Model

𝑅ℎ𝑜𝑠𝑖𝑚𝑝𝑙𝑒 𝑀𝑜𝑑𝑒𝑙 (𝑚𝑖𝑐𝑟𝑜𝑛𝑠/𝑚𝑆) =𝑀𝑒𝑑𝑖𝑎𝑛 𝑃𝑜𝑟𝑒 𝐷𝑖𝑎𝑚 (𝑚𝑖𝑐𝑟𝑜𝑛𝑠)

𝑀𝑒𝑎𝑛 𝑇2 (𝑚𝑆)

Scaling Factor (Rho) = 0.04 microns/ms

Example of a match between MICP & NMR in the time domain.

Comparison of the ‘raw’ MICP pore size and inverted T2 distribution

Comparison of the pore size and T2 distributions after time domain matching in inversion.

One criticism of previous methods used to calculate the single scaling factors is that the pore size distributions from the mercury injection data and the NMR T2 distribution from the CPMG echo train data are derived in very different ways.

We present a new method to convert MICP injection data into a time domain equivalent so that it can be matched directly with the NMR raw data

After matching both sets of data can be inverted (NMR echo train and MICP time domain equivalent data) with identical parameters to produce distributions with identical smoothing and similar x axis scales, which makes comparison easier.

The single scaling factor can then be extracted, we call this RhoInversion Model

Single Scaling factors to convert T2 distributions to Capillary Pressure

How to calculate RhoInversion Model

K=186mD, Phi=13.3%RhoInversion Model = 0.0588 microns/ms

K=1.52mD, Phi=15.1%RhoInversion Model = 0.0435 microns/ms

To match in the time domain, first the MICP pore size distribution data must be transformed into a sum of exponentialfunctions with time constants based on pore sizes. This is done using:

𝑅 𝑡𝑖 = σ𝑗=1𝑚 𝐺𝑗 . 𝑒

−𝑡𝑖𝑌.𝐴𝑗

Where Gj is the MICP distribution amplitude at the particular pore size Aj. This equation is evaluated for ti valuescorresponding to the NMR echo acquisition times.

Rho is the scaling factor, it can then be obtained by choosing a value for Y such that:

𝑀 𝑡𝑖 − 𝑅(𝑡𝑖) = 0

Where M(ti) are the echo amplitudes of the corresponding NMR data at time ti.

The single value scaling factor obtained using this method will be referred to as the RhoInversion Model

Rho Aj

Constructing the Rho Variable Function

• The Rho value for every saturation ‘bin’ is calculated by minimising the differences between the mercury injection and cumulative T2 distribution.

• In this case Rho has the units psi/ms.

• A relationship between Rho and T2 time is defined

• This model is called the RhoVariable Model

The Data Set

All plugs, 174 plugs All plugs with Porosity diff< 0.015 (78 plugs)MICP porosity vs NMR porosity.

• Data from the ART NMR Sandstone Rock Catalogue is used in this study.

• The dataset includes 174 sandstone plug samples with high pressure mercury injection capillary pressure (MICP) curves and NMR T2 measurements on brine saturated plugs.

• The sandstone samples come from oil and gas reservoirs around the world.

• The depositional environments for these samples include; aeolian, fluvial, coastal and shallow and deep marine. The samples used have a wide variety of mineralogy and diagenetic overprints.

• Only samples with a porosity difference of less than 1.5 P.U. are used

Rh

o s

imp

le (

mic

ron

s/m

s)

Rh

o in

vers

ion

(m

icro

ns/

ms)

Rhosimple Model versus nitrogen permeability. Rhoinversion model versus nitrogen permeability for the two FZI groups.

RhoSimple Model and RhoInversion Model From the 78 Plug Quality Checked Data Set

• A RhoSimple Model and RhoInversion Model value is calculated from the MICP & NMR data for each of the 78 QC’ed plugs

• These values are then correlated against rock properties (K, Phi & FZI) to obtain a usable predictive model

• The following relationships were the most successful:

Four examples of modelled versus measured mercury injection capillary pressure curves using plug specific variable scaling factor relationships.

RhoVariable Model From the 78 Plug Quality Checked Data Set

• A RhoVariable Model function is calculated from the MICP & NMR data for each of the 78 QC’ed plugs:

For samples with a flow zone index less than 0.83:

𝑅ℎ𝑜 = 16,080 𝑇2−2.189𝐾0.035

RhoVariable Model From the 78 Plug Quality Checked Data Set

• To produce a predictive RhoVariable Model model we need to find a correlation between the multipliers and powers in these functions and common rock properties i.e. permeability, porosity or flow zone index

For samples with a flow zone index greater than 0.83:

𝑅ℎ𝑜 = 20,457 𝑇2−2.0256𝐾0.0247

Rho=Surface Relaxivity (psi/ms), T2=T2 relaxation time (ms), K=Nitrogen Permeability (mD)

• We found a relationship between the ‘power’ and permeability

• No usable relationships were found for the ‘multiplier’, therefore we used an average value

• The final predictive models are:

Comparison of the Three Global Model Results

RhoSimple Model – Sum Saturation Differences = 34.99 S.U.RhoInversion Model – Sum Saturation Differences = 27.97 S.U.RhoVariable Model – Sum Saturation Differences = 18.86 S.U.

For the six samples below:

XX40

XX50

XX60

XX70

XX80

Application of the Three Global Models to an NMR Log Data Set

High permeability sands,drilled with water based mud, CMR+ NMR log.

FWL

xx

xx

xx

xx

xx

xx

xx

xx

xx

Archie HPVTh = 4.51ftRho Simple Model HPVTh = 4.87ftRho Inversion Model HPVTh = 4.35ftRho Variable Model HPVTh = 4.42ft

Conclusions

• NMR and capillary pressure data from a large database has been used to construct and testdifferent methods for modelling capillary pressure curves from saturated sample NMR T2

distributions.

• These models can be applied to NMR log data to convert the T2 distribution at each depth to acapillary pressure curve.

• The modelled capillary pressure curves can be used to estimate water saturation at eachdepth without the need to revert to a T2 cutoff or irreducible water saturation.

• The use of single scaling factor models is found to be enhanced if the mercury injection data isinverted and handled in the same way than the NMR T2 data.

• Overall the variable scaling factor model is found to be the most successful.

• This methodology will be more successful in gas or water-wet light oil reservoirs wells drilledwith water-based muds with high degrees of mud filtrate invasion.

Thank You for Listening

Any Questions?