Pore scale modeling and interpretation of borehole NMR logsTrevor Irons1; Jason Heath2; Brian J. McPherson1; Tom Dewers2; Eric Bower2

1University of Utah, Energy & Geoscience Institute, Dept. of Civil & Environmental Engineering2Sandia National Laboratoratories

SUMMARY

Multiphase fluid flow through porous media is of interest to the oil and gas industry and ge-ologic carbon capture and sequestration (CCS) projects. In most of these applications, subsurfaceflow simulations are used to manage resources and projects by predicting responses due to drivingforces such including production and injection activities. In most instances, the only practical wayto model complex systems is at the continuum scale where physical (hydrologic) flow properties areaggregated over large volumes. This imposes several complications affecting model-based manage-ment. Geologic media is inherently inhomogeneous and anisotropic–properties which can be difficultto simulate accurately at large scales. Confounding this, robust measurements of relative perme-ability are expensive and time consuming to perform; this generally limits sampling to a few pointmeasurements, which may or may not be characteristic. Geophysical characterization techniques arepromising means by which to improve our understanding of multiphase systems. In particular nu-clear magnetic resonance (NMR) methods provide signal that is directly proportional to the amountof hydrogen in pore fluids. Additionally, since NMR methods are sensitive to the surface area to vol-ume ratio of pores, it is often possible to estimate hydraulic flow properties from the data. BoreholeNMR logs provide in situ estimates of porosity and permeability, however these logs need to be cal-ibrated in order to ensure the accuracy of the estimates. This is particularity important if more thanone fluid phase are present. In this poster we compare borehole NMR measurements of multiphasesystems with random walk simulations of NMR responses at the pore scale. The simulations providea powerful interpretation tool for the data and provide insight into the fluid distribution. Additionally,anisotropy and inhomogeneity can easily be investigated in computer simulations.

PORE MATRIX FROM µCT IMAGES

(a) (b)

0 100 200 300µCT bin

0

50

100

150

200

250

300

µC

Tbi

n

µCT image segment

65.067.570.072.575.077.580.082.585.0

0 100 200 300µCT bin

0

50

100

150

200

250

300

pore matrix

grain

pore

(c)

64 66 68 70 72 74 76 78µCT intensity bin

0.000.050.100.150.200.250.300.350.40

freq

uenc

y

freq′freq′′Threshold

1porosity

(m3/m3

)0.000.050.100.150.200.250.300.350.400.45

freq

uenc

y

(d) (e)

A µCT image (at 11.5 µmvoxel resolution) of theMorrow B Sandstone unitis shown (a). In order toextract a pore matrixsuitable for simulation (b)appropriate thresholdvalues must bedetermined. Since imageintensity variesthroughout the volume, aglobal threshold value isnot appropriate. Instead,subsets of the image areanalysed as shown in(c,d). The 320 × 320 ×10 voxel image subset in(c) has a porosity of 9%;the porosity distributionfor similar sized subsetsof the while volume isshown in (e).

NMR DYNAMICS

Hydrogen atoms in liquid water develop bulk magnetization moments M(0)N in a static magnetic

field (B0). These moments precess at the Larmor frequency and may be tipped away from theirequilibrium position using RF radiation at the same frequency. After the tipping pulse the momentsdecay back to equilibrium, macroscopically characterized by three parameters T1, T2, and T∗2 [1].

M(0)N (r,T) =2nH2OB0

γ2H~

2

4kBTf (r)B̂0

MN(r, t) =M(0)N (r)

{1− e−(t−τp)/T1(r) + e−(t−τp)/T1(r) cos

[θT(r, τp)

]}

+ e−(t−τp)/T∗2(r) ×[M(0)

N (r)× B̂+T (r, t)

]sin[θT(r, τp)

](1)

x

y

zB̂0

x

y

zB̂0

x

y

zB̂0

x

y

zB̂0

Where γH is the gyromagnetic ratio of hydrogen, f is the porosity of the media, and nH2O is thenumber density of water. B+

T is the corotating part of the transmitter field (BBBT) and τp is the durationof the tipping pulse which together determine the tip angle θT . In magnetic media nuclear spinsdephase causing T∗2 to dephase and deviate from T2; refocusing CPMG pulses are used such thatT∗2 → T2. In porous media the permeability can be related using, for example, the Schlumberger-Doll (SDR) equation κSDR = cpφ

mNT2n

2ML, where T2ML is the logorithmic mean of the T2 decay timedistribution, φN is the NMR derived porosity (initial amplitude), and cp, N, and M are tunable andlithology-dependent scaling factors determined through calibration.

NMR RANDOM WALK SIMULATION

(a)

10−3 10−2 10−1 100 101

time (s)

0.000.010.020.030.040.050.060.070.080.09

NM

Rsi

gnal

(Mt/M

bw)

simulatedinverted

(b)

The simplified NMR equation of motion (1), aswell as the SDR relation, are appropriate onlyon the macroscopic level and are not applica-ble to pore scale NMR. Instead, stochastic ran-dom walk simulations where individual spinswithin a pore matrix are tracked as they diffusedue to Brownian motion can be used to simu-late the NMR response of media at this scale.Single phase NMR code developed by the Im-perial College London (ICL) [2] was extendedfor multiple phases and used to perform syn-thetic NMR simulations on the extracted porematrices (a), the simulated data are shown in(b) for a single subcube of 100×100×100 vox-els. The simulations shown in this block aresingle phase; the permafrost example demon-strates the multiple phase NMR simulation ca-pabilities.Random walk simulations of subsets of the en-tire image volume were similiarily generated.The results were then stiched together to forma composite simulated NMR image of the corewith the pore space filled 100% with water. Oneslice of the synthetic NMR image is shown in-cluding estimates of NMR porosity, log meanT2 and uncalibrated permeability.

0 2 4 6 8 10 12subvoxel bin

0

2

4

6

8

10

12

subv

oxel

bin

T2ML(s)

0 2 4 6 8 10 12subvoxel bin

φ(m3/m3)

0 2 4 6 8 10 12subvoxel bin

∝ κ(cp/m2)

020040060080010001200140016001800

0.000.020.040.060.080.100.120.140.16

060012001800240030003600420048005400

CMR LOGS

Schlumberger CMR log at Farnsworth Unit, well 1310-A

Porosity comparison ofCMR data to coremeasurements,µ-porosity from claycontent is poorlyresolved in CMR logs.

7672 7680 7688 7696 7704 7712Depth (ft)

10−5

10−4

10−3

10−2

10−1

100

101

102

103

Perm

eabi

lity

(mD

)

SDRTimur-Coateslab measured

CMR-derivedpermeability is in goodagreement with corescale measurements

ACKNOWLEDGEMENTS

Funding for this project is provided by the U.S. Department of Energy’s (DOE) National EnergyTechnology Laboratory (NETL through the Southwest Regional Partnership on Carbon Sequestra-tion (SWP) under Award No. DE-FC26-05NT42591. Additional support has been provided by siteoperator Chaparral Energy, L.L.C. and Schlumberger Carbon Services.

REFERENCES

[1] A. Abragam. The principles of nuclear magnetism. International series of monographs on physics. Clarendon Press, 1961.[2] Olumide Talabi, Saif AlSayari, Stefan Iglauer, and Martin J. Blunt. Pore-scale simulation of NMR response. Journal of

Petroleum Science and Engineering, 67(3–4):168–178, 2009.

Carbon Science & Engineering Research Group http://co2.egi.utah.edu/; Sandia National Laboratories http://www.sandia.gov/ Trevor Irons <tirons@egi.utah.edu>