A Simulation Approach To Validate Petrophysical Data From NMR Imaging
- Elizabeth Zuluaga (U. of Texas at Austin) | Paul D. Majors (U. of Texas at Austin) | Ekwere J. Peters (U. of Texas at Austin)
- Document ID
- Society of Petroleum Engineers
- SPE Journal
- Publication Date
- March 2002
- Document Type
- Journal Paper
- 35 - 39
- 2002. Society of Petroleum Engineers
- 5.3.2 Multiphase Flow, 5.5.1 Simulator Development, 1.8 Formation Damage, 5.6.1 Open hole/cased hole log analysis, 5.1 Reservoir Characterisation, 5.5.2 Core Analysis, 5.4.7 Chemical Flooding Methods (e.g., Polymer, Solvent, Nitrogen, Immiscible CO2, Surfactant, Vapex), 5.3.1 Flow in Porous Media, 3 Production and Well Operations, 1.6.9 Coring, Fishing
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Nuclear magnetic resonance (NMR) imaging was used to map the 3D porosity and permeability distributions in heterogeneous sandstone cores under controlled laboratory conditions. The porosity and permeability distributions so obtained were used to numerically simulate first-contact miscible displacements in the cores. The spatial and temporal solvent concentrations from the numerical simulations were compared to those from imaging experiments in the cores in an effort to validate the porosity and permeability data. The results show that with calibration, useful 3D porosity and permeability distributions of heterogeneous cores can be derived from NMR imaging (NMRI).
Measurement of the basic petrophysical properties of porosity and permeability in situ has always been a challenge in the petroleum industry. Several logs are available to indirectly measure in-situ porosity such as resistivity, sonic, neutron, and density logs. However, quantitative measurement of absolute permeability of the formation in situ has been a major challenge until the advent of NMR logging. The literature shows several similar relationships that can be used to derive the porosity and permeability of rocks from NMR measurements.1-9
The objective of this study was to further test the idea of deriving the absolute permeabilities of porous media from NMR measurements under controlled laboratory conditions. We used NMRI techniques to derive 3D porosity and permeability distributions in heterogeneous sandstone cores under controlled laboratory conditions. To validate the results, the porosity and permeability data obtained by NMRI were used to numerically simulate a 3D first-contact miscible displacement in the cores. The first-contact miscible displacement experiments were then performed in the cores and imaged by NMR. Good agreement between the simulated solvent concentration distributions and the experimentally measured solvent concentration distributions is deemed to be a satisfactory verification of the porosity and permeability distributions obtained by NMRI. Results show that the 3D porosity and permeability distributions obtained by NMRI yield a reasonable estimate of the porosity and permeability distributions of the highly heterogeneous porous media under controlled laboratory conditions.
NMR is based on the interaction between externally applied magnetic fields and nuclear magnetic moments. NMR yields chemical information via chemical shift, spin coupling interactions, physical information via spin-lattice (T1) and spin-spin (T2) relaxation times, and molecular diffusion measurements. NMR imaging and flow measurements yield positional and coherent displacement information, respectively.10
NMRI involves performing NMR measurements in the presence of temporally and spacially varying magnetic fields (i.e., pulsed magnetic field gradients).10-13 Magnetic field gradients are created along three mutually perpendicular (x, y, and z) directions in concert with nuclear spin excitation and detection, making it possible to reconstruct an image of the sample, and yielding a spatial map of NMR observables (spin concentrations, T1, T2, diffusion, and flow).
Conventional NMRI techniques are rendered semiquantitative due to signal coherence losses during signal formation. Signal coherence losses are caused by T2 relaxation and by molecular diffusion in the presence of applied and background magnetic field gradients, which cause the contributions from individual nuclei within the image voxel to lose phase coherence. Quantitative NMRI techniques must therefore be employed to obtain measurements suitable for porosity mapping.14 Quantitative techniques simultaneously measure the signal decay rates and intensities I for each voxel, providing information for extrapolation of the intensity before signal loss I0. I0 is proportional to the number of mobile hydrogen atoms in the voxel, and consequently to the volume of water. Porosity information can be derived from these corrected image intensities.
The CPMG sequence used in this study yields a linear signal decay with respect to time so that a general multi-exponential decay model can be employed. The resulting expression for signal decay (including gradient cross terms and assuming a negligible pulse duration when ga is switched off) is given by
where I=the measured pixel intensity, I0=the extrapolated intensity before coherence loss, n=the echo number, TE=the interecho time, T2 =the local spin-spin relaxation rate, ?=the gyromagnetic ratio constant for 1H, g0=the local background magnetic field gradient strength, ga=the applied imaging magnetic field gradient strength, and Deff=the effective molecular diffusion constant for the pore fluid. The time variable is n*TE and is descretized to the center of each echo.
Several relationships have been proposed for deriving permeability from NMR measurements.1-9 Most are based on the Carman- Kozeny equation for transport in porous media and contain a quadratic T1 or T2 term to represent the characteristic length of the porous medium and a power of porosity term to account for the relationship between the NMR signal and pore throat size.6 Thus,
This expression has been modified by various researchers using parametric analysis to correlate NMR data with traditional permeability measurements,5-8 to employ various forms of mean relaxation time,15 and to include other data such as the electrical formation factor to account for connectivity effects.7,8,16
Kenyon et al.6 found an optimal empirical relationship between permeability and T1 of the form
where Cpm=a constant scaling factor based on fluid-surface interactions. This relationship has been shown to estimate permeability to within a factor of about three for brine-saturated sandstones. We chose to use this relation in the present study because it has been shown to yield accurate estimates of permeability in sandstones and because it employs T1, which provides a more reliable representation of pore size than T2 at the higher magnetic field strengths employed in this study.5
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