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Permeability estimation with NMR logging
The ability to estimate formation permeability is one of the earliest benefits of nuclear magnetic resonance (NMR) logging and remains the most important application. This artcle provides an overview of permeability estimation techniques by use of NMR logging.
Laboratory studies demonstrate that pore-water relaxation time is inversely related to the surface area-volume (S/V) ratio of the pore space (Fig.1). The NMR estimate of permeability is based on theoretical and core-based models that show that permeability increases with increasing porosity and pore size (S/V).
Fig.1 – Variation in T2 decay with permeability. This plot illustrates the difference between echo trains obtained from formations with similar porosity but different pore sizes. In terms of T2 distribution, this difference is expressed in different FFI/BVI ratios. The permeabilities were computed using the Timur-Coates model.
The measurement of formation permeability, in general, is greatly influenced by the method used, the limitations of each, and the scale at which the measurements are made. As stated previously, mercury-injection capillary pressure (MICP) curves obtained on core samples correlate to pore-throat size, while NMR measures pore-body size.
NMR logging does not provide direct and continuous measurement of permeability; rather, a formation-permeability estimate, or index, is calculated from the spectral-porosity measurements using permeability models that are based on a combination of empirical and theoretical relationships. Several permeability models have been developed, and two are in common use:
- The free-fluid (Timur-Coates or Coates) model
- The mean-T2 [the Schlumberger-Doll-Research (SDR)] model.
The free-fluid model can be applied to water-saturated and hydrocarbon-saturated reservoirs, and the mean-T2 model can be applied to water-saturated reservoirs. These permeability models assume that a good correlation exists between porosity, pore-body and pore-throat size, and pore connectivity. This assumption is generally valid in clastic (e.g., sand/shale) sequences, but in carbonates or other lithologies, model-derived permeabilities may not be reliable.
Typically, a permeability model is calibrated over a particular zone of interest and verified, wherever possible, by core or well/formation test data. Once this is done, the NMR log can provide a robust continuous-permeability estimate within the zone of interest.
Both models treat permeability as an exponential function of porosity, ϕ4, and include a parameter to account for the fact that NMR measures pore-body size, not pore-throat size (Fig.2). In the Coates model, the pore-size parameter enters implicitly through T2cutoff, which determines the ratio of FFI to BVI. In the SDR model, the size parameter enters through the geometrical mean of the relaxation spectra, T2gm. In water-saturated rocks, both models provide similar and good results; however, when hydrocarbons are present, the SDR model fails because T2gm is no longer controlled exclusively by pore size.
Free-fluid (Timur-Coates or Coates) model
In the simplest form of the free-fluid model, permeability, kCoates, is expressed as follows (Eq.1):
where ϕ is MSIG, MBVI is obtained through the CBVI or SBVI method, MFFI is the difference between MSIG and MBVI (assuming that there is no clay-bound water, see Fig.3), and C is a formation-dependent variable. The free-fluid model is very flexible and has been calibrated using core data for successful use in different formations.
To calibrate the model to core, Eq.1 is solved in the form of a straight line, y = mx + b:
Assuming b = 0 in the equation (2), core permeability is substituted for k. The slope of the line, m (i.e., C value in Eq.2), is determined using a least-squares regression (Fig.3).
Despite the flexibility of this model there are formation conditions that limit the effectiveness of the model and may require a correction (Table 1). The presence of hydrocarbons (i.e., oil, oil filtrate, or gas) in the BVI component may result in an overestimate of BVI by either the CBVI or SBVI methods, leading to an underestimate of permeability. An HI correction can be applied when gas is present. The very short T2 values associated with heavy oil may be counted in the BVI component and result in an underestimate of permeability.
Schlumberger-Doll-Research (SDR) model
Using the SDR model, permeability is expressed as
where ϕ is NMR effective porosity (MPHI), T2gm is the geometric mean of the T2 distribution, and C is a formation-dependent variable. The SDR model works very well in water-saturated zones. In the presence of oil or oil filtrates, the mean T2 is skewed toward the T2bulk, because of the effects of partial polarization, leading to an overestimate of permeability. In unflushed gas zones, mean-T2 values are too low relative to the flushed-gas zone; and permeability is underestimated. Because hydrocarbon effects on T2gm are not correctable, the SDR model fails in hydrocarbon-bearing formations. The Coates and SDR models represent matrix permeability and, therefore, are not applicable to estimation of permeability in fractured formations.
Table 1 compares the Coates and SDR models under different reservoir conditions, and it may be advisable to use both methods in an effort to constrain values for permeability.
There are a number of benefits in having available NMR-derived permeability and BVI. This information enables more-accurate quantification of reservoir heterogeneity and improves estimation of reserves and ultimate recovery. Other applications include:
- Optimizing the locations of perforations
- Well spacing
- Tailoring completions to maximize recovery rates and efficiencies
- Improving primary and secondary recovery design schemes
|C||=||coefficient in the Coates permeability model|
|kCoates||=||permeability derived using the Timur-Coates model, darcy|
|kSDR||=||permeability derived using the mean-T2 model, darcy|
|T2||=||transverse relaxation time, seconds|
|T2bulk||=||pore-fluid bulk-T2 relaxation time, seconds|
|T2cutoff||=||T2 cutoff value, seconds|
|T2gm||=||T2 geometric mean value, seconds|
- Timur, A. 1969. Effective Porosity and Permeability of Sandstones Investigated Through Nuclear Magnetic Principles. The Log Analyst 10 (1): 3.
- Seevers, D.O. 1966. A Nuclear Magnetic Method for Determining the Permeability of Sandstones. Presented at the SPWLA 7th Annual Logging Symposium, Tulsa, 8–11 May. Paper L.
- Timur, A. 1969. Pulsed Nuclear Magnetic Resonance Studies of Porosity, Movable Fluid, and Permeability of Sandstones. J Pet Technol 21 (6): 775-786. SPE-2045-PA. http://dx.doi.org/10.2118/2045-PA
- Timur, A. 1968. An Investigation of Permeability, Porosity, and Residual Water Saturation Relationships for Sandstone Reservoirs. The Log Analyst 9 (4): 8.
- Ahmed, U., Crary, S.F., and Coates, G.R. 1991. Permeability Estimation: The Various Sources and Their Interrelationships. J Pet Technol 43 (5): 578-587. SPE-19604-PA. http://dx.doi.org/10.2118/19604-PA
- Worthington, P.F. 2003. The Effect of Scale on the Petrophysical Estimation of Intergranular Permeability. Presented at the SPWLA 44th Annual Logging Symposium, Galveston, Texas, USA, 22–25 June. SPWLA-2003-A.
- Kenyon, W.E., Day, P.I., Straley, C. et al. 1988. A Three-Part Study of NMR Longitudinal Relaxation Properties of Water-Saturated Sandstones. SPE Form Eval 3 (3): 622–636. SPE-15643-PA. http://dx.doi.org/10.2118/15643-PA
- Bryant, S.L., Cade, C.A., and Melor, D.W. 1993. Permeability prediction from geological models. AAPG Bulletin 77 (8): 1338–1350.
- Chang, D., Vinegar, H., Morris, C. et al. 1997. Effective Porosity, Producible Fluid and Permeability in Carbonates From NMR Logging. The Log Analyst 38 (2): 60-72.
- Babadagli, T. and Al-Salmi, S. 2002. Improvement of Permeability Prediction for Carbonate Reservoirs Using Well Log Data. Presented at the SPE Asia Pacific Oil and Gas Conference and Exhibition, Melbourne, Australia, 8-10 October. SPE-77889-MS. http://dx.doi.org/10.2118/77889-MS
- Marschall, D., Gardner, J.S., and Curby, F.M. 1997. MR Laboratory Measurements—Requirements to Assure Successful Measurements that Will Enhance MRI Log Interpretation. Presented at the Society of Core Analysts International Symposium, Calgary, 8–10 September. SCA-9704.
- Kenyon, W.E. 1997. Petrophysical Principles of Applications of NMR Logging. The Log Analyst 38 (2): 21–43.
- Prammer, M.G. 1994. NMR Pore Size Distribution and Permeability at the Well Site. Presented at the SPE Annual Technical Conference and Exhibition, New Orleans, 25–28 September. SPE-28368-MS. http://dx.doi.org/10.2118/28368-MS
Noteworthy papers in OnePetro
Chen, S., Jacobi, D., Kwak, H., Altunbay, M., & Kloos, J. (2008, January 1). Pore-Connectivity Based Permeability Model For Complex Carbonate Formations. Society of Petrophysicists and Well-Log Analysts.
Zhang, G., Chen, S., & Fang, S. (2001, January 1). Evaluation Of Models And Methods For Nmr Total Porosity And Permeability Estimation. Society of Petrophysicists and Well-Log Analysts.
Sezginer, A., Mirth, C. C., Van Dort, G., Herron, M., Heaton, N., & Freedman, R. (1999, January 1). An Nmr High-Resolution Permeability Indicator. Society of Petrophysicists and Well-Log Analysts.
Lehne, K. A., Altunbay, M., Kelder, O., Geerits, T. W., & Tang, X. M. (1999, January 1). Comparison Between Stoneley, Nmr, And Core-Derived Permeabilities. Society of Petrophysicists and Well-Log Analysts.
Tang, X. M., Altunbay, M., & Shorey, D. (1998, January 1). Joint Interpretation Of Formation Permeability From Wireline Acoustic, Nmr, And Image Log Data. Society of Petrophysicists and Well-Log Analysts.
Prammer, M. G. (1994, January 1). NMR Pore Size Distributions and Permeability at the Well Site. Society of Petroleum Engineers. doi:10.2118/28368-MS
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