Porosity determination with NMR logging

Evaluating porosity is an important petrophysical task as part of formation evaluation. This article provides an overview of techniques used in determining porosity by nuclear magnetic resonance (NMR) logging techniques.

Measuring porosity

The initial amplitude of the spin-echo train is proportional to the number of hydrogen nuclei associated with the fluids in the pores within the sensitive volume. This amplitude is calibrated in porosity units. The accuracy of this amplitude measurement depends on three factors:

1. A sufficiently long polarization time, T_W, is needed to achieve complete polarization of the hydrogen nuclei in the fluids. If T_W is too short, then the NMR porosity will be underestimated.
2. A sufficiently short inter-echo spacing, T_E, is needed to record the decays for fast relaxing fluids associated with highly viscous oils and/or fluids residing in micro pores. If T_E is too long, micro porosity quantification will be inaccurate.
3. The number of hydrogen nuclei in the fluid should equal the number in an equivalent volume of water (i.e., HI = 1); if the HI of any of the pore fluids is significantly less than 1, a correction to porosity is necessary.

Porosity was one of the earliest NMR measurements and is still an important one. Assuming that the logging tool is properly calibrated and functioning normally, interpretation of the porosity measurement depends on several other factors, including vintage of the logging tool, whether hydrocarbons are present, and fluid type.

There are two major contrasts between NMR porosity and conventional density and neutron-nuclear-porosity logs.

1. NMR porosity does not depend on the mineralogy of the matrix, except in cases in which the formation contains significant amounts of ferromagnetic or paramagnetic materials. Hence, it is considered a lithology-independent measurement for most cases.

1. NMR porosity is not sensitive to either borehole or mudcake and does not require corrections because the measurement zone (i.e., sensitive volume) is focused within the formation, beyond the borehole wall and these influences. However, the rugosity of the wellbore will have to stay less than the range of DOI (depth of investigation of the tool) to keep the sensitive volume of measurement in the formation. The frequency of the NMR experiments, bottomhole temperature and the conductivity of the borehole fluid are the main controls of the DOI for the NMR tool as a function of its hardware specifics.

The accuracy and precision of NMR-derived porosity can be confirmed through comparisons with core porosity obtained using conventional laboratory measurement methods (Fig.1), after thorough quality control of the core analysis measurements (Al-Muthana et al., 2008) with proper considerations of core sample mineralogy (Al-Ofi et al., 2024) and effect of fluids (Shao et al., 2023).

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  Fig.1 – Comparison of core- and log-NMR porosity. In this clean sandstone example, there is good agreement between porosity derived from laboratory-NMR measurements and porosity derived from conventional core analysis. NMR-porosity values typically fall within ±1 p.u. of the measured core-porosity values. Here, NMR-laboratory data were measured at T_E = 0.5 ms and T_E = 1.2 ms.

Influence of tool version on the porosity measurement

The original nuclear-magnetic-log (NML) tool had such a large dead time (e.g., minimum echo spacing, T_E) that it could not measure clay- and capillary-bound fluids; thus, it was only capable of measuring free-fluid porosity, which is now called NMR effective porosity (MPHI). The minimum T_E used in the early versions of pulse-NMR tools was still relatively large, and those tools still could not see all the clay-bound fluids. With improvements in logging technology, most NMR logs recorded after 1997 are considered "total-porosity" logs. Current logging tools use a minimum T_E of 0.3 ms in continuous mode and a T_E as small as 0.1 ms in stationary mode.

In clean, water-filled formations, MPHI should approximately equal neutron-density crossplot porosity. In shaly sands, MPHI should approximately equal density porosity, calculated with the correct grain density; however, the MPHI may not equal effective porosity because of the effects of HI and long T₁ components (Eq. 1):

....................(1)

where MPHI is measured by the NMR tool; ϕ_e is effective porosity of the formation; HI is related to the amount of fluid in the effective porosity system; T_W is polarization time used during logging; and T₁ is longitudinal relaxation time of the fluid in the effective porosity system. Older NMR logs may indicate very low porosity in shales.

MPHI is almost always less than NMR total porosity (MSIG):

....................(2)

where MSIG is measured by NMR total-porosity logging, and clay-bound-water porosity (MCBW) is measured by the NMR tool with partial-polarization acquisition. In very clean formations, however, NMR MCBW is virtually zero, and then MPHI equals MSIG (see Fig.2).

NMR total porosity may approximate density or neutron-density porosity. The reported clay-bound volume should not be considered absolute because the boundary between clay- and capillary-bound porosity components can vary with clay type and distribution. Whenever possible, the relationship of clay type and volume should be confirmed through core analysis and comparison with other log data.

Porosity logging modes

Several modes of porosity logging are currently in use:

• Standard T₂ mode
• Short T W (e.g., bound-fluid logging)
• Intermediate T_W (e.g., polarization correction and the "clean, wet formation" method)
• Long T_W, or multiple-wait-time acquisition (e.g., total-porosity logging)

Total-porosity-logging mode provides data to determine porosity, permeability, and productivity (mobile fluids). Total-porosity acquisition is a multiple-wait-time acquisition that acquires two echo trains to obtain the total porosity. One echo-train acquisition uses a long T_E (e.g., 0.9 or 1.2 ms) and a long T_W (3 to 8 seconds) to achieve complete polarization. This echo train provides the effective porosity. The second echo-train acquisition uses a short T_E (0.2 to 0.6 ms) and a short T_W (20 ms) that is only long enough to achieve complete polarization of the fluids in the micro pores (i.e., clay-bound porosity). Although the long T_W acquisition may achieve full polarization in gas zones, the porosity may still require HI correction. The short T_W echo trains are stacked to improve S/N. Total porosity is obtained by combining the two separate T₂ distributions, usually at 4 ms. The standard T₂ acquisition is used in situations in which there is little to no diffusion or T₁ contrast. The benefits of standard T₂ acquisition are increased logging speed without degradation of data quality; or superior data quality at normal logging speeds.

In bound-fluid logging mode, T_W is kept relatively short, ranging from 0.3 to 1.0 seconds. The benefit of using a short T_W is faster logging speeds while determining the clay and capillary-bound fluid volumes. The drawback is underpolarization of the free-fluid volume.

When this logging mode is used, the free-fluid volume is computed from other log data (e.g., density, neutron-density crossplot, or acoustic). In polarization mode (CMR tool), a correction to the free-fluid volume is made using the observed relationship of T₁ to T₂, on the basis of the T₂ acquired while logging. The magnitude of the polarization correction must be monitored because, in addition to porosity, the T₁/T₂ ratio is also influenced by changes in the types of formation and pore fluid. This method generally works well in clastics, but in conditions of high T₁ and T₂, such as in carbonates or light oil, the correction may actually introduce additional error.

Another mode of operation is to find a clean, wet formation and perform a sweep of different wait times (T_W) ranging from 2 to 5 seconds to determine the one needed for full polarization. Because light oil and gas may have very long T₁ values or require an HI correction, the use of intermediate T_W methods does not guarantee that the NMR porosity will be fully reported.

Optimization of the acquisition is critical to accurate NMR measurements and interpretation (see Planning for NMR log data collection). The effect of incorrect acquisition parameters on the T₂ distribution is illustrated in Fig.3. In this figure, the sequence of graphs shows the effects of T_E, T_W, pulsing time (T_P), and S/N on the measured NMR characteristics of a core sample:

• A: Initial acquisition results show an apparent unimodal distribution.
• B: Increasing the T_P shows that this sample is, in fact, bimodal. There is a significant change in the T₂ distribution, but little to no change in the cumulative porosity.
• C: Decreasing the echo spacing (T_E) reveals fast components in this sample that were previously masked by a T_E that is too long. There is a significant change in the cumulative porosity with a characteristic shift of the fastest components in the distribution to shorter T₂ values.
• D: Increasing the wait time (T_W) has significantly increased cumulative porosity. After correction for a T_W that is too short, there is a characteristic shift in the slow T₂ components to longer T₂ values.
• E: Increasing the S/N results in sharper resolution of the two major components. Although the definition of each component in the T₂ distribution improves, little change is noted in the cumulative porosity.
• F: The final result, in which all acquisition parameters have been optimized (red), is compared with the initial result (blue).

BVI determination

Determining the bulk volume irreducible (BVI) of water in a formation is one of the earliest and most widely used applications of NMR logging. BVI refers to the immovable or bound water in a formation. BVI is a function of pore-throat size distribution where high threshold pressure due to smaller pore throats retains the fluids in the pores. The ratio of BVI against effective porosity is the irreducible saturation for the wetting phase (S_wirr and can be compared to the same, obtained from core capillary pressure data as the pressure approaches to infinity. (Fig.4).

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  Fig.3 – Dependence of T₂ distribution on NMR-acquisition parameters. In all figures, blue represents previous results, red represents new results, solid lines represent incremental T₂ (read on the left axis), and dashed lines represent cumulative T₂ vs. T₂ relaxation time (read on the right axis).

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  Fig.4 – Correlating NMR T_2cutoff to capillary pressure: (a) grains are shown in gray, capillary-bound water (BVI) in light blue, and free fluids in a gradient tone blue/red; (b) capillary pressure curve (black dots) defines capillary pressure (P_c) in which water saturation becomes irreducible (S_wirr); (c) a single-porosity cutoff value on the T₂ distribution, corresponding to this pressure.

In practice, BVI serves as an indicator of, and is used for, estimating producibility and permeability. There are two methods currently used for BVI determination. One is the cutoff-BVI (CBVI) model, which is based on a fixed-T₂ value (T_2cutoff) that divides BVI and free-fluid index (FFI). The second is the spectral BVI (SBVI) model, which assumes the coexistence of free and bound fluids in any pore described by the T₂ distribution at water saturation (S_w) = 100%. This coexistence is expressed through a weighting factor that defines the fraction of bound water associated with each pore size. The SBVI method is used primarily for quantifying movable water and, secondarily, for estimating permeability.

It is noted that laboratory NMR measurements are often conducted at ambient conditions. When applying those ambient condition laboratory results downhole, effect of reservoir conditions, such as temperature, may need to be considered (Shao et al., 2022). In addition, NMR cutoff based pore typing may be strongly affected by pore surface roughness (Singer et al., 2023), an issue we may need to take into consideration when talking about macro, meso, and micro pores (a term often used interchangeably with BVI).

CBVI (cutoff) model

The T₂ signal from the rock matrix is actually so rapid that even modern logging tools cannot detect it. Consequently, the recorded T₂ distribution represents only the porosity occupied by movable (FFI) water and immovable BVI and clay-bound-water (CBW) components. Assuming that the mobility of reservoir fluids is primarily controlled by pore size (i.e., the producible fluids reside in large pores and the immobile, or bound, fluids reside in small pores), a fixed-T₂ value can relate directly to a pore size at or below which fluids will not move. This value (T_2cutoff) is used to divide the T₂ distribution into movable (i.e., producible or free fluids and FFI) and immovable (i.e., bound-fluid, BVI, and CBVI) components (Fig.5). T_2cutoff is a variable that differs from one formation to another and is influenced by a variety of factors including:

• Capillary pressure
• Lithology
• Grain size
• Compaction
• Pore characteristics

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  Fig.5 – Illustration of the T_2cutoff used in the CBVI model to divide NMR porosity into movable and immovable components.

In practical use, T_2cutoff is either determined in the laboratory or a default value is assumed. If time and expense permit, accurate T_2cutoff values can be defined by comparing the T₂ distributions obtained on fully and partially water-saturated core samples taken from the logged interval (Fig.6).

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  Fig.6 – Determination of T_2cutoff from core measurements. NMR measurements on fully saturated (S_W = 100%) core samples at irreducible saturation (S_wirr) can be used to establish a T_2cutoff for use in CBVI model. The T₂ distributions are displayed as incremental porosity and cumulative porosity. The cumulative curves are used to determine T_2cutoff.

In the absence of laboratory data, lithology-dependent default values are used for T_2cutoff. Default T_2cutoff values are based on local field experience or common practice; for example, typical values used in the Gulf of Mexico are 33 ms for clastics (sandstones) and 92 or 100 ms for carbonates. When using a default value, remember that, in fact, the T_2cutoff can actually vary within a single lithology because the capillary pressure at which irreducible water saturation (S_wirr) is achieved, varies between the actual rocks. In addition, T_2cutoff is also influenced by pore-wall chemistry, the presence of minor paramagnetic or ferromagnetic components, texture, and pore-throat to pore-body ratios. The use of an incorrect value for T_2cutoff may result in underestimation of recoverable reserves or in bypassing a pay zone.

SBVI (spectral) model

The SBVI model was developed to address the limitations of the CBVI model in some rocks, particularly in very-well-sorted rocks in which there is a very narrow range of grain and pore sizes. In these rocks, the NMR echo-decay can typically be fit by a single-exponential decay that produces a sharp peak in the T₂ distribution. When a fixed cutoff is used for determining BVI, it may result in significant error because of the presence of immovable water contained in microporosity associated with pore irregularities. This microporosity component is apparent at S_wirr, but not at S_w = 100% (Fig.7).

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  Fig.7 – BVI associated with microporosity in a coarse-grained rock having a narrow range in pore sizes. The T₂ distribution at S_w=100% exhibits a single sharp peak (upper). The T₂ distribution at S_w<100% exhibits two peaks (lower). One appears below the T_2cutoff value, the result of the irreducible water on the pore surfaces. The other appears above the T_2cutoff and represents the oil in the pore fluid. The T₂ value of the second peak is close to the T₂ of bulk oil. This same effect is seen in a North Sea chalk.

A weighting function defines the fraction of bound water in each pore size that is present in the T₂ distribution at S_w = 100% (Fig.8). Several methods have been proposed for obtaining the weighting function.

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  Fig.8 – SBVI model. For a given T₂, the SBVI-weighting factor provides the fractional volume of irreducible fluids in the pores whose size is associated with that T₂. The model shown is a step function and is commonly used to describe the weighting factors.

In general, the SBVI method is superior to the CBVI method for determining BVI in rocks in which S_w = 100%. The presence of hydrocarbons (i.e., S_w < 100%), however, introduces complications to the SBVI method. To overcome the limitations of both methods for determining BVI, the recommended practice is to compute two bound-water values—one from the cutoff (CBVI) and one from the spectral (SBVI) method—and take the larger of the two.

Nomenclature

Sw	=	water saturation, %
Swirr	=	irreducible water saturation, %
T1	=	longitudinal relaxation time, seconds
T2	=	transverse relaxation time, seconds
T2bulk	=	pore-fluid bulk-T2 relaxation time, seconds
T2cutoff	=	T2 cutoff value, seconds
TE	=	CMPG interecho spacing, seconds
Tp	=	pulsing time, seconds
TW	=	polarization (wait) time, seconds
ϕe	=	effective porosity, %

Noteworthy papers in OnePetro

Freedman, R. (2006, January 1). Advances in NMR Logging. Society of Petroleum Engineers. doi:10.2118/89177-JPT

Reppert, M., Akkurt, R., Howard, J., & Bonnie, R. (2005, January 1). Porosity and Water Saturation from LWD NMR in a North Sea Chalk Formation. Society of Petrophysicists and Well-Log Analysts.

Cannon, D. E., Minh, C. C., & Kleinberg, R. L. (1998, January 1). Quantitative NMR Interpretation. Society of Petroleum Engineers. doi:10.2118/49010-MS

Coates, G. R., Menger, S., Prammer, M., & Miller, D. (1997, January 1). Applying NMR Total and Effective Porosity to Formation Evaluation. Society of Petroleum Engineers. doi:10.2118/38736-MS

Lonnes, Steve, Guzman-Garcia, Angel, Holland, Robert- Nmr Petrophysical Predictions On Cores 2003-DDD SPWLA Conference Paper - 2003

Mai, A., Kantzas, A. - Porosity Distributions in Carbonate Reservoirs Using Low-Field NMR 07-07-02 PETSOC Journal Paper - 2007

Al-Muthana, A., Ma, S., and Okasha, T. (2008). Best practices in conventional core analysis- a laboratory investigation. Paper SPE 120814, SPE Saudi Arabia Annual Technical Symp, 10-12 May. https://doi.org/10.2118/120814-MS

Al-Ofi, S., Ma, S., Al-Hammad, R., and Zhang, J. (2024). Challenges of laminated shaly rocks evaluation and fit-for-purpose core analysis workflow. Paper IPTC-23905, IPTC, 12-14 Feb, Dhahran, Saudi Arabia. https://doi.org/10.2523/IPTC-23905-MS

Shao, W., Chen, S., Hursan, G., and Ma, S. (2022). Temperature dependence of NMR relaxation time in carbonate reservoirs. SPE Res Eval & Eng 1-16, 16 Feb. https://doi.org/10.2118/206184-PA

Singer, G., Ma, S.,  Chen, S., and Eid, E. (2023). 2D surface roughness quantification for enhanced petrophysical applications. SPE Journal, 6 Jan. https://doi.org/10.2118/210178-PA

Shao, W., Chen, S., Hursan, G., and Ma, S. (2023). NMR fluid substitution for multimodal carbonate pore systems, SPWLA 64^th Annual Symposium, 10-14 June, Conroe, Texas, USA. https://doi.org/10.30632/SPWLA-2023-0101

External links

Use this section to provide links to relevant material on websites other than PetroWiki and OnePetro

See also

Nuclear magnetic resonance (NMR) logging

Porosity determination

Porosity evaluation with acoustic logging

Porosity for resource in place calculations

NMR petrophysics

NMR logging tools