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.
Contents [hide hide]]
1 Estimating permeability 2 Free-fluid (Timur-Coates or Coates) model 3 Schlumberger-Doll-Research (SDR) model 4 Applications 5 Nomenclature 6 References 7 Noteworthy papers in OnePetro 8 External links 9 See also
Estimating permeability 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 ( Fig.1). ). The NMR estimate of permeability is based on theoretical and core-based models that show that permeability increases with increasing porosity and [1][2][3][ 2][3][4][5] 4][5] pore size (S/V). (S/V).[1][
Fig.1 – Variation in
T 2 decay
with permeability. This plot illustrates the difference between echo trains
obtained from formations with similar porosity but different pore sizes. In terms of
T 2 distribution,
this
difference is expressed in different FFI/BVI ratios. The permeabilities were computed using the TimurCoates 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 .[6] 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-T 2 [the Schlumberger-Doll-Research (SDR)] model.[7][8][9][10]
The free-fluid model can be applied to water-saturated and hydrocarbon-saturated reservoirs, and the mean-T 2 model can be applied to water-saturated reservoirs .[11] 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 [12] (Fig.2). In the Coates model, the pore-size parameter enters implicitly through T 2cutoff , which determines the ratio of FFI to BVI. In the SDR model, the size parameter enters through the geometrical mean of the relaxation spectra, T 2gm. In water-saturated rocks, both models provide similar and good results; however, when hydrocarbons are present, the SDR model fails because T 2gm is no longer controlled exclusively by pore size.[13]
Fig.2 – NMR-permeability models. The free-fluid permeability, Coates, model (top) uses the MFFI/MBVI ratio to describe the changes in the S/V ratio. The S DR permeability model (bottom) uses an average
T 2 value
to describe changes in S/V.
Free-fluid (Timur-Coates or Coates) model In the simplest form of the free-fluid model, permeability, k Coates, is expressed as follows (Eq.1):
....................(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 formationdependent 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:
....................(2) 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).
Fig.3 – Crossplot of core and NMR data used for determining the Coates permeability constant, Assuming b = 0 in Eq.2, core permeability is substituted for
k ,
and the slope of the line,
m ,
C .
is the
C value
in Eq.1.
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 T 2 values associated with heavy oil may be counted in the BVI component and result in an underestimate of permeability.
Table 1
Schlumberger-Doll-Research (SDR) model Using the SDR model, permeability is expressed as
....................(3) where ϕ is NMR effective porosity (MPHI), T 2gm is the geometric mean of the T 2 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 T 2 is skewed toward the T 2bulk, because of the effects of partial polarization, leading to an overestimate of permeability. In unflushed gas zones, mean- T 2 values are too low relative to the flushed-gas zone; and permeability is underestimated. Because hydrocarbon effects onT 2gm 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.
Applications 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
Nomenclature C
=
coefficient in the Coates permeability model
k
=
permeability, darcy
k Coates
=
permeability derived using the Timur-Coates model, darcy
k SDR
=
permeability derived using the mean-T 2 model, darcy
T 2
=
transverse relaxation time, seconds
T 2bulk
=
pore-fluid bulk-T 2 relaxation time, seconds
T 2cutoff
=
T 2 cutoff value, seconds
T 2 gm
=
T 2 geometric mean value, seconds
ϕ
=
porosity, %
