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Permeability determination
The "gold" standard for permeability is to make measurements on core samples and to determine permeability with the methods outlined in API RP 40.^{[1]} All other techniques are calibrated back to core measurements. However, because core measurements sample such a minute part of the reservoir, we must rely on techniques that can be applied in a widespread fashion across the reservoir. These methods rely on measurements on sidewall samples, correlation to wireline logging responses, interpretation of nuclear magnetic resonance (NMR) logs, wireline formation tester pressure responses, and drillstem tests.
Measurement approaches
Sidewall samples
This technique is valid for slightly to unconsolidated sandstone rock types. Carbonate rock types are generally too heterogeneous for small samples to provide any meaningful reservoir-wide value for permeability. Sidewall samples of sandstone rock types are inherently contaminated with drilling mud particles and are of little use for direct measurement of permeability. However, we can inspect the rock sample with a binocular microscope to estimate median grain size, sorting, and degree of consolidation, and to characterize pore fills. With these data, we can develop correlations to permeability on the basis of whole core measurements. An alternative is to disaggregate the sample and determine a grain size analysis with laser light scattering, which can then be correlated to permeability on the basis of whole core analysis.
Wireline logging correlations
Permeabilities measured in cores can be correlated to wireline measurements taken in the cored borehole. At various times and places, almost every wireline log has been used to correlate to permeability. The porosity-permeability crossplot is, perhaps, the most used; however, it is subject to considerable error. In select basins, the GR log response can be used to correlate to permeability while, in other basins, the neutron log or acoustic log seems to provide the correlation with least statistical scatter.
NMR logs
Interpretation of NMR logging responses provides a volumetric distribution of pore sizes. If the pores are assumed to be spherical in shape, a value for permeability can be computed. These size-dependent data have been coupled with NMR pore volumes and NMR fluid saturations to produce an NMR permeability log. The chapter on NMR logging in this section of the Handbook shows examples of these techniques.
Wireline formation testers
All wireline tester vendors provide answer products that take the drawdown and buildup pressure vs. time responses and compute mobility. Mobility can be converted into permeability if a value of fluid viscosity is assumed. This permeability must be used with some caution. First, the pressure measurements are made on the borehole wall that has suffered possible drilling damage and pore throat plugging from mud solids. Second, one must take note if the measurement is in an invaded zone with two phases and, hence, the permeability determined is an effective permeability, not an absolute permeability. Depending on rock type and fluid saturations, the effective permeability may be an order of magnitude too small. The chapter on fluid sampling in the General Engineering section of this Handbook presents examples of wireline formation tester responses and derived permeability and the use of these pressure measurements to determine fluid gradients.
Drillstem tests
See discussions in Acquiring bottomhole pressure and temperature data and Formation testing while drilling (FTWD)
Determining permeability
Point-by-point permeability values are needed over the reservoir interval at the wellbores for several purposes. First, the distribution and variation of the permeabilities are needed by the engineers to develop completion strategies. Second, this same information is needed as input to the geocellular model and dynamic-flow calculations (e.g., numerical reservoir-simulation models). For both of these, the first consideration is the location of shales and other low-permeability layers that can act as barriers or baffles to vertical flow. A second consideration is the nature of the permeability variation (i.e., whether the high-permeability rock intervals occur in specific layers and the low-permeability intervals occur in other layers, or that there is so much heterogeneity that the high- and low-permeability intervals are intimately interbedded with each other).
When good-quality core data are not available, estimates of permeability can be made from empirical equations. Permeability is controlled by such factors as pore size and pore-throat geometry, as well as porosity. To take some account of these factors, the widely used Timur equation^{[2]} relates permeability to irreducible S_{w} and porosity, and therefore can be applied only in hydrocarbon-bearing zones. This form of his equation applies to a medium-gravity oil zone:
where k = absolute permeability in millidarcies, ϕ_{e} = effective (not total) porosity as a bulk volume fraction, and S_{w} = effective water saturation above the transition zone as a fraction of PV. Estimates that are based only on porosity are likely to have large prediction errors, especially in carbonate reservoirs. Equations of the following form, or a logarithmic-linear form, are useful particularly in sandstones:
where parameters C and D are very approximate and equal to about 7, and k and ϕ_{e} are as defined following Eq. 1. They should be adjusted according to local knowledge.
In field evaluation, the starting point for calculations of permeability is the routine-core-analysis data. These data, and the associated SCAL measurements of permeability and porosity as a function of overburden stress, are input to calculations to develop permeability values at reservoir conditions and the permeability vs. porosity correlation. The permeability vs. porosity correlation is often taken as semilogarithmic but usually with a steeper slope at low-porosity values. Figs. 1 and 2 demonstrate the characteristics of these relationships. Fig. 1 presents a typical permeability vs. porosity relationship from routine-core-analysis data (the scatter in these data increases at the lower-porosity levels). Fig. 2 shows the permeability ratio (stressed permeability divided by unstressed permeability) vs. unstressed permeability. This ratio is much smaller for low-permeability values and approaches a value of 1.0 for the high-permeability values.
Fig. 2 – Crossplots of core permeability at stressed vs. surface conditions and core permeability ratio vs. core permeability at surface conditions; data from an Asian gas field. “Stressed” refers to the rock being subjected to simulated overburden pressure of approximately 4,500 psia. The permeability correction is larger at low permeabilities.
In developing the permeability vs. porosity relationships, the technical team needs to identify the extent to which the reservoir interval needs to be subdivided into zones or layers. The subdividing of the core data over the reservoir interval should be into logical subdivisions that are strongly influenced by the geologists’ understanding of the depositional environment. This will naturally account for major differences in grain size, sorting, and key mineralogical factors. Alternatively, a sufficiently thick reservoir interval can be subdivided into layers of 50 to 100 ft each. A superior petrophysical methodology will be developed if a thick reservoir is appropriately subdivided, compared with treating the full reservoir interval with a single permeability vs. porosity correlation. A single permeability vs. porosity correlation for a reservoir interval with different depositional environments can lead to underprediction of permeability by an order of magnitude in an interval of better-sorted rocks compared with poorly sorted rocks (see Fig. 3). Identifying the location and correct values of highest-permeability rocks is very important for reservoir flow modeling.
The result of modeling the relationship with the least-squares regression method is that the range of predicted permeability values is smaller than that of the original routine-core permeability data. This loss of range is made worse when the logarithm of permeability is used as the y -variable because the logarithmic model is a predictor of the geometric-average permeability. ^{[3]} While the permeability vs. porosity relationship is developed from the routine and SCAL core-analysis data, the application to the point-by-point well-log database requires the use of porosity values calculated from the logs. It is preferable to model the prediction equation directly with core permeability and the basic log values^{[3]} (see Fig. 4 and the calibration line-fitting on the core/log calculation approaches page). The y-on-x (dashed) line-fit in Fig. 4 follows a curved trend on the logarithmic-linear plot and uses an arctangent function as the transformation. The solid line gives arithmetic average permeabilities at various bulk-density values. The arithmetic averages, which may be more appropriate in some reservoirs, are 2 to 3 times larger than the geometric averages. Alternative predictions of permeability may also be estimated using two-log or multiple regression analysis methods.
After the permeability values have been calculated point-by-point over the reservoir interval from the various wells’ logs, these permeability values need to be compared with those derived at each well from the pressure-transient analysis (PTA) of the pressure-buildup (PBU) or falloff data. The PBU permeability values are average values for the interval open to flow into the wellbore. The type of average (arithmetic, geometric, harmonic, or somewhere in between) to use with the point-by-point permeability values depends on the nature of the depositional environment and whether the perforated intervals are a small fraction of the full reservoir interval. If there are significant differences between the two sets of average permeability values, then the technical team needs to determine the likely cause of the differences—small-scale fractures, relative permeability effects, or some other geological factors. The point-by-point permeability values may need to be adjusted on the basis of the technical teams’ conclusions.
Nomenclature
k | = | absolute permeability in millidarcies |
ϕ_{e} | = | effective (not total) porosity as a bulk volume fraction |
S_{w} | = | effective water saturation above the transition zone as a fraction of PV |
C | = | very approximate and equal to about 7 |
D | = | very approximate and equal to about 7 |
References
- ↑ API RP 40, Recommended Practices for Core Analysis, second edition. 1998. Washington, DC: API.
- ↑ Timur, A. 1968. An Investigation of Permeability, Porosity and Residual Water Saturation Relationships for Sandstone Reservoirs. The Log Analyst 9 (4).
- ↑ ^{3.0} ^{3.1} ^{3.2} Woodhouse, R. 2003. Statistical Regression Line-Fitting in the Oil and Gas Industry. Tulsa, Oklahoma: PennWell.
Noteworthy papers in OnePetro
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External links
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See also
Permeability estimation with NMR logging
Permeability estimation with Stoneley waves
Permeability estimation in tight gas reservoirs
Water saturation determination