Method determines vuggy carbonate permeability

April 13, 1998
Equations For Determining Permeability [70,130 bytes] An improved method determines vuggy carbonate permeability on the basis of specific surface area per unit pore volume and a flow zone indicator (FZI). Comparisons of fit standard error estimates show that this approach is superior to the multivariable empirical correlations of Chilingarian, et al., 1 and to the ANN-estimated permeabilities.
Emmanuel O. Udegbunam
Illinois State Geological Survey
Champaign, Ill.
An improved method determines vuggy carbonate permeability on the basis of specific surface area per unit pore volume and a flow zone indicator (FZI).

Comparisons of fit standard error estimates show that this approach is superior to the multivariable empirical correlations of Chilingarian, et al.,1 and to the ANN-estimated permeabilities.

Unlike the multivariable empirical regression approach and the ANN model, this model is derived from the causal relationships among permeability, a flow zone indicator (FZI), and the specific surface area, and hence, is nonsubjective.

This method is important because over half of the world's petroleum reserves occur in carbonate formations.2

In many significant geological regions of the world, such as the Middle East, Canada, and Mexico, almost all oil and gas production is from carbonate reservoirs. In the U.S., all major oil-producing areas except Pennsylvania have oil-bearing carbonate formations.2

The correlating functions for the method were tested with data from four Russian carbonate reservoirs3 and compared to the multivariable empirical models of Chilingarian, et al.,1 and to permeabilities estimated from an artificial neural network (ANN) model of the data.

Permeability

Knowledge of permeability and permeability distribution is essential for effective reservoir description. Laboratory-measured permeability of rock samples requires a simple geometric shape that is not possible with vuggy carbonate rocks.

On the other hand, porosity, specific surface area, irreducible water saturation, and pore size distribution can be measured.4-6 This rationale led Chilingarian, et al., to empirically correlate permeability, effective porosity, specific surface area, and irreducible water saturation of carbonate rocks from four Russian oil and gas fields by a multiple regression approach.

Although the authors reported high correlation coefficients, their multivariable regression equations are not based on theoretical relationships between permeability and the other carbonate rock parameters. Furthermore, the rock properties used by the authors for correlating permeability values were subjective and varied from one carbonate reservoir to another.

Consequently, these empirical relationships are not transportable to other carbonate reservoirs.

A recent advance in petrophysics provides relationships between permeability and other rock properties of both carbonates and siliciclastics on the basis of the hydraulic unit concept.7 8 Starting from a generalized Carman-Kozeny relationship, Amaefule, et al., defined the FZI that is a representative volume of the total reservoir rock volume by Equation 1 (see equation box).

The terms in the equation are as follows:

Fs = Shape factor,t = Tortuosity, K = Permeability, md,f = Porosity Ss = Surface area per unit pore volume, mm-1

The correlating functions presented here were tested with core data from four Russian carbonate reservoirs.1 3

It is hoped that the methodology presented in this article can also be applied in vuggy carbonate reservoirs associated with the Sub-Kaskaskia unconformity in the Illinois basin.

Correlating functions

A plot of porosity vs. permeability for a carbonate reservoir of any appreciable size commonly results in a scatter such as in Fig. 1 [51,309 bytes]. According to Equation 1, the appropriate relationship between permeability and porosity should include an FZI as shown in Equation 2.

By its definition (Equation 1), FZI can be independently correlated to the specific surface area and the square root of the Kozeny constant (Fs1/2t). It has been shown that the Kozeny constant (Fst2) could vary from 5 to 100 in real reservoir rocks.7

The plot of FZI vs. specific surface area of samples from four Russian carbonate reservoirs (Table 1 [164,329 bytes]) yields a strong reciprocal relationship (Fig. 2 [48,355 bytes]) with the best correlating function being of the form shown in Equation 3.

In Equation 3, A and B are variables that express the relationship of the Kozeny constant and the matrix volume to pore volume ratio to the specific surface area of the rock. Hence, the permeability-specific surface area-porosity function is expressed as Equation 4.

Data verification

Equation 4 was validated with data from four Russian carbonate reservoirs previously published by Bagrintseva3 and Chilingarian, et al.1 According to Chilingarian, et al., these data (Table 1) were derived from carbonate samples from the Vuktyl'skiy gas condensate deposits, a central Asian reservoir, the reservoirs of the Kuybyshev, along Volga region, and the Orenburg deposit.

These carbonate samples had varying textural properties (porous, porous-vuggy, crystalline, slightly calcareous, crystalline dense, micrograined, etc.).

Parameters measured include the effective porosity, permeability, specific surface area per unit pore volume, and irreducible water.

The FZI value corresponding to each sample was calculated from the observed permeability and porosity values according to Equation 1. Constants A and B in Equation 3, and their corresponding correlation coefficient (R2) and F-statistics, are shown in Table 2 [45,581 bytes] for each carbonate reservoir.

Correlation coefficients that ranged from 0.996 to 0.9995 indicated excellent goodness of fit of the FZI-Ss correlations to the data. The F-statistics were also consistently very high (3,575 to 27,696) indicating that, to a large extent, the four correlations represent the data from the four carbonate reservoirs, respectively.

Composite data

When data of the four carbonate reservoirs are merged, the best correlation describing the relationship between the specific surface area per unit pore volume and the FZI is shown as Equation 5.

Both R2 (0.995) and F (5,359) values indicate that a strong correlation still exists between FZI and Ss for all the samples from four geographically diverse carbonate deposits.

According to Equation 4, the permeability of a sample from any of the four carbonate reservoirs can be expressed as Equation 6.

Comparisons

The calculated and observed permeabilities of the four carbonate reservoirs ( Fig. 3 [122,426 bytes]) show very good agreement. The values calculated with Equation 4 were also compared to results of the empirical correlations of Chilingarian, et al., using fit standard error estimates or the root MSE, defined by Equation 7. The root MSE is the square root of the variance of N residuals, ei. The closer the root MSE value is to zero, the better the least-squares fit.

Table 3 [40,181 bytes] shows that the root MSE estimates for Equation 4 were consistently smaller than those determined with the empirical correlations of Chilingarian, et al. Hence, the carbonate rock permeabilities calculated with Equation 4 came closer to the observed permeabilities than the values calculated with the multivariable empirical correlations of Chilingarian, et al.

Neural network estimates

The validity of Equation 6 for data from all four Russian carbonate reservoirs was demonstrated by comparing it to permeabilities estimated with an artificial neural network model (ANN). The artificial neural network (ANN) modeling approach is considered the best estimation tool in use today and is increasingly being utilized for estimating permeability from other rock properties. 9-11

Loosely modeled after the neuronal structure of the mammalian brain, the ANN is capable of applying knowledge gained from past experience to new problems and situations. It uses a "learning" experience to build a system of neurons and weight links that allow it to make new predictions, decisions, or classifications.

The ANN method used for modeling these data is the back-propagation network.11 12 About 75% of the composite data were used in the "learning or training" process, 10% of the data were used for testing, and another 15% were used for validation of the ANN model.

The input parameters for this ANN model were porosity, irreducible water saturation, and the specific surface area. The target parameter was permeability.

The validation data set consisted of a random selection of ten samples from the combined set for all four reservoirs.

Porosity and specific surface area values from the validation data set were used to calculate permeabilities with Equation 4. These values were compared to the observed permeabilities and to the permeabilities estimated by the ANN model.

Although the results (Fig. 4 [79,254 bytes]) appear to have the same degree of accuracy, the fit standard error estimate for the permeabilities calculated with Equation 6 was 23.5 while the fit standard error estimate for the ANN-estimated permeabilities was 49.7.

This showed that the permeabilities estimated with Equation 4 were closer to the observed values than the ANN-estimated permeabilities.

References

1. Chilingarian, G.V., Chang J., and Bagrintseva, K.I., "Empirical expression of permeability in terms of porosity, specific surface area, and residual water saturation of carbonate rocks," Journal of Petroleum Science and Engineering, Vol. 4, 1990, pp. 317-22.

2. Tanner, R.S., Udegbunam, E.O., McInerney, M.J., and Knapp, R.M., "Microbially Enhanced Recovery from Carbonate Reservoirs," Geomicrobiology Journal, Vol. 9, pp. 169-95.

3. Bagrintseva, K.I., Carbonate Rocks-Oil and Gas Reservoirs. Nedra, Moscow, 1977.

4. Tiab, D., and Donaldson, E.C., Petrophysics: Theory and Practice of Measuring Reservoir Rock and Fluid Transport Properties, Gulf Publishing Co., Houston, 1996.

5. Amyx, J.W., Bass D.M., and Whiting, R.L., Petroleum Reservoir Engineering-Physical Properties, McGraw-Hill Publishing Co., New York, 1960.

6. Dullien, F.A.L., Porous Media, Academic Press, New York, 1979.

7. Amaefule, J.O., Altunbay. M., Tiab, D., Kersey, D.G., and Keelan, D., "Enhanced Reservoir Description: Using Core and Log Data to Identify Hydraulic (Flow) Units and Predict Permeability in Uncored Intervals/Wells, Paper No. SPE 26436, SPE Annual Technical Conference and Exhibitions, Houston, 1993.

8. Abbaszadeh, M., Fujii, H., and Fujimoto, F., "Permeability Prediction by Hydraulic Flow Units,", SPE Formation Evaluation Journal, December 1996, pp. 263-71.

9. Rogers, S.J., Chen, H.C., Kopaska-Merkel, D.C., and Fang, J.H., Predicting Permeability from Porosity using Neural Networks, AAPG Bulletin, Vol. 79, No. 12, 1995, p. 1786.

10. Balan, B., Mohaghegh, S., and Ameri, S., "State-Of-The-Art in Permeability Determination from well log data: Part 1: A comparative Study, Model Development," Paper No. SPE 30978, SPE Eastern Regional Conference and Exhibition, Morgantown, W.Va., 1995, pp. 33-42.

11. Mohaghegh, S., Arefi, R., Ameri, S., and Rose, D., "Design and Development of An Artificial Neural Network for Estimation of Formation Permeability," Paper No. SPE 28237, SPE Petroleum Computer Conference, Dallas, July 31-Aug. 3, 1994.

12. SPSS Inc./Recognition Systems Inc., Neural Connection 2.0, Applications Guide, SPSS Inc., Chicago, 1997.

The Author

Emmanuel Udegbunam is a petroleum engineer at the Illinois State Geological Survey, Champaign, Ill. He provides technical support for the oil and gas program. Udegbunam has a BS in petroleum engineering, and an MS in chemical engineering from the University of Tulsa, and a PhD in chemical engineering from the University of Michigan, Ann Arbor.

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