NEURAL NETWORKS PROVIDE MORE ACCURATE RESERVOIR PERMEABILITY

Debra A. Osborne
Texaco Exploration & Production Inc.
Midland, Tex.

For Texaco Exploration & Production Inc.'s proposed Roberts Unit CO2 flood, neural networks almost doubled the correlation coefficient of the crossplot of core-derived permeability vs. predicted permeability.

The higher correlation coefficient gives more accurate and reliable permeabilities. Accurate permeability estimates are an essential element of such flood projects.

The Roberts Unit is a mature waterflood project located on the northwestern edge of the Wasson field about 100 miles northwest of Midland, Tex. The field is on the Northern shelf of the Permian basin (Fig. 1). The unit produces oil from the upper Permian, San Andres formation.

To recover the maximum amount of oil, the Wasson field includes several active CO2 floods, areas with planned CO2 flood expansion, and the Roberts Unit proposed CO2 flood.

Texaco has designed a four-phase CO2 for the Roberts Unit.

GEOLOGY

The San Andres formation was deposited on a broad carbonate platform. Deposition was cyclic with the cycles displaying an overall upward shoaling character.1 Regionally, these shallowing-upward cycles gradually prograded southward across the Midland basin.

The Roberts Unit is along the northwestern limb of the Wasson field anticline. Although the primary trapping mechanism is structural, internal reservoir heterogeneity plays a significant role in controlling local variations in productivity and infectivity .2 At the Wasson field, the San Andres formation is a 1,400-ft thick regressive sequence overlain by the Grayburg formation.

The Wasson field reservoir is divided into two parts. The "first porosity" is mainly intertidal and restricted marine dolomites. The other part is the "main pay" that is predominantly subtidal dolomites .3

The Roberts Unit's stratigraphy (Fig. 2) includes the main pay that forms the reservoir and overlying tight intertidal dolomites and sabkha anhydrites/dolomites that form the seal.

Although the San Andres has been thoroughly dolomitized, five depositional environments can be recognized at the Roberts Unit. These are:

Open shelf
Sponge-bryozoan bank
Restricted shelf
Tidal flat
Sabkha.

Of the depositional environments, the best pay intervals are developed in open shelf wackestones/packstones and in some of the restricted shelf wackestones.

The seal and tight intervals are commonly developed in the sponge-bryozoan bank and restricted shelf and tidal flat mudstones/wackestones .2

The reservoir was subdivided vertically into reservoir flow units based on porosity log characteristics that were correlative over the field. Seven zones (Fig. 3) were used in the reservoir simulation and the neural network.'

The reservoir flow units are characterized by a porous top becoming tight toward the base. Zone thickness is commonly 30-60 ft.

PERMEABILITY ESTIMATION

Permeability is defined as a porous rock's capacity to transmit fluid. The accurate estimation of permeability is a basic element in designing and implementing a CO2 flood.5 Depending on available data, permeability can be determined by several methods.

The most reliable method for estimating permeability is pressure build-up analysis. However, lack of sufficient data restricts this method.

In the Robert's Unit, permeability obtained from wire line log analysis is scarce. Also, permeability from modeling cores lacks accuracy because most Permian basin fields have insufficient core coverage.

Commonly, linear regression analysis is used to develop linear relationships between core-derived porosity and permeability data. This method assumes a linearity between porosity and permeability. In many fields, this linearity may be poor.

By using nonlinear regression with multiple inputs, neural networks provide another method for estimating permeability.

For the Roberts Unit, regression analysis was used to develop a linear transform to convert porosity to permeability. The regression used core analysis data from six cored wells in the Roberts Unit study area.

The porosity-permeability relationship from the cored wells then was used to estimate permeability from existing porosity logs in non-cored wells.

Fig. 4a shows a general trend of increasing permeability with increasing porosity. The regression analysis produced permeabilities with a correlation coefficient of 0.44, a less than ideal correlation.

NEURAL NETWORKS

A neural network is a computer model that attempts to emulate human thought processes. The human brain contains over 100 billion neurons. The connections between neurons are called synapses (Fig. 5a). The strength of the synapse is modified when the brain learns.

Neural networks contain artificial neurons called processing elements. Processing elements are linked via one way information channels called connections. Associated with these connections are weights that control the level of the input signal entering the processing element.

Connection weights simulate the biological synapse. Each processing element sums the scaled inputs and then applies a nonlinear function to the sum to determine the processing element's output.6 Fig. 5b is a generalized cross section of a processing element.

Neural networks learn by example and are not programmed. A neural network must be given sample data containing both the inputs and a known output. However, a neural network rarely produces the expected output on the first iteration. Therefore, a neural network changes the output by modifying connection weights.

In the Roberts Unit study, the backpropagation algorithm was used to modify the connection weights. Backpropagation functions by first sending the inputs forward through the network and then computing the output error between the actual output and the desired output.

Beginning with the output layer, the network adjusts the weights layer by layer, propagating each layer's error back to the previous layer and computing connection weight changes during the processing. The process adjusts the connection weights until a minimum network global error is obtained .7 1

Neural networks are useful in solving problems that traditionally trip up computers. These problems include associations and generalizations, pattern recognition, classifying data, and disregarding errors.

Because neural networks can "learn" from examples, they are extremely useful in pattern recognition. 6 By recognizing patterns from available core data, these networks are suitable for estimating permeability.

ROBERTS UNIT ANALYSIS

A commercially available PC-based program was used to develop the neural network at the Roberts Unit. The training set consisted of 1,105 sample cases from the six cored wells in the Roberts Unit study area.

Approximately 10% (134 sample cases) of the training set was randomly extracted for the test set that checked the network's reliability.

The Roberts Unit neural network was trained on a 386 DOS computer with a math coprocessor. Central processing unit (CPU) training time was 17 hr.

To arrive at an optimum network configuration, various networks were tested by adjusting output scaling, the number of processing elements in the hidden layer, and the number of learning iterations.

The best network was found to have 30 processing elements in the hidden layer and learned after 3.1 million iterations. The network had five inputs (the geographic well location in XY coordinates, subsea depth, porosity, and reservoir flow unit) with a corresponding output of the permeability adjustment factor (Fig. 5c).

Permeability was needed for each reservoir flow unit in every well in the study area. Therefore, five inputs and an output were used and available for every well.

For the Roberts Unit neural network, the permeability adjustment factor was the difference between the actual core-derived permeability and the regression-derived permeability.

This adjustment factor plus the regression-derived permeability equals the network-derived permeability. Because the permeability adjustment factor took into account the existing porosity-permeability relationship, the network was freed to learn other relationships.

Other tested neural networks used a permeability output and a log of permeability output. These took longer to converge and did not improve the correlation.

Porosity contributed most to the output, as follows:

Porosity - 31.9%
Subsea depth - 18.9%
X coordinate - 17.5%
Reservoir flow unit - 17.2%
Y coordinate - 14.5%.

Fig. 4b crossplots core-derived permeability-vs.-predicted permeability of the regression-derived permeabilities. From regression analysis, the correlation coefficient was 0.44.

Neural networks almost doubled the correlation coefficient. In Fig. 4c the crossplot of core-derived permeability-vs.-predicted permeability of the network-derived permeabilities has a correlation coefficient to 0.81.

Isopermeability maps (Fig. 6) of the regression-derived permeabilities and network-derived permeabilities show that the network-derived map exhibits more definition in permeability throughout the study area.

This is a more realistic permeability distribution. However, the 0.81 correlation coefficient does indicate that some relevant data are missing.

Work done by Rogers and Wiener 9 indicates that higher correlation coefficients can be obtained by including a complete set of wire line log data as the inputs into the permeability estimation neural network.

ACKNOWLEDGMENTS

The author expresses her appreciation to Texaco for permission to publish this article and to the enhanced oil recovery department, Midland producing division, for its support in its preparation. Thanks go to Robert Boomer for his help with neural networks and to Jimmy Bent, Dennis Dull, and Ed Horvath for their assistance in preparing this article.

REFERENCES

Ramondetta, P.J., "Facies and stratigraphy of the San Andres formation, Northern and Northwestern shelves of the Midland basin, Texas and New Mexico," the University of Texas Austin, Bureau of Economic Geology Report of Investigations No. 128, 1982, P. 56.
Ginger, E.P., Danielli, H.M.C., Week, J.W., and Byrd, D.W., "Geological and petrophysical characterization of the San Andres reservoir, Roberts unit (west sector), Wasson field, Yoakum county, Texas," Texaco EPTD Technical Report 90-143, 1990, p. 64.
Mathis, R.L., "Reservoir geology of the Denver unit-Wasson San Andres field, Gaines and Yoakum counties, Texas," Bebout, D.G., and Harris, P.M. eds., "Hydrocarbon reservoir studies, San Andres/Grayburg formations, Permian basin," PBS-SEPM Publication No. 86-26, 1986, pp. 43-47.
Hindi, R., Cheng, C.T., and Wang, B., "CO2 miscible flood simulation study, Roberts unit, Wasson field, Yoakum county, Texas," SPE/DOE Paper No. 24185, SPE/DOE Eighth Symposium on Enhanced Oil Recovery, Tulsa, Apr. 21-24.
Ahmed, U., Crary, S.F., and Coates, G.R., "Permeability estimation: the various source sand their interrelationships," journal of Petroleum Technology, May 1991, pp. 578-87.
Wasserman, P.D., Neural computing, theory and practice, Van Nostrand Reinhold, New York, 1989, p. 230.
Caudill, M., "Neural network primer, Part III," Al Expert, June 1988, pp. 53-59.
Caudill, M., "Neural network primer, Part I," AI Expert, December 1987, pp. 46-52.
Rogers, J.A., and Weiner, J.M., "Predicting carbonate permeabilities from wire line logs using a neural network," Texaco internal report, 1990, P. 10.

BIBLIOGRAPHY

Schneider, W.T., "Geology of Wasson field, Yoakum and Gaines counties, Texas," American Association of Petroleum Geologists, Vol. 27, No. 4, 1943, pp. 479-523.