Predicting Rock and Fluid/Rock Properties by Modeling Diagenesis

Steven L. Bryant
Department of Petroleum and Geosystems Engineering and Institute for Computational and Engineering Sciences
The University of Texas at Austin

Predictions of reservoir quality, efforts to improve formation evaluation, and methods for assigning properties in reservoir simulation models have traditionally relied on correlations between petrophysical properties. Most correlations are empirical. These are particularly useful when logs or core are available. A theoretical basis for these correlations would be of great benefit when extrapolation to new areas is required and when few measurements are available. Although a great deal of research has been devoted to the subject, a theoretical framework for relating the engineering properties of sedimentary rocks remains elusive. In this talk I illustrate a method for quantifying rock properties as a function of various diagenetic processes. The approach holds considerable promise as a means for establishing physics-based forms of correlations, for defining more rigorous cross-property relationships, and for translating a geologic description of a formation into a quantitative engineering model.
The premise of this approach is that many engineering properties – porosity, permeability, resistivity, acoustic impedance – are strong functions of the pore space geometry. The approach seeks to relate that geometry to geology. The idea is to develop simple but physically representative models of the processes that form sedimentary rocks: deposition, compaction, cementation, etc. For example, a sediment of well-sorted sand can be modeled as a dense, randomly packed assemblage of equal spheres. Burial and compaction of this model sediment can be modeled by numerically moving the spheres closer together. Pressure solution at grain contacts could be modeled by allowing the spheres to interpenetrate. Elastic deformation during compaction could be modeled by direct solution of the stress-strain equations at sphere contacts. The growth of epitaxial quartz cement could be modeled by numerically increasing the radius of the spheres while keeping the sphere centers fixed in space. The precipitation of patchy carbonate cement can be approximated by randomly filling individual pores within the sphere packing. 
These models are simplistic, but they capture essential aspects of how geologic processes affect pore-scale geometry. For example, even perfectly sorted sand is not made up of smooth, spherical grains. But in any depositional environment, those grains will be packed randomly rather than in some regular structure. A random sphere packing captures this aspect of the grain- and pore-scale geometry, which proves to influence transport properties significantly. Similarly, quartz overgrowths are neither smooth nor of uniform thickness, but the simple “onion-skin” model turns out to capture the macroscopic effect of such cement on porosity, permeability, formation factor, etc. 
The key to making this approach quantitative is knowing the spatial locations of all the grains in the model sediment. Given the grain size (sphere radius) this information completely determines the geometry of grain space, and by inference the geometry of void space, in the model sediment. The grain locations can be determined by experiment (in this work we use the coordinates of a random sphere pack measured by Finney and reported in 1970) or by numerically generating a dense random packing. A Delaunay tessellation of the sphere centers provides an unambiguous means of identifying pore bodies and pore throats in the model rocks. A network representation of these pore bodies and throats is a convenient means of computing transport properties of the model rocks. 
We illustrate this approach by quantifying porosity-permeability trends arising from quartz cementation and illite precipitation. The results highlight both strengths and pitfalls for attempts to correlate porosity and permeability. Predictions of formation factor provide insight into the variation of Archie’s cementation exponent m. It is also possible to compute unprecedentedly realistic configurations of multiple fluids within pore space, and this provides a foundation for better understanding multiphase flow and transport properties. Comparison of a priori predictions with measurements are encouraging, motivating a discussion of potential new applications of the approach.

SELECTED REFERENCES

Gladkikh, M. and Bryant, S., "Prediction of Interfacial Areas During Imbibition in Simple Porous Media," Advances in Water Resources, Vol. 26, pp.609-622, 2003. 
Bryant, S., Mason, G., and Mellor, D., “Quantification of Spatial Correlation in Porous Media and Its Effect on Mercury Porosimetry,” Journal Colloid and Interface Science, Vol. 177, pp.88-100, 1996. 
Bryant, S. and Raikes, S., “Prediction of Elastic Wave Velocities in Sandstones Using Structural Models,” Geophysics, Vol. 60, No. 2, pp. 437-446, March - April 1995.
Bryant, S., Cade, C. and Mellor, D., “Permeability Prediction from Geologic Models," American Association of Petroleum Geologist (AAPG) Bulletin, Vol. 77, pp. 1338 - 1350, 1993.

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