Applied Mathematics, **Machine** VP, CM

Research School of Physical Sciences and Engineering

**Co-Investigators** X Zhang, M Sahimi, D Y C Chan and L Paterson

Applied Mathematics, Research School of Physical Sciences and Engineering,

Chemical Engineering, University of Southern California, USA ,

Mathematics, University of Melbourne and

CSIRO Petroleum Resources

**Lattice Gas Simulations of Complex Flows**

A study of conductivity and fracture properties of disordered media has been undertaken. It has also enabled study of fracture in materials exhibiting a realistic (non-classical) heterogeneity. Classical fracture mechanics is based around the growth of flat planar fractures. Applications to the design of hydrofractures for the stimulation of production from oil and gas wells is based on an ideal flat penny shaped model. This is not achieved in reality, especially in a heterogeneous material such as coal, where branched irregular fractures occur. Important applications of the work concern the search for high permeability fractured zones in coal seams, necessary for the successful economic extraction of coalbed methane, and the design of hydraulic fractures in coal for effective enhancement of methane production.

We have also considered flow across fracture surfaces. There is considerable interest concerning the relationship between the aperture distance and the intrinsic permeability of a natural fracture. In the modelling of the flow of fluids in single fractures one usually assumes flow through the fracture is analogous to laminar flow between two perfectly smooth parallel plates. In reality, this is not a good model. Deviations are expected because real fracture surfaces are rough and contact each other at discrete points. This latter work involves a large collaborative research effort with other Australian and overseas groups.

**What are the basic questions addressed?**

What are the flow properties (conductivity, permeability, etc.) of media with physically realistic heterogeneities? What is the relationship between these properties and the nature and structure of fractures in the media?

**What are the results to date and the future of the work?**

Excellent speeds achieved when solving the conductivity of water-saturated porous media on the CM-5 have enabled us to solve for the first time large scale three dimensional fracture problems in three dimensional media. It has also enabled study of fracture in materials exhibiting a realistic (non-classical) heterogeneity. We have considered both heterogeneity associated with uncorrelated microstructure, and correlated heterogeneity on all scales derived from observations of sedimentary rock (S L Painter and L Paterson, CSIRO Petroleum Resources, preprint). Comparison of the resultant fractures are made with photographs of coal taken using optical microscopy.

To examine the problem of flow across fracture surfaces, we consider a simulation of flow between rough surfaces (see Figure 1). At large separations the surface topography has little effect. At small separations strong deviations from the predicted behaviour are in agreement with laboratory studies of flow in natural fractures. We find that the permeability (k)/aperture-distance(d) power law relationship k u dn gives a range of n for different surface roughness (see Figure 1).

Figure 1: Flow between two rough fractures (a) morphology of rough fracture surface (b) Flow pattern when fracture surfaces approach; the background (grey-scale) shows the local flow velocity, the brighter colour denoting a faster flow rate. Individual streamlines at different heights along the fracture illustrate the strong deviation from planar laminar flow.

**What computational techniques are used and why is a supercomputer
required?**

The method is based on lattice gas automata (LGA). Models based on LGA are discrete in time and space, require only local rules for updating and are performed by a series of simple logical operations. By virtue of their construction, LGA models of hydrodynamics are amenable to the study of very complex geometries. The method is particularly suitable for massively parallel computers like the Connection Machine.

**Publications**

*Hydrodynamic properties of fractal aggregates, *M A Knackstedt, M
Sahimi and X Zhang, presented at the American Chemical Society Meeting,
Stanford, CA, June 26, 1994.

*Drag across fractal aggregates*, M A Knackstedt, M Sahimi and X Zhang,
Phys. Fluids, in press.

*Direct evaluation of length scales and structural parameters associated with
flow in porous media,* M A Knackstedt and X Zhang, Phys. Rev. E50, 2134
(1994).

*Viscous Fingers do not exist in Oil Reservoirs*, M Sahimi and M.
Knackstedt, J. de Physique I, **7**, (1994).

*Percolation and the Pore Geometry of Crustal Rocks*, M A Knackstedt and S
F Cox, Phys. Rev. E, in press.

*On the Universality of Fracture Roughness*, X Zhang, D Y C Chan, M A
Knackstedt, L Paterson, Europhys. Lett., submitted.

*Flow properties across fracture surfaces*, M A Knackstedt, M Sahimi and X
Zhang, Water Res. Research, submitted.

*Percolation in Sedimentary Rocks*, S Painter, L Paterson, M A Knackstedt
and X Zhang, Phys. Rev. E, submitted.

*Measurement of Tortuosity of Porous Media, X Zhang and M A Knackstedt,
Geophys. Res. Lett., *submitted.

*Ternary Microemulsions as model disordered media*, M A Knackstedt and B W
Ninham, Phys. Rev. E, **50**, 2566 (1994).