Principal Investigator Mark Knackstedt Project s25

Applied Maths, Machine VP

Research School of Physical Sciences and Engineering

Co-investigators: X. Zhang, Applied Maths, Research School of Physical Sciences and Engineering, Prof. M. Sahimi, Chemical Engineering, University of Southern California, U.S.A.,Prof. D.Y.C. Chan, Mathematics, University of Melbourne. Lincoln Paterson, CSIRO Petroleum Resources. Prof. W.V. Pinczewski, Petroleum Engineering, Univ. of NSW. Prieur DuPlessis, Applied Maths, U. of Stellenbosch, South Africa. Prof. S.F. Cox, Geology Department, U. of Newcastle

Flow and Fracture in Heterogeneous Materials.

Single phase fluid flow in porous solids is of wide interdisciplinary concern. Knowledge of flow characteristics in porous solids strongly impacts upon oil and gas production, the disposal of hazardous wastes, ground-water flow and transport and reaction in porous catalysts. In many applications the permeability of a porous solid is the physical parameter of primary interest. Despite numerous theoretical investigations, attempts to predict the permeability from measurable properties of porous solids are often in error by an order of magnitude or more. The commercial development of polymeric materials, paints, oils and industrial suspensions and the resulting need for rational design procedures has spurred great interest in non-Newtonian flows. Despite their importance, flow properties of Non-Newtonian fluids in even the simplest geometries are not fully understood. A new computational method based on lattice gas automata (LGA) offers a promising new approach to the study of these complex flows.

Classical textbook fracture mechanics is based around the growth of flat planar fractures. In reality, however, many fractures are not flat, but are serrated with branches. For instance, 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. Furthermore, modelling of the flow of fluids in fractured rocks (such as coal) usually assumes a regular array of flat fractures. Again, in reality, this is not a good model, particularly for important questions like connectivity of the fracture network.

What are the basic questions addressed?

What are the flow and fracture properties of media with physically realistic heterogeneities?

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

Flow properties of three dimensional periodic and random porous media. Direct analysis of microscopic parameters associated with empirical models of flow in porous media.

Study of flow across fracture surfaces.

Analysis of the drag force across fractal aggregates. Measurement of roughness of heterogeneous fractures. Analysis of Flow in Crustal Rocks.

Analysis of Tortuosity Factor in Heterogeneous Rocks. Displacement properties of Heterogeneous Fields.

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

The flow properties are measured using the method 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 generous present allocation has enabled us to study for the first time fracture properties of three dimensional disordered media at a large scale. The results of the research completed within the present (still ongoing) allocation period is summarised below. Consultation with groups in both industry and within CSIRO has led to proposed studies of important problems in fracture mechanics including borehole breakouts. Recently a collaborative group at CSIRO has visualised three dimensional fractures in coal seams via an X-ray CAT scanner. A large scale study of fracture in three dimensional coal seams with the inclusion of heterogeneity is proposed


Direct Evaluation of Length Scales and Structural Parameters associated with Flow in Porous Media, M.A. Knackstedt and X. Zhang, Phys. Rev. E.

Direct Simulation of Electrical and Hydraulic Tortuosity in Porous Solids, X. Zhang and M.A. Knackstedt, Geophysical Research Letters, 22, 2333-2336 (1995).

Percolation and the Pore Geometry of Crustal Rocks, Mark A. Knackstedt and S.F. Cox, Phys. Rev. E Rapid Communications, R5181-R5184 (1995).

Diffusion in Model Disordered Media, Mark A. Knackstedt, B.W. Ninham and M. Monduzzi, Phys. Rev. Lett., 75, 653-656, (1995).