Fluid velocity fields in 2D heterogeneous porous media: empirical measurement and validation of numerical prediction

The scale invariance of geological material and the consequent absence of a length scale on which to base the upscaling of measurements made on geological samples represent a serious challenge to the prediction of fluid behaviour in rock at economically interesting scales. Numerical simulation is an important tool for understanding constraints in this problem and current discrete fluid models in which complex boundary conditions can be represented have the potential for testing many possible upscaling schemes. At present, however, there are no accurate empirical data on the distributions of fluid velocities in complex, scale-invariant geometries, with which to validate such models.To address this, fluid velocity fields in complex 2D media with fractal heterogeneity were measured. Digital models of rock geometries were created and translated into physical form using electric discharge machining and stereolithography. These physical models were then enclosed between parallel sheets of glass and Perspex forming a Hele-Shaw cell which was permeated with water, doped with small neutrally buoyant spheres and pumped at accurately steady and reproducible velocities. Local velocity vectors were estimated by the analysis of sequential images captured using high-resolution video. Precision digital control systems were used to move the cell relative to the camera and repeated measurements allowed the construction of full 2D velocity fields. The accuracy of the technique was assessed by comparison between automated and manual measurements, confirming the accuracy over approaching three orders of magnitude in velocity.The results have been compared to the output of lattice Boltzmann (LB) simulations of flow in identical geometries, showing that the correlation between simulated and measured velocity fields is strongly dependent on the viscosity used in the numerical simulation. In particular, the LB scheme used in these tests is incapable of simulating correct viscosities for complex geometries. Some important effects are shown to be strongly viscosity dependent and it is concluded that some simulations may be able to predict the behaviour of high viscosity fluids only. Nonlinear effects between fracture and matrix flow are likely to be more important in these cases.