A fractal model ofr predicting permeability around perforation tunnels using size distribution of fragmented grains

摘要

A methodology to predict the permeability distribution around the perforation tunnels is presented.The resulting equation describes the permeability by modeling the distribution of grain fragments and by fractal concepts.The equation allows the calculaton of permeability from the particle size data obtained from the rock material surrounding the tunnel.The fractal model constructs a flow equation for an incompletely fragmented porous media by describing the geometry and size of the pores using the grain size distribution and setting upa hierarchical scaling concept for fragmentation to eliminate the extra porosity of a completely fragmented fractal porous medium.Predicted permeabilities (as compared to measured ones for the 2.4-and 5.1-MPa underbalance shots)using the developed equation showed that hte predictions are successful at almost all radial positions around the tunnel.Relative errors between predictions and measurements increae towards the tunnel wall.This may be attributed to the unfavorable particle shapes,which are assumed to be spherical in the model,and aspect ratios of fragmented grains.It also was observed that predictions for higher underbalance test are better due to better surfe flow cleaning,which eliminates most of the small particles affecting the calculations due to their unfavorable shapes.The developed equation provides an easier and cheaper way of mappying the permeability distribution aroudn the perforation tunnels compared to the viscous fluid injection and pressure transient measurmenet techniques.The proposed techique can be valuable to obtain permeability distribvution data for near-wellbore modeling of specific formatiosn perforated at laboratory conditions and also for the assessment of the permeability damage created by differnet charge and gun designs.