Drilling Fluid Loss Model in Rough Fractures Based on Fractal Theory

Conventional lost-circulation models failed to consider impacts of fracture roughness on losses of drilling fluids.Consequently,patterns of lost circulation in rough fractures were not fully understood,whereas fracture widths derived through inversion were usually characterized by huge errors.In the concerned study,a two-dimensional model for rough fractures was established based on fractal theory.With non-Newtonian rheological behaviors of the drilling fluid were highlighted by using the Herschel-Buckley mode,and with non-linear deformation features highlighted by index equations,a model for losses of drilling fluid could be established.Midpoint displacement method was used to derive numerical solution of the equation to determine the impacts of mesh sizes,number of fractal dimensions and standard deviation on drilling fluid loss rates and cumulative loss.Research results showed when sizes of mesh grids were large enough,numerical simulation might generate results with higher reliability.Loss rates and the cumulative loss might decrease significantly with increases in the standard deviation.The effect of the number of fractal dimensions on fluid loss behavior was related to contact of the two fracture surfaces.Minor effects on the loss could be observed when the contact rate was zero,and the impacts might be enhanced with increases in contact areas.Research results showed the newly established lost-circulation model might provide theoretical references for identification of lost circulation mechanisms and to determine the widths of fractures through inversion.