Modeling and Numerical Analysis of Mud Filtration for a Well with aFinite-Conductivity Vertical Fracture: Based on Convection-Dispersion Filtrate Transport

摘要

Most of the drilled wells are conducted on acidizing inorder to eliminate the permeability reduction due to mudfiltration. This type of formation damage is more sever innaturally fractured wells due to the high conductivity offracture. If the radius of the damage due to lostcirculation of drilling fluid is determined, the volume ofacid needed to conduct any acid job could be calculated.Also, prediction of the near-wellbore conditions, such asmud filtrate radius, is important for accurateinterpretation of the well-logs used for measuring andmonitoring the properties of the near-wellboreformations. In this paper a mathematical model isdeveloped to investigate the amount of mud filtrationduring drilling operation in a well with a finiteconductivity vertical fracture in an infinite slab reservoir.Convection-dispersion filtrate transport model isdeveloped in which the drilling mud can be mixed with theformation fluid. A systematic step-by-step procedureillustrating the methodology of the proposed model for theanalysis of mud filtration in a finite conductivity fracturedwell is presented. This model is formulated for linear flowin both fracture and matrix. The effect of the filter cake issimulated by means of an empirically decaying filter rateequation. The developed model is solved by numericalanalysis. The consistency of the numerical solution ischecked and the best situation is considered. The sensitiveanalysis has been done on all the parameters of the modeland the effect of each parameter such as wellborepressure, fracture permeability, fracture diffusioncoefficient, matrix permeability, matrix diffusioncoefficient, matrix porosity, viscosity, constants related tothe filter cake formation and fracture width on the amountof filtration are investigated. By means of the proposedmodel, the mud filtration can be plotted against positionin both fracture and matrix for different wellbore andreservoir properties. The position in the fracture andmatrix at which the curve of concentration reaches zerocould be considered to represent skin radius. This radiuscould be used for the determination of the acid volumewhich is needed for the acidizing operation. Also, thismodel is a useful tool for accurate interpretation of theresistivity profiles which are essential for the developmentof efficient well-log interpretation.