Most of the drilled wells are conducted on acidizing in order to eliminate the permeability reduction due to mud filtration. This type of formation damage is more sever in naturally fractured wells due to the high conductivity of fracture. If the radius of the damage due to lost circulation of drilling fluid is determined, the volume of acid needed to conduct any acid job could be calculated. Also, prediction of the near-wellbore conditions, such as mud filtrate radius, is important for accurate interpretation of the well-logs used for measuring and monitoring the properties of the near-wellbore formations. In this paper a mathematical model is developed to investigate the amount of mud filtration during drilling operation in a well with a finite conductivity vertical fracture in an infinite slab reservoir. Convection-dispersion filtrate transport model is developed in which the drilling mud can be mixed with the formation fluid. A systematic step-by-step procedure illustrating the methodology of the proposed model for the analysis of mud filtration in a finite conductivity fractured well is presented. This model is formulated for linear flow in both fracture and matrix. The effect of the filter cake is simulated by means of an empirically decaying filter rate equation. The developed model is solved by numerical analysis. The consistency of the numerical solution is checked and the best situation is considered. The sensitive analysis has been done on all the parameters of the model and the effect of each parameter such as wellbore pressure, fracture permeability, fracture diffusion coefficient, matrix permeability, matrix diffusion coefficient, matrix porosity, viscosity, constants related to the filter cake formation and fracture width on the amount of filtration are investigated. By means of the proposed model, the mud filtration can be plotted against position in both fracture and matrix for different wellbore and reservoir properties. The position in the fracture and matrix at which the curve of concentration reaches zero could be considered to represent skin radius. This radius could be used for the determination of the acid volume which is needed for the acidizing operation. Also, this model is a useful tool for accurate interpretation of the resistivity profiles which are essential for the development of efficient well-log interpretation.
Water block or invasion of water into the pores of reservoir forms during the operations of water-based drilling, injection, many perforations, completion fluids, and some other particular processes in the reservoir (such as fingering and conning). Subsequently, the alteration in the shape or composition of the fine particles such as clay (water-wet solids), as a result of the stress on it, in the flow path of the second phase can lead to the permeability decline of reservoir. Consequently, the solvents such as surfactants (as demulsifiers) to lower the surface tension as a phenomenon associated with intermolecular forces (known as capillary action) during flowback are consumed to avoid the emulsions and sludge mostly in the near-wellbore zone or undertreatment and under-injection radius of the reservoir. However, in addition to surging or swabbing the wells to lower the surface tension, using solvents as the wettability changing agent along with base fluid is a common method in the water block elimination from the wellbore, especially in the low permeability porous media or the reservoirs latter its average pressure declined below bubble point. For more profitability, after using solvents in various reservoir characterizations, the trend of their behavior variations in the different lithologies is required to decide on the removed damage percentage. The investigations on this subject involve many experimental studies and have not been presented any mathematical formulas for the damage of water block in the water, oil, and gas reservoirs. These formulas determine selection criteria for the applied materials and increase variable performance. An integrated set of procedures and guidelines for one or more phases in a porous media is necessary to carry out the step-by-step approach at wellhead. Erroneous decisions and difficult situations can also be addressed in the injection wells or saltwater disposal wells, in which water block is a formation damage type. Misconceptions and difficult situations resulting from these injuries can increase water saturation in borehole and affect the fluid transmissibility power in reaching far and near distances of the wellbore, which results in injection rate loss at the wellhead. Accordingly, for the equations of water block here, a set of variables, of a particular domain, for defining relationships between rock-and fluid-based parameters are required. For these equations, at first, the structural classifications of fracture and grain in the layers (d 1 ,d 2 , and d 3) are defined. Afterward, the equations of overburden pressure (P ob) for a definite sectional area surrounding the wellbore for any lithology (in the three categories relative to porosity) are obtained by these structural classifications and other characteristics of rock and fluid. Naturally, prior to equations of overburden pressure in 2 Oil and Gas Wells
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