A rate decline model for acidizing and fracturing wells in closed carbonate reservoirs

Combined with micro-seismic exploration results, an unsteady production model for multi-branched fractures in bounded tight fractured reservoirs has been established in this paper, and by means of Laplace transform, point source integration, Stehfest numerical inversion, and semi-analytical solutions to the production model have been obtained. The accuracy of model simulation has been verified through the fitting analysis of the theoretical model and field production data. The influences of fracture branch number, inter-porosity flow coefficient, storage coefficient, branched fracture density, and drainage area on production have been analyzed. According to the calculation results, the larger the fracture branch number, the higher the decline rate in the early stage; in addition, the dimensionless production curves in the late stage coincided with each other; basically, inter-porosity flow coefficient affects the productivity of only the inter-porosity flow interval; the greater the inter-porosity flow coefficient, the higher the production; storage coefficient mainly affects the early productivity of volume-fractured wells; the greater the storage coefficient, the higher the early production, but the productivity decline rate is similar at different storage coefficients; fracture density mainly affects the early productivity of volume-fractured wells; the larger the fracture density, the smaller the productivity, but with the reduction of fracture density, the influence of fracture density on productivity is less obvious; a larger reservoir drainage radius leads to later entering of energy depletion stage. Much attention shall be paid to the optimization of productivity influence factors, and they shall be taken into account as comprehensively as possible in the actual production process.