Perforation cluster design method and system based on a hybrid model to predict proppant distribution

A method for forming perforations in a casing which is placed in a well, the method comprising:

• determining the distribution of a proppant and associated slurry exiting perforations to be made in the casing, the determining step comprising:
• receiving settling data describing the proppant settling in the casing;
• receiving a slip parameter describing a casing velocity of the proppant relative to a perforation velocity of the proppant;
• calculating with a computing device, based on a constant proppant concentration model, (1) initial flow rates Q′(i) of the proppant through the perforations and (2) initial flow rates Q′case(i) of the proppant through the casing, wherein i is the number of perforations;
• and
• calculating with the computing device, based on (1) a variable proppant concentration model, (2) the settling data, (3) the slip parameter, (4) the initial flow rates Q′(i) of the proppant through the perforations, and (5) the initial flow rates Q′case(i) of the proppant through the casing, normalized flow rates Q′s(i) of the proppant through the perforations;
• placing the casing in a well adjacent to a formation;
• based on the normalized flow rates Q′s(i), forming perforations in the casing with a size, orientation, and location to provide a substantially uniform placement of proppant and fluid in the formation;
• and
• pumping slurry comprising proppant and fluid into the casing, through the perforations, and into the formation.