...-order Padé-type thermoelastic constants derived by the approximation of Padé rational function to the total strain energy. The Padé thermoelastic constants are characteristics of a reasonable theoretical prediction for acoustic velocities of solid rocks even at high temperature. The results demonstrate...

... values match well with the measured values during the actual hydraulic fracturing operations. hydraulic fracturing compute breakdown pressure wellbore integrity approximation wellbore design pore pressure algorithm formula upstream oil & gas lower bound formula poroelastic stress...

.... The approach integrates subsurface characterization, well placement and spacing, completion and treatment designs, production forecasts and economic considerations. We leverage scientific computing and modeling technology to cover relevant parameter space and utilize approximations and response surfaces...