Determining geometries of hydraulic fractures

A structured data processing system for determining geometries of hydraulic fractures, the system comprising:

• one or more hardware processors;
• a memory in communication with the one or more hardware processors, the memory storing a data structure and an execution environment, the data structure storing data that comprises a plurality of hydraulic fracture identifiers and a plurality of observed fluid pressures, at least one of the plurality of hydraulic fracture identifiers associated with a first hydraulic fracture formed from a monitor wellbore that extends from a terranean surface into a subsurface rock formation and at least another of the plurality of hydraulic fracture identifiers associated with a second hydraulic fracture formed from a treatment wellbore that extends from the terranean surface into the subsurface rock formation, at least one of the plurality of observed fluid pressures comprising a pressure change in a fluid in the first hydraulic fracture that is induced by formation of the second hydraulic fracture, the execution environment comprising:
• a hydraulic fracture geometry solver configured to perform operations comprising:
• (i) executing a single- or multi-objective, non-linear constrained optimization analysis to minimize at least one objective function associated with the plurality of observed fluid pressures, the at least one objective function comprising a first objective function, and minimizing the first objective function comprises minimizing a difference between the observed pressure and a modeled pressure associated with the first and second hydraulic fractures, the modeled pressure determined with a finite element method that outputs the modeled pressure based on inputs that comprise parameters of a hydraulic fracture operation and the respective sets of hydraulic fracture geometries of the first and second hydraulic fractures,
• (ii) applying a constraint to the single- or multi-objective, non-linear constrained optimization analysis associated with at least one of a center of the first hydraulic fracture or a center of the second hydraulic fracture, the operation of applying the constraint comprising at least one of constraining a distance between the center of the first hydraulic fracture and the radial center of the monitor wellbore to be no greater than a fracture half-length dimension of the first hydraulic fracture and no greater than a fracture height dimension of the first hydraulic fracture, or constraining a distance between the center of the second hydraulic fracture and the radial center of the treatment wellbore to be no greater than a fracture half-length dimension of the second hydraulic fracture and no greater than a fracture height dimension of the second hydraulic fracture, and
• (iii) based on minimizing the at least one objective function, determining respective sets of hydraulic fracture geometries associated with at least one of the first hydraulic fracture or the second hydraulic fracture;
• a user interface module that generates a user interface that renders one or more graphical representations of the determined respective sets of hydraulic fracture geometries;
• and
• a transmission module that transmits, over one or more communication protocols and to a computing device, data that represents the one or more graphical representations.