Calculating pull for a stuck drill string

A system, comprising:

• a data transceiver, capable of receiving input parameters from one or more of downhole sensors of a borehole undergoing drilling operations, surface sensors proximate the borehole, a data store, a previous survey data, a well site controller, a drilling controller, or a computing system, wherein the input parameters include sensor data of a fluid composition of a mud at a first depth in the borehole, a drill string is coupled to a surface location and extends into the borehole, the drill string is in a stuck state, and wherein the fluid composition comprises a percentage of liquid of the mud and a percentage of solids of the mud that have settled out of the mud at a time when at least some material sag has occurred at the first depth;
• a result transceiver, capable of communicating an output parameter;
• and
• a pull force processor, capable of using at least one of the input parameters and a first insitu friction parameter and a second insitu friction parameter to generate the output parameter, wherein a first insitu friction parameter is determined from the percentage of liquid and the second insitu friction parameter is determined from the percentage of solids, and calculating a total drag utilizing terms that include a shear force, the first insitu friction parameter, the second insitu friction parameter, and a fluid drag of a fluid inside the drill string, wherein each of the terms is calculated over a length of a portion of the drill string being evaluated, and where the output parameter comprises at least an overpull force and a backoff depth, the overpull force is sufficient to conduct a back-off operation of the drill string at the backoff depth, the overpull force is applied to a drill string hook coupled to the drill string, and the overpull force utilizes a safety factor.