A distillation tower management system comprising: a measurement unit that is a pressure measurement unit that measures pressures at a plurality of different sites in a height direction of a distillation tower which is for use in facilities for a process of at least one of petroleum refinery processes, petroleum chemical processes or coal chemical processes; an operation data unit that produces operation data containing measurement data measured with the measurement unit; an analysis unit that analyzes a state of the distillation tower from the operation data and produces analysis data regarding the state of the distillation tower, the state comprising presence or absence of salting-out; and a control unit that produces, based on the analysis data, control data regarding a differential pressure-eliminating agent that is added to the distillation tower, wherein the differential pressure-eliminating agent is a salt remover comprising a quaternary ammonium compound, wherein the operation data unit produces operation data containing differential pressure data regarding a differential pressure between the pressures at the plurality of different sites in the height direction, measured with the pressure measurement unit, wherein the analysis unit analyzes a predicted alteration of a future differential pressure from a differential pressure alteration that is obtained from the differential pressure data and determines whether or not the predicted alteration reaches an upper limit differential pressure set as a state in which an operation of the distillation tower is hindered and produces the analysis data containing the determination result, wherein, in a case where the operation of the distillation tower is predicted not to be hindered in the analysis data, the control unit produces the control data that maintains the kind of the differential pressure-eliminating agent that is added to the distillation tower and the amount of the differential pressure-eliminating agent added, and in a case where the operation of the distillation tower is predicted to be hindered in the analysis data, the control unit produces the control data that changes the kind of the differential pressure-eliminating agent that is added to the distillation tower and/or increases the amount of the differential pressure-eliminating agent added. a measurement unit that is a pressure measurement unit that measures pressures at a plurality of different sites in a height direction of a distillation tower which is for use in facilities for a process of at least one of petroleum refinery processes, petroleum chemical processes or coal chemical processes; an operation data unit that produces operation data containing measurement data measured with the measurement unit; an analysis unit that analyzes a state of the distillation tower from the operation data and produces analysis data regarding the state of the distillation tower, the state comprising presence or absence of salting-out; and a control unit that produces, based on the analysis data, control data regarding a differential pressure-eliminating agent that is added to the distillation tower, wherein the differential pressure-eliminating agent is a salt remover comprising a quaternary ammonium compound, wherein the operation data unit produces operation data containing differential pressure data regarding a differential pressure between the pressures at the plurality of different sites in the height direction, measured with the pressure measurement unit, wherein the analysis unit analyzes a predicted alteration of a future differential pressure from a differential pressure alteration that is obtained from the differential pressure data and determines whether or not the predicted alteration reaches an upper limit differential pressure set as a state in which an operation of the distillation tower is hindered and produces the analysis data containing the determination result, wherein, in a case where the operation of the distillation tower is predicted not to be hindered in the analysis data, the control unit produces the control data that maintains the kind of the differential pressure-eliminating agent that is added to the distillation tower and the amount of the differential pressure-eliminating agent added, and in a case where the operation of the distillation tower is predicted to be hindered in the analysis data, the control unit produces the control data that changes the kind of the differential pressure-eliminating agent that is added to the distillation tower and/or increases the amount of the differential pressure-eliminating agent added.