Process for controlling a pump to account for compressibility of liquids in obtaining steady flow

A method for forming a solvent composition comprised of a major solvent component and one or more minor solvent components in a system for pumping said solvent composition through a liquid chromatography column using a two piston pump having a shaft coupled to an intake piston running in an input cylinder and coupled to a damper piston, said intake cylinder in fluid communication with a solvent input and said damper piston in fluid communication with said input cylinder and with a solvent output which is in fluid communication with said column, each said piston having an intake stroke and a pumping stroke, each said stroke having a constant velocity portion and each said piston pumping stroke having an overlap region defined as a region of overlap between the pumping strokes of said two pistons and further defined by an overlap angle of rotation through which the shaft of said pump moves while traversing said overlap region, and further comprising a computer controller stepper motor driving said two piston pump and a plurality of electrically operated valves coupling the input of said pump to a plurality of reservoirs for storing said major and minor solvent components and having a control system which alters motor speed of said stepper motor automatically in accordance with a programmable, selected flow rate represented by a target pressure signal to maintain constant flow rate even during said overlapping region of the pumping strokes of each said piston comprising the steps of:

• (1) obtaining data regarding a desired, selected solvent composition, and calculating a number of steps of said stepper motor to keep each electrically operated valve controlling flow of a minor solvent open during said constant velocity portion of said intake stroke of said intake piston by multiplying a selected percentage for each minor solvent component by a constant, AV, said constant AV being equal to the number of steps during said constant velocity portion of said intake stroke of said intake piston one of said electrically operable valves would have to be open to obtain 0.1% of the selected solvent in the final selected solvent composition:
• (2) driving said pump using said stepper motor at a speed so as to obtain a selected, programmable flow rate and separately opening each said electrically operated valve during a corresponding separate portion of said intake stroke of said intake piston, said opening interval being equal to the time taken by said stepper motor to step through the number of steps calculated in step 1 for the corresponding electrically operated valve and the corresponding solvent component, said opening for each said electrically operated valve occurring during an intake stroke;
• (3) calculating a compressibility correction factor for said selected solvent composition by measuring a time A taken by the intake piston to move through said overlapping region of said pumping stroke and dividing time A by a time B taken by said intake piston to move through an angle equal to said overlap angle while said intake piston is travelling through said constant velocity portion of said pumping stroke to derive a ratio and subtracting 1 from said ratio to derive a factor C;
• (4) calculating the ratio of time D equal to the time taken for said intake piston to move through said overlap region of said pumping stroke for an incompressible solvent at a low pressure and constant flow rate divided by a time E equal to the time taken by said input piston to move through an angle equal to said overlap angle during said constant velocity portion of said pumping stroke at said selected flow rate and the same low pressure used for measuring said time D to derive a ratio F and subtracting 1 from said ratio F;
• (5) calculating a correction factor, CF, by subtracting from Z the quantity where Z is the volume displaced by said intake piston while moving through said pumping stroke;
• (6) correcting said constant AV by multiplying AV by a quantity equal to 1 minus a moving average of a plurality of correction factors, CF;
• (7) during an intake stroke subsequent to the correction of the constant AV, opening each electrically operated valve individually for the number of steps calculated in step 1 for the corresponding solvent using the corrected constant AV as corrected in step 6 for compressibility during the constant velocity portion of said intake stroke of said input piston with only one electrically operable valve to be open at any particular time;
• (8) after all the minor solvent valves have been opened, opening the major component solvent valve for the remainder of said intake stroke to obtain a final solvent composition which is corrected for compressibility of the selected solvent composition at the selected flow rate;
• and
• (9) calculating a new target pressure and converting said new target pressure into a corrected target pressure signal, said new target pressure being defined as the old target pressure times a quantity equal to said moving average of said compressibility correction factor CF plus 1, and using said new target pressure to control the motor speed thereby obtaining said selected flow rate which is constant and corrected for the compressibility of said selected solvent composition at the selected flow rate.