Method of simulating flow-through area of a pressure regulator

A method of simulating flow-through area of a pressure regulator positioned in a branch of a fluid flow network, said method comprising the steps of:

• defining a target pressure at a location along the branch that is downstream of the pressure regulator;
• generating a projected flow-through area for a next time step in a sequence of time steps, said projected flow-through area being a non-linear function of (i) said target pressure, (ii) a flow-through area of the pressure regulator for a current time step and a previous time step, and (iii) pressure at said location for said current time step and said previous time step, wherein said step of generating said projected flow-through area includes the step of generating a sum by adding said flow-through area for said current time step to a differential area term, said differential area term defined as the product of (i) a difference between said flow-through area for said current time step and said flow-through area for said previous time step, and (ii) a pressure ratio, wherein said pressure ratio is defined as a difference between said pressure at said location for said current time step and said pressure at said location for said previous time step relative to a difference between said pressure at said location for said current time step and said target pressure, and wherein said step of generating said projected flow-through area includes the step of controlling a rate of change of said projected flow-through area by multiplying said sum by a ratio of said target pressure to said pressure at said location for said current time step;
• generating a simulated flow-through area for said next time step as a sum of (i) said flow-through area for said current time step, and (ii) a difference between said projected flow-through area and said flow-through area for said current time step multiplied by a user-defined rate control parameter;
• and
• repeating said steps of generating for a next sequential time step from said sequence of time steps until said pressure at said location is approximately equal to said target pressure, wherein said simulated flow-through area becomes said flow-through area for said current time step when performing said steps of generating for said next sequential time step.