This paper discusses a method of simulating rate of change using pipeline dynamic simulation. There are situations in the oil industry, where it is critical to simulate the rate of change of process variables to ensure proper, safe and economic pipeline operation. The equations of motion and PID error function were used to obtain solutions to solve a complex dynamic problem. In this paper, the motion and PID error function equations were solved and then followed by pipeline dynamic simulation to evaluate check valves dynamic performance and pipeline rate of pressure rise surge protection. The new method helps to estimate the permissible level to which the pressure can be allowed to rise without unacceptable conditions developing in the system and calculates the deceleration of the liquid column downstream of the check valve. Examples of an industrial application on a specific field are described.


This paper introduces a simple method of simulating a process variable (PV) rate of change with respect to time (time derivative d(PV)/dt), that is usually not readily available or directly calculated by some dynamic pipeline simulators. The method makes use of elementary concepts of Proportional-Integral-Derivative (PID) controllers along with commercial software packages of pipeline dynamic simulators, like Stoner Pipeline Simulator™ (SPS). The method is described in the next section. Its application in the oil and gas industry is illustrated by two examples. One is related to overpressure protection of cross-country pipelines. The other example applies to the proper selection of a check valve as an integral part in a pipeline system. In pipelines process dynamic simulation packages, flow, pressure and temperature are the most commonly used calculated PVs. Flow, on the other hand, is the most common PV rate of change of mass or volume with respect to time. Fluid velocity (V) in a pipeline is another example of a PV rate of change of the fluid traveled-distance with respect to time which is usually calculated from flow rate based on physical properties of fluid (e.g., density and viscosity) and pipe size and material. The pressure rate of change (dP/dt) such as pressure rate of rise (PRR), or velocity rate of change (dV/dt = a), that is, acceleration or deceleration are not standard calculated outputs in pipelines hydraulics and surge analysis software programs. A PV rate of change like dP/dt is very useful in surge analysis to simulate rate-of-rise types of surge relief valves [1]. Also, knowing a PV rate of change like dV/dt from a transient analysis simulation, very much helps identifying the suitable check valve for a specific system and application [2]. There are also situations where PV rate of change is needed to be observed almost continuously and displayed before an operator in the form of "rate of change" alarms, where abnormal variation of PV data with respect to time, such as sudden increase or decrease of pressure can trigger rate of change alarms.

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