Pressure changer

Authors: Kedric Daly ^[2016]

Stewards: David Garcia, Fengqi You

Date Presented: February 5, 2016

Introduction

Pressure changers are any piece of equipment where the main goal is to increase or decrease the pressure of a stream. Typically, pressure changers are used mostly for increasing pressure, due to the fact that pressure losses occur within a system due to friction with pipes, pipe bends, valves, and other pieces of equipment . Lowering the pressure of a system can also be useful however, such as to favor the products of a chemical reaction through Le Chatelier's principle. It is important however to ensure proper pressure is maintained throughout a chemical process so that blowback does not occur, and any fluids actually reach their destination as expected, at the proper conditions.

There are many different types of modeling software for chemical processing, Aspen HYSYS, and Aspen Plus being well known. Like any piece of process equipment, it is necessary to specify a number of independent variables in order for the simulation to converge and produce unknown values. There are different combinations of independent variables that will suffice and cause the model to converge. Different parameters of the pump or compressor can also be specified, such as efficiency, which will impact the results of the simulation. It is therefore important to ensure the equipment is correctly specified to ensure accurate results.

Pumps

Pumps do work on fluids, causing them to increase in pressure at a constant volume, due to the assumption that liquids that enter pumps are mostly incompressible. To find the power outlet required by a pump to pressurize a fluid, an energy balance can be done on the system. The result is the mechanical balance equation, below:

Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mathbf{P} = -mW_s = m\left ( \Delta \left (\frac{u^2}{2\alpha} \right ) +g\Delta z + \int_{P_1}^{P_2} vdP + F \right ) }

Where Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mathbf{P} } is the power required, Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle m } is the mass flow rate, Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle W_s } is that shaft work, Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle u } is the velocity of the fluid, Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \alpha } describes the flow in the system (0.5 for laminar, 1 for turbulent), Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle g } is the gravitational acceleration, Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \Delta z } is the change in height, Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \int_{P_1}^{P_2} vdP } is the constant volume PV work done, and Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle F } is the force acting on the fluid. Each grouping deals with different aspects of the fluid flow. The first term deals with the kinetics, the second term with the statics, the third term with the pressure head, and the fourth term with the viscous losses. It should also be noted that a pressure head is the height of a fluid that results in an equivalent pressure via the Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle P = \rho g h } relation.


While the mechanical balance equation can be used to find the outlet power required, no pump is 100% efficient. The efficiency, Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \eta } , of a pump is defined as:

Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \eta = \frac{\mathbf{P_{out}}}{\mathbf{P_{in}}} }

The efficiency of a pump is related to the pressure head and the fluid flow rate because the work can be converted to either a higher velocity or a larger pressure head.. Manufacturers often supply characteristic pump curves in order to inform their customers which pumps will meet their needs. Using these types of curves, it can be seen where the best operating range is for a pump in order to maximize efficiency, and therefore minimize losses in the system. An example curve can be seen below.

Characteristic Pump Curve Example

Another important consideration for pumps is that a Net Positive Suction Head (NPSH) must be maintained within the pump, in order to avoid cavitation. Specifically, the available NPSH (Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle NPSH_{avail} } ) must exceed the required NPSH (Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle NPSH_{reqd} } ), which is specified by the manufacturer of the pump because Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle NPSH_{reqd} } depends on the pump design. The Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle NPSH_{avail} } can be found by using equation (20.21) in Towler, below:

Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle NPSH_{avail} = \frac{P}{\rho g} + H - \frac{P_f}{\rho g} - \frac{P_v}{\rho g} }

Where Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle P } is the pressure above the liquid in the feed vessel, Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle H } is the height of the liquid above the pump section, Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle P_f} is the pressure loss in the suction piping, Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle P_v } is the vapor pressure of the liquid at the pump suction, Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \rho } is the density of the liquid, and $g$ is the acceleration due to gravity. Regardless of what Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle NPSH_{reqd} } is, the Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle NPSH_{avail} } from the above equation must exceed it to avoid cavitation.