Equations for quantifying the quality of industrial steam in feed mills

Quantifying the quality of industrial steam should be a recurring action in a plant, as it depends on being able to maintain the useful life of the equipment and provide quality end products. In general terms, steam quality is defined as a measure of the amount of saturated steam coexisting with its condensate in a given system.

Steam generators enable efficient food processing, so quantifying the quality of steam in food industry systems is of great importance to minimise moisture damage to machinery.

This article will focus on the benefits and equations for quantifying the quality of industrial vapour. Although it is difficult to eliminate liquid carryover in condensate, it is possible to measure this percentage of liquid to avoid irreversible damage within the system and its components.

Similarly, high velocity condensate can cause other problems related to erosion and corrosion. So one way to achieve the optimisation and control of energy costs in industrial steam systems is to quantify the quality of the industrial steam.

Benefits of quantifying the quality of industrial steam

• Increased heat transfer efficiency:

The main problem with poor steam quality is the effect on heat transfer in equipment and processes. In some cases, low steam quality can reduce heat transfer with efficiencies of no more than 65%. Therefore, less usable energy is available.

Quantifying the quality of industrial steam allows for a reduction of liquid build-up in the heat exchanger, indicating a higher latent energy capacity of the steam to be transferred to the product.

• Prevents premature valve failure:

By quantifying the vapour quality, the passage of liquid through the vapour control valves can be reduced, resulting in less erosion of the internal parts of the valves and preventing premature failure.

• Prevents failure of internal turbine components:

Quantifying the amount of liquid and industrial vapour provides insight into the amount of liquid that is introduced with the vapour in an operation, thus providing information on how much to reduce it to help maintain the life of internal components.

• Reduces water hammer problems:

Because steam systems are generally not designed to accommodate the additional liquid in liquid vapour, the potential for water hammer is created, so quantifying the quality of industrial steam allows action to be taken to reduce the likelihood of water hammer failures.

Equations for quantifying the quality of industrial steam in the system

As a first equation to find the amount of saturated steam with condensate, the mass of steam is divided by the total mass of steam and condensate.

Where:

Msteam= Mass of vapour within the system.

Mcond= Mass of vapour coexisting in the condemned.

Once the general equation is known, we will start to calculate the vapour quality with a throttling calorimeter. It is clear that a small amount of vapour is throttled through an orifice from system pressure (PS) to atmospheric pressure.

The vapour temperature at the orifice outlet (TE) is recorded. This expansion is adiabatic. Thus the following expression describes the energy balance associated with the throttling process:

HM= HL (1-X) + HGX   (Equation 2)

By rearranging equation 2, x= Steam Quality can be found as follows:

X=

Where:

• HM = Enthalpy of superheated steam at temperature.
• TE = Outlet temperature at atmospheric pressure.
• HL and HG = Enthalpy of condensate and steam, respectively, at system pressure PS.
• X= Steam quality

In order to calculate the steam quality with the thermodynamic data, it must be carried out by means of the ASME Steam Tables, The Enthalpy - Entropy Chart is shown here.), TE (Temperature at atmospheric pressure) on the abscissa and vapour quality (X) on the ordinate.

Also shown in the diagram is a series of isobars for PS (System Pressure) in the range 50 to 1500 psi. This diagram provides a quick estimate of steam quality when TE and PS are known, either directly, interpolating or extrapolating.

Action that applies to a third equation that allows us to find the quality of steam at pressures ranging from 2 bar (29 psi) to 200 bar (2900 psi) and is expressed as follows:

X = A + B(TE) (equation 3)

This formula describes the vapour quality at each pressure, PS as a function of TE. Each set of coefficients A and B (constant vapour terms as a function of temperature see table 1) is valid for one pressure only. The coefficients for pressures not included in the list must be interpolated. Solving equations 2a and 3 requires the user to look up the data prescribed above.

Table 1. Dielectric constant of vapour as a function of pressure and temperature

A fourth equation is also used to quantify the quality of the industrial steam when the pressure and temperature of the calorimeter are known. It is valid for steam quality between 0.95 and 1.00 and for pressures between 30 psi and 600 psi, as follows:

X = 0.9959 - 0.000442TE - ln [(PS + 6.8) 0.03218 (PS + 374) -0.0001581TE].

Solving for TE will take Equation 4a, whereby it is expressed as a single continuous function, thus eliminating the need for graphical data representation or interpolation.

TE = [0.9959 -X - 0.03218 ln (PS + 6.8)] / [0.000442 - 0.001581 ln (PS + 374)] / [0.000442 - 0.001581 ln (PS + 374)].

By adjusting the data available in the ASME steam tables, the P-T relationship for saturated steam in the range 30 to 600 psi, an equation 5 remains, which can be expressed as follows:

PS = 1.5 + (TS120.62) 4.5886

Solving for the saturated vapour temperature TS:

TS = 120.62 (PS - 1.5) 0.21793 (Equation 5a)

Where:

TS= System temperature.

Another way to quantify the quality of industrial vapour is to rely on the basic principles of saturated vapour. Knowing that vapour is an invisible dry gas and only becomes visible with entrained air or liquid. Therefore, opening a vapour valve and allowing vapour to be released into the atmosphere provides an estimate of vapour quality.

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