Quantifying steam quality

One equation comprising two independent variables gives an accurate assessment of steam quality

By Frank A. Rusche

By Frank A. Rusche

Steam quality is a measure of the amount of saturated steam that coexists with its condensate in a given system. Calculate it by dividing the mass of steam by the total mass of steam and condensate.

Steam quality = Msteam/(Msteam + Mcond) (Eqn. 1)

Others have pointed out the importance of identifying steam quality in systems supporting industrial applications. For example, excessive moisture in the form of free droplets carried along with the main steam flow might impinge on turbine blades and cause mechanical damage. Likewise, high-velocity condensate can score valve seats and cause other erosionand corrosionrelated problems.

Ganapathy(1) gives a detailed explanation of how to calculate steam quality with a throttling calorimeter. A small quantity of the steam is throttled through an orifice from system pressure (PS) down to atmospheric pressure. The steam temperature at the orifice exit (TE) is recorded. This expansion is adiabatic. The following expression describes the energy balance associated with the throttling process:

ADVERTISEMENT

HM = HL (1-X) + HGX (Eqn. 2)

And after rearranging:

X = (HL-HM)/(HL - HG) (Eqn. 2a)

Where:

HM = enthalpy of superheated steam at temperature.

TE = exit temperature at atmospheric pressure.

HL and HG = the enthalpy of condensate and steam, respectively, at system pressure PS.

X = the steam quality.

Thermodynamic data for calculating steam quality may be obtained from ASME Steam Tables(2) or any other library source(3). Ganapathy developed a diagram, which displays TE on the abscissa and X on the ordinate. A series of isobars for PS in the 50 to 500 psia range also is shown on the diagram. The diagram provides a quick estimate of steam quality when TE and PS are known.

Liley(4) calculated steam quality at pressures ranging from 2 bars (29 psia) to 20 bars (290 psia) in one bar increments. He developed an equation of the form:

X = A + BTE (Eqn. 3)

It describes the steam quality at each pressure, PS as a function of TE. Each set of coefficients A and B is valid for only a single pressure. Coefficients for pressures not included in the list must be interpolated. Solving equations 2a and 3 requires a user to look up recorded data.

The following equation was developed to quantify steam quality when the pressure and calorimeter temperature are known. It is valid for a steam quality between 0.95 and 1.00 and for pressures between 30 psia and 600 psia:

X = 0.9959 - 0.000442TE - ln[(PS + 6.8)0.03218(PS + 374)-0.0001581TE] (Eqn. 4)

Solving for TE:

TE = [0.9959 -X - 0.03218 ln(PS + 6.8)]/[0.000442 - 0.001581 ln(PS + 374)] (Eqn. 4a)

Expressing steam quality by means of a single continuous function eliminates the need for graphical data representation or interpolation. The equations can be used for online steam quality monitoring with a programmable process controller using orifice exit temperature and steam system pressure as input values, or they can simply be stored in the memory of a pocket calculator for use when the information is required.

By curve fitting available data in the ASME Steam Tables, the P-T relationship for saturated steam in the 30 to 600 psia range can be expressed as:

PS = 1.5 + (TS/120.62)4.5886 (Eqn. 5)

Solving for the saturated steam temperature TS:

TS = 120.62 (PS - 1.5)0.21793 (Eqn. 5a)

Substituting Eqn. 5 into Eqn. 4 allows the latter to be expressed entirely in terms of TE and TS. The graph in Figure 1 gives a quick method for calculating steam quality when saturation pressure and temperature and calorimeter temperature are known.

The validity of the above equations has been tested against a known example presented in one of the referenced articles and, at a more elevated pressure level, against steam data obtained from the Engineering Data Book(3).

The fast way

 

Figure 1. Steam quality X can be quickly assessed graphically when the exit temperature TE and the saturated steam temperature TS and pressure PS are known.

Try these examples

Example 1. Calculate the steam quality of a 200 psia system when the orifice exit temperature is 250 F.

Page 1 of 2

<< < 1 | 2 > >>

Sponsored Links