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empirical temperature correction equations can be developed. One equation developed for the EPM dilution probe is given in Equation 3‐5.

(3‐5)

      This correction equation appears to be system specific (Jahnke and Marshall 1994) and should only be used as a first approximation for small changes in temperature (e.g. ± 50 °F). It is recommended that the user check the expression for his or her own installation and adjust it as appropriate. It does not appear to work well in cycling units where large swings in temperature are frequent.

       Molecular Weight Correction Equation.

      Since the flow through the critical orifice is dependent on gas density, molecular weight of the sample gas also affects the dilution ratio. Fluctuation of flue gas moisture and CO₂ concentrations can cause errors in the dilution measurements since their concentrations are respectively low (18) and high (44) relative to the usual combustion gas molecular weight of ~30. Also, with regard to earlier Scenario 4, the use of multi‐blend calibration gases containing CO₂ initially caused considerable confusion in conducting calibration error (drift) and linearity tests. The higher molecular weight of CO₂ increases the density and will cause lower readings if the dilution system was previously calibrated with a cylinder gas containing nitrogen (MW 28) only, as a background gas. Errors due to fluctuations in molecular weight have been calculated to approach up to 7%, depending upon the initial calibration conditions and measurement conditions (McGowan 1994).

      This issue was first resolved by Miller (1994) who calculated relative sonic velocities for a variety of multicomponent gas mixtures. A molecular weight correction expression was developed by Appel (1994) for changes in flue gas composition valid under the condition that the dilution system is calibrated initially with single‐blend, nitrogen background cylinder gases:

(3‐6)

       Combined Corrections.

      If pressure, temperature, and molecular weight changes are affecting the dilution system response, the equations given above can be cascaded to obtain the following:

      (3‐7)

      Such an expression may not be necessary for all applications, but it does indicate that some insight must be put into the application and that more than one correction may be necessary.

       Theoretical Corrections.

      Although the theory of the critical orifice has been examined in detail, the construction and operation of dilution probe and its analogues may not satisfy all the underlying assumptions of the theory. Theoretical aspects of dilution systems were studied by Munukutla (1992) and Jahnke and Marshall (1994), Romero and Associates (1999), and Batug and Associates (2004). The extended formulation of Jahnke is provided here.

      Dilution system theory begins from the theoretical equation for critical flow (see ASME 1971; Green and Perry 2007; Sadegh and Worek 2017; Shapiro 1953). This equation is used to obtain a corrected dilution ratio, D, from a new set of gas conditions that differ from the conditions under which the system was originally calibrated for the initial dilution ratio, D_o (Jahnke and Marshall 1994; Munukutla 1992):

      (3‐8)

Instead of using Equation 3‐3 (c = c_measD_o) to calculate the source‐level concentration from the measured analyzer data, the following equation can be used to correct the data to the actual conditions of measurement:

(3‐9)

      This equation has been shown to adequately represent the effect of pressure and molecular weight changes on dilution system data (note: it is simplified by not incorporating changes in specific heat) (Jahnke and Marshall 1994; McGowan 1994; Miller 1994). Critical orifice theory predicts that the temperature variation . However, this expression is incomplete since it does not account for changes in the dilution air temperature. Baugham (1996) has done this and has developed an instrument control method that corrects for both probe and dilution air temperature variations. In later work, Romero et al. (1999) and Batug et al. (2004) applied computational fluid dynamic techniques to develop a model for evaluating temperature, pressure, and molecular weight effects in the EPM dilution probe.

Equation 3‐9 is especially useful for calculating molecular weight corrections that would apply to changing flue gas composition or cylinder gas audits using different gas blends. One can simply input the molecular weight of the initial calibration gas, M_o, and correct subsequent readings if the molecular weight of the test gas, M, is known.

      Note that these corrections may not be necessary if data are reported as an emission rate, E, in terms of lb/mmBtu (ng/J). If emissions are reported in units of lbs pollutant emitted/10⁶ Btu generated (or ng/J),

      the F factor expression can be used (see Appendix A).

(3‐10)

      where

       Fc = “F” factor in scf/106 Btu

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