Air Preheater X-Ratio Calculator

On the air preheater side, X-ratio is not a number to be read as “efficiency” by itself; rather, it is used to check the heat capacity balance between the air and gas sides. In particular, the gas outlet temperature looked at without making a leakage correction can give the impression that the APH is performing better than it actually is. This calculator is prepared to calculate the X-ratio value using temperature data, with a ready no-leakage gas outlet temperature, or with the flow × specific heat method. The result is most accurate when read with temperature, flow, and leakage data taken from the same load point.

What exactly does X-ratio show?

In air preheater performance, X-ratio is a practical ratio used to read the heat capacity balance between the gas side and the air side. It is used to approach some of these questions: Is the APH clean or dirty, have seal leakages increased, is the air side being loaded more than expected?

The most common temperature-based expression is written as:

$$
X = \frac{T_{g,in} - T_{g,out,nl}}{T_{a,out} - T_{a,in}}
$$

Here \(T_{g,in}\) is the gas inlet temperature. \(T_{g,out,nl}\) is the no-leakage gas outlet temperature corrected for the leakage effect. \(T_{a,in}\) denotes the air inlet, and \(T_{a,out}\) denotes the air outlet.

The main issue is that the gas outlet temperature should not be taken with raw measurement. In a rotary APH, if there is seal leakage, air leaks into the gas side. The gas outlet appears low on the DCS screen. It looks good on paper, but it is often not a value to be trusted too much.

That is why the no-leakage temperature is discussed separately.

X-ratio calculation is especially used for comparison with design after a performance test, pre- and post-maintenance tracking, monitoring the effect of APH washing, separating the leakage effect after seal adjustment, and roughly seeing the air-gas side capacity balance. The word “roughly” is important here. If the measurement point, load, fuel, excess air, O2 trim, and flow calculation are not proper at the same time, the interpretation can shift even if the formula is correct.

In an engineering report, simply writing “X-ratio = 0.76” is not enough. It should also be stated by which method it was found, which temperatures were used, and whether the leakage correction was applied. Otherwise, there is a number, but no trace.

Leakage correction when calculating with temperature

The temperature + leakage correction method derives the no-leakage gas outlet temperature from the measured gas outlet temperature:

$$
T_{g,out,nl} = T_{g,out,measured} + \left(\frac{L}{100}\right) \times (T_{g,out,measured} - T_{a,in})
$$

\(L\) is the leakage rate and is entered as a percentage. If \(L = 8\), then \(8 / 100\) is used in the formula.

For example, if the gas inlet is 350 °C, the measured gas outlet is 150 °C, the air inlet is 30 °C, the air outlet is 280 °C, and the leakage rate is taken as 8 percent, the no-leakage gas outlet becomes approximately 159.6 °C. With this value, the X-ratio comes out to approximately 0.7616. If the design value is 0.80, the deviation is around -4.8%.

These values are clean example values. In the field, you often see 347.8 °C instead of 350; the air outlet gets stuck at 276.4 °C instead of 280; the leakage report says 7.6 percent instead of 8 percent. The calculator also works with these fractional values. Seeing fractions in real data is more normal.

The unit issue is short but critical. You can work with °C, °F, or K; since the calculation is based on temperature differences, if the conversion is done correctly, the result stays on the same line. The error usually doesn't come from unit conversion, but from putting data that doesn't belong to the same load point into the same calculation.

If the no-leakage value is already available, do not re-correct

Some test reports already give the no-leakage gas outlet temperature. In such a case, there is no need to regenerate no-leakage from the measured gas outlet temperature with the leakage correction. You would have applied the same correction twice.

In this method, the following calculation is done directly:

$$
X = \frac{T_{g,in} - T_{g,out,nl}}{T_{a,out} - T_{a,in}}
$$

For 350 °C gas inlet, 160 °C no-leakage gas outlet, 30 °C air inlet, and 280 °C air outlet, the X-ratio is 0.76. If the design is 0.80, the deviation comes out to -5%.

Here, what needs to be checked is the source rather than the number. Where did the \(T_{g,out,nl}\) value come from? Is it from a guarantee test, a site performance test, the manufacturer's datasheet value, or from another calculation file? Two values carrying the same label sometimes do not tell the same thing.

In APH reports, a small note line saves a lot of work:

• Load: for example, 85 percent MCR
• Fuel: coal, gas, fuel-oil, biomass; whichever is used
• Leakage: measured or assumed
• Temperatures: instantaneous value or average
• No-leakage: calculated or taken from the report

There's no need to embellish this at length. But if it is not written at all, six months later the person opening the same report will fight with the calculation.

X-ratio via flow and Cp

The temperature method is sometimes sufficient, sometimes not. If the flow and specific heat information is reliable, the capacity ratio gives a more direct reading:

$$
X = \frac{\dot{m}_{air} \times C_{p,air}}{\dot{m}_{gas} \times C_{p,gas}}
$$

\(\dot{m}_{air}\) is the air mass flow rate, \(\dot{m}_{gas}\) is the gas mass flow rate. \(C_{p,air}\) and \(C_{p,gas}\) are the specific heat values of the respective fluids.

If 120 kg/s air flow, 130 kg/s gas flow, 1.005 kJ/kg·K for air and 1.09 kJ/kg·K for gas are taken, the X-ratio comes out to approximately 0.8503. If the design is 0.80, the deviation becomes +6.29%.

In this method, the temperature probe error falls back a bit; flow and Cp assumptions come to the forefront. Where the flow comes from is important. Is it from the fan curve, a test measurement, or a DCS calculation tag? The Cp side is the same. If the gas composition changes, the constant \(C_{p,gas}\) assumption remains a bit shaky.

In a coal boiler, excess air changes, flue gas moisture changes, O2 trim plays. If you are burning biomass, things get even messier. Reading all loads with the same Cp value may be practical, but this assumption needs to be written in the report.

There is also a unit error. If kg/h and kg/s are used side by side, the result becomes nonsense. The calculator can do unit conversion; nevertheless, knowing what the entered value represents remains on the user's side. 120 kg/s and 120 kg/h are not the same thing. When this mistake is made, the X-ratio doesn't deviate slightly; it goes completely elsewhere.

How should the design deviation be read?

The expression used for the design comparison is straightforward:

$$
Sapma\ (\%) = 100 \times \frac{X_{mevcut} - X_{tasarım}}{X_{tasarım}}
$$

If \(X_{mevcut}\) is 0.7616 and \(X_{tasarım}\) is 0.80, the deviation is approximately -4.8%. This indicates that the current value remains below the design. It is still too early to render a performance verdict in a single sentence.

If there is a negative deviation, the data is looked at first. Is the gas inlet temperature stable? Was the air outlet read from a single point? Is there stratification in the APH outlet duct? Was leakage measured at the same test point? Issues such as basket fouling, fouling, seal gap, bypass, cold-end plugging come into play here.

A positive deviation is not always “better” either. The air flow may have been entered too high. The gas flow may have been underestimated. The Cp assumption may have been chosen higher than necessary. Sometimes the brightest-looking line of a report comes from the weakest assumption.

X-ratio should be read not alone, but together with gas outlet temperature, air outlet temperature, leakage rate, and APH pressure drop. If these speak in the same direction, the interpretation strengthens. If one is playing a different tune, the measurement side should be examined first.

Method selection in the calculator

This calculator works with three different methods.

Temperature + leakage correction is used when you have the measured gas outlet temperature and the leakage rate. The no-leakage gas outlet is derived within the calc. It is a practical way for a quick check after maintenance.

The no-leakage temperature direct method is for cases where this value is given ready in the test report. Here, the leakage rate is not brought into play again.

The flow × specific heat method compares the heat capacity flow rates on the air and gas sides. It is based not on temperature difference, but on mass flow and Cp values. If the flow data is not reliable, it produces a good-looking result, but it is hard to trust.

Temperature units can be °C, °F, and K. On the flow side, units such as kg/s, kg/h, lbm/h, lbm/s, klbm/h, or t/h can be used. The tool converts them to a common base. It is good for the chosen units to remain clear when writing a report; especially in plants where different teams enter data into the same file.

The Design X-ratio field is for comparison. Whatever the manufacturer's datasheet, guarantee test, or accepted operating target is, that value is entered. If the design value is not known, the default 0.80 can be used, but it should not be presented as design data. It would be more honest to write “reference assumption”.