Loss of steam through steam traps accounts for significant energy waste at many plants. Quantifying the extent of the loss often poses difficulties. Indeed, to date, no simple-to-use predictive tool can accurately estimate the actual rates of lost steam as a function of steam line pressure and saturation temperature of sub-cooled condensate. Here, however, we present an accurate and reliable method that requires fewer computations than conventional approaches.

**Tuned Coefficients**

**Table 1.**These coefficients, suitable for Eqs. 2–5, cover flow rates of condensate for steam traps with CV = 1 for data reported by Branan.The tool predicts the condensate flow,

*Q*, in kg/h, via a simple equation: Ln

*(Q) = a + b/P + c/P*(1) where

^{2}+ d/P^{3}*P*is steam line pressure in kPa (abs) and the four coefficients relate to the sub-cooled condensate's saturation temperature,

*T*, in K, via:

*a = A*(2)

_{1}+ B_{1}T + C_{1}T^{2}+ D_{1}T^{3}*b = A*(3)

_{2}+ B_{2}T + C_{2}T^{2}+ D_{2}T^{3}*c = A*(4)

_{3}+ B_{3}T + C_{3}T^{2}+ D_{3}T^{3}*d = A*(5) The optimum tuned coefficients (

_{4}+ B_{4}T + C_{4}T^{2}+ D_{4}^{T3}*A, B, C and D*) appear in

**Table 1**. They cover condensate flow rates for steam traps with a flow capability, C

_{V}, of 1 in data reported in the 4th edition of C. R. Branan's "Rules of Thumb for Chemical Engineers," Gulf Publishing (2005). In the next step, the result from Eq. 1 is used to estimate actual loss of steam. Equation 6 gives the corrected steam-trap flow factor:

*F*(6) Equation 7 then predicts actual steam loss, SA, as a function of trap inlet pressure, in kPa (abs), and the corrected flow factor:

_{C}= Q_{C}/Q*S*= (0.093P – 9.4589)

_{A }*F*(7)

_{C}**Condensate Flow Rate**

**Figure 1.**Tool's predictions of sub-cooled condensate flow rate in steam trap agree well with data from Branan (2005).

**Figure 1**compares the tool's predictions of condensate flow rates in steam traps with C

*= 1 as a function of steam line pressure and saturation temperature of sub-cooled condensate with data reported by Branan. The results agree well with these data.*

_{V}**Figure 2**depicts the tool's performance for estimating condensate flow rates as a function of steam line pressure and saturation temperature of sub-cooled condensate. Figure 3 compares predicted steam loss as a function of inlet pressure with Branan's data.

**Table 2**highlights the very good agreement with the reported data — the average absolute deviation is 2.87%.

**Effect of Pressure and Saturation Temperature**

**Figure 2.**Estimates of sub-cooled condensate flow rate cover a wide range of conditions. (Color bar shows sub-cooled condensate flow rate).

**AN EXAMPLE**Contact pyrometer measurements taken immediately upstream and downstream of a steam trap on a 1,136-kPa (abs) steam line indicate it's blowing live steam. The catalog rating of the trap at that pressure is 2,270 kg/h at saturation temperature (255.4 K sub-cooled). So:

*a*= 8.0217665022 (from Eq. 2);

*b*= -1.453738401 × 10

^{3}(from Eq. 3);

*c*= 4.301678566 × 10

^{5}(from Eq. 4); and

*d*= -4.40231517 × 10

^{7}(from Eq. 5). Therefore, condensate flow rate = 1,147.4389 × 10

^{3}kg/h (from Eq. 1). The flow factor is:

**Tool Accuracy**

**Table 2.**Predictions of sub-cooled condensate flow as a function of steam trap inlet pressure and sub-cooled condensate temperature show good agreement with published data.

*F*= 2,270/1,147.44 = 1.9783 (from Eq. 6). Equation 7 then gives 190 kg/h steam flow. For the trap in question, assuming a rather modest steam cost of $3 per thousand kg, the loss of steam is estimated to cost: 190/1,000($3) = $0.57/h or $113/wk. The results show good agreement with the $117/week from Branan.

_{C}**SIMPLE AND USEFUL**We have introduced a method that's superior in accuracy and ease of use. Relevant coefficients can be re-tuned quickly for various cases and if new data become available. This predictive tool enables process engineers to easily monitor steam loss for a wide variety of operating conditions. It also should immensely help combustion engineers estimate the total amount of heat recoverable from boilers using blowdown systems. The method should speed analysis of design and operational modifications.

*ALIREZA BAHADORI is a postgraduate student in the School of Chemical and Petroleum Engineering, Curtin University, Perth, Australia. HARI B. VUTHALURU is an associate professor in the School of Chemical and Petroleum Engineering, Curtin University, Perth, Australia. E-mail them at *[email protected] *and* [email protected].

**NOMENCLATURE**

*A --*Tuned coefficient

*a*-- Coefficient

*B*-- Tuned coefficient

*b*-- Coefficient

*C*-- Tuned coefficient

*c*-- Coefficient

*C*-- Flow capability

_{V}*D --*Tuned coefficient

*d*-- Coefficient

*F*-- Corrected flow factor

_{C }*P*-- Trap inlet pressure or steam line pressure, kPa (abs)

*Q*-- Condensate flow rate, kg/h

*Q*-- Catalog flow rating of trap, kg/h

_{C}*S*-- Actual steam loss, kg/h

_{A}*T*-- Temperature, K