Jul-2010

Estimation of steam losses using a predictive tool

A predictive mathematical tool estimates condensate flow rate and flow correction factor to obtain steam losses in steam traps

Alireza Bahadori and Hari B Vuthaluru
Curtin University of Technology

Article Summary

Steam traps are generally used on steam mains, headers, separators and purifiers, where they remove water formed as a result of unavoidable condensation or carry-over from the boilers. They are also used on all kinds of steam heating equipment, in which the steam gives up heat and is converted to condensate. Whether a trap is used to keep condensate from accumulating in a steam line or to discharge water from a steam-heated machine, its operation is important. From a quantitative perspective, it is necessary to estimate steam losses in steam traps.

In the present work, a predictive tool, which is easier to use than existing approaches, with fewer computations, has been formulated to arrive at an appropriate estimation of the condensate flow rate and flow factor. The resulting information can then be applied to estimate actual loss of steam, for pressures up to 3500 kPa(abs) and saturation temperatures of sub-cooled condensates up to 100°C. 

The proposed predictive tool shows good agreement with the reported data, wherein the average absolute deviation hovered around 2.87%. This approach can be of practical value for engineers and scientists to gain a quick estimate of the actual loss of steam in steam traps for a wide range of operating conditions, without the necessity for a pilot plant or experimental trials. In particular, process engineers would find the tool involves transparent calculations with no complex expressions for their applications.

Boilers and other steam producers and plants are the most significant energy consumers in a refinery.¹ An important issue with regard to steam and condensate systems is the ability to predict consumed/wasted energy and opportunities for reducing energy consumption during the operation of boiler and steam plants.²

Steam traps must be used in these systems to automatically purge condensate and non-condensable gases, such as air, from the steam system. However, a steam trap should never discharge live steam. Such discharges are dangerous as well as costly.³ A steam trap is a device attached to the lower portion of a steam-filled line or vessel that passes condensate, but does not allow the escape of steam.⁴ It is also a piece of equipment that automatically controls the removal of condensate, air and carbon dioxide from a piping system with minimal steam loss.⁴ Removal of hot condensate is necessary to prevent water hammer, which can damage or misalign piping instruments.⁴

There are mechanical, thermostatic, thermodynamic and instrumented steam traps, and many steam trap functional characteristics and operating conditions.^5,6 In order to obtain the best performance for any type of steam trap under prevailing working conditions, the literature^7,8 rating tables for steam trap types can be used. Process steam traps comprise the highest potential for losses and costs related to process functions.^9,10,11

In view of the issues mentioned, it is necessary to develop an accurate and simple method that is 
less complicated than existing approaches, with fewer computations for predicting the actual loss of steam from steam traps. The results of the proposed predictive tool can be used in follow-up calculations to determine the extent of losses and costs related to process functions.

Methodology to develop a predictive tool
The data required to develop a predictive tool includes the actual loss of steam, as a function of pressures and saturation temperatures for sub-cooled condensate. In this work, the actual loss of steam in steam traps is predicted rapidly by proposing a simple tool, and the following methodology has been applied to develop this tool.

First, the flow rates of condensate for C= 1 in a steam trap are correlated as a function of steam line pressure (trap inlet pressure) in kPa(abs) for different saturation temperatures of sub-cooled condensate in 0K. Then, the calculated coefficients for these polynomials are correlated as a function of 
saturation temperatures of sub-cooled condensate. The derived polynomials are applied to calculate new coefficients for Equation 1 to predict condensate flow rates. Table 1 shows the tuned coefficients for Equations 2 to 5 for the flow rates of condensate according to the available data.¹²

In brief, the following steps13,14 are repeated to tune the correlation’s coefficients:
1    Correlate the flow rates of condensate in a steam trap as a function of steam line pressure in kPa(abs) for a given saturation temperature of sub-cooled condensate
2    Repeat step 1 for other saturation temperatures of sub-cooled condensate
3    Correlate the corresponding polynomial coefficients, which are obtained in the previous steps, against the saturation temperatures of sub-cooled condensate, a = f(T), b = f(T), c = f(T), d = f(T) (see Equations 2 to 5).

So Equation 1 represents the proposed governing equation in which four coefficients used to correlate the flow rates of condensate in a steam trap are correlated as a function of steam line pressure (P) in kPa(abs) for different saturation temperatures of sub-cooled condensate, where the relevant coefficients have been reported in Table 1:
                                                                             
In(Q) = a + b + c + d                      (1)
                        P    P2   P3 

where:
                                                                             
a = A1 + B1T + C1T2 + D1T3       (2)
                                                                                      b = A2 + B2T + C2T2 + D2T3        (3)
                                                                                      c = A3 + B3T + C3T2 + D3T3        (4)
                                                                                      d = A4 + B4T + C4T2 + D4T3        (5)