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A software simulation had to be designed that could compare theoretical inputs and outputs with that of an existing simulation used to design steam tracing, as well as compare it to existing installed steam tracing, in order to determine where improvements in the software could be made.

The new software had to use the outputs from the existing software as inputs and its outputs had to correspond to the inputs of the existing software. Other important evaluations were also included in the new software.

Electrical heat tracing may be described as an insulated electrical heating cable, which is spiralled around the process fluid pipe, after which the pipe and tracing is insulated with the appropriate type and thickness of insulation lagging material.  While this method of heat tracing may be installed with

relative ease compared to steam tracing, it is more expensive, and poses several risks.  The most important of these, being the risk of electric spark, which may cause electric shock or ignite flammable substances resulting in explosions or fire.   If electrical heat tracing is not carefully controlled, there is also the possibility that the cable could overheat and damage the pipe or insulation.  This also renders the tracing cable unusable and the cable needs to be replaced.

Steam tracing is described by attaching a smaller pipe containing saturated steam, also known as the “tracer”, parallel to the process fluid pipe. The two pipes are then also insulated together with the specified insulation and jacketed if necessary.  Steam tracing is more labor intensive to install than electrical heat tracing, but there are very few risks associated with it.  The temperature of the tracer also cannot exceed the maximum saturation temperature of the steam, as it operates at specific steam pressures.

Steam tracing may be done in one of two ways.  Bare steam tracing is the most popular choice as it is fairly easily installed and maintained and it is ideally suited to lower temperature requirements.  It is simply composed of a half inch or three quarters of an inch pipe attached to the process fluid pipe by straps and both pipes are then insulated together.   The other available option is to make use of cemented steam tracing, during which heat conductive cement is placed around the steam tracer running parallel to the process fluid pipe, (shown in figure 1b), in an attempt to increase the contact area available for heat transfer, between the tracer and the process fluid pipe.

It is necessary to foster a better understanding of the heat loss distribution through an insulated pipe containing steam tracing, before continuing the discussion. For this purpose, detailed diagrams depicting the cross-sections of the two types of tracing methods are given below, in figures 1a and b:

Because the area around the process fluid pipe and tracer cannot be accurately described simply by assuming perfect cylindrical geometry, provision had to be made for a realistic impression of the true geometry. Detailed derivations of formulas are included in Appendix 1.

Heat transfer across a surface occurs according to the following equation: (Coulson & Richardson, 1999:634-688)

(2.1)

The following equations were derived in determining the different areas across which heat transfer occurs:

(2.2)

For bare tracing, the following formulas were derived:

	(2.3)
	(2.4)
	(2.5)
	(2.6)
	(2.7)
	(2.8)
	(2.9)
	(2.10)
	(2.11)
	(2.12)

The following equation was used to determine the hottest surface temperature for bare tracing: (Le Roux, D.F. (1997) “Thermal Insulation and Heat Tracing”, Guideline presented by D.F. le Roux, Secunda)

	(2.13)
	(2.14)
	(2.15)
For cemented tracing, the following formulas were derived:
	(2.16)
	(2.17)
	(2.18)
	(2.19)
	(2.20)
	(2.21)
	(2.22)
	(2.23)
	(2.24)
	(2.25)
The following equation was used to determine the hottest surface temperature for cemented tracing:
	(2.26)
where
	(2.27)
Refer to Appendix 2 for a table of qt vs. NPS. (Table 3)

 

The independent variables for the design were as follows, and were all specified variables in the software simulation:

• Time, s
• Pipe Length,                                         (0 to maximum length for steam trap), m
• Steam Pressure,                                   (240 to 1700kPa)
• Nominal process fluid pipe size,             (0.5 to 48 inches)
• Amount of available tracers                    (0 to 5)
• Nominal pipe size of tracer pipe,           (0.5 or 0.75 inches)
• Insulation thickness,                              (0 to process fluid pipe diameter), m
• Emissivity of insulation lagging               (0 to 1)
• Ambient Temperature,                           (-10 to 50 șC)
• Wind velocity,                                        (0 to 72km/h)

The dependent variables for the simulation were as follows:

• Annulus Temperature,                           (Process fluid temperature to Steam Temperature)
• Saturated Steam Temperature,              (126.1 to 204.3șC)
• Steam Consumption,                             (0 to 50kg/h)
• Process Fluid Temperature,                   (0 to 600șC)
• Pipe Outer Radius,                                (10.668 to 609.62mm)
• Pipe Wall Thickness,                             (1.3974 to 15.6869mm)
• Pipe Inner Radius,                                 (6.401 to 1219.2mm)
• Pipe Wall Thermal Conductivity,             (16 to 401W/mK)
• Steam Tracer Outside Radius,               (6.35 to 9.53mm)
• Maximum Tracer Length,                       (30 to 60m)
• Thermal Conductivity of insulation          (0.01241 to 0.1120 W/mK)
• Average Insulation Temperature,      (Ambient temp. to Steam temp.)
• Surface Temperature,                           (N/A), K
• Surface Film Coefficient,                        (N/A), W/m²K

The main deliverable was to obtain the minimum temperature at which the process fluid had to enter the pipeline, but other information such as the wall temperature and steam consumption were also important.

The interface designed for the simulation is shown in Fig. 3c and was written in Microsoft Excel:

Fig. 3c, Interface

The detailed design and calculations can be found in Appendix 1. The design was done following an unconventional approach, in an attempt to make as few assumptions as possible.

Most of the equations were fundamentally derived, but some equations were employed from other sources. (See References)

All the necessary equations were developed and simplified to eliminate ambiguity. The equations were then solved simultaneously and by making use of iterations.

The inputs to the simulation were highlighted in yellow, on the left side of the page, and the outputs were highlighted blue, on the right hand side, to eliminate ambiguity in deciding which were inputs and which were outputs.

The inputs section mostly made use of drop-down menus to facilitate data input, and mostly made use of referencing techniques to look up the necessary values used in the calculations. For example, the user was only required to choose the NPS of the process fluid pipe, and the schedule number, and the program automatically looked up the outer diameter, inside diameter and wall thicknesses from a table containing accurate standard values for pipe sizes.

Also, the user was only required to specify the insulation material type, steam pressure, and ambient temperature, which the program used to calculate an average insulation temperature, and interpolate between different k-values, to obtain the specific thermal conductivity at that specific temperature, since thermal conductivity is temperature dependent. The program also used the lagging emissivity, together with the ambient temperature, surface temperature and wind velocity, to calculate an exact value for the surface film coefficient on the outside, which needed to be very accurate.

The program was also able to calculate a maximum surface temperature, to ensure safety protection for personnel, as the surface temperature, by standard, is not allowed to exceed 60 șC. Temperatures higher than this would result in injury caused by touching the outside surface.

The steam consumption was also calculated by determining the heat loss from the system for a certain length of pipe. The steam is invariably subject to heat loss, and thus condensation, when sufficient heat has been lost. This corresponds to the maximum length of a tracer. Fresh, saturated steam then needs to be re-introduced into the system, to ensure efficient operation, and a steam trap needs to be installed at the end of the maximum length, to collect all the condensate which has formed. The condensate may be recycled to create new steam.

The simulation made use of macros, in the sense that the program automatically performs the calculations necessary to converge the answers to a final answer, by simply requiring the user to press a shortcut key.

Due to the nature of the project, definite answers are not possible to obtain, but rather different simulations could be run and each time the answers could be evaluated. As an example, one specific run could be described in terms of its equations as follows:

Consider the Bare Tracer.

Firstly, the inputs field has to be completed (see Table 1):

Table 1: Input Fields

After this has been done, the outputs section may be calculated:

Some of the outputs are values found in making use of references from other tables. These are shown first in Table 2.

Table 2: Output Fields

This information can now be used together with the inputs section to calculate the remaining outputs.

Firstly, the Average Insulation Temperature is calculated from equation (2.9):

it is found that   T_ins=36.67 șC

It should be noted that the Process fluid Temperature is not known yet, so this is not a final answer.

Secondly, the Annulus Temperature may be calculated from eq. (2.8):

T_ann=76.4 șC

Since T_p is not known yet, and T_ins has not yet been assigned a definite value, this value is also not fixed yet.

Now, the Average Surface Temperature needs to be calculated.  This value may be approximated by assuming that about 80% of the average surface temperature is due to the process fluid temperature and the remaining 20% is made up of the surface temperature on the tracer side.  The Average Surface Temperature may then be calculated as follows.

From Eq.(2.13) and (2.14):

for the tracer side

and

for the process fluid pipe side.

The surface temperature is now calculated by making use of iterations to obtain the final value of
                   
T_surf)Avg = 14.991 șC 

This causes the value of q to change until it stabilizes to its final answer

Technically speaking, one has to calculate the area ratios that the process fluid pipe, annulus length and tracer each contribute, calculate each area’s surface temperature, and obtain the average value for the surface temperature accordingly, but due to the limited capacity of Microsoft Excel, this method was tried and it failed, because Excel could not perform all the iterations necessary to do the calculations.  The above calculation has shown to give satisfactory results for most situations.

The value for the surface coefficient then becomes:
h₀=10.1
k₁ is calculated using Eq.(2.10):

but according to Eq.(2.5),

and

therefore, k₁=18.21340591
k₂ may then be calculated using Eq.(2.11):

and therefore amounts to     k₂= 0.489641399

Finally the Process Fluid Temperature can be calculated using Eq.(2.12):

Excel is then programmed to perform iterations automatically, since a circular reference is created, but it causes all of the values to converge consequently, and the final answers are obtained, and with the final values of T_ins known, the correct thermal conductivity values can be obtained and used in the equations:

k_ins=0.02712 W/mK
k_w=53.3 W/mK

Le Roux, D.F. (1997) “Thermal Insulation and Heat Tracing”, Guideline presented by line manager D.F. le Roux, Secunda.

Foo, K.W. (1994) “Sizing tracers quickly (Part 1)”. Hydrocarbon Processing, p93-97. January. “Sizing tracers quickly (Part 2)”. Hydrocarbon Processing, p93-97. February.

Fisch, E. (1984) “Winterising process plants”. Chemical Engineering, p128-143, 20 August.

Kenny, T.M. (1992) ”Steam tracing: do it right”. Chemical Engineering Progress, p40-44, August.

Coulson, J.M and Richardson, J.F. (1999) Chemical Engineering, R.K. Sinnot, London.

Le Roux, D.F. (2005) Theoretical discussion and problem description, Sasol Limited, Secunda.

Van der Spuy, E. (2005) Theoretical advice, and steam traps, Spirax Sarco, Secunda.

Smit, J. (2005) Practical information, Sasol Limited, Secunda.

Technical committee of specification SP 50-4, (2004) Specification SP 50-4 Revision 2 for Steam and Hot Water Tracing, Sasol Limited, Secunda.