Maximum Tube Temperature

 

The maximum tube temperature is a crucial aspect of the heater performance that must be assessed during both design phase and operation. Alongside the process pressure, the tube temperature has a fundamental role in determining tube material selection, since each material will have prescribed temperature limits that they can withstand.

Thankfully, there are reliable calculation methods that can be utilised in order to determine maximum tube temperature, hence the appropriate tube material can be selected. The temperature calculation is more accurate for single phase process fluids (i.e. either 100% liquid flow, or 100% vapour flow), since the respective heat transfer properties can be reliably calculated for each case respectively.

For two-phase fluids, the calculation will have a wider degree of accuracy due to the inherent error margin in estimating physical property characteristics in combination with a particular flow regime.

API 530 Maximum Tube Temperature Calculation

The API 530 Standard (API 530 Calculation of Heater Tube Thickness in Petroleum Refineries) details a method for calculating the maximum tube temperature that has been proven and used widely across the industry. 

The API 530 method is based on the following equation:

T_{max =}  T_{bf +} ΔT_{ff +} ΔT_{f +} ΔT_tw

Where:

• T_max   is the maximum tube temperature, C or F
• T_bf   is the fluid bulk temperature, C or F
• ΔT_f   is the temperature difference across the internal fouling layer, C or F
• ΔT_tw   is the temperature difference across the tube wall, C or F
• ΔT_ff   is the temperature difference across the fluid film, C or F

Calculation of Temperature across the fluid film, ΔT_ff 

Note that ΔT_ff   is defined as follows:

                       ΔT_ff   =  ( Q_rMax  *  Do ) / ( K_ff  *  Di )

Where:

• K_ff  is the fluid film heat transfer coefficient, W/m² C or  BTU/hr ft² F
• Q_rMax  is the maximum radiant heat flux, W/m²  or  BTU/hr ft² 
• D_o   is the outside tube diameter, m or ft
• D_i   is the inside tube diameter, m or ft

Calculation of Temperature across internal fouling layer, ΔT_f

Note that ΔT_f   is defined as follows:

                          ΔT_{tw  =}  Q_rMax  *  R_f  *   / Do  ( Do  /  (Di  -  d_f ) )

where:

• d_{f  is the coke and/or scale thicknesses, m or ft}
• _Rf  is the fouling factor inside the tube

Calculation of Temperature across the Tube Wall, ΔT_tw

Note that ΔT_tw  is defined as follows:

                      ΔT_{tw  =}  Q_rMax  *  [ (Do  *  ln (Do / Di))  /  ( 2 * λtm ) ]

where:

• λtm is the tube thermal conductivity at the average temperature, W/mk or BTU/hr ft F

Maximum Tube Heat Flux

The heat flux is a measure of the intensity of heat absorption over a particular heat transfer surface. The greater the heat flux density, the higher the resultant tube temperature.

The average tube heat flux is evaluated based on the total heat absorbed, divided by the available area of the heat transfer surface.

For example, if the calculated duty (heat absorption) within the radiant section is 7MW, and the total tube area of the radiant tubes is 241m², the calculation of the heat flux is as follows:

7 MW = 7,000,000 W

Flux = 7,000,000 / 241

        = 29,045.6 W/m²

Determining the average heat flux, is a straightforward calculation as shown above. However, in reality, the heat absorption will not be completely uniform due to certain physical aspects such as certain tubes being closer to the flame than others, variation in flame height to the radiant section height, and flue gas distribution variations.

This means that the maximum heat flux is based on empirical correlation methods based the tube distance to wall and also whether the tubes are double fired or not.

According to API 530, the maximum flux can be estimated from the following equation:

Q_rMax = Fcir  *  FL *  FT * Q_rAvg + Qconv

where:

• Fcir   is the factor accounting for circumferential variations around the tube (determined from the graph B.1 above)
• FL      is the factor variations in longitudinal heat flux
• FT      is the factor for the temperature effect of radiant tube flux
• Q_rAvg   is the Average Radiant Heat Flux, W/m²  or  BTU/hr ft²
• Qconv   is the Average Convective Heat Flux,  W/m²  or  BTU/hr ft²

Note: further discussion of deriving suitable values for the FT and FT factors are not detailed within this article. Please refer to the API 530 standard for further details on suitable values to use. Alternatively, please get in touch with us to review the specific performance case of your particular fired heater. 

Fired Heater Tube Temperature Transmitters

Monitoring the tube temperatures during fired heater operation is an important factor to ensure that the heater is operating within safe design limits. Excessive tube temperatures may lead to extensive strain within the tubes, shortening the tube life and in worst cases result in tube rupture which can have catastrophic consequences.

Heat Transfer Coefficient inside Fired Heater Tubes

There have been numerous documented methods in literature for calculating the heat transfer coefficient of flowing fluids. Each method has their merits, limitations and best application scenarios.

API 530 also provides calculation methods for determining the inside heat transfer coefficient of the fluid flowing inside the tubes. The heat transfer coefficient is required to calculate the temperature across the fluid film, which is then used to calculate the tube temperature.

The heat transfer coefficient depends upon fluid physical properties, characteristics and vapour fraction. API 530 provides separate calculation for Liquid flow, Vapour flow and two-phase flow conditions.

Many engineers consider the API 530 method for two-phase flow is too simplistic and prone to error especially at higher vapour fractions. Therefore other correlation methods have been produced over a number of years to deduce the heat transfer coefficient.

Potential Root Causes for High Tube Temperatures in Fired Heaters

The following list details some of the common root cause factors that cause high tube temperatures readings in Fired Heaters:

• Low Process Flow Rates
• Flame-Tube Impingement (burners flames in contact with tubes)
• Uncontrolled fire within the heater
• Excessively high fuel supply pressure
• Failure in Temperature Measurement Instruments (thermocouple and/or transmitter)

Note: this list is not exhaustive and also some of the items mentioned above, may in turn have other problems that cause them to arise. For example, the case of Excessively high fuel pressure may arise because of multiple different reasons, such as failure in the firing rate controller or fuel control valve.

We would recommend installation of at very least 1 Tube Skin Thermocouple (TSTC) per pass, located on the final tube of each pass in the radiant section. We would also recommend that the TSTC be located at approximately 66% the height of the radiant section, to coincide appropriately with the flame height.

Tube Temperature Alarms and Trips

For most Fired Heaters, a high tube temperature trip would be considered excessive. However, alarming at sensible setpoints is considered a standard good safety practice. 

Sensible engineering judgement is required for defining the appropriate Alarm setpoints , which should be below the design temperature stated on the fired heater datasheet.