Engineering ToolBox - Resources, Tools and Basic Information for Engineering and Design of Technical Applications!

This is an AMP page - Open full page! for all features.

Search is the most efficient way to navigate the Engineering ToolBox!

WABT - Weighted Average Bed Temperature

Sponsored Links

WABT - Weighted Average Bed Temperature is a way to get one representative temperature from an adiabatic reactor (no heat loss or gain to the surroundings), which in reality have an increasing or decreasing temperature profile from inlet to outlet. The temperature profile occurs due to exothermic or endothermic reactions taking place in the reactor. The WABT is used to indicate the catalyst activity in catalytic processes, where a deactivation of the catalyst starts to take place from the start-up after a catalyst change. To maintain the catalyst activity despite the deactivation, the inlet temperature is gradually increased by the operators and the temperature profile through the reactor changes over time. WABT at start of a run is compared to WABT at a given time after start-up, and the difference is telling something about the degree of catalyst deactivation. 

WABT is the average temperature of each catalytic bed between two temperatur indicators, and Tin and Tout are the inlet and outlet temperatures in each catalytic bed, respectively. The global WABT is calculated with


where

N = the number of catalyst beds
Wci = the weight fraction of catalyst in each bed with respect to the total

In real life the number of temperatur indicators may be limited to one at the inlet and one at the outlet, only. Other places there might be a lot of thermocouples throughout the reactor, both in radial and length direction. Below, examples of calculation of WABT in different cases are given.

.

Example 1: One reactor and two thermocouples


In this case both N and Wci are 1, and Tin = T1 and Tout = T2

WABT = (T1 + 2*T2)/3 * 1

If T1=350 °C and T2=395°C,

WABT = (350°C + 2*395°C)/3 = 380°C

Example 2: Three reactors and Tin and Tout of each reactor


T1=345°C, T2=380°C, T3=370°C, T4=390°C, T5=385°C and T6=395°C

In this case we have temperature indicators, but we must also know the bulk density of the catalyst beds to do the right weighting of the temperature.

Lets say that the catalyst bulk dencities ρ1= 550 kg/m3, ρ2= 800 kg/m3 and ρ3=750 kg/m3 are for catalyst beds in reactor 1, 2 and 3, respectively. Then, first we calculate weight fraction the total catalyst mass in each reactor:

Catalyst weight in R1: 18 [m3]*550[kg/m3] = 9 900 [kg]
Catalyst weight in R2: 30 [m3]*800[kg/m3] = 24 000 [kg]
Catalyst weight in R3: 30 [m3]*750[kg/m3] = 22 500 [kg]
Total catalyst weight: 56 400 [kg]

WcR1 = 9900/56400 = 0.18
WcR2 = 24000/56400 = 0.42
WcR3 = 22500/56400 = 0.40

Then, we can calculate the WABT:

WABT = WABTR1*WcR1 + WABTR2*WcR2 + WABTR3*WcR3

        = (T1+2T2)/3*0.18 + (T3+2T4)/3*0.42 + (T5+2T6)/3*0.40

        = (345 + 2*380)/3*0.18 + (370 + 2*390)/3*0.42 + (385 + 2*395)/3*0.40  = 384°C

.


Example 3: One reactor with two chains of thermocouples throughout the reactor


T1=351°C, T2=350°C, T3=368°C, T4=386°C, T5=399°C, T6=406°C, T7=411°C, T8=413°C, T9=350°C, T10=370°C, T11=387°C, T12=398°C, T13=405°C, T14=410°C, T15=412°C and T16=411°C

In this case there is a 1/6 top layer of catalyst, with density ρ1= 550 kg/m3, while the rest of the catalyst mass (5/6) has density ρ2= 800 kg/m3. Then the catalyst weight fractions for each of the fractions of the catalyst bed will be:

Catalyst weight top layer: 18*1/6 [m3] * 550 [kg/m3] = 1 650 [kg]
Catalyst weight layer 2 to 6: 18*1/6 [m3] * 800 [kg/m3] = 2 400 [kg]
Total catalyst weight: 1 650 [kg] + 2 400[kg]*5 = 13 650 [kg]

Wc1 = 1650/13650= 0.12
Wc2 = Wc3 = Wc4 = Wc5 = Wc6 = 2400/13650 = 0.176

WABT = WABT1*Wc1 + WABT2*Wc2 + WABT3*Wc3 + WABT4*Wc4 + WABT5*Wc5 + WABT6*Wc6

           = WABT1*Wc1 + Wc2*(WABT2 + WABT3 + WABT4 + WABT5 + WABT6)

In this case, there are two thermocouples at each height level in the reactor, and Tin and Tout of each fraction is the average of these two. Then, WABT is:

WABT = ((T2+T9)/2+2*(T3+T10)/2)/3*0.12 + 0.176*(((T3+T10)/2+2*(T4+T11)/2)/3 + ((T4+T11)/2+2*(T5+T12)/2)/3 + ((T5+T12)/2+2*(T6+T13)/2)/3 + ((T6+T13)/2+2*(T7+T14)/2)/3 + ((T7+T14)/2+2*(T8+T15)/2)/3)

          = ((350+350)/2+2*(368+370)/2)/3*0.12 + 0.176*(((368+370)/2+2*(386+387)/2)/3 + ((386+387)/2+2*(399+398)/2)/3 + ((399+398)/2+2*(406+405)/2)/3 + ((406+405)/2+2*(411+410)/2)/3 + ((411+410)/2+2*(413+412)/2)/3  = 395.3°C

It should be obvious that this is a more precise measurement/calculation than the more simple

WABT = (T1 + 2*T16)/3 * 1

          = (351 + 2*411)/3*1 = 391.0 °C

The figure above shows the given temperature profile, which is typical for a gas oil hydrotreater in a refinery. Calculating WABT from T1 and T16, only, gives 391°C, while using the catalyst bed temperatures, measured by T2 to T15, gives WABT = 395°C. If calculating the average bed temperature, simply as the average of T1 and T16, you get 381°C, which is much less representative for the temperature in the catalyst bed than the WABT using the same temperatures.

The reason for the actual shape given in this figure, is that the fastest reactions, in this case, are the most exothermic (giving a fast temperature increase at the reactor inlet), and when their potential is used up (reach equilibrium or reactants are consumed), more slow, and less exothermic reactions take place. 

Sponsored Links

Related Topics

Thermodynamics

Work, heat and energy systems.

Related Documents

1st Law of Thermodynamics

The First Law of Thermodynamics simply states that energy can be neither created nor destroyed (conservation of energy). Thus power generation processes and energy sources actually involve conversion of energy from one form to another, rather than creation of energy from nothing.

2nd Law of Thermodynamics

Entropy and disorder.

Arithmetic and Logarithmic Mean Temperature Difference

Arithmetic Mean Temperature Difference in Heat Exchangers - AMTD - and Logarithmic Mean Temperature Difference - LMTD - formulas with examples - Online Mean Temperature Calculator.

Standard enthalpy of formation, Gibbs energy of formation, entropy and molar heat capacity of organic substances

The standard enthalpy of formation, Gibbs energy of formation, entropy and molar heat capacity are tabulated for more than hundred organic substances.

Standard State and Enthalpy of Formation, Gibbs Free Energy of Formation, Entropy and Heat Capacity

Definition and explanation of the terms standard state and standard enthalpy of formation, with listing of values for standard enthalpy and Gibbs free energy of formation, as well as standard entropy and molar heat capacity, of 370 inorganic compounds.

Symbols Used to Denote a Chemical Reactions and Process or Condition

Explanation of symbols used as subscripts or superscripts to tell more about the type of chemical reaction, process or condition.

Thermodynamic Terms - Functions and Relations

Common thermodynamic terms and functions - potential energy, kinetic energy, thermal or internal energy, chemical energy, nuclear energy and more.

Sponsored Links

Search Engineering ToolBox

Search is the most efficient way to navigate the Engineering ToolBox!

SketchUp Extension - Online 3D modeling!

Add standard and customized parametric components - like flange beams, lumbers, piping, stairs and more - to your Sketchup model with the Engineering ToolBox - SketchUp Extension - enabled for use with the amazing, fun and free SketchUp Make and SketchUp Pro . Add the Engineering ToolBox extension to your SketchUp from the Sketchup Extension Warehouse!

Privacy

We don't collect information from our users. Only emails and answers are saved in our archive. Cookies are only used in the browser to improve user experience.

Some of our calculators and applications let you save application data to your local computer. These applications will - due to browser restrictions - send data between your browser and our server. We don't save this data.

Google use cookies for serving our ads and handling visitor statistics on the AMP pages. Please read Google Privacy & Terms for more information about how you can control adserving and the information collected.

AddThis use cookies for handling links to social media. Please read AddThis Privacy for more information.