AlPrg Table of Contents Cell Voltage Haupin Diagrams

Haupin Diagrams

Warren Haupin was the first (Lit.) to published a diagram that showed the components of cell voltage and their relation to energy consumption (see Publications). AlPrg draws a similar diagram:

AlPrg Version of Haupin Diagrams.

The left diagram shows cell voltage components and the right side the corresponding energy balance diagram.

The meaning of the symbols is:

I_ref, I_act: reference, actual current intensity,
η: current efficiency,
IPD: interpolar distance,

ΣU_bus: sum of the busbars voltage drop,
U_bath: bath voltage,
U_bub: bubble voltage drop,
U_Ω: ohmic bath voltage,
U_IPD: electrolyte voltage drop,
η_AC: anodic concentration overvoltage,
η_AR: anodic reaction overvoltage,
η_CC: cathodic concentration overvoltage,
E₀: reversible decomposition voltage,
E_el: electrochemical bath voltage.

ΣU_bus(ext): sum of the external busbars voltage drop,
E_(int): total internal energy,
ΣU_bus(int): sum of the internal busbars voltage drop,
ΔH_f(CO2): enthalpy of formation of carbon dioxide,
ΔH_f(CO): enthalpy of formation of carbon monoxide,
ΔH_f(Al2O3): enthalpy of decomposition of alumina,
ΔH_Al2O3: enthalpy to heat alumina,
ΔH_C: enthalpy to heat the carbon anodes,
ΔH_total: total enthalpy to produce aluminum.

AlPrg helps you to get informations about a symbol: when you move the mouse cursor over a symbol it changes its form to a question mark and a small information window opens that tells you the meaning of the symbol (see Cell Geometry Diagrams).

Examples of Information Windows.

When you move the mouse cursor over a symbol (IPD, U_bub, ΔH_f(CO2), ΔH_total as examples in this figure) the mouse cursor changes its form to a question mark. A small window tells you the meaning of the symbol. You get also information what actions you can make.

You switch the appearance of these information popup windows on or off by pressing the Info ON/OFF button. If this button is turned off the cursor shape does not change to a question mark over a symbol and consequently you can not open an information window.
When you move the mouse cursor around the Haupin Diagrams Window it may change its form to a hand. That means you can make some action by pressing the left mouse button (see GUI). Perhaps you remember, pressing the right mouse button opens the popup menu.

Information ON/OFF Button.

If you know the meaning of the symbols you may want to switch off the appearance of the information windows. You do it by clicking on the Info ON/OFF button.

Publications

The following section will compare the values found in the literature with the calculation results of AlPrg.

Light Metals (1998)

The next picture shows a genuine Haupin Diagram namely the Fig. 7 on page 536 of Lit. 1998:

Please compare these values with the result of AlPrg on the Bath Voltage Page:

Comparison with AlPrg Results.

This figure shows the Bath Voltage Page with the results of AlPrg to calculate bath volt components with the same starting values (bath composition, current densities) as Figure 7. The ohmic voltage drops are not interesting because they can be adjusted.

and on the Energy Balance Page:

Comparison with the Energy Balance Page.

On this figure you compare the reaction enthalpy and the heat losses. The differences are probably due to the bath temperature (the paper specifies only the superheat) and the relations for the temperature dependence of the enthalpies.

Light Metals (2000)

The next figures compare several diagrams from Lit. 2000:

Figure 1.

Comparison of typical values of the cell voltage and power components of the publication and determined by AlPrg.

+ larger figure.

The next figure shows the influence of a current efficiency reduction from 96% to 90%.

Figure 2.

This figure shows the influence of a current efficiency reduction from 96% to 90%.

+ larger figure.

For the next figure the carbon anodes were replaced by inert not consumable anodes. Using AlPrg you press the Carbon/Inert Anode Button on the Status Bar or on one of the Cell Voltage Pages.

Figure 3.

For this case the carbon anodes were replaced by inert not consumable anodes.

+ larger figure.

Graphical User Interface (GUI)

The Haupin Diagram Window is conceived as a graphical user interface (GUI) e.g. you may change values by moving the mouse pointer and pressing a mouse button. When you move, for instance, the mouse pointer over the current efficiency value rectangle the mouse pointer changes its form to hand. After you have clicked into the value rectangle AlPrg shows a small dragging window, the dragging rectangle containing an ordinate and a value bar. When you move the mouse pointer in this rectangle with pressed left mouse button also the small value rectangle changes its position. The current efficiency gets a new value according to the modified position of the value rectangle.

Current Efficiency Dragging Rectangle.

After after you have clicked into the current efficiency rectangle AlPrg shows a dragging rectangle with ordinate and value bar. You change the position of the value bar e.g. the current efficiency value by moving up and down the bar with the mouse pointer.

The next figure shows part of the Haupin Diagrams Window after you have moved the current efficiency bar to 95%. AlPrg updates correspondingly the values in the Haupin Diagrams Window and all other open pages and diagrams to the new current efficiency value.

Change of Current Efficiency from 93% to 95% .

This figure shows part of the Haupin Diagrams Window after you have changed the current efficiency from 93% to 95% by dragging the value bar to the new position.

You close a dragging rectangle by clicking again into the value rectangle. to the new current efficiency value.
The following figures show the Haupin Diagrams version of the examples of the Cell Voltage Page and Energy Balance Page.

Haupin Diagrams Version of the Cell Voltage and Energy Balance Examples.

With the input of Reference Current (I_ref): 200 kA, Cell Voltage: 4.2 V and Current Efficiency (η): 95% AlPrg calculates the Interpolar Distance (IPD): 4.8 cm, the Electric Power: 840 kW and the Heat Loss: 377 kW.

As shown on the Cell Voltage Page: Input Heat Loss you click on the Heat Loss value rectangle to select the Heat Loss as input and you change the Reference Current to I_ref = 210 kA.

Input Heat Loss.

This figure shows what happens when you select the Heat Loss as input (to keep it constant) and you increase the Actual Current Intensity (I_act) from 200 kA to 210 kA: the Cell Voltage and Interpolar Distance (IPD) must consequently be decreased. As on the Cell Voltage Page the value fields are dark gray to indicate that Input Heat Loss is selected.

You may decide, for instance, to select the Bath Voltage Value (U_bath) together with the Heat Loss as input to determine the current intensity. The next figure shows the corresponding Haupin Diagrams after the Bath Voltage was increased from 3.60 V to 3.80 V.

Input Heat Loss and Bath Voltage.

The Bath Voltage was changed by mouse dragging on the dragging rectangle to the new value of 3.80 V. AlPrg changes the Actual Current Intensity to 184 kA to keep the Heat Loss constant at 377 kW.