The object of this tutorial is to examine the simultaneous solution of mass and energy balance. The example chosen concerns an interesting development in the cooling of leaching autoclaves.

The flowsheet and the calculations are more difficult than those examined to date.

The flowsheet consists of a mixing tank, a feed tank, an autoclave, and a flash drum. The plant accepts a feed mainly of CuS and Cu2S, mixes this with spent solution from electrowinning.

The mixed slurry flows from the mixing tank to the feed tank, which combines a flash recycle from the autoclave with the mixed slurry. The product from the feed tank forms the feed to the autoclave. Leach solution is flashed to atmosphere in a flash drum.

There are a number of challenges here:

  • The first challenge is to determine the amount of material to be recycled so that the temperature is at the desired level of 140°C.
  • The second challenge is how do we handle the energy balance for the feed tank and for the flash drum. Clearly a large amount of water must evaporate from both these vessels.
  • The third challenge is to ensure that the acid concentration leaving the autoclave is 16 g/L.
  1. Draw the flowsheet
  2. Add components to the mass balance
  3. Setup the stream compositions
  4. Enter the reactions
  5. Setup Process Unit properties
  6. Running each unit individually
  7. Change Calculation Properties
  8. Calculating the flowsheet
  9. Examining the results

Step 1: Draw the flowsheet

Draw the flowsheet so that it looks like that shown in Figure 1.


Figure 1. Flowsheet for the autoclave flash recycle.

The units that have been added are, from left to right, two tanks, an autoclave, and a flash drum.

Provide the units with tags, descriptions and type data, as discussed earlier.

For the autoclave, navigate to the "Equipment" properties on the Property Viewer, and select "True" for CompartmentWalls and type in 4 for "NumberOfAgitators". This is shown in Figure 2.


Figure 2. Setting the number of agitators in an autoclave

In order to get a line break when two lines representing streams cross, select the one that is horizontal when it crosses.

Then from the main menu, choose Format>Order>Bring To Front.

Step 2: Add components to the mass balance

Add the following components to the mass balance:

Cu2S           (s)              chalcocite

CuS             (s)              covellite

SiO2            (s)              silica

H2O             (l)               water

H2SO4         (aq)           sulphuric acid

CuSO4         (aq)            copper sulphate

H2SO4         (l)              sulphuric acid

H2O             (g)             water vapour

N2               (g)             nitrogen

O2               (g)             oxygen

Note the two different states for the acid.

This is because the acid is typically supplied as concentrated sulphuric acid (98% w/w) and will be diluted either when used or before for specific applications (stripping, solvent extraction).

In order to account for the heat of mixing, we need to "react" the concentrated solution to produce the dilute one.

Note that you must still include the 2% water in the concentrated sulfuric acid stream.

Step 3: Setup the stream compositions

Setup the stream compositions so that the four inlet streams have the compositions shown in Figure 3.


Figure 3. Input streams compositions.

Please note that the Feed stream temperature is set to 50°C and the Spent stream temperature is set to 30°C. The Acid and Oxygen streams remain at the default stream temperature of 25°C.

Step 4: Enter the reactions

Select the second tank (TK-020) and add the reaction shown in Figure 4:

H2SO4 (l) -> H2SO4 (aq)


Figure 4. The reaction in the feed tank representing the dilution of acid.

Select the autoclave (AU-010/020/030/040) and add the reactions shown in Figure 5:

CuS (s) + 2 O2 (g) -> CuSO4 (aq), ext = 0.85

Cu2S (s) + 2.5 O2 (g) + H2SO4 (aq) -> 2 CuSO4 (aq) + H2O (l), ext = 0.95


Figure 5. The reactions in the autoclave.

Step 5: Setup Process Unit properties

Do the following:

  1. For the feed tank (TK-020):
    1. Set the Energy Balance property to "NonIsothemal"
    2. Change the OffGasSaturated property, which can be found on expanding the evaporation rate in the property viewer, to YES.
  2. For the Autoclave:
    1. Set the Flash Fraction to 80%
    2. Set the Energy Balance" property to "NonIsothermal"
    3. Set the Pressure to 1050 kPaG.
    4. Under EvaporationRate, set the OffGasSaturated to YES
  3. For the flash drum (FV-010):
    1. Set energy balance to “NonIsothermal;

Step 6: Running each unit individually

Often when starting on a new flowsheet, there is the possibility of letting the calculation "run away with itself".

For this reason check that all the inputs make sense; it is advisable to run each Unit on its own prior to running the entire project.

Use the Run Selected Unit button on the Process Toolbar.

This button is the fourth button from the left on the Calculate Process Toolbar, shown in Figure 6.


Figure 6 Process Toolbar.

Check the following:

  • Check that the Overall Mass Balance error in the Convergence Form is very low (< 1e-5), for each element.
  • Check the temperatures of the non-isothermal units behave sensibly and are in the right ball-park.
  • Ensure flowrates and concentrations are within expected limits.

Step 7: Change Calculation Properties

Press the ‘Calculation Options’ button on the Calculate toolbar shown in Figure 7.

In the window that opens, under Calculation Options, change the following parametes to the value specifed:

MaximumIterations -> 60

Tolerance -> 1E-09

The tolerance specifies how small the errors must be for the run to complete. The smaller the tolerance the longer the simulation will take in order for the errors to reduce. However, if it set too low then it may never reach that error.

This is why the MaximumIterations is important. It prevents the simulation from running indefintely. However, care must be taken not to set the value too low else the error tolerance will not be reached.

Step 8: Calculating the flowsheet

Once you are sure that each unit is responding as required, then it is time to run the entire flowsheet.

Press the ‘Run Project’ button on the Calculate toolbar, shown in Figure 7.


Figure 7. The Process Toolbar, with the cursor hovering over the Run Project button.

The Convergence Form that is displayed once the Flowsheet has run. This is shown, below, in Figure 8.


Figure 8. Convergence Form

These results indicate that Stream 107 was chosen as the Tear Stream and that this has converged to a root mean square deviation tolerance of 9.23e-10.

In addition, the relative errors for the overall balance on an element basis are small so we can accept these results.

Step 9: Examining the results

The results that are of interest are the following:

  1. The temperature of the autoclave is °C.
  2. The water evaporated in the feed tank is t/hr.
  3. The concentration of acid in the product stream (112) is g/L.

Another engineering design consideration is the recycle ratio, which is the mass flowrate of the autoclave flash recycle stream divided by the total slurry mass flow to the feed tank. This is equal to 82.15/23 = 3.6. This corresponds with the industrial practice.

Yet another consideration is the concentration of copper in the product solution (112), which is 146.5 g/L. This is close to saturation but is acceptable if there is some dilution on cooling.

As an extension of this tutorial, add Designers to constrain the following: the solution to a temperature of 140°C, to add acid so that the exit concentration is 15 g/L, to add oxygen so that the oxygen utilization is 75%, and to adjust the leaching reactions so that the concentration of copper in solutions is 120 g/L .