Heat exchangers initialization

[GioCrl]

Hi everyone,

I am modelling the autothermal reforming process in IDAES following the flowsheet in the image below. Three heat exchangers are used to make steam from liquid water removing heat from the hot gasses produced by the reactors.

I have created and connected each component like this:

`# Biogas path
m.fs.s01 = Arc(source=m.fs.BIOGAS.outlet, destination=m.fs.C101.inlet)
m.fs.s02 = Arc(source=m.fs.C101.outlet, destination=m.fs.H101.inlet)
m.fs.s03 = Arc(source=m.fs.H101.outlet, destination=m.fs.M101.biogas_feed)

# Steam path
m.fs.s04 = Arc(source=m.fs.STEAM.outlet, destination=m.fs.P101.inlet)
m.fs.s05 = Arc(source=m.fs.P101.outlet, destination=m.fs.H103.water_inlet)
m.fs.s06 = Arc(source=m.fs.H103.water_outlet, destination=m.fs.H104.water_inlet)  
m.fs.s07 = Arc(source=m.fs.H104.water_outlet, destination=m.fs.H105.water_inlet)  
m.fs.s08 = Arc(source=m.fs.H105.water_outlet, destination=m.fs.M101.steam_feed)   

# Oxygen path
m.fs.s09 = Arc(source=m.fs.OXYGEN.outlet, destination=m.fs.V101.inlet)
m.fs.s10 = Arc(source=m.fs.V101.outlet, destination=m.fs.H102.inlet)
m.fs.s11 = Arc(source=m.fs.H102.outlet, destination=m.fs.M101.oxygen_feed)

# Reactors and heat exchangers path
m.fs.s12 = Arc(source=m.fs.M101.outlet, destination=m.fs.R101.inlet)
m.fs.s13 = Arc(source=m.fs.R101.outlet, destination=m.fs.H105.syngas_inlet)
m.fs.s14 = Arc(source=m.fs.H105.syngas_outlet, destination=m.fs.R102.inlet)
m.fs.s15 = Arc(source=m.fs.R102.outlet, destination=m.fs.H104.syngas_inlet)        
m.fs.s16 = Arc(source=m.fs.H104.syngas_outlet, destination=m.fs.H103.syngas_inlet) 
m.fs.s17 = Arc(source=m.fs.H103.syngas_outlet, destination=m.fs.SYNGAS.inlet)` 

After fully defining the problem (degrees of freedom = 0) I moved to the initialization sequence.
I used I used SequentialDecomposition with Wegstein to determine the tear streams:

`# Create sequential decomposition object
seq = SequentialDecomposition()
seq.options.select_tear_method = "heuristic"
seq.options.tear_method = "Wegstein"
seq.options.iterLim = 3

# Create computational sequence
G = seq.create_graph(m)
heuristic_tear_set = seq.tear_set_arcs(G, method="heuristic")
order = seq.calculation_order(G)

# Print debug information
print('\nTear streams: ')
for o in heuristic_tear_set:
    print(o.name)

print('\nFlowsheet solving order: ')
for o in order:
    print(o[0].name)

print('\n')`

I then provided adequate guesses for the three tear streams: s06, s07, and s12

`# Steam from evaporator to superheater
tear_guesses_s06 = {
    "flow_mol": {0: 29.8},
    "mole_frac_comp": {
        (0, "CH4"): 0.01,
        (0, "CO2"): 0.01,
        (0, "CO"): 0.01,
        (0, "H2O"): 0.95,
        (0, "O2"): 0.01,
        (0, "H2"): 0.01,
    },
    "temperature": {0: 423.15},
    "pressure": {0: 1.5e5},
}
seq.set_guesses_for(m.fs.H104.water_inlet, tear_guesses_s06)

# Steam after superheater
tear_guesses_s07 = {
    "flow_mol": {0: 29.8},
    "mole_frac_comp": {
        (0, "CH4"): 0.01,
        (0, "CO2"): 0.01,
        (0, "CO"): 0.01,
        (0, "H2O"): 0.95,
        (0, "O2"): 0.01,
        (0, "H2"): 0.01,
    },
    "temperature": {0: 623.15},
    "pressure": {0: 1.5e5},
}
seq.set_guesses_for(m.fs.H105.water_inlet, tear_guesses_s07)

# Reactor inlet
tear_guesses_s12 = {
    "flow_mol": {0: 56.5},
    "mole_frac_comp": {
        (0, "CH4"): 0.22,
        (0, "CO2"): 0.15,
        (0, "CO"): 0.01,
        (0, "H2O"): 0.50,
        (0, "O2"): 0.11,
        (0, "H2"): 0.01,
    },
    "temperature": {0: 773.15},
    "pressure": {0: 1.5e5},
}
seq.set_guesses_for(m.fs.R101.inlet, tear_guesses_s12)`

And finally I used the following function to initialize the flowsheet

`# Define initialization function
def function(unit):
    # Try initializing using default initializer,
    # if it fails (probably due to scaling) try solving directly
    try:
        initializer = unit.default_initializer()
        initializer.initialize(unit, output_level=idaeslog.INFO)
    except InitializationError:
        solver = configure_solver()
        solver.solve(unit)

# Run sequential initialization
seq.run(m, function)`

However, despite achieveing the desired input conditions for reactor R101 (Gibbs reactor) the results are way different from those that I get with a simplified flowsheet where I assume the three feeds to the mixer to be already at the desired pressure and temperature, which I created and initialized as follow:

`m.fs.s01 = Arc(source=m.fs.STEAM.outlet, destination=m.fs.M101.steam_feed)
m.fs.s02 = Arc(source=m.fs.OXYGEN.outlet, destination=m.fs.M101.oxygen_feed)
m.fs.s03 = Arc(source=m.fs.BIOGAS.outlet, destination=m.fs.M101.biogas_feed)
m.fs.s04 = Arc(source=m.fs.M101.outlet, destination=m.fs.R101.inlet)
m.fs.s05 = Arc(source=m.fs.R101.outlet, destination=m.fs.H101.inlet)
m.fs.s06 = Arc(source=m.fs.H101.outlet, destination=m.fs.R102.inlet)
m.fs.s09 = Arc(source=m.fs.R102.outlet, destination=m.fs.SYNGAS.inlet)

m.fs.BIOGAS.initialize()
propagate_state(arc=m.fs.s03)

m.fs.STEAM.initialize()
propagate_state(arc=m.fs.s01)

m.fs.OXYGEN.initialize()
propagate_state(arc=m.fs.s02)

m.fs.M101.initialize()
propagate_state(arc=m.fs.s04)

m.fs.R101.initialize(outlvl=idaeslog.INFO_HIGH)
propagate_state(arc=m.fs.s05)

m.fs.H101.initialize()
propagate_state(arc=m.fs.s06)

m.fs.R102.initialize(outlvl=idaeslog.INFO_HIGH)
propagate_state(arc=m.fs.s09)

m.fs.SYNGAS.initialize()`

I therefore believe the issue lies in the initialization procedure.

What would be the correct way to initialize the flowsheet with the heat exchangers?
Any advice or suggestions would be really helpful. Thanks in advance!

[dallan-keylogic]

Do you believe that the results are in error, or is the issue that there are multiple steady states (for example, an ignited, quenched, and unstable triplet)?

If the issue is multiple steady states, you'll need to specify the desired steady state in a different way than the inputs. To do this, you should run the SequentialDecomposition with the option solve_tears=False in order to converge all the state blocks but avoid converging the recycle streams. Then you'll want to unfix some control variable(s) and fix instead some other variable(s) like a reactor inlet or outlet temperature. Then use IPOPT to try to solve your flowsheet as a square problem.