1 name, title of the presentation canonical thermodynamics & modelling tore haug-warberg bjørn...

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Name, title of the presentation

Canonical Thermodynamics & Modelling

Tore Haug-WarbergBjørn Tore Løvfall

Olaf Trygve Berglihn

Cybernetica21 June 2006

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Programme

1. Executive summary (THW) 2. Symbolic differentiation (BTL)3. Thermodynamic algebra (THW)4. Dynamic simulation (OTB)


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What is thermodynamic modelling?• Thermodynamic modelling is about physical

state models. In the current context only simple systems shall be considered. Thus, the models assume uniform states (no gradients), and they are insensitive to geometry, to external fields, and to the previous history. In practice f (x) can be G(T, p, n), A(T, V, n) or (T, V, µ ).


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When is it important?

• Thermodynamic modelling is important when there is a significant coupling between two or more of the system variables. This includes unit operations such as: Valves, compressors, expanders, reactors and separation units. Specialized units like hydraulic networks or heat exchanger networks are on the side-line of what we shall talk about.


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Why bother?

• If done awkwardly, thermodynamic calculations require a lot of man-power and occupy excess CPU-time. One of the most difficult questions to ask is about standard states. As soon as two or more engineers are playing around with different simulators the result is quite often a big mess. Controlling the thermodynamic calculations means better modularity, increased re-usability and reduced maintenance costs.


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Where does it fit in?• Good question, and this is why we are here to

listen to your problems. For many people in industry it is tempting to claim that ”the proof of the pudding lies in its eating”. However, we are talking about new technology and new thinking patterns here, and the biggest obstacle is maybe that people will not even taste the pudding because they do not recognize it as proper food.


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Thermodynamic formalism


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Newton-Raphson


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Newton-Lagrange-Euler


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Additional constraints


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Canonical block structure (reactive flash)


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Conclusions

• Canonical representation implies a highly structured equation system.

• Intensive and extensive variables are solved simultanously.

• The updated state is solved for explicitly.• Equilibrium and balance equations are solved

only once (linear functional) while iterating the transport equations many times.


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Symbolic differentiation

• Traditional coding requires that all functions derivatives are implemented by hand.

• By collecting the function in a computer graph symbolic operations are possible.

• The derivatives can then be calculated by automatic procedures and exported to e.g. C.

• Higher order (>2) derivatives are feasible.


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Declarations

• d1 = Dim.new• t = Variable.new(’T’)• dg = Parameter.new(’deltag’, d1, d1)• nrtl = Model.new(’nrtl’, t, n, r, dg, al)


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Modelling• sumn = nrtl.expr(’sumn’, n).sum• x = nrtl.expr(’x’, n,sumn[nil]){|q,w| q/w}

etc. (5 more lines)

• dgex = nrtl.expr(’DeltaGex’,r[nil,nil],t[nil,nil],

x[nil,d1],x[d1,nil],

tmp3){|q,w,e,y,u| e*y*u*q*w}.sum


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Ruby vs Matlab

• tmp1 = nrtl.expr(’tmp1’,x[nil,d1],

expG,x[d1,nil]){|q,w,e| q + w*e}

The same code written in MATLAB is:

• tmp1 = repmat(x,1,3) + expg.*repmat(x’,3,1);


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• [x11, x21][nil,d1],

[[G11, G12], [G21, G22]],

[x12, x22][d1,nil]

• [x11, x21][d1], [G11, G12], [x12][nil]

[x11, x21][d1], [G21, G22], [x22][nil]

• [[ (x11, G11, x12), (x21, G12, x12)],

[ (x11, G21, x22), (x21, G22, x22)]]


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Instantiation• d1.init(3)• r.init([8.314])

• dg.init([[0,-105.43,285.39],

[-36.852,0,-2.3302],

[754.56,11.362,0]])

• al.init([[0, 0.2, 0.2],[0.2, 0, 0.2],[0.2, 0.2, 0]])


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API• Require ´rbct´

• c,d = SRKmodule::init([0,0,1])

• SRKmodule::set(d,SRKmodule::N,[4.3])• SRKmodule::set(d,SRKmodule::T,[298.15])• SRKmodule::set(d,SRKmodule::V,[5.0e-4])

• SRKmodule::srk(c,d)


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Thermodynamic frameworks

• Thermodynamic process models consist of several sub-models (heat capacity, ideal gas, equation of state, etc.).

• Different frameworks are needed for metallurgy, oil & gas, polymers, etc.

• It would be great to represent all frameworks into one generic structure rather than programming several chains of explicit function calls.


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Text book example


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Ruby interface

n = [’nitrogen’,’methane’,’ethane’,

’propane’,’n-butane’]

A = Surface * Helmholtz * StandardState * [

MuTcp.extend(:poly3) *

MuThs.fun(:h0) + MuThs.extend(:s0).mix(n)] +

EquationOfState * [

ModTVNideal.extend(:idealgas).mix(n) ] +

EquationOfState * [ ModTVN.extend(:srk).mix(n) ]


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Conclusions

• Thermodynamic frameworks can be captured in computer graphs using simple algebra.

• The graph acts as a wrapper and exports the entire model framework into C.

• Symbolic differentiation (gradients) is available to arbitrary order.

• Automatic documentation eliminates a common source of error.


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Dynamic simulation using YASIM

• One-step solver with steplength control. Newton-Lagrange-Euler formulation.

• Thermodynamic state-estimator• Modularized, flexible interface.• Aggregation of simple units into complex units.• Export to simplified/linearlized models in Taylor-

expansion manifold for process control analysis.• Plug-flow and transport delay


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Canonical representation

• A full thermodynamic problem is always stated.• Solve for both intensive and extensive variables.• Additional constraints are implemented as lambda

functions:• Analytical inverse is possible for the thermo-

dynamic coefficient matrix (at fixed topology).


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Dynamic 2-phase flash


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Simulation factory

• Node factory.• Thermo surface import.• Thermo model propagator (graph coloring

algorithm).• Species propagator (graph coloring algorithm).• Node aggregator. Injects flowsheet constitutive

equations (flow relations) and handles DOF-assignment.


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Executive conclusions


• YASIM ≠ ASPEN (simulation vs design)• DASIM = YASIM + PFR + CSTR

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High priority development


• Transport delay (PFR)• Dynamic reactive flash (multiphase reactor)• Stirred tank (CSTR)• Electrolyte handling• ATLAS-binding in Ruby• Simulation API • Automatic documentation

1 name, title of the presentation canonical thermodynamics & modelling tore haug-warberg bjørn...

Documents

presentation slide

thermodynamic modelling

thermodynamic calculations

thermodynamic formalism

thermodynamic algebra

symbolic operations

symbolic differentiation

declarations d1