public void CanSolveMaxProblem()
{
var problem = new EquationSystem();
var x1 = new Variable("x1", 10);
problem.AddVariables(x1);
problem.AddConstraints((Sym.Max(x1, 5)).IsEqualTo(25));
var solver = new Newton();
solver.Solve(problem);
Assert.AreEqual(25, x1.ValueInSI, 1e-5);
Assert.AreEqual(true, solver.IsConverged);
}
public void Test_MinMax()
{
var x = new Variable {
Name = "x", ValueInSI = 3
};
var y = new Variable {
Name = "y", ValueInSI = 6
};
var eval = new Evaluator();
Assert.AreEqual(3, Sym.Min(x, y).Eval(eval), 1e-5);
Assert.AreEqual(6, Sym.Max(x, y).Eval(eval), 1e-5);
}
public void CanSolveMinMaxProblem()
{
var problem = new EquationSystem();
var x1 = new Variable("x1", 0);
var x2 = new Variable("x2", 6);
var x3 = new Variable("x3", 25);
problem.AddVariables(x2);
problem.AddConstraints((Sym.Max(x1, Sym.Min(x2, x3))).IsEqualTo(5));
var solver = new Newton();
solver.Solve(problem);
Assert.AreEqual(5, x2.ValueInSI, 1e-5);
Assert.AreEqual(true, solver.IsConverged);
}
/// <summary>
/// Creates a new instance of the liquid phase activity coefficient calculation object
/// </summary>
/// <param name="sys">Thermodynamic system to take parameters from</param>
/// <param name="T">Temperature variable</param>
/// <param name="x">Vector of composition variables (molar fractions)</param>
/// <param name="idx">Index of the active variables to calculate for</param>
public ActivityCoefficientUNIQUAC(ThermodynamicSystem sys, Variable T, List <Variable> x, int idx)
{
Symbol = "UNIQUAC_GAMMA";
_system = sys;
index = idx;
//Bind variables to this instance
this.T = T;
this.x = x;
Parameters.Add(T);
foreach (var comp in x)
{
Parameters.Add(comp);
}
NC = _system.Components.Count;
tau = new Expression[NC, NC];
int i = index;
var parameterSet = _system.BinaryParameters.FirstOrDefault(ps => ps.Name == "UNIQUAC");
if (parameterSet == null)
{
throw new ArgumentNullException("No UNIQUAC parameters defined");
}
double[,] a = parameterSet.Matrices["A"];
double[,] b = parameterSet.Matrices["B"];
double[,] c = parameterSet.Matrices["C"];
double[,] d = parameterSet.Matrices["D"];
double[,] e = parameterSet.Matrices["E"];
for (int ii = 0; ii < NC; ii++)
{
for (int j = 0; j < NC; j++)
{
tau[ii, j] = Sym.Exp(a[ii, j] + b[ii, j] / T + c[ii, j] * Sym.Ln(T) + d[ii, j] * T + e[ii, j] / Sym.Pow(T, 2));
}
}
Expression lnGamma = 0.0;
Expression lnGammaComb = 0.0;
Expression lnGammaRes = 0.0;
Expression Vi = 0;
Expression Fi = 0;
Expression FiP = 0;
Expression Sxl = 0;
var ri = _system.Components.Select(co => co.GetParameter(MethodTypes.Uniquac, "R").ValueInSI).ToList();
var qi = _system.Components.Select(co => co.GetParameter(MethodTypes.Uniquac, "Q").ValueInSI).ToList();
var qpi = _system.Components.Select(co => co.GetParameter(MethodTypes.Uniquac, "Q'").ValueInSI).ToList();
double[] li = new double[NC];
for (int j = 0; j < NC; j++)
{
li[j] = 5 * (ri[j] - qi[j]) - (ri[j] - 1);
}
Vi = ri[i] * x[i] / Sym.Sum(0, NC, (j) => ri[j] * x[j]);
Fi = qi[i] * x[i] / Sym.Sum(0, NC, (j) => qi[j] * x[j]);
FiP = qpi[i] * x[i] / Sym.Sum(0, NC, (j) => qpi[j] * x[j]);
//Sxl = Sym.Sum(0, NC, (j) => (5 * (_system.Components[j].GetParameter(MethodTypes.Uniquac, "R").ValueInSI - _system.Components[j].GetParameter(MethodTypes.Uniquac, "Q").ValueInSI) - (_system.Components[j].GetParameter(MethodTypes.Uniquac, "R").ValueInSI - 1)) * x[j]);
lnGammaComb = Sym.Ln(Vi / Sym.Max(1e-10, x[i])) + 5 * qi[i] * Sym.Ln(Fi / Vi) + li[i] - Vi / Sym.Max(1e-10, x[i]) * Sym.Sum(0, NC, j => x[j] * li[j]);
Expression[] FPj = new Expression[_system.Components.Count];
for (int j = 0; j < NC; j++)
{
FPj[j] = qpi[j] * x[j] / Sym.Sum(0, NC, (kj) => qpi[kj] * x[kj]);
}
var doubleSum = Sym.Sum(0, NC, (j) => FPj[j] * tau[i, j] / (Sym.Sum(0, NC, (k) => FPj[k] * tau[k, j])));
var SFP = Sym.Sum(0, NC, (j) => FPj[j] * tau[j, i]);
lnGammaRes = qpi[i] * (1.0 - Sym.Ln(SFP) - doubleSum);
lnGamma = lnGammaComb + lnGammaRes;
_gamma_exp = Sym.Exp(lnGamma);
_dgamma_dx = new Expression[NC];
DiffFunctional = (cache, v) => _gamma_exp.Diff(cache, v);
EvalFunctional = (cache) => _gamma_exp.Eval(cache);
}
public override void FillEquationSystem(EquationSystem problem)
{
int NC = System.Components.Count;
var vliq = Sym.Sum(0, NC, i => Liquid.ComponentMolarflow[i] * Liquid.ComponentMolarVolume[i]);
var vvap = Vapor.TotalMolarflow / Vapor.DensityMolar;
MW.BindTo(System.EquationFactory.GetAverageMolarWeightExpression(System, Mixed.ComponentMolarFraction.ToArray()));
Liquid.TotalVolumeflow.BindTo(vliq);
Vapor.TotalVolumeflow.BindTo(vvap);
Mixed.TotalVolumeflow.BindTo(vliq + vvap);
Mixed.TotalMassflow.BindTo(Sym.Sum(Mixed.ComponentMassflow));
Liquid.TotalMassflow.BindTo(Sym.Sum(Liquid.ComponentMassflow));
Vapor.TotalMassflow.BindTo(Sym.Sum(Vapor.ComponentMassflow));
//Liquid.SpecificEnthalpy.BindTo(Sym.Par(Sym.Sum(0, NC, (idx) => Liquid.ComponentMolarFraction[idx] * Liquid.ComponentEnthalpy[idx])));
//Vapor.SpecificEnthalpy.BindTo(Sym.Par(Sym.Sum(0, NC, (idx) => Vapor.ComponentMolarFraction[idx] * Vapor.ComponentEnthalpy[idx])));
Liquid.SpecificEnthalpy.BindTo(new EnthalpyRoute(System, Mixed.Temperature, Mixed.Pressure, Liquid.ComponentMolarFraction, PhaseState.Liquid));
Vapor.SpecificEnthalpy.BindTo(new EnthalpyRoute(System, Mixed.Temperature, Mixed.Pressure, Vapor.ComponentMolarFraction, PhaseState.Vapour));
Mixed.Density.BindTo(Mixed.TotalMassflow / Mixed.TotalVolumeflow);
Liquid.Density.BindTo(Liquid.TotalMassflow / Liquid.TotalVolumeflow);
Vapor.Density.BindTo(Vapor.TotalMassflow / Vapor.TotalVolumeflow);
Mixed.DensityMolar.BindTo(Mixed.TotalMolarflow / Mixed.TotalVolumeflow);
Liquid.DensityMolar.BindTo(Liquid.TotalMolarflow / Liquid.TotalVolumeflow);
Vapor.DensityMolar.BindTo(System.EquationFactory.GetAverageVaporDensityExpression(System, Mixed.Temperature, Mixed.Pressure, Vapor.ComponentMolarFraction));
for (int i = 0; i < NC; i++)
{
Mixed.ComponentMassflow[i].BindTo(Mixed.ComponentMolarflow[i] * Sym.Convert(System.Components[i].GetConstant(ConstantProperties.MolarWeight), SI.kg / SI.mol));
Mixed.ComponentMassFraction[i].BindTo(Mixed.ComponentMassflow[i] / Sym.Max(1e-12, Mixed.TotalMassflow));
Liquid.ComponentMassflow[i].BindTo(Liquid.ComponentMolarflow[i] * Sym.Convert(System.Components[i].GetConstant(ConstantProperties.MolarWeight), SI.kg / SI.mol));
Liquid.ComponentMassFraction[i].BindTo(Liquid.ComponentMassflow[i] / Sym.Max(1e-12, Liquid.TotalMassflow));
Liquid.ComponentMolarVolume[i].BindTo((1.0 / System.EquationFactory.GetLiquidDensityExpression(System, System.Components[i], Mixed.Temperature, Mixed.Pressure)));
Liquid.ComponentEnthalpy[i].BindTo(System.EquationFactory.GetLiquidEnthalpyExpression(System, i, Mixed.Temperature));
Vapor.ComponentMassflow[i].BindTo(Vapor.ComponentMolarflow[i] * Sym.Convert(System.Components[i].GetConstant(ConstantProperties.MolarWeight), SI.kg / SI.mol));
Vapor.ComponentMassFraction[i].BindTo(Vapor.ComponentMassflow[i] / Sym.Max(1e-12, Vapor.TotalMassflow));
Vapor.ComponentEnthalpy[i].BindTo(System.EquationFactory.GetVaporEnthalpyExpression(System, i, Mixed.Temperature));
}
Mixed.TotalEnthalpy.BindTo(((Mixed.TotalMolarflow * Mixed.SpecificEnthalpy)));
Liquid.TotalEnthalpy.BindTo(((Liquid.TotalMolarflow * Liquid.SpecificEnthalpy)));
Vapor.TotalEnthalpy.BindTo(((Vapor.TotalMolarflow * Vapor.SpecificEnthalpy)));
if (!Mixed.SpecificEnthalpy.IsFixed)
{
Mixed.SpecificEnthalpy.BindTo((Sym.Par(Vapor.TotalMolarflow * Vapor.SpecificEnthalpy + Liquid.TotalMolarflow * Liquid.SpecificEnthalpy) / Mixed.TotalMolarflow));
}
else
{
AddEquationToEquationSystem(problem, (Mixed.SpecificEnthalpy * Mixed.TotalMolarflow).IsEqualTo(Vapor.TotalMolarflow * Vapor.SpecificEnthalpy + Liquid.TotalMolarflow * Liquid.SpecificEnthalpy), "Enthalpy Balance");
}
AddEquationToEquationSystem(problem, Mixed.TotalMolarflow.IsEqualTo(Sym.Sum(Mixed.ComponentMolarflow)), "Mass Balance");
for (int i = 0; i < NC; i++)
{
// AddEquationToEquationSystem(problem, (Mixed.ComponentMolarFraction[i] * Mixed.TotalMolarflow).IsEqualTo(Liquid.ComponentMolarFraction[i] * Liquid.TotalMolarflow + Vapor.ComponentMolarFraction[i] * Vapor.TotalMolarflow));
AddEquationToEquationSystem(problem, (Mixed.ComponentMolarflow[i]).IsEqualTo(Liquid.ComponentMolarflow[i] + Vapor.ComponentMolarflow[i]));
// Mixed.ComponentMolarflow[i].BindTo(Liquid.ComponentMolarflow[i] + Vapor.ComponentMolarflow[i]);
}
for (int i = 0; i < NC; i++)
{
AddEquationToEquationSystem(problem, (Mixed.ComponentMolarFraction[i] * Mixed.TotalMolarflow).IsEqualTo(Mixed.ComponentMolarflow[i]));
//Mixed.ComponentMolarFraction[i].BindTo(Mixed.ComponentMolarflow[i]/ Mixed.TotalMolarflow);
}
for (int i = 0; i < NC; i++)
{
AddEquationToEquationSystem(problem, (Liquid.ComponentMolarFraction[i] * Liquid.TotalMolarflow).IsEqualTo(Liquid.ComponentMolarflow[i]));
//Liquid.ComponentMolarFraction[i].BindTo(Liquid.ComponentMolarflow[i] / Sym.Max(1e-12, Liquid.TotalMolarflow));
}
for (int i = 0; i < NC; i++)
{
AddEquationToEquationSystem(problem, (Vapor.ComponentMolarFraction[i] * Vapor.TotalMolarflow).IsEqualTo(Vapor.ComponentMolarflow[i]));
// Vapor.ComponentMolarFraction[i].BindTo(Vapor.ComponentMolarflow[i] / Sym.Max(1e-12, Vapor.TotalMolarflow));
}
AddEquationToEquationSystem(problem, (Vfmolar * Mixed.TotalMolarflow).IsEqualTo((Vapor.TotalMolarflow)), "Vapor Fraction");
switch (State)
{
case PhaseState.BubblePoint:
AddEquationToEquationSystem(problem, (Sym.Sum(Liquid.ComponentMolarFraction) - Sym.Sum(Vapor.ComponentMolarFraction)).IsEqualTo(Beta), "Equilibrium");
AddEquationToEquationSystem(problem, Beta.IsEqualTo(0), "Equilibrium");
AddEquationToEquationSystem(problem, Liquid.TotalMolarflow.IsEqualTo(Sym.Sum(Liquid.ComponentMolarflow)), "Mass Balance");
break;
case PhaseState.DewPoint:
AddEquationToEquationSystem(problem, (Sym.Sum(Liquid.ComponentMolarFraction) - Sym.Sum(Vapor.ComponentMolarFraction)).IsEqualTo(Beta), "Equilibrium");
AddEquationToEquationSystem(problem, Beta.IsEqualTo(0), "Equilibrium");
AddEquationToEquationSystem(problem, Vapor.TotalMolarflow.IsEqualTo(Sym.Sum(Vapor.ComponentMolarflow)), "Mass Balance");
break;
default:
if (Vfmolar.IsFixed)
{
AddEquationToEquationSystem(problem, (Sym.Sum(Liquid.ComponentMolarFraction) - Sym.Sum(Vapor.ComponentMolarFraction)).IsEqualTo(Beta), "Equilibrium");
AddEquationToEquationSystem(problem, Beta.IsEqualTo(0), "Equilibrium");
}
else
{
AddEquationToEquationSystem(problem, (Sym.Sum(Liquid.ComponentMolarFraction) - Sym.Sum(Vapor.ComponentMolarFraction)).IsEqualTo(Beta), "Equilibrium");
AddEquationToEquationSystem(problem, Sym.Mid(Vfmolar, Beta, Vfmolar - 1).IsEqualTo(0), "Equilibrium");
}
AddEquationToEquationSystem(problem, (Mixed.TotalMolarflow).IsEqualTo(Vapor.TotalMolarflow + Liquid.TotalMolarflow), "Mass Balance");
break;
}
for (int i = 0; i < NC; i++)
{
System.EquationFactory.EquilibriumCoefficient(System, KValues[i], Mixed.Temperature, Mixed.Pressure, Liquid.ComponentMolarFraction, Vapor.ComponentMolarFraction, i);
AddEquationToEquationSystem(problem, Vapor.ComponentMolarFraction[i].IsEqualTo(KValues[i] * Liquid.ComponentMolarFraction[i]), "Equilibrium");
}
base.FillEquationSystem(problem);
}