id	summary	reporter	owner	description	type	status	priority	milestone	component	version	resolution	keywords	cc
6385	Overdetermined system	anonymous	Shravya Hebbur Murali <shravya2535@…>	"Does anyone have a system for how they determine where the errors are in their overdetermined model? I find that the errors from the simulation do not directly lead me to the error


package SplitM_1
  connector Inlet
  
   flow Real Q[17] (each quantity=""volumetric flowrate"", each unit=""L/h"") ""Flowrate""; 
   input Real c[17] (each quantity=""concentration"",each unit=""mg/L"");
    Real P[17] (each quantity = ""pressure"", each unit = ""Pa"") ""Potential variable"";
    
  end Inlet;

  connector Outlet
    
   flow Real Q[17] (each quantity=""volumetric flowrate"", each unit=""L/h"") ""Flowrate""; 
   output Real c[17] (each quantity=""concentration"",each unit=""mg/L"");
    Real P[17] (each quantity = ""pressure"", each unit = ""Pa"") ""Potential variable"";
    
  end Outlet;

  record membrane_properties
    parameter Real n = 7 ""Number of capillaries per fiber"";
    parameter Real m = 15 ""Number of Membrane Fibers"";
    parameter Modelica.SIunits.Length d_cap = 0.0009 ""Capillary diameter"";
    parameter Modelica.SIunits.Length l_m = 1.5 ""Capillary membrane length"";
  end membrane_properties;

  record set_flow_parameters
   parameter Modelica.SIunits.Velocity u_cf[17] ={0.25, 0.5, 1, 1.5, 2, 2.5, 3, 3.5, 4, 4.5, 5, 5.5, 6, 6.5, 7, 7.5, 8}; //Crossflow velocity at the membrane inlet
    parameter Real J_p_overall = 35;
    //in m^3/sm^2 Average permeate flux as the permeate leaves the membrane 35 L/hm^2
    parameter Real Y = 0.45;
    //Water conversion factor (Q_p/Q_raw)
    parameter Real k_w = 10.67;
    //water permeability through the membrane in L/hm^2
    //parameter Real P_feed = 2.75; // used to calculate potential presure terms
  end set_flow_parameters;

  record Conc_pol_parameters
    //output
  Real Re[17]; //Reynoldsnumber
  Real Sc[17]; //Schmidtnumber
  Real Sh[17]; //Sherwoodnumber
  Real CP[17]; //concentration polarization
  Real delta[17]; //d_h/Sh
  Real k[17]; //D_i.Sh/d_h"";
    //input
    constant Real D_i = 1.07 * 10 ^ (-9) ""Diffusion coefficient / m²/s"";
  end Conc_pol_parameters;

  record osmopressure_solute
    constant Real R_gasconstant = Modelica.Constants.R;
    parameter Real alpha = 1 ""disscociation constant
      between 0 and 1"";
    parameter Real T = 293 ""temperature /K"";
    //why error
    parameter Real v = 2 ""stoichiometric coefficient"";
    //c_f is the only variation from one membrane module to the next
  Real P_osmotic[17];
  Real B;
  end osmopressure_solute;

  class calculated_flows
    constant Real pi = 3.141592;
    Real d_h ""hydraulic diameter"";
    extends membrane_properties;
    extends set_flow_parameters;
    output Real A_cf ""Crosssectional flow area / m²"";
    output Real A_act ""Active Membrane area / m²"";
  equation
    d_h = d_cap * m * n;
    A_cf = pi * (d_cap / 2) ^ 2 * n * m;
    A_act = pi * d_h * l_m;
  end calculated_flows;

  model Raw_water
    //Inlet In_MO;
    Outlet Out_F;
    extends calculated_flows;
    //Permeate Perm;
    parameter Real c_raw_init = 248 ""Concentration of contaminant / mg/L"";
    Real Q_raw_f[17] ""raw water flowrate set / L/h "";
    Real c_raw[17];
    //Real Q_p;
    Real V[17]""Volume of water in the raw water tank varying with progression of the filtration process with time"";
    Real V_initial = 500 * 10 ^ 3 ""Volume of water present in the tank"";
   
  
  initial equation
  
  for i in 1:17 loop
  
   c_raw[i] = c_raw_init;
   V[i] = V_initial;
   Q_raw_f[i] = J_p_overall * A_act / Y;
    
   end for;
  
  equation
  for i in 1:17 loop
   
  //initial equation
  //c_raw[i] = c_raw_init;
  //V[i] = V_initial;
    
  //equation
    Out_F.c[i] = c_raw[i];
    Out_F.Q[i] = - Q_raw_f[i];
    der(V[i]) = - Q_raw_f[i];
    der(c_raw[i] * V[i]) = Out_F.Q[i] * Out_F.c[i];
//der(V) = In_MO.Q + Out_F.Q ;
//der(c_raw * V) = In_MO.Q * In_MO.c ;
//In_MO.P = 1;
    Out_F.P[i] = 1;
    
   end for; 
   
  end Raw_water;

  model Feed
    Inlet In_raw, In_cyc;
    Outlet Out;
    extends calculated_flows;
    //feed flowrate calculated based on fixed feed velocity
    //Real P_head;
    Real Q_f[17];
    Real P_f[17];
    //just display
    Real P_rec[17];
    //just display
    Real P_increase_f[17];
    Real P_increase_rec[17];
    Real P_feed[17];
  
  equation
  
    for i in 1:17 loop
    
    Q_f[i] = u_cf[i] * A_cf * 3600 * 1000;
    
    In_raw.c[i] * In_raw.Q[i] + In_cyc.c[i] * In_cyc.Q[i] + Out.c[i] * Out.Q[i] = 0;
    Out.Q[i] = -abs(Q_f[i]);
    In_cyc.Q[i] + Out.Q[i] + In_raw.Q[i] = 0;
    
    In_raw.P[i] = P_f[i];
    In_cyc.P[i] = P_rec[i];
    P_increase_f[i] = P_feed[i] - P_f[i];
    P_increase_rec[i] = P_feed[i] - P_rec[i];
    Out.P[i] = P_feed[i];
    
    end for;
    
  end Feed;

  model Membrane
    Inlet In;
    Outlet Out_P, Out_M;
    
    Real sn ""segment number"";  
    Real R_obssn[17] ""rejection considering CP"";
    Real c_msn[17] ""concentration along the membrane / mg/L"";
    Real c_fsn[17] ""concentration of feed or bulk / mg/L"";
    Real tsn[17] ""thickness of boundary layer / m"";
    Real TMP[17] ""transmembrane pressure /bar"";
    Real WCF[17] ""water conversion factor"";
    Real k[17] ""beta, mass transfer coefficient"";
    
    //Real P_loss ""Pressure loss"";
    Real P_loss_HP[17] ""Pressure loss along the membrane length using Hagen-poiseuille equation"";
    //Real P_loss_sn ""Pressure loss in each segment"";
    Real e_sn[17] ""energy used in each segment unit"";
    //Real TMP_test;
    
    Real Q_psn[17] ""permeate leaving segment n"";
    Real J_psn[17] ""permeate flux through segment sn"";
    Real u_cfsn[17];
    //Parameter assumption to test the model-
    //Pressure varies with velocity and a relationship must be attained experimentally, or J_p(TMP) must be calculated by another method and not Darcy's law
    //Intrinsic retetntion can be obtained from experimental calculations
    Real P_in[17];
    Real P_out[17];
    Real f_D[17];
    parameter Real R_int = 0.9;
    //intrinsic retention of membrane
      
    parameter Real rho = 998.2 ""density of water kg/m^3"";
    parameter Real mu = 1 * 10 ^ (-3) ""dynamic viscosity / Pa.s"";
    
    extends calculated_flows;
    extends Conc_pol_parameters;
    extends osmopressure_solute;
  
  equation
  
  for i in 1:17 loop
  
   f_D[i] = 64 / Re[i] ""friction factor"";
  
    abs(In.c[i]) = c_fsn[i];
//Out_P.c = In.c * (1-R); // permeate from the membrane calculated based on assumed R value
    u_cfsn[i] = In.Q[i] / (A_cf * 3600 * 1000);
    
    P_in[i] = In.P[i];
    Out_P.P[i] = 0;
//P_loss_sn =  f_D * rho * l_m/4 * u_cfsn ^ 2 / (2 * d_cap) * 10^(-5);
//P_loss = f_D * rho * l_m * sn/4 * u_cfsn ^ 2 / (2 * d_cap) * 10^(-5);
    
    P_loss_HP[i] = 0.25 *l_m * sn/4 * u_cfsn [i];
  //P_loss_HP[i] = In.Q[i] * (8 / (m * n)) * mu * l_m * sn / 4 * 10 ^ (-5) / ((d_cap / 2) ^ 4 * pi * 3.6 * 10 ^ 6);
// convert from pa to bar - Q from l/h to m3/s, flow is considered to be equally distributed through the m capillaries in the n fibres
    
    P_out[i] = P_in[i] - P_loss_HP[i];
    TMP[i] = (P_in[i] + P_out[i]) / 2 - Out_P.P[i];
    Out_M.P[i] = P_out[i];
//TMP_test = (In.P + Out_M.P)/2;
    Q_psn[i] = k_w * TMP[i] * (A_act / 4);
    J_psn[i] = Q_psn[i] / (A_act / 4);
    Out_P.Q[i] = -abs(Q_psn[i]);
    In.Q[i] + Out_P.Q[i] + Out_M.Q[i] = 0;
    WCF[i] = abs(Out_P.Q[i] / In.Q[i]);
    (CP[i], Re[i], Sc[i], Sh[i], delta[i], k[i]) = Concentration_polarization(d_cap, D_i, l_m * sn / 4, c_fsn[i], u_cfsn[i], J_psn[i], R_int);
    (B, P_osmotic[i]) = osmotic_pressure(R_gasconstant, alpha, T, c_msn[i], v);
    
    c_msn[i] = CP[i] * c_fsn[i];
    //Out_P.c = (1 - R_int) * c_fsn;
    //R_obssn = 1 - Out_P.c / c_msn;
    Out_P.c[i]=(1-R_int)*c_msn[i];
    R_obssn[i]=1-(Out_P.c[i]/c_fsn[i]);
    tsn[i] = D_i / k[i];
    Out_P.c[i] * Out_P.Q[i] + Out_M.c[i] * Out_M.Q[i] + In.c[i] * In.Q[i] = 0;
    e_sn[i] = P_loss_HP[i] * u_cfsn[i] * A_cf * 3600 * 1000;
  
  end for;
  
  end Membrane;

  model Permeate
    Inlet In_P1, In_P2, In_P3, In_P4;
    output Real Q_p[17];
    output Real c_permeate[17];
    extends calculated_flows;
    
  equation
  
  for i in 1:17 loop
  
    Q_p[i] = In_P1.Q[i] + In_P2.Q[i] + In_P3.Q[i] + In_P4.Q[i];
    c_permeate[i] = (In_P1.c[i] * In_P1.Q[i] + In_P2.c[i] * In_P2.Q[i] + In_P3.c[i] * In_P3.Q[i] + In_P4.c[i] * In_P4.Q[i]) / Q_p[i];
  
  end for;
  
  end Permeate;

  model Membrane_outlet
    Inlet In;
    Outlet Out_cyc, Out_Ret;
    //Out_RW
    //parameter Real rec = -1 ""recirculation"";
  
  equation
  for i in 1:17 loop
  
    Out_Ret.c[i] = In.c[i];
    Out_cyc.c[i] = In.c[i];
//Out_cyc.Q = -abs(rec);
    Out_cyc.Q[i] + Out_Ret.Q[i] + In.Q[i] = 0;
    Out_cyc.P[i] = 1;
    Out_Ret.P[i] = 1;
    
   end for;
    
  end Membrane_outlet;


  model Retentate
    
    Inlet In_Ret;
    output Real Q_ret[17];
    output Real c_ret[17];
    extends calculated_flows;
  equation
  
for i in 1:17 loop
  
    Q_ret[i] = In_Ret.Q[i];
    c_ret[i] = In_Ret.c[i];
// In_P1.P + In_P2.P + In_P3.P + In_P4.P = 0;

end for;
  
  end Retentate;

  class Run
    
    Real WCF_overall[17];
    Real Y_overall[17];
    Real R_overall[17];
    Real P_loss_overall[17];
    Real R_raw_overall[17];
    Real TMP_overall[17];
    
    extends calculated_flows;
    
    Raw_water RW;
    Feed F;
    Membrane M1(sn = 1);
    Membrane M2(sn = 2);
    Membrane M3(sn = 3);
    Membrane M4(sn = 4);
    Permeate Pn;
    Membrane_outlet MO;
    Retentate Ret;
    
  equation
    connect(RW.Out_F, F.In_raw);
    connect(F.Out, M1.In);
    connect(M1.Out_P, Pn.In_P1);
    connect(M2.Out_P, Pn.In_P2);
    connect(M3.Out_P, Pn.In_P3);
    connect(M4.Out_P, Pn.In_P4);
//final permeate stream is made up of the 4 permeate streams
    connect(M1.Out_M, M2.In);
    connect(M2.Out_M, M3.In);
    connect(M3.Out_M, M4.In);
    connect(M4.Out_M, MO.In);
    connect(MO.Out_Ret, Ret.In_Ret);
    connect(MO.Out_cyc, F.In_cyc);
    
  for i in 1:17 loop
  
    WCF_overall[i] = abs(Pn.Q_p[i] / F.Out.Q[i]);
    Y_overall[i] = Pn.Q_p[i] / RW.Q_raw_f[i];
    R_overall[i] = 1 - Pn.c_permeate[i] / F.Out.c[i];
    R_raw_overall[i] = 1 - Pn.c_permeate[i] / RW.c_raw_init;
    P_loss_overall[i] = M1.P_loss_HP[i] + M2.P_loss_HP[i] + M3.P_loss_HP[i] + M4.P_loss_HP[i];
    J_p_overall = (M1.Q_psn[i] + M2.Q_psn[i] + M3.Q_psn[i] + M4.Q_psn[i]) / A_act;
    TMP_overall[i] = (M1.P_in[i] + M4.P_out[i]) / 2;
    
  end for;
  
  end Run;

  function Concentration_polarization
    input Real d_cap, D_i, l_m, c_f, u_cf, J_p, R_int;
    output Real CP ""Concentration polarization / c_0/c_f"", Re ""Reynold's number"", Sc ""Schmidt number"", Sh ""Sherwood number"", delta ""thickness of boundary layer laminar flow / m"", k ""Mass transfer coefficient"";
  protected
    constant Real e = Modelica.Constants.e;
    Real mu = 1 * 10 ^ (-3) ""dynamic viscosity / Pa.s"";
    Real rho = 998.2 ""density of water kg/m^3"";
  algorithm
    Re := d_cap * u_cf * rho / mu;
    Sc := mu / (rho * D_i);
    if Re < 2300 then
      Sh := 1.62 * (Re * Sc * d_cap / l_m) ^ (1 / 3);
    else
      Sh := 0.04 * Re ^ (3 / 4) * Sc;
    end if;
    delta := d_cap / Sh ""thickness of boundary layer laminar flow / m"";
    k := D_i / delta ""Mass transfer coefficient"";
    CP := e ^ (J_p / 1000 / 3600 / k) / (R_int + (1 - R_int) * e ^ (J_p / 1000 / 3600 / k)) ""Concentration polarization / c_0/c_f"";
  end Concentration_polarization;

  function osmotic_pressure
    input Real R_gasconstant, alpha, T, c_f, v;
    //c_f is the only varaiation from one membrane module to the next
    output Real B, P_osmotic;
  algorithm
    B := 1 + alpha * (v - 1);
    P_osmotic := B * R_gasconstant * 10 ^ (-2) * T * c_f / (1000 * 120.3676);
// Use magnesium sulphate in moles
  end osmotic_pressure;
end SplitM_1;"	defect	assigned	high		OMEdit	1.16.2		Overdetermined, openmodelicabeginner, nanofiltration	Andreas Heuermann Philip Hannebohm