Objects are available in Python GEKKO and the APMonitor language to simplify the description of complex models.

Python GEKKO Object Library

Python GEKKO has equation functions and pre-built objects. GEKKO has objects in the Deep Learning (Brain) and Thermo & Flowsheet Chemical libraries. Some of the other pre-built objects and equation functions are:

In Python GEKKO, objects are defined as components of the model as m.object_name().

Python GEKKO Example Usage (abs3)

from gekko import GEKKO
# define new GEKKO model
m = GEKKO()
# variable
x = m.Var(-0.5)
# calculate y=abs(x) with abs3
y = m.abs3(x)
# solve with APOPT (MINLP solver)
# print solution
print('x: ' + str(x.value))
print('y: ' + str(y.value))

Python GEKKO Example Usage (Array, abs3, sum)

from gekko import GEKKO
import numpy as np
m = GEKKO()
x1 = m.Param(-2)
x2 = m.Param(-1)
x3 = np.linspace(0,1,6)
x4 = m.Array(m.Param,3)
y4 = m.Array(m.Var,3)
for i in range(3):
    y4[i] = m.abs3(x4[i])
# create variable
y = m.Var()
# y = 0.6 =          -2 -1   + 3       + 0.6
m.Equation(y == sum([x1,x2]) + sum(x3) + sum(y4))
m.solve() # solve
print('x1: ' + str(x1.value))
print('x2: ' + str(x2.value))
print('y: '  + str(y.value))

APMonitor Object Library

In APMonitor, objects are defined in the Objects ... End Objects section of the model file. New instances of an object are defined by declaring a new object name equal to the parent object type.

new_child = parent_object

 ! example use of ABS as MPEC
   a = abs
 End Objects

   x = a.x
   y = a.y
 End Connections

   x = -5
 End Parameters

 End Variables

The object library consists of common mathematical functions and chemical processing equipment such as feed streams, reactors, pumps, mixers, flash columns, vessels, and distillation stages. It also includes other elements that support distributed control system emulation such as a LAG and a PID controller.

Thermo objects

Thermo objects access data from the underlying thermodynamic database. There are many compounds accessible in the database. To reduce the size of the APMonitor executable, only some of the more common compounds are currently incorporated. Additional compounds can be easily added but require a rebuild of the executable.

Temperature Independent Property Data

Temperature independent property data do not vary with temperature. They are defined as constants for each of the species declared in the Compounds ... End Compounds section of the model. If the Compounds ... End Compounds section is missing, all available compounds are included in the model.

thermo_mw Molecular Weight kg/kmol
thermo_tc Critical Temperature K
thermo_pc Critical Pressure Pa
thermo_vc Critical Volume m^3/kmol
thermo_ccf Crit Compress Factor unitless
thermo_mp Melting Point K
thermo_tpt Triple Pt Temperature K
thermo_tpp Triple Pt Pressure Pa
thermo_nbp Normal Boiling Point K
thermo_lmv Liq Molar Volume m^3/kmol
thermo_ighf IG Heat of Formation J/kmol
thermo_iggf IG Gibbs of Formation J/kmol
thermo_igae IG Absolute Entropy J/kmol*K
thermo_shf Std Heat of Formation J/kmol
thermo_sgf Std Gibbs of Formation J/kmol
thermo_sae Std Absolute Entropy J/kmol*K
thermo_hfmp Heat Fusion at Melt Pt J/kmol
thermo_snhc Std Net Heat of Comb J/kmol
thermo_af Acentric Factor unitless
thermo_rg Radius of Gyration m
thermo_sp Solubility Parameter (J/m^3)^0.5
thermo_dm Dipole Moment c*m
thermo_r van der Waals Volume m^3/kmol
thermo_q van der Waals Area m^2
thermo_ri Refractive Index unitless
thermo_fp Flash Point K
thermo_lfl Lower Flammability Limit K
thermo_ufl Upper Flammability Limit K
thermo_lflt Lower Flamm Limit Temp K
thermo_uflt Upper Flamm Limit Temp K
thermo_ait Auto Ignition Temp K

Temperature Dependent Property Data

The temperature dependent thermo objects produce values based on a specified temperature. When a temperature dependent property object is declared, a new temperature variable will be created. This variable can be adjusted or linked to an existing temperature of interest.

thermo_sd Solid Density kmol/m^3
thermo_ld Liquid Density kmol/m^3
thermo_svp Solid Vapor Pressure Pa
thermo_lvp Liquid Vapor Pressure Pa
thermo_hvap Heat of Vaporization J/kmol
thermo_scp Solid Heat Capacity J/kmol*K
thermo_lcp Liquid Heat Capacity J/kmol*K
thermo_igcp Ideal Gas Heat Capacity J/kmol*K
thermo_svc Second Virial Coefficient m^3/kmol
thermo_lv Liquid Viscosity Pa*s
thermo_vv Vapor Viscosity Pa*s
thermo_sk Solid Thermal Conductivity W/m*K
thermo_lk Liq Thermal Conductivity W/m*K
thermo_vk Vap Thermal Conductivity W/m*K
thermo_st Surface Tension N/m
thermo_sh Solid Enthalpy J/kmol
thermo_lh Liq Enthalpy J/kmol
thermo_vh Vap Enthalpy J/kmol

Example - MIN Function

Example - Mixer Application

Example - Distillation Column

 Model distill

 End Compounds

  ! feed stream
  feed           = Feed
  feed_lag       = Stream_Lag
  feed_cooler    = Vessel
  feed_flash     = Flash
  liq_mixer      = Mixer
  vap_mixer      = Mixer

  ! condenser and reflux
  condenser      = Vessel
  drum           = Flash
  reflux         = Splitter

  ! column stages
  stage[1:8]     = Stage_1

  ! reboiler
  sump           = Vessel
  reboiler       = Vessel
  reboiler_flash = Flash

  ! mass and massflows
  sump_mass      = Mass
  feed_massflow  = Massflow
  cleu_massflow  = Massflow
  btms_massflow  = Massflow
 End Objects

  ! feed streams
  feed.*                      = feed_lag.inlet.*
  feed_lag.outlet.*           = feed_cooler.inlet.*
  feed_cooler.outlet.*        = feed_flash.inlet.*
  feed_flash.outlet_vap.*     = vap_mixer.inlet[1].*
  feed_flash.outlet_liq.*     = liq_mixer.inlet[1].*

  ! liquid down the column
  liq_mixer.inlet[2].*        = stage[1].l_out.*
  liq_mixer.outlet.*          = stage[2].l_in.*
  stage[2:7].l_out.*          = stage[3:8].l_in.*
  stage[8].l_out.*            = sump.inlet.*

  ! reboiler
  sump.outlet.*               = reboiler.inlet.*
  reboiler.outlet.*           = reboiler_flash.inlet.*

  ! vapor up the column
  reboiler_flash.outlet_vap.* = stage[8].v_in.*
  stage[3:8].v_out.*          = stage[2:7].v_in.*
  vap_mixer.inlet[2].*        = stage[2].v_out.*
  vap_mixer.outlet.*          = stage[1].v_in.*

  ! condenser
  stage[1].v_out.*            = condenser.inlet.*
  condenser.outlet.*          = drum.inlet.*
  drum.outlet_liq.*           = reflux.inlet.*
  reflux.outlet[2].*          = stage[1].l_in.*

  ! mass and massflow meters
  sump.reserve.*              = sump_mass.acc.*
  feed.*                      = feed_massflow.stream.*
  drum.outlet_vap.*           = cleu_massflow.stream.*
  reboiler_flash.outlet_liq.* = btms_massflow.stream.*

  ! stream pressures
  strm_p                            = stage[1].v_out.p
  strm_p                            = stage[2:8].l_out.p
  strm_p                            = stage[3:8].v_out.p

  ! feed and stage pressures
  fd_p                              = stage[1:8].l_res.p
 End Connections

 Model custom

     fd_t     = 370.0  ! K
     fd_p     = 3.11e6 ! Pa
     fd_c2h4  = 0.28   ! mol%
     fd_c3h6  = 0.6184 ! mol%
     fd_c3h8  = 0.0916 ! mol%
     fd_h2    = 0.01   ! mol%

     strm_p   = fd_p   ! Pa
     fd_ndot  = 1.0
  End Parameters

     fd_mdot  = 0.395  ! kg/sec
  End Variables

     fd_t     = feed.t
     fd_p     = feed.p
     fd_c2h4  = feed.x[1]
     fd_c3h6  = feed.x[2]
     fd_c3h8  = feed.x[3]
     fd_h2    = feed.x[4]
     fd_mdot  = feed_massflow.mdot
     fd_ndot  = feed.ndot
  End Connections

  End Intermediates

  End Equations

 End Model
Home | Objects