add liquid volume for reactive distillation

biosteam/units/design_tools/column_design.py

@@ -345,7 +345,7 @@ def compute_max_vapor_velocity(C_sbf, sigma, rho_L, rho_V, F_F, A_ha):
  F_F : 
  Foaming factor
  A_ha : 
- Ratio of open area, A_h, to active area, A_a
+ Ratio of open area, A_h, to active area, A_a.
  
  Notes
  -----
@@ -407,7 +407,7 @@ def compute_tower_diameter(V_vol, U_f, f, A_dn):
  The tower diameter is given by [3]_. See source code for details.
  
  """
- Di = np.sqrt(4.*V_vol/(f*U_f*np.pi*(1.-A_dn)))
+ Di = np.sqrt(4. * V_vol/(f * U_f * np.pi* (1. - A_dn)))
  if Di < 0.914:
  # Make sure diameter is not too small
  Di = 0.914

biosteam/units/distillation.py

@@ -53,7 +53,7 @@
 from scipy.optimize import brentq
 from warnings import warn
 import biosteam as bst
-from math import inf
+from math import inf, sqrt, exp, pi
 from .heat_exchange import HXutility
 from ._flash import Flash
 from .stage import MultiStageEquilibrium
@@ -218,8 +218,8 @@ class Distillation(Unit, isabstract=True):
  flooding.
  foaming_factor=1.0 : float
  Must be between 0 to 1.
- open_tray_area_fraction=0.1 : float
- Fraction of open area to active area of a tray.
+ open_tray_area=0.1 : float
+ Ratio of open area to active area of a tray.
  downcomer_area_fraction=None : float
  Enforced fraction of downcomer area to net (total) area of a tray.
  If None, estimate ratio based on Oliver's estimation [1]_.
@@ -309,13 +309,14 @@ def _init(self,
  stage_efficiency=None,
  velocity_fraction=0.8,
  foaming_factor=1.0,
- open_tray_area_fraction=0.1,
+ open_tray_area=0.1,
  downcomer_area_fraction=None,
  is_divided=False,
  vacuum_system_preference='Liquid-ring pump',
  condenser_thermo=None,
  reboiler_thermo=None,
  partial_condenser=True,
+ weir_height=0.1,
  ):
  self.check_LHK = True
 
@@ -332,10 +333,11 @@ def _init(self,
  self.tray_type = tray_type
  self.tray_material = tray_material
  self.tray_spacing = tray_spacing
+ self.weir_height = weir_height
  self.stage_efficiency = stage_efficiency
  self.velocity_fraction = velocity_fraction
  self.foaming_factor = foaming_factor
- self.open_tray_area_fraction = open_tray_area_fraction
+ self.open_tray_area = open_tray_area
  self.downcomer_area_fraction = downcomer_area_fraction
  self.is_divided = is_divided
  self.vacuum_system_preference = vacuum_system_preference
@@ -508,12 +510,29 @@ def Hr(self):
  return self._Hr
  @Hr.setter
  def Hr(self, Hr):
- assert self.product_specification_format == "Recovery", (
- "product specification format must be 'Recovery' "
- "to set heavy key recovery")
- assert 0 < Hr < 1, "heavy key recovery in the bottoms product must be a fraction" 
+ if not self.product_specification_format == "Recovery":
+ raise ValueError(
+ "product specification format must be 'Recovery' "
+ "to set heavy key recovery"
+ )
+ if not 0 < Hr < 1:
+ raise ValueError(
+ "heavy key recovery in the bottoms product must be a fraction" 
+ )
  self._Hr = Hr
 
+ @property
+ def weir_height(self):
+ """Weir height as a fraction tray spacing."""
+ return self._WH
+ @weir_height.setter
+ def weir_height(self, WS):
+ if not 0 < WS < 1:
+ raise ValueError(
+ "weir height must be a fraction" 
+ )
+ self._WH = WS
+
  @property
  def tray_spacing(self):
  return self._TS
@@ -549,11 +568,11 @@ def foaming_factor(self, F_F):
  self._F_F = F_F
 
  @property
- def open_tray_area_fraction(self):
- """Fraction of open area, A_h, to active area, A_a."""
+ def open_tray_area(self):
+ """Ratio of open area, A_h, to active area, A_a."""
  return self._A_ha
- @open_tray_area_fraction.setter
- def open_tray_area_fraction(self, A_ha):
+ @open_tray_area.setter
+ def open_tray_area(self, A_ha):
  self._A_ha = A_ha
 
  @property
@@ -915,7 +934,7 @@ def _complete_distillation_column_design(self):
  U_f = design.compute_max_vapor_velocity(C_sbf, sigma, rho_L, rho_V, F_F, A_ha)
  A_dn = self._A_dn
  if A_dn is None:
- self._A_dn = A_dn = design.compute_downcomer_area_fraction(F_LV)
+ A_dn = design.compute_downcomer_area_fraction(F_LV)
  f = self._f
  R_diameter = design.compute_tower_diameter(V_vol, U_f, f, A_dn) * 3.28
 
@@ -1135,7 +1154,7 @@ class BinaryDistillation(Distillation, new_graphics=False):
  flooding.
  foaming_factor=1.0 : float
  Must be between 0 to 1.
- open_tray_area_fraction=0.1 : float
+ open_tray_area=0.1 : float
  Fraction of open area to active area of a tray.
  downcomer_area_fraction=None : float
  Enforced fraction of downcomer area to net (total) area of a tray.
@@ -1656,7 +1675,7 @@ class ShortcutColumn(Distillation, new_graphics=False):
  flooding.
  foaming_factor=1.0 : float
  Must be between 0 to 1.
- open_tray_area_fraction=0.1 : float
+ open_tray_area=0.1 : float
  Fraction of open area to active area of a tray.
  downcomer_area_fraction=None : float
  Enforced fraction of downcomer area to net (total) area of a tray.
@@ -1986,7 +2005,7 @@ class AdiabaticMultiStageVLEColumn(MultiStageEquilibrium):
  flooding.
  foaming_factor=1.0 : float
  Must be between 0 to 1.
- open_tray_area_fraction=0.1 : float
+ open_tray_area=0.1 : float
  Fraction of open area to active area of a tray.
  downcomer_area_fraction=None : float
  Enforced fraction of downcomer area to net (total) area of a tray.
@@ -2084,8 +2103,9 @@ def _init(self,
  stage_efficiency=None,
  velocity_fraction=0.8,
  foaming_factor=1.0,
- open_tray_area_fraction=0.1,
- downcomer_area_fraction=None, 
+ open_tray_area=0.1,
+ downcomer_area_fraction=None,
+ weir_height=0.1,
  use_cache=None,
  collapsed_init=False,
  method=None,
@@ -2106,8 +2126,9 @@ def _init(self,
  self.stage_efficiency = stage_efficiency
  self.velocity_fraction = velocity_fraction
  self.foaming_factor = foaming_factor
- self.open_tray_area_fraction = open_tray_area_fraction
+ self.open_tray_area = open_tray_area
  self.downcomer_area_fraction = downcomer_area_fraction
+ self.weir_height = weir_height
  self._last_args = (
  self.N_stages, self.feed_stages, self.vapor_side_draws, 
  self.liquid_side_draws, self.use_cache, *self._ins, 
@@ -2143,11 +2164,12 @@ def vapor(self):
  def liquid(self):
  return self.outs[1] 
 
+ weir_height = Distillation.weir_height
  tray_spacing = Distillation.tray_spacing
  stage_efficiency = Distillation.stage_efficiency
  velocity_fraction = Distillation.velocity_fraction
  foaming_factor = Distillation.foaming_factor
- open_tray_area_fraction = Distillation.open_tray_area_fraction
+ open_tray_area = Distillation.open_tray_area
  downcomer_area_fraction = Distillation.downcomer_area_fraction
  tray_type = Distillation.tray_type
  tray_material = Distillation.tray_material
@@ -2291,7 +2313,7 @@ class MESHDistillation(MultiStageEquilibrium, new_graphics=False):
  flooding.
  foaming_factor=1.0 : float
  Must be between 0 to 1.
- open_tray_area_fraction=0.1 : float
+ open_tray_area=0.1 : float
  Fraction of open area to active area of a tray.
  downcomer_area_fraction=None : float
  Enforced fraction of downcomer area to net (total) area of a tray.
@@ -2371,11 +2393,11 @@ class MESHDistillation(MultiStageEquilibrium, new_graphics=False):
  Electricity Power kW 0.918
  Cost USD/hr 0.0718
  Cooling water Duty kJ/hr -9.13e+06
- Flow kmol/hr 6.23e+03
+ Flow kmol/hr 6.24e+03
  Cost USD/hr 3.04
  Low pressure steam Duty kJ/hr 9.62e+06
  Flow kmol/hr 249
- Cost USD/hr 59.1
+ Cost USD/hr 59.2
  Design Theoretical stages 5
  Actual stages 6
  Height ft 22.9
@@ -2390,7 +2412,7 @@ class MESHDistillation(MultiStageEquilibrium, new_graphics=False):
  Pump - Motor USD 390
  Reboiler - Floating head USD 2.41e+04
  Total purchase cost USD 1.17e+05
- Utility cost USD/hr 62.2
+ Utility cost USD/hr 62.3
  
  Notes
  -----
@@ -2435,11 +2457,12 @@ class MESHDistillation(MultiStageEquilibrium, new_graphics=False):
  _max_agile_design = AdiabaticMultiStageVLEColumn._max_agile_design
  _units = AdiabaticMultiStageVLEColumn._units
 
+ weir_height = Distillation.weir_height
  tray_spacing = Distillation.tray_spacing
  stage_efficiency = Distillation.stage_efficiency
  velocity_fraction = Distillation.velocity_fraction
  foaming_factor = Distillation.foaming_factor
- open_tray_area_fraction = Distillation.open_tray_area_fraction
+ open_tray_area = Distillation.open_tray_area
  downcomer_area_fraction = Distillation.downcomer_area_fraction
  tray_type = Distillation.tray_type
  tray_material = Distillation.tray_material
@@ -2458,7 +2481,8 @@ def _init(self,
  stage_efficiency=None,
  velocity_fraction=0.8,
  foaming_factor=1.0,
- open_tray_area_fraction=0.1,
+ open_tray_area=0.1,
+ weir_height=0.1,
  downcomer_area_fraction=None,
  vacuum_system_preference='Liquid-ring pump',
  partition_data=None,
@@ -2495,14 +2519,15 @@ def _init(self,
  maxiter=maxiter)
 
  # Construction specifications
+ self.weir_height = weir_height
  self.vessel_material = vessel_material
  self.tray_type = tray_type
  self.tray_material = tray_material
  self.tray_spacing = tray_spacing
  self.stage_efficiency = stage_efficiency
  self.velocity_fraction = velocity_fraction
  self.foaming_factor = foaming_factor
- self.open_tray_area_fraction = open_tray_area_fraction
+ self.open_tray_area = open_tray_area
  self.downcomer_area_fraction = downcomer_area_fraction
  self.vacuum_system_preference = vacuum_system_preference
  self._load_components()
@@ -2634,16 +2659,34 @@ def _actual_stages(self):
  else:
  return self.N_stages, np.ceil(self.N_stages / eff)
 
- def _design(self):
- self._simulate_condenser_and_reboiler()
- Design = self.design_results
+ def update_liquid_holdup(self):
+ diameter = self.estimate_diameter()
+ hw = weir_height = diameter * self.weir_height * 12 # inches
+ area = diameter * diameter * pi / 4
+ b = 2/3
+ partitions = self.partitions
+ for i in self.stage_reactions:
+ partition = partitions[i]
+ vapor, liquid = partition.outs
+ rho_V = vapor.rho
+ rho_L = liquid.rho
+ active_area = area * (1 - partition.downcomer_area_fraction)
+ Ua = vapor.get_total_flow('ft3/s') / active_area
+ Ks = Ua * sqrt(rho_V / (rho_L - rho_V)) # Capacity parameter
+ Phi_e = exp(-4.257 * Ks**0.91) # Effective relative froth density 
+ Lw = 0.73 * diameter * 12 # Weir length [in] assuming Ad/A = 0.1
+ # TODO: Compute weir length or other Ad/A
+ qL = liquid.get_total_flow('gal/min')
+ CL = 0.362 + 0.317 * exp(-3.5 * weir_height)
+ hL = Phi_e * (hw + CL * (qL / (Lw * Phi_e)) ** b) # equivalent height of clear liquid holdup [in]
+ partition.liquid_volume = hL * area * 0.00236155 # m3 
+
+ def estimate_diameter(self): # ft
+ diameters = []
  TS = self._TS
  A_ha = self._A_ha
  F_F = self._F_F
  f = self._f
-
- ### Get maximum required diameter of column across stages ###
- diameters = []
  for i in self.stages:
  vapor, liquid = i.partition.outs
  if liquid.isempty() or vapor.isempty(): continue
@@ -2657,22 +2700,29 @@ def _design(self):
  C_sbf = design.compute_max_capacity_parameter(TS, F_LV)
  U_f = design.compute_max_vapor_velocity(C_sbf, sigma, rho_L, rho_V, F_F, A_ha)
  A_dn = self._A_dn
- if A_dn is None: A_dn = design.compute_downcomer_area_fraction(F_LV)
+ if A_dn is None: i.partition.downcomer_area_fraction = A_dn = design.compute_downcomer_area_fraction(F_LV)
  diameters.append(
  design.compute_tower_diameter(V_vol, U_f, f, A_dn)
  )
- diameter = max(diameters) * 3.28
+ return max(diameters) * 3.28 # ft
+
+ def _design(self):
+ self._simulate_condenser_and_reboiler()
+ Design = self.design_results
+
+ ### Get maximum required diameter of column across stages ###
  Po = self.P * 0.000145078 # to psi
  rho_M = material_densities_lb_per_in3[self.vessel_material]
  if Po < 14.68:
  warn('vacuum pressure vessel ASME codes not implemented yet; '
  'wall thickness may be inaccurate and stiffening rings may be '
  'required', category=RuntimeWarning)
  N_theoretical, N_actual = self._actual_stages()
+ TS = self._TS
  Design['Theoretical stages'] = N_theoretical
  Design['Actual stages'] = actual_stages = N_actual - (bool(self.condenser) + bool(self.reboiler))
  Design['Height'] = H = design.compute_tower_height(TS, actual_stages) * 3.28
- Design['Diameter'] = Di = diameter
+ Design['Diameter'] = Di = self.estimate_diameter()
  Design['Wall thickness'] = tv = design.compute_tower_wall_thickness(Po, Di, H)
  Design['Weight'] = design.compute_tower_weight(Di, H, tv, rho_M)