Video summary

Balance de Energía en un reactor-enfriador

Main summary

Key takeaways

Educational

Main ideas / concepts conveyed

  • Goal of the case study: Compute heat duty for two connected units in a process that produces hydrogen chloride (HCl):

    1. A reactor where Cl₂ + H₂ → 2 HCl
    2. A heat exchanger (cooler) that cools the reactor exhaust from 200°C down to 50°C

  • Feed and reaction setup (given conditions):

    • Target production: 10,000 tons HCl per year
    • Reactor operating pressure: 1.5 bar (assumed constant for the energy method)
    • Reactor temperature: 200°C
    • Chlorine feed: at saturation point, gas phase
    • Hydrogen feed: mixed with nitrogen (inert) at 95% H₂ / 5% N₂
    • Hydrogen is fed with 11% excess relative to stoichiometry
    • Reaction degree of conversion: complete chlorine conversion

  • Methodology used:

    • Treat the problem as two separate boundaries/systems:
      1. Reactor as a reacting system
      2. Heat exchanger as a non-reacting system
    • Use degrees of freedom analysis to confirm the system is solvable.
    • Perform material balances first, then energy balances.

Reactor system: degrees of freedom, material balance, energy balance

A) Degrees of freedom analysis (reactor)

  • Streams and species counts (as described):
    • Stream 1: 1 species
    • Stream 2: 1 species
    • Stream 3: 3 species
  • Total “species per stream” = 6
  • Add the reaction as an additional equation/unknown contribution: +1
  • Subtract known compositions per stream:
    • Only one known composition → −1
  • Result: a solvable system with 0 degrees of freedom

Next steps: solve material balance then energy balance.

B) Basis change for calculation (unit conversion)

  • Convert production basis:
    • 10,000 tons/year → 1 × 10⁷ kg/year
  • Convert mass flow to a molar basis using molecular weights
  • Convert time units to avoid unwieldy magnitudes
    • Ultimately uses a basis in moles per second
  • The video reports an intermediate molar flow basis for product/outlet:
    • 8.7 (moles per second) for HCl production flow basis (as stated in the subtitles)

C) Reactor material balance (component-wise)

Stoichiometry: Cl₂ + H₂ → 2 HCl

  • Chlorine balance

    • Since chlorine is completely consumed, the chlorine outlet is effectively 0
    • Setup (conceptual): chlorine in − reaction progress = 0

  • Hydrogen balance

    • Because hydrogen is in excess, hydrogen outlet is nonzero
    • Setup: hydrogen out = hydrogen in − reaction progress

  • HCl balance

    • HCl is formed
    • Setup (conceptual): product term proportional to 2 × reaction progress

  • Auxiliary equation: excess fraction

    • Uses the 11% excess hydrogen condition to relate hydrogen feed to the stoichiometric requirement

  • Outcome stated:

    • Determine reaction progress
    • Then determine required feed molar flows (Cl₂, H₂, and N₂ from the 95/5 mixture)

D) Determining nitrogen feed

  • The hydrogen feed stream is 95% H₂ and 5% N₂
  • Once H₂ feed is computed:
    • N₂ feed = (5/95) × H₂ feed
  • The subtitles give final numeric molar values (in mol/s) for the reactor outlet context:
    • N₂ = 23.12 mol/s (as stated later for exchanger inlet, implying it carries through unchanged)

E) Reactor energy balance

  • The method uses:
    • A reaction-rate term (based on literature formation rates at 25°C reference state)
    • Plus sensible enthalpy changes computed via heat capacities Cp(T)

Key steps described:

  • Reaction rate / formation rates

    • Literature formation rates referenced to 25°C
    • For pure reactants “as pure components,” the formation rates used are 0 for Cl₂ and H₂
    • The nonzero contribution comes from HCl formation rate
    • Reaction advancement rate is determined at 25°C, then used in the reactive energy balance

  • Compute enthalpy/entropy changes using “trajectories”

    • Gas-phase assumption; no phase change
    • Pressure constant → only temperature effects considered
    • Reference state: 25°C
    • Compute integrals using a Cp polynomial:
      • Entropy change uses ∫ Cp dT / T-type logic (as described in the subtitles)
      • Emphasis on unit compatibility (bibliography uses kJ/mol·°C)

  • Energy balance structure for a reactive system

    • Combines:
      • Reaction term (reaction progress × reaction heat term)
      • Outlet enthalpy contributions minus inlet contributions

Result stated:

  • The reaction is exothermic
  • Heat to remove from the reactor to hold 200°C is reported as:
    • 728 (heat must be removed; subtitle is partially garbled)
    • Then concretely: 0.25 kg/s of heat removal is mentioned (intended meaning: remove heat equal to X to maintain reactor temperature)
  • Safety implication noted:
    • If too little heat is removed, reactor temperature could rise

Heat exchanger system: degrees of freedom, material balance, energy balance

A) Degrees of freedom analysis (heat exchanger)

  • No reaction occurs in the exchanger
  • One inlet and one outlet
  • Therefore:
    • Degrees of freedom = 0
  • Inert and reacting species pass through with flow rates conserved

B) Heat exchanger material balance

  • Subtitles provide molar flows (mol/s) carried through:
    • HCl / combined outlet basis = 8.7 mol/s
    • H₂ = 0.435 mol/s
    • N₂ (inert) = 23.12 mol/s
  • Nitrogen remains unchanged (inert)

C) Heat exchanger energy balance (non-reactive)

  • Reference temperature can be chosen for non-reactive energy balances
  • Chosen reference state:
    • 200°C, aligned with the inlet operating temperature

  • Temperature change across exchanger:

    • Inlet: 200°C
    • Outlet: 50°C

  • Cp polynomial values are used to compute sensible energy/“entropy” terms for each species from 200°C → 50°C

    • Values come out negative because temperature decreases (heat must be removed)

Non-reactive steady-state duty equation described:

  • Heat flow = Σ( moles × (specific output term − specific input term) )
  • Since inlet is at the reference state, inlet terms simplify/eliminate

Numerical result stated:

  • Heat exchanger heat removal duty:
    • 39.16 (kg/s) appears in the subtitles
    • Intended meaning: the heat flow rate required to be removed to reach 50°C outlet
  • Conclusion:
    • The exchanger acts as a cooler

Main lessons conveyed (method summary)

  • Divide the plant into subsystems (reactor vs heat exchanger) and analyze each separately.
  • Use degrees of freedom to confirm the model can be solved.
  • Perform material balances first (including excess fraction and complete conversion).
  • Then perform energy balances:
    • For reactive systems: include reaction heat/formations plus sensible contributions from Cp(T).
    • For non-reactive systems: only sensible enthalpy/entropy changes using a chosen reference state.
  • Use unit-consistent Cp polynomial data and careful basis conversion (e.g., tons/year → mol/s).

Speakers / sources featured

Speakers

  • The subtitles do not name a specific person; it appears to be a single unnamed presenter (e.g., “Hello and welcome…”).

Sources referenced

  • Literature: for formation rates and Cp polynomial data
  • Bibliography (in the video description): for Cp units and polynomial form

Original video