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# Single Fluid System (TCU) Heating & Cooling Sizer Documentation

# 1. Executive Summary & Objective

The Single Fluid Temperature Control Unit (TCU) / Monofluid System Calculator provides complete thermodynamic and hydraulic engineering sizing for industrial single working fluid utility skids.

In pharmaceutical Active Pharmaceutical Ingredient (API) synthesis, switching different utility fluids (e.g. steam →\to cooling water →\to sub-zero chilled brine) directly inside the reactor jacket causes severe thermal shock, glass-lining stress cracks, utility cross-contamination, corrosion, and sluggish process transitions.

A Monofluid TCU Skid maintains a single continuous working fluid (such as Syltherm XLT, Marlotherm SH, Therminol 55, or 50% Aqueous Glycol) circulating continuously through the reactor jacket. Process heating, cooling, and chilling duties are accomplished indirectly via three dedicated Plate Heat Exchangers (PHEs) located on the skid:

  1. PHE-1 (Steam / Heating Exchanger): For batch ramp-up and endothermic reactions.
  2. PHE-2 (Cooling Tower Water Exchanger): For high-to-medium temperature ramp-down (+150∘C→+35∘C+150^\circ\text{C} \to +35^\circ\text{C}).
  3. PHE-3 (Chilled Glycol / Brine Exchanger): For sub-zero cryogenic chilling (+35∘C→−25∘C+35^\circ\text{C} \to -25^\circ\text{C}) and exothermic reaction heat removal.

# 2. Governing Engineering Thermodynamic Equations

# 2.1 Process Thermal Capacitance (M⋅CpM \cdot C_p)

The total thermal mass heated or cooled during batch ramp operations combines the process batch contents and the vessel metal mass:

(M⋅Cp)total=Mbatch⋅Cp,batch+Mmetal⋅Cp,metal[kJ/K](M \cdot C_p)_{total} = M_{batch} \cdot C_{p,batch} + M_{metal} \cdot C_{p,metal} \quad [\text{kJ/K}]

Where:

  • Mbatch=Vbatch⋅ρbatchM_{batch} = V_{batch} \cdot \rho_{batch} = Batch mass (kg\text{kg})
  • MmetalM_{metal} = Wetted vessel inner shell + agitator metal mass (kg\text{kg})
  • Cp,batch,Cp,metalC_{p,batch}, C_{p,metal} = Specific heat capacities (kJ/kg⋅K\text{kJ/kg}\cdot\text{K})

# 2.2 Dynamic Heating & Cooling Thermal Duties

# 1. Heating Ramp-Up Duty (Q˙heat\dot{Q}_{heat}):

Q˙heat=(M⋅Cp)total⋅(Ttarget−Tstart)theat_ramp×60×LossFactor+Q˙rxn,endo[kW]\dot{Q}_{heat} = \frac{(M \cdot C_p)_{total} \cdot (T_{target} - T_{start})}{t_{heat\_ramp} \times 60} \times \text{LossFactor} + \dot{Q}_{rxn,endo} \quad [\text{kW}]

# 2. Stage 1 Cooling Water Duty (Q˙cw\dot{Q}_{cw}):

Q˙cw=(M⋅Cp)total⋅(Ttarget−Tcw_target)tcw_ramp×60×1.05[kW]\dot{Q}_{cw} = \frac{(M \cdot C_p)_{total} \cdot (T_{target} - T_{cw\_target})}{t_{cw\_ramp} \times 60} \times 1.05 \quad [\text{kW}]

# 3. Stage 2 Sub-Zero Chilling Duty (Q˙chill\dot{Q}_{chill}):

Q˙chill=(M⋅Cp)total⋅(Tcw_target−Tfinal)tchill_ramp×60×1.10+Q˙rxn,exo[kW]\dot{Q}_{chill} = \frac{(M \cdot C_p)_{total} \cdot (T_{cw\_target} - T_{final})}{t_{chill\_ramp} \times 60} \times 1.10 + \dot{Q}_{rxn,exo} \quad [\text{kW}]
Refrigeration Tonnage (TR)=Q˙chill3.51685[TR]\text{Refrigeration Tonnage } (\text{TR}) = \frac{\dot{Q}_{chill}}{3.51685} \quad [\text{TR}]

# 2.3 Monofluid Circulation Flow Rate (V˙HTF\dot{V}_{HTF})

To guarantee rapid temperature response and maintain a tight temperature differential (ΔTloop≈3∘C−5∘C\Delta T_{loop} \approx 3^\circ\text{C} - 5^\circ\text{C}) across the reactor jacket:

V˙HTF=max⁡(Q˙heat,Q˙cw,Q˙chill)ρHTF⋅Cp,HTF⋅ΔTloop×3600[m3/h]\dot{V}_{HTF} = \frac{\max(\dot{Q}_{heat}, \dot{Q}_{cw}, \dot{Q}_{chill})}{\rho_{HTF} \cdot C_{p,HTF} \cdot \Delta T_{loop}} \times 3600 \quad [\text{m}^3/\text{h}]

# 2.4 Circulation Pump Hydraulics & Motor HP

# Total Dynamic Head (TDHTDH):

ΔPtotal=ΔPpipe_friction+ΔPjacket+ΔPPHE+ΔPvalves+ΔPelevation[bar]\Delta P_{total} = \Delta P_{pipe\_friction} + \Delta P_{jacket} + \Delta P_{PHE} + \Delta P_{valves} + \Delta P_{elevation} \quad [\text{bar}]
TDH=ΔPtotal×105ρHTF⋅g[m of HTF]TDH = \frac{\Delta P_{total} \times 10^5}{\rho_{HTF} \cdot g} \quad [\text{m of HTF}]

# Motor Sizing:

Ppump,electric=V˙HTF⋅ρHTF⋅g⋅TDH3600⋅ηpump⋅1000×1.25[kW→HP]P_{pump,electric} = \frac{\dot{V}_{HTF} \cdot \rho_{HTF} \cdot g \cdot TDH}{3600 \cdot \eta_{pump} \cdot 1000} \times 1.25 \quad [\text{kW} \to \text{HP}]

# 2.5 Expansion Tank Sizing (VtankV_{tank})

Over the full operating temperature span (ΔTspan=Tmax−Tmin\Delta T_{span} = T_{max} - T_{min}):

ΔVexpansion=Vtotal_system_charge⋅βHTF⋅ΔTspan[Liters]\Delta V_{expansion} = V_{total\_system\_charge} \cdot \beta_{HTF} \cdot \Delta T_{span} \quad [\text{Liters}]
Vtank≥(ΔVexpansion×2.2+Vresidence_buffer)×1.35[Liters]\mathbf{V_{tank} \ge (\Delta V_{expansion} \times 2.2 + V_{residence\_buffer}) \times 1.35} \quad [\text{Liters}]

# 2.6 Plate Heat Exchanger Sizing & Utility Consumptions

# PHE-1 (Steam Heating Exchanger):

APHE,steam=Q˙heat×1000Usteam⋅LMTDsteam[m2]A_{PHE,steam} = \frac{\dot{Q}_{heat} \times 1000}{U_{steam} \cdot \text{LMTD}_{steam}} \quad [\text{m}^2]
Steam Consumption m˙steam=Q˙heat×3600hfg,steam[kg/h]\text{Steam Consumption } \dot{m}_{steam} = \frac{\dot{Q}_{heat} \times 3600}{h_{fg,steam}} \quad [\text{kg/h}]

# PHE-2 (Cooling Water Exchanger):

APHE,cw=Q˙cw×1000Ucw⋅LMTDcw[m2]A_{PHE,cw} = \frac{\dot{Q}_{cw} \times 1000}{U_{cw} \cdot \text{LMTD}_{cw}} \quad [\text{m}^2]
Cooling Water Flow V˙CW=Q˙cw×3600ρw⋅Cp,w⋅(Tcw,out−Tcw,in)[m3/h]\text{Cooling Water Flow } \dot{V}_{CW} = \frac{\dot{Q}_{cw} \times 3600}{\rho_w \cdot C_{p,w} \cdot (T_{cw,out} - T_{cw,in})} \quad [\text{m}^3/\text{h}]

# PHE-3 (Chilled Glycol Exchanger):

APHE,chill=Q˙chill×1000Uchill⋅LMTDchill[m2]A_{PHE,chill} = \frac{\dot{Q}_{chill} \times 1000}{U_{chill} \cdot \text{LMTD}_{chill}} \quad [\text{m}^2]
Chilled Glycol Flow V˙glycol=Q˙chill×3600ρglycol⋅Cp,glycol⋅(Tglycol,out−Tglycol,in)[m3/h]\text{Chilled Glycol Flow } \dot{V}_{glycol} = \frac{\dot{Q}_{chill} \times 3600}{\rho_{glycol} \cdot C_{p,glycol} \cdot (T_{glycol,out} - T_{glycol,in})} \quad [\text{m}^3/\text{h}]
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