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 ($+150^\circ\text{C} \to +35^\circ\text{C}$).
3. PHE-3 (Chilled Glycol / Brine Exchanger): For sub-zero cryogenic chilling ($+35^\circ\text{C} \to -25^\circ\text{C}$) and exothermic reaction heat removal.

2. Governing Engineering Thermodynamic Equations

2.1 Process Thermal Capacitance ($M \cdot C_p$)

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

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

Where:

• $M_{batch} = V_{batch} \cdot \rho_{batch}$ = Batch mass ($\text{kg}$)
• $M_{metal}$ = Wetted vessel inner shell + agitator metal mass ($\text{kg}$)
• $C_{p,batch}, C_{p,metal}$ = Specific heat capacities ($\text{kJ/kg}\cdot\text{K}$)

2.2 Dynamic Heating & Cooling Thermal Duties

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

$$\dot{Q}{heat} = \frac{(M \cdot C_p){total} \cdot (T_{target} - T_{start})}{t_{heat_ramp} \times 60} \times \text{LossFactor} + \dot{Q}_{rxn,endo} \quad [\text{kW}]$$

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

$$\dot{Q}{cw} = \frac{(M \cdot C_p){total} \cdot (T_{target} - T_{cw_target})}{t_{cw_ramp} \times 60} \times 1.05 \quad [\text{kW}]$$

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

$$\dot{Q}{chill} = \frac{(M \cdot C_p){total} \cdot (T_{cw_target} - T_{final})}{t_{chill_ramp} \times 60} \times 1.10 + \dot{Q}{rxn,exo} \quad [\text{kW}]$$ $$\text{Refrigeration Tonnage } (\text{TR}) = \frac{\dot{Q}{chill}}{3.51685} \quad [\text{TR}]$$

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

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

$$\dot{V}{HTF} = \frac{\max(\dot{Q}{heat}, \dot{Q}{cw}, \dot{Q}{chill})}{\rho_{HTF} \cdot C_{p,HTF} \cdot \Delta T_{loop}} \times 3600 \quad [\text{m}^3/\text{h}]$$

2.4 Circulation Pump Hydraulics & Motor HP

Total Dynamic Head ($TDH$):

$$\Delta P_{total} = \Delta P_{pipe_friction} + \Delta P_{jacket} + \Delta P_{PHE} + \Delta P_{valves} + \Delta P_{elevation} \quad [\text{bar}]$$ $$TDH = \frac{\Delta P_{total} \times 10^5}{\rho_{HTF} \cdot g} \quad [\text{m of HTF}]$$

Motor Sizing:

$$P_{pump,electric} = \frac{\dot{V}{HTF} \cdot \rho{HTF} \cdot g \cdot TDH}{3600 \cdot \eta_{pump} \cdot 1000} \times 1.25 \quad [\text{kW} \to \text{HP}]$$

2.5 Expansion Tank Sizing ($V_{tank}$)

Over the full operating temperature span ($\Delta T_{span} = T_{max} - T_{min}$): $$\Delta V_{expansion} = V_{total_system_charge} \cdot \beta_{HTF} \cdot \Delta T_{span} \quad [\text{Liters}]$$ $$\mathbf{V_{tank} \ge (\Delta V_{expansion} \times 2.2 + V_{residence_buffer}) \times 1.35} \quad [\text{Liters}]$$

2.6 Plate Heat Exchanger Sizing & Utility Consumptions

PHE-1 (Steam Heating Exchanger):

$$A_{PHE,steam} = \frac{\dot{Q}{heat} \times 1000}{U{steam} \cdot \text{LMTD}{steam}} \quad [\text{m}^2]$$ $$\text{Steam Consumption } \dot{m}{steam} = \frac{\dot{Q}{heat} \times 3600}{h{fg,steam}} \quad [\text{kg/h}]$$

PHE-2 (Cooling Water Exchanger):

$$A_{PHE,cw} = \frac{\dot{Q}{cw} \times 1000}{U{cw} \cdot \text{LMTD}{cw}} \quad [\text{m}^2]$$ $$\text{Cooling Water Flow } \dot{V}{CW} = \frac{\dot{Q}{cw} \times 3600}{\rho_w \cdot C{p,w} \cdot (T_{cw,out} - T_{cw,in})} \quad [\text{m}^3/\text{h}]$$

PHE-3 (Chilled Glycol Exchanger):

$$A_{PHE,chill} = \frac{\dot{Q}{chill} \times 1000}{U{chill} \cdot \text{LMTD}{chill}} \quad [\text{m}^2]$$ $$\text{Chilled Glycol Flow } \dot{V}{glycol} = \frac{\dot{Q}{chill} \times 3600}{\rho{glycol} \cdot C_{p,glycol} \cdot (T_{glycol,out} - T_{glycol,in})} \quad [\text{m}^3/\text{h}]$$