Hot Water Temperature (HWT) System Sizer Documentation

1. Executive Summary & Objective

The Hot Water Temperature (HWT) / TCU Generation & Circulation System Calculator provides a rigorous thermodynamic and hydraulic sizing engine for industrial hot water utility skids in pharmaceutical API synthesis, solvent recovery, and fine chemical plants.

It sizes closed-loop hot water systems serving:

1. Solvent Distillation & Stripping Columns (reboiler evaporation duty).
2. Vacuum Contact Dryers (ANFD, Rotary Cone Vacuum Dryers - RCVD, Vacuum Tray Dryers - VTD).
3. Jacketed Chemical Reaction Vessels (batch heat-up and isothermal temperature maintenance).
4. General Heat Exchangers & Process Evaporators.

The calculator sizes circulation flow rate, piping hold-up volume across distance, expansion/buffer tank capacity, circulation pump Total Dynamic Head (TDH) & motor HP, and steam-to-water heat exchanger surface area ($m^2$) & steam consumption ($\text{kg/h}$).

2. Governing Engineering Thermodynamic Equations

2.1 Process Thermal Duty ($Q_{process}$)

Mode A: Solvent Distillation Reboiler:

$$Q_{reboiler} = \dot{m}{evap} \cdot (1 + R/D) \cdot \Delta H{vap} + \dot{m}{feed} \cdot C{p,liquid} \cdot (T_{boil} - T_{feed}) \quad [\text{kW}]$$

Mode B: Vacuum Contact Drying:

$$Q_{drying} = \frac{(M_{dry_solid} \cdot C_{p,solid} + M_{solvent} \cdot C_{p,solvent}) \cdot (T_{dry} - T_{init}) + M_{solvent} \cdot \Delta H_{vap}}{t_{drying} \cdot 3600} \quad [\text{kW}]$$

Mode C: Jacketed Reactor Batch Heating:

$$Q_{reactor} = \frac{(M_{liquid} \cdot C_{p,liquid} + M_{vessel_metal} \cdot C_{p,metal}) \cdot (T_{target} - T_{init})}{t_{heatup} \cdot 3600} \quad [\text{kW}]$$

Total HWT Design Thermal Capacity:

$$Q_{design} = Q_{process} \times (1 + \text{Margin}_{loss}) \quad [\text{kW}]$$

2.2 Hot Water Circulation Flow Rate ($F_{HW}$)

$$F_{HW} = \frac{Q_{design}}{\rho_{water} \cdot C_{p,water} \cdot (T_{supply} - T_{return})} \times 3600 \quad [\text{m}^3/\text{h}]$$

2.3 Piping Distance & System Hold-Up Volume ($V_{loop}$)

For a one-way distance $L_{distance}$ from the HWT skid to the user vessel: $$L_{total_pipe} = 2 \cdot L_{distance} \times 1.25 \quad [\text{m}]$$ $$V_{piping} = \frac{\pi \cdot D_{pipe,ID}^2}{4} \cdot L_{total_pipe} \times 1000 \quad [\text{Liters}]$$ $$V_{total_loop} = V_{piping} + V_{jacket} + V_{HEX_internal} \quad [\text{Liters}]$$

2.4 Thermal Expansion & Buffer Tank Sizing ($V_{tank}$)

Volumetric water thermal expansion between ambient ($20^\circ\text{C}$) and operating supply temperature ($T_{supply}$): $$\Delta V_{expansion} = V_{total_loop} \cdot \beta_{water} \cdot (T_{supply} - 20^\circ\text{C}) \quad [\text{Liters}]$$ $$\text{Buffer Residence Volume } V_{buffer} = F_{HW} \cdot t_{retention} \quad [\text{Liters}]$$ $$\mathbf{V_{tank_recommended} \ge (\Delta V_{expansion} \times 2.5 + V_{buffer}) \times 1.30} \quad [\text{Liters}]$$

2.5 Circulation Pump Hydraulics & Motor HP

Total Dynamic Head ($TDH$):

$$\Delta P_{total} = \Delta P_{pipe_friction} + \Delta P_{jacket} + \Delta P_{HEX} + \Delta P_{control_valve} \quad [\text{bar}]$$ $$TDH = \frac{\Delta P_{total} \times 10^5}{\rho_{water} \cdot g} \quad [\text{meters of water}]$$

Pump Motor Sizing:

$$P_{hydraulic} = \frac{\rho_{water} \cdot g \cdot (F_{HW}/3600) \cdot TDH}{1000} \quad [\text{kW}]$$ $$P_{motor} = \frac{P_{hydraulic}}{\eta_{pump} \cdot \eta_{motor}} \times 1.15 \quad [\text{kW}]$$

2.6 Steam Heat Exchanger Surface Area & Steam Consumption

Log Mean Temperature Difference (LMTD):

$$\text{LMTD} = \frac{(T_{steam} - T_{return}) - (T_{steam} - T_{supply})}{\ln\left( \frac{T_{steam} - T_{return}}{T_{steam} - T_{supply}} \right)} \quad [^\circ\text{C}]$$

Required Surface Area ($A_{HEX}$):

$$A_{HEX} = \frac{Q_{design} \cdot 1000}{U \cdot \text{LMTD}} \quad [\text{m}^2]$$ (where $U \approx 2800\text{ W/m}^2\cdot\text{K}$ for Plate Heat Exchangers)

Plant Saturated Steam Consumption:

$$\dot{m}{steam} = \frac{Q{design} \cdot 3600}{\lambda_{steam}} \quad [\text{kg/h}]$$

3. Standard Pipe Sizing Guidelines (Hot Water Systems)

4. Reference Standards

1. ASHRAE Handbook — HVAC Systems and Equipment: Chapter 13 Hydronic Heating and Cooling System Design.
2. ASME B31.3: Process Piping Code.
3. ISPE Good Practice Guide: Heating, Ventilation, and Air Conditioning (HVAC) & Process Utilities.
4. Spirax Sarco: Design of Steam and Hot Water Heat Exchange Systems.