# 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:

Solvent Distillation & Stripping Columns (reboiler evaporation duty).
Vacuum Contact Dryers (ANFD, Rotary Cone Vacuum Dryers - RCVD, Vacuum Tray Dryers - VTD).
Jacketed Chemical Reaction Vessels (batch heat-up and isothermal temperature maintenance).
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)

Nominal Pipe Size	Inside Diameter (mm)	Max Recommended Flow ( $v \le 1.8\text{ m/s}$ )	Piping Hold-Up (L / 100 m)
DN 25 (1")	26.6 mm	3.5 m³/h (58 L/min)	55.6 L
DN 40 (1.5")	40.9 mm	8.5 m³/h (142 L/min)	131.4 L
DN 50 (2")	52.5 mm	15.0 m³/h (250 L/min)	216.5 L
DN 65 (2.5")	62.7 mm	22.0 m³/h (367 L/min)	308.8 L
DN 80 (3")	77.9 mm	35.0 m³/h (583 L/min)	476.6 L
DN 100 (4")	102.3 mm	60.0 m³/h (1000 L/min)	821.9 L

# 4. Reference Standards

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