# Single Fluid System (Monofluid TCU) Sizing & Engineering Design Guide: Monofluid vs Multi-Utility, Hydraulics, DIN 4754 Expansion Tank, 3-PHE Skid Selection & PLC Temperature Control Logic

# Executive Summary & Industrial Background

In modern pharmaceutical Active Pharmaceutical Ingredient (API) plants and fine chemical batch synthesis facilities, temperature control of reactors is critical to product yield, polymorphism, enantiomeric purity, and process safety.

Historically, batch reactors utilized Direct Multi-Utility Changeover, where distinct utility fluids—such as LP steam, cooling water, chilled water, and sub-zero brine ( $-20^\circ\text{C}$ ethylene glycol)—were sequentially injected directly into the reactor jacket.

However, direct multi-utility jackets suffer from severe operational and safety limitations:

Glass Lining Enamel Thermal Shock: Rapid switching from $140^\circ\text{C}$ steam to $5^\circ\text{C}$ cooling water exceeds the maximum permissible temperature differential (typically $\Delta T_{\text{wall}} \le 50 - 80^\circ\text{C}$ per De Dietrich and Pfaudler guidelines), cracking glass lining and causing catastrophic corrosion.
Salt & Scale Precipitation: Cross-mixing of steam condensate and cooling water causes calcium carbonate scaling, clogging jacket passages and deteriorating overall heat transfer ( $U$ ).
Fluid Cross-Contamination: Leaking automated changeover valves allow toxic glycol or brine to contaminate clean steam condensate loops or cooling towers.
Sluggish Thermal Response: Purging water from a jacket with compressed air before introducing sub-zero brine takes $15 - 30 \text{ minutes}$ , during which reaction temperature control is lost.

To overcome these hazards, chemical process plants have standardized on Single Fluid Thermal Control Units (Monofluid TCUs). In a TCU system, a single Heat Transfer Fluid (HTF)—such as Marlotherm N, Therminol VP-1, Syltherm 800, or DW-Therm—continuously circulates through the reactor jacket at high, constant fluid velocity. Thermal energy modulation is executed externally across secondary Plate Heat Exchangers (PHEs).

                  MONOFLUID SINGLE FLUID TCU SCHEMATIC ARCHITECTURE
+-----------------------------------------------------------------------------------+
|                                                                                   |
|    +------------------+         +----------------+         +-----------------+    |
|    |   PHE-1: STEAM   |         |   PHE-2: CW    |         | PHE-3: CHILLER  |    |
|    |  Heating Exch.   |         | Cooling Exch.  |         | Sub-Zero Exch.  |    |
|    +--------+---------+         +-------+--------+         +--------+--------+    |
|             |                           |                           |             |
|  ==========+===========================+===========================+==========   |
|  HTF Loop   |                           |                           |             |
|             v                           v                           v             |
|    +------------------+       +-------------------+       +------------------+    |
|    | Modulating 3-Way |       | Modulating 3-Way  |       | Modulating 3-Way |    |
|    |  Control Valve   |       |   Control Valve   |       |  Control Valve   |    |
|    +--------+---------+       +---------+---------+       +--------+---------+    |
|             |                           |                          |              |
|             +---------------------------+--------------------------+              |
|                                         |                                         |
|                                         v                                         |
|                             +-----------------------+                             |
|                             | HTF Circulation Pump  |                             |
|                             +-----------+-----------+                             |
|                                         |                                         |
|                                         v                                         |
|                             +-----------------------+                             |
|                             | DIN 4754 Expansion    |                             |
|                             | Tank (N2 Cushioned)   |                             |
|                             +-----------+-----------+                             |
|                                         |                                         |
|                                         v                                         |
|                             +-----------------------+                             |
|                             | Reactor Jacket Loop   |                             |
|                             | (v = 1.5 - 2.0 m/s)   |                             |
|                             +-----------------------+                             |
+-----------------------------------------------------------------------------------+

# 1. Fundamentals of Monofluid System Sizing

Sizing a Monofluid TCU requires a coupled thermodynamic, hydraulic, and mechanical evaluation. The total system must govern:

Sensible Thermal Capacitance ( $M \cdot C_p$ ) of the process mass and reactor vessel steel/glass.
Exothermic and Endothermic Heat of Reaction Load ( $Q_{\text{rxn}}$ ) during active reagent dosing.
Circulation Pump Hydraulics to deliver turbulent heat transfer inside the jacket.
Thermal Expansion Vessel Volume ( $V_{\text{tank}}$ ) under DIN 4754 Monofluid criteria.
Plate Heat Exchanger (PHE) Skid Selection to optimize heat surface area and prevent utility thermal shock.

# 2. Step-by-Step Engineering Equations

# 2.1 Thermal Capacitance & Peak Phase Duties

The process batch thermal capacitance ( $C_{\text{process}}$ ) and vessel metal thermal capacitance ( $C_{\text{metal}}$ ) are defined as:

C_{\text{process}} = M_{\text{batch}} \cdot C_{p,\text{batch}} = \left( \frac{V_{\text{batch}}}{1000} \cdot \rho_{\text{batch}} \right) \cdot C_{p,\text{batch}} \qquad [\text{kJ/K}]

C_{\text{metal}} = M_{\text{vessel}} \cdot C_{p,\text{vessel}} \qquad [\text{kJ/K}]

C_{\text{total}} = C_{\text{process}} + C_{\text{metal}} \qquad [\text{kJ/K}]

# Phase 1: Heating Duty ( $Q_{\text{heat}}$ )

To heat a reactor from $T_{\text{start}}$ to $T_{\text{target}}$ over ramp time $t_{\text{heat}}$ (seconds):

Q_{\text{sensible, heat}} = \frac{C_{\text{total}} \cdot (T_{\text{target}} - T_{\text{start}})}{t_{\text{heat}}} \qquad [\text{kW}]

Q_{\text{peak, heat}} = (Q_{\text{sensible, heat}} \cdot 1.10) + Q_{\text{endothermic, rxn}} \qquad [\text{kW}]

(where $1.10$ represents a $10\%$ heat loss allowance to ambient surroundings).

# Phase 2: Cooling Water Duty ( $Q_{\text{cw}}$ )

To cool the batch from high reaction temperature down to ambient cooling water limit ( $35^\circ\text{C}$ ) over ramp time $t_{\text{cw}}$ :

Q_{\text{peak, cw}} = \left( \frac{C_{\text{total}} \cdot (T_{\text{cw, start}} - T_{\text{cw, target}})}{t_{\text{cw}}} \right) \cdot 1.05 \qquad [\text{kW}]

# Phase 3: Sub-Zero Chilling Duty ( $Q_{\text{chill}}$ )

To cool the process mass from ambient down to sub-zero temperature (e.g., $-20^\circ\text{C}$ ) over ramp time $t_{\text{chill}}$ while controlling an exothermic reaction load ( $Q_{\text{exo}}$ ):

Q_{\text{peak, chill}} = \left( \frac{C_{\text{total}} \cdot (T_{\text{chill, start}} - T_{\text{chill, target}})}{t_{\text{chill}}} \cdot 1.10 \right) + Q_{\text{exothermic, rxn}} \qquad [\text{kW}]

\text{Tons of Refrigeration (TR)} = \frac{Q_{\text{peak, chill}}}{3.51685}

# 2.2 HTF Circulation Flow Rate & Hydraulic Line Sizing

The overall pump flow rate ( $Q_{\text{HTF}}$ ) is governed by the highest thermal load ( $Q_{\text{governing}} = \max(Q_{\text{heat}}, Q_{\text{cw}}, Q_{\text{chill}})$ ) and the allowable HTF loop temperature drop ( $\Delta T_{\text{loop}}$ , typically $10 - 15^\circ\text{C}$ ):

Q_{\text{HTF, m}^3/\text{s}} = \frac{Q_{\text{governing, kW}}}{\rho_{\text{HTF}} \cdot C_{p,\text{HTF}} \cdot \Delta T_{\text{loop}}}

Q_{\text{HTF, m}^3/\text{h}} = Q_{\text{HTF, m}^3/\text{s}} \times 3600, \qquad Q_{\text{HTF, LPM}} = Q_{\text{HTF, m}^3/\text{h}} \times 16.6667

# Line DN Selection & Velocity

To maintain turbulent flow without excessive pressure drop, line velocity ( $v$ ) is sized between $1.5 - 2.0 \text{ m/s}$ (target default $1.7 \text{ m/s}$ ):

A_{\text{req}} = \frac{Q_{\text{HTF, m}^3/\text{s}}}{v_{\text{target}}} \implies D_{\text{inner, req}} = \sqrt{\frac{4 \cdot A_{\text{req}}}{\pi}}

The nearest standard Nominal Pipe Diameter (DN 25 to DN 150 Sch 40) is selected.

# Total Dynamic Head (TDH) & Pump Motor Power

Total Dynamic Head includes pipe friction, jacket drop, PHE drop, control valve drop, and static elevation:

H_{\text{friction}} = f \cdot \left(\frac{L_{\text{total}}}{D_{\text{inner}}}\right) \cdot \frac{v^2}{2g} \qquad [\text{m}]

\text{TDH}_{\text{meters}} = H_{\text{friction}} + H_{\text{jacket}} + H_{\text{PHE}} + H_{\text{valves}} + H_{\text{static}}

P_{\text{hydraulic, kW}} = \frac{Q_{\text{HTF, m}^3/\text{s}} \cdot \rho_{\text{HTF}} \cdot g \cdot\text{TDH}_{\text{m}}}{1000}

P_{\text{brake, kW}} = \frac{P_{\text{hydraulic, kW}}}{\eta_{\text{pump}}}, \qquad P_{\text{motor, HP}} = (P_{\text{brake, kW}} \times 1.34102) \times (1 + \text{Margin}\%)

# 2.3 DIN 4754 Expansion Tank Sizing Methodology

Unlike hydronic HVAC expansion vessels, Monofluid TCU expansion tanks operate under DIN 4754 Standards (Thermal Oil Installations). The expansion tank must absorb volumetric liquid expansion across the entire operating range ( $T_{\text{min}}$ to $T_{\text{max}}$ ) plus maintain a cold liquid seal reserve under an inert Nitrogen ( $N_2$ ) blanket.

# 1. System Hold-Up Volume ( $V_{\text{charge}}$ )

V_{\text{charge}} = V_{\text{piping}} + V_{\text{jacket}} + V_{\text{PHEs}} + V_{\text{skid}} \qquad [\text{Leters}]

# 2. Volumetric Thermal Expansion ( $\Delta V$ )

\Delta V = V_{\text{charge}} \cdot \beta_{\text{HTF}} \cdot (T_{\text{max}} - T_{\text{min}}) \qquad [\text{Leters}]

(where $\beta_{\text{HTF}}$ is the volumetric thermal expansion coefficient of the HTF, e.g., $0.00095 \text{ K}^{-1}$ for Marlotherm N).

# 3. Cold Liquid Seal Reserve ( $V_{\text{seal}}$ )

Per DIN 4754, at minimum system temperature ( $T_{\text{min}}$ ), a liquid reserve must remain in the vessel to prevent pump cavitation and fluid oxidation:

V_{\text{seal}} = \max(15\% \times \Delta V,\; 5\% \times V_{\text{charge}}) \qquad [\text{Leters}]

# 4. Total DIN 4754 Expansion Tank Volume

Factoring safety margin (k_{\text{\exp}} = 1.20 - 1.25) and Nitrogen vapor space cushion ( $30\% \text{ N}_2$ space):

V_{\text{tank, DIN 4754}} = \frac{\Delta V \cdot k_{\text{\exp}} + V_{\text{seal}}}{1 - \%N_2 \text{ Vapor Space}} \qquad [\text{Leters}]

                   DIN 4754 MONOFLUID EXPANSION TANK LAYER STRUCTURE
   +------------------------------------------------------------------+
   |  Nitrogen (N2) Vapor Space Cushion (30% Total Vessel Volume)     |  <-- Prevents HTF Oxidation
   +------------------------------------------------------------------+
   |  Thermal Expansion Volume ΔV · k_exp (Absorbs liquid expansion)  |  <-- T_min to T_max Expansion
   +------------------------------------------------------------------+
   |  Cold Liquid Seal Reserve V_seal (Min 15% ΔV or 5% System Charge) |  <-- Prevents Pump Cavitation
   +------------------------------------------------------------------+

# 3. Comparison of 3-PHE Skid Architectures

When designing a Monofluid TCU, selecting the layout of secondary utility Plate Heat Exchangers (PHEs) determines thermal shock safety, equipment footprint, and operational reliability:

Feature / Criteria	Option 1: Single Max Governing PHE	Option 2: Combined Steam/CW + Separate Chiller (Recommended)	Option 3: Dedicated 3-PHE Skid Architecture
Number of PHEs	1 PHE (Sequential utility switching)	2 PHEs (1 Dual Steam/CW PHE + 1 Sub-Zero Chiller)	3 PHEs (Dedicated Steam, CW, and Chiller)
Hardware Footprint	Lowest Footprint & Hardware Cost	Balanced Footprint & High Safety	Highest Footprint & Capital Cost
Thermal Shock Risk	High risk during steam-to-chiller transition	Eliminated (Chiller isolated on dedicated loop)	Zero (Complete physical isolation)
Operational Control	Requires complex automated flush manifolds	Smooth changeover between ambient and sub-zero	Simultaneous utility readiness & fast ramping
Freezing Hazard	High risk of steam condensate freezing in brine	Zero risk of steam/brine freezing interaction	Zero risk of utility cross-contamination

# 4. PLC Temperature Control Logic Architecture & PID Tuning

Controlling temperature in a batch reactor with a Monofluid TCU requires a robust Programmable Logic Controller (PLC) Automation Strategy to maintain process temperature precisely at setpoint, eliminate overshoot during exothermic reactions, and protect glass-lined vessel enamel from thermal shock.

                    PLC CASCADE & SPLIT-RANGE CONTROL ARCHITECTURE
  [ Master Setpoint SP_process ] 
                 │
                 ▼
     +-----------------------+
     | Master PID (TIC-101)  | <--- PV_master: Reactor Mass Temp (T_process)
     +-----------+-----------+
                 │
                 │ Output = Desired Jacket Temp (T_HTF_set)
                 v
     +-----------------------+
     | Thermal Shock Clamp   | <--- Ensures |T_HTF_set - T_process| <= 50°C
     +-----------+-----------+
                 │
                 ▼
     +-----------------------+
     |  Slave PID (TIC-102)  | <--- PV_slave: HTF Supply Temp (T_HTF_supply)
     +-----------+-----------+
                 │
                 │ Controller Output CO (0.0% to 100.0%)
                 v
     +-----------------------------------------------------------------+
     | Split-Range Utility Control Valve Logic                         |
     |                                                                 |
     |   CO: 0% ─── 45%         CO: 45% ─ 55%       CO: 55% ─── 80%    |   CO: 80% ─── 100%
     |  [ Steam PHE Valve ]      [ Deadband ]     [ CW PHE Valve ]     |  [ Chiller PHE Valve ]
     |    100% -> 0% Open         All Closed        0% -> 100% Open    |   0% -> 100% Open
     +-----------------------------------------------------------------+

# 4.1 Master-Slave Cascade PID Loop Design

Direct single-loop PID control fails in batch reactors due to massive thermal inertia and dead time between jacket heat transfer and core fluid response. A Cascade Control Architecture is mandatory:

Master PID Controller (TIC-101):
- Process Variable ( $PV_M$ ): Reactor internal mass temperature ( $T_{\text{process}}$ measured via redundant Pt100 duplex RTD probes).
- Setpoint ( $SP_M$ ): Desired batch temperature profile or dynamic linear ramp rate ( $^circ\text{C}/\text{min}$ ).
- Manipulated Output ( $CV_M$ ): Calculates the required HTF supply temperature setpoint ( $T_{\text{HTF, set}}$ ) for the slave loop.
Slave PID Controller (TIC-102):
- Process Variable ( $PV_S$ ): HTF jacket supply line temperature ( $T_{\text{HTF, supply}}$ ).
- Setpoint ( $SP_S$ ): Clamped output from Master PID ( $T_{\text{HTF, set}}$ ).
- Manipulated Output ( $CV_S$ ): Overall Controller Output ( $CO$ ) spanning $0.0\%$ to $100.0\%$ .
Enamel Thermal Shock Safeguard Clamp:
- To prevent glass lining cracking, the slave setpoint is dynamically constrained in PLC logic:

SP_S = \min\Big(\max(CV_M,\; T_{\text{process}} - \Delta T_{\text{shock, max}}),\; T_{\text{process}} + \Delta T_{\text{shock, max}}\Big)

(where $\Delta T_{\text{shock, max}} = 50.0^\circ\text{C}$ for glass-lined reactors).

# 4.2 Split-Range Control Logic for Modulating 3-Way Valves

The slave controller output $CO$ ( $0 - 100\%$ ) modulates the 3 utility PHE control valves across distinct split-range zones:

Zone 1: Steam Heating ( $CO = 0.0\% \text{ to } 45.0\%$ ):
- $TCV_{\text{steam}} \text{ Position } (\%) = \frac{45.0 - CO}{45.0} \times 100.0\%$
- Cooling Water & Chiller Valves remain $0\%$ Fully Closed.
Zone 2: Thermal Neutral / Deadband ( $CO = 45.0\% \text{ to } 55.0\%$ ):
- All 3 utility valves remain $0\%$ Fully Closed. HTF circulates at current temperature without utility heat addition or extraction.
Zone 3: Cooling Water ( $CO = 55.0\% \text{ to } 80.0\%$ ):
- $TCV_{\text{cw}} \text{ Position } (\%) = \frac{CO - 55.0}{80.0 - 55.0} \times 100.0\%$
- Steam & Chiller Valves remain $0\%$ Fully Closed.
Zone 4: Sub-Zero Chilling ( $CO = 80.0\% \text{ to } 100.0\%$ ):
- $TCV_{\text{chill}} \text{ Position } (\%) = \frac{CO - 80.0}{100.0 - 80.0} \times 100.0\%$
- Steam & CW Valves remain $0\%$ Fully Closed.

# 4.3 Feedforward Action & Anti-Reset Windup

# Exothermic Reaction Feedforward ( $FF$ )

During highly exothermic reagent additions (e.g. nitrations or acid-base additions), feedback control alone experiences temperature spikes. A Feedforward Signal ( $FF$ ) scaled to reagent dosing pump speed ( $Q_{\text{dosing}}$ in L/h) pre-cools the HTF jacket before heat is generated:

SP_S = SP_S - (k_{\text{feedforward}} \cdot Q_{\text{dosing}})

# Anti-Reset Windup Protection

When the slave controller output $CO$ hits $0\%$ or $100\%$ limits, integral action accumulation is frozen in PLC memory (Clamping Anti-Windup Method) to prevent long recovery delays when transitioning between heating and cooling.

# 4.4 PID Tuning Methodology (Internal Model Control / Cohen-Coon)

Because thermal lag ( $L_{\text{lag}}$ ) in glass-lined reactors ranges from $2 - 5 \text{ minutes}$ with time constant $\tau = 15 - 30 \text{ minutes}$ , standard aggressive tuning causes severe hunting. Internal Model Control (IMC) tuning parameters are recommended:

Loop Level	Proportional Gain ( $K_p$ )	Integral Time ( $T_i$ )	Derivative Time ( $T_d$ )	Tuning Objective & Behavior
Master Loop (TIC-101)	1.2 - 2.5 \text{ %/%}	$300 - 600 \text{ sec}$	$0 \text{ sec (Off)}$	Smooth, non-overshooting process temp tracking
Slave Loop (TIC-102)	3.5 - 6.0 \text{ %/%}	$45 - 90 \text{ sec}$	$10 - 20 \text{ sec}$	Fast, robust jacket supply temperature stabilization

# 4.5 IEC 61131-3 Structured Text (ST) PLC Implementation Code

Below is the production-ready Structured Text (ST) logic implemented in PLCs (Siemens S7-1500 / Rockwell ControlLogix / Schneider M580) for TCU temperature control:

// ============================================================================
// PLC STRUCTURED TEXT LOGIC: MONOFLUID TCU CASCADE & SPLIT-RANGE CONTROL
// ============================================================================
PROGRAM TCU_Temperature_Control
VAR_INPUT
    bAutoMode             : BOOL := TRUE;        // Auto/Manual Selection
    rProcessTemp_PV       : REAL;                // Reactor Internal Mass Temp (°C)
    rProcessTemp_SP       : REAL;                // Target Process Setpoint (°C)
    rHTF_SupplyTemp_PV    : REAL;                // HTF Jacket Supply Line Temp (°C)
    rDosingFlowRate_Lh    : REAL;                // Reagent Dosing Pump Rate (L/h)
    rMaxThermalShock_degC : REAL := 50.0;        // Max Permissible ΔT (°C)
END_VAR

VAR_OUTPUT
    rSteamValve_Cmd       : REAL;                // Steam PHE 3-Way Valve (0-100%)
    rCWValve_Cmd          : REAL;                // CW PHE 3-Way Valve (0-100%)
    rChillerValve_Cmd     : REAL;                // Chiller PHE 3-Way Valve (0-100%)
    rHTF_Supply_SP_Clamped: REAL;                // Calculated Safe HTF Setpoint (°C)
END_VAR

VAR
    fbMasterPID           : PID_FIXED;           // Master Controller Instance
    fbSlavePID            : PID_FIXED;            // Slave Controller Instance
    rMaster_Output_Raw    : REAL;                // Raw Desired HTF Temp (°C)
    rSlave_Controller_CO  : REAL;                // Slave Controller Output (0-100%)
    rFeedForward_Offset   : REAL;                // Exothermic Dosing FF Offset (°C)
END_VAR

// ----------------------------------------------------------------------------
// 1. MASTER PID CONTROL LOOP (Reactor Mass Temperature -> HTF Setpoint)
// ----------------------------------------------------------------------------
fbMasterPID.PV := rProcessTemp_PV;
fbMasterPID.SP := rProcessTemp_SP;
fbMasterPID.Kp := 1.8;                           // Master Proportional Gain
fbMasterPID.Ti := 450.0;                         // Master Integral Time (sec)
fbMasterPID.Td := 0.0;                           // Derivative Off to Prevent Spikes
fbMasterPID();                                   // Execute Master PID

rMaster_Output_Raw := fbMasterPID.Output;

// Exothermic Reaction Feedforward Compensation
rFeedForward_Offset := rDosingFlowRate_Lh * 0.15; // 0.15°C offset per L/h dosing rate
rMaster_Output_Raw  := rMaster_Output_Raw - rFeedForward_Offset;

// ----------------------------------------------------------------------------
// 2. GLASS ENAMEL THERMAL SHOCK SAFEGUARD CLAMP (Max ΔT <= 50°C)
// ----------------------------------------------------------------------------
IF (rMaster_Output_Raw > (rProcessTemp_PV + rMaxThermalShock_degC)) THEN
    rHTF_Supply_SP_Clamped := rProcessTemp_PV + rMaxThermalShock_degC;
ELSIF (rMaster_Output_Raw < (rProcessTemp_PV - rMaxThermalShock_degC)) THEN
    rHTF_Supply_SP_Clamped := rProcessTemp_PV - rMaxThermalShock_degC;
ELSE
    rHTF_Supply_SP_Clamped := rMaster_Output_Raw;
END_IF;

// ----------------------------------------------------------------------------
// 3. SLAVE PID CONTROL LOOP (HTF Supply Temp -> Split-Range CO 0-100%)
// ----------------------------------------------------------------------------
fbSlavePID.PV := rHTF_SupplyTemp_PV;
fbSlavePID.SP := rHTF_Supply_SP_Clamped;
fbSlavePID.Kp := 4.2;                            // Slave Proportional Gain
fbSlavePID.Ti := 60.0;                           // Slave Integral Time (sec)
fbSlavePID.Td := 12.0;                           // Slave Derivative Time (sec)
fbSlavePID();                                    // Execute Slave PID

rSlave_Controller_CO := fbSlavePID.Output;      // Range: 0.0% to 100.0%

// ----------------------------------------------------------------------------
// 4. SPLIT-RANGE VALVE POSITION SCALING LOGIC
// ----------------------------------------------------------------------------
IF (rSlave_Controller_CO <= 45.0) THEN
    // Zone 1: Steam Heating Phase (CO: 0% -> 45%)
    rSteamValve_Cmd   := ((45.0 - rSlave_Controller_CO) / 45.0) * 100.0;
    rCWValve_Cmd      := 0.0;
    rChillerValve_Cmd := 0.0;

ELSIF (rSlave_Controller_CO > 45.0 AND rSlave_Controller_CO <= 55.0) THEN
    // Zone 2: Deadband Neutral Region (All Valves Closed)
    rSteamValve_Cmd   := 0.0;
    rCWValve_Cmd      := 0.0;
    rChillerValve_Cmd := 0.0;

ELSIF (rSlave_Controller_CO > 55.0 AND rSlave_Controller_CO <= 80.0) THEN
    // Zone 3: Cooling Water Phase (CO: 55% -> 80%)
    rSteamValve_Cmd   := 0.0;
    rCWValve_Cmd      := ((rSlave_Controller_CO - 55.0) / 25.0) * 100.0;
    rChillerValve_Cmd := 0.0;

ELSE
    // Zone 4: Sub-Zero Chilling Phase (CO: 80% -> 100%)
    rSteamValve_Cmd   := 0.0;
    rCWValve_Cmd      := 0.0;
    rChillerValve_Cmd := ((rSlave_Controller_CO - 80.0) / 20.0) * 100.0;
END_IF;
END_PROGRAM

# 5. Fully Worked Industrial Numerical Case Study

# Case Study Specification: 5,000 L Glass-Lined API Reactor

A pharmaceutical production plant requires a Monofluid TCU for a 5,000 L Glass-Lined Reactor (GLR) performing a multi-stage synthetic API batch process:

# Process & Equipment Inputs:

Reactor Nominal Capacity: $5,000 \text{ L}$ , Vessel Steel Mass = $2,500 \text{ kg}$ ( $C_p = 0.50 \text{ kJ/kg}\cdot\text{K}$ ).
Batch Liquid Charge: $4,000 \text{ L}$ Organic Solvent (Density $\rho = 1,000 \text{ kg/m}^3$ , $C_p = 2.50 \text{ kJ/kg}\cdot\text{K}$ ).
Heat Transfer Fluid (HTF): Marlotherm N ( $\rho = 875 \text{ kg/m}^3$ , $C_p = 2.15 \text{ kJ/kg}\cdot\text{K}$ , $\beta = 0.00095 \text{ K}^{-1}$ ).
Phase 1 Heating: $25^\circ\text{C} \rightarrow 130^\circ\text{C}$ in $60 \text{ min}$ ( $1 \text{ hour}$ ) with $0 \text{ kW}$ endothermic load.
Phase 2 CW Cooling: $130^\circ\text{C} \rightarrow 35^\circ\text{C}$ in $45 \text{ min}$ ( $0.75 \text{ hours}$ ).
Phase 3 Sub-Zero Chilling: $35^\circ\text{C} \rightarrow -20^\circ\text{C}$ in $60 \text{ min}$ ( $1 \text{ hour}$ ) with $45 \text{ kW}$ exothermic reaction load.
Hydraulic Loop: Piping length = $45 \text{ m}$ , Loop $\Delta T = 15^\circ\text{C}$ , Target Velocity = $1.7 \text{ m/s}$ .

# Step-by-Step Calculation Solution:

# Step 1: Thermal Capacitances & Mass

M_{\text{batch}} = \left(\frac{4000}{1000}\right) \times 1000 = 4,000 \text{ kg}

C_{\text{process}} = 4,000 \text{ kg} \times 2.50 \text{ kJ/kg}\cdot\text{K} = 10,000 \text{ kJ/K}

C_{\text{metal}} = 2,500 \text{ kg} \times 0.50 \text{ kJ/kg}\cdot\text{K} = 1,250 \text{ kJ/K}

C_{\text{total}} = 10,000 + 1,250 = 11,250 \text{ kJ/K}

# Step 2: Peak Thermal Phase Duties

# Phase 1: Heating Duty ( $25^\circ\text{C} \rightarrow 130^\circ\text{C}$ )

\Delta T_{\text{heat}} = 130 - 25 = 105^\circ\text{C}, \qquad t_{\text{heat}} = 3,600 \text{ seconds}

Q_{\text{sensible, heat}} = \frac{11,250 \text{ kJ/K} \times 105 \text{ K}}{3,600 \text{ s}} = 328.13 \text{ kW}

Q_{\text{peak, heat}} = (328.13 \times 1.10) + 0 = 360.94 \text{ kW} \quad (310.35 \text{ Mcal/h})

# Phase 2: CW Cooling Duty ( $130^\circ\text{C} \rightarrow 35^\circ\text{C}$ )

\Delta T_{\text{cw}} = 130 - 35 = 95^\circ\text{C}, \qquad t_{\text{cw}} = 2,700 \text{ seconds}

Q_{\text{sensible, cw}} = \frac{11,250 \times 95}{2,700} = 395.83 \text{ kW}

Q_{\text{peak, cw}} = 395.83 \times 1.05 = 415.63 \text{ kW} \quad (357.38 \text{ Mcal/h})

# Phase 3: Sub-Zero Chilling Duty ( $35^\circ\text{C} \rightarrow -20^\circ\text{C}$ with $45 \text{ kW}$ Exotherm)

\Delta T_{\text{chill}} = 35 - (-20) = 55^\circ\text{C}, \qquad t_{\text{chill}} = 3,600 \text{ seconds}

Q_{\text{sensible, chill}} = \frac{11,250 \times 55}{3,600} = 171.88 \text{ kW}

Q_{\text{peak, chill}} = (171.88 \times 1.10) + 45.0 = 234.06 \text{ kW} \quad (66.55 \text{ TR})

# Governing Thermal Duty for Pump Sizing:

Q_{\text{governing}} = \max(360.94,\; 415.63,\; 234.06) = 415.63 \text{ kW} \quad (\text{Cooling Water Phase})

# Step 3: Circulation Pump Hydraulics & Line DN Sizing

# HTF Volumetric Flow Rate ( $Q_{\text{HTF}}$ ):

Q_{\text{HTF, m}^3/\text{s}} = \frac{415.63 \text{ kW}}{875 \text{ kg/m}^3 \times 2.15 \text{ kJ/kg}\cdot\text{K} \times 15 \text{ K}} = 0.01473 \text{ m}^3/\text{s}

Q_{\text{HTF, m}^3/\text{h}} = 0.01473 \times 3600 = 53.03 \text{ m}^3/\text{h} \quad (883.8 \text{ LPM})

# Header Line DN Selection:

For target velocity $v = 1.7 \text{ m/s}$ :

A_{\text{req}} = \frac{0.01473}{1.7} = 0.008665 \text{ m}^2 \implies D_{\text{inner, req}} = \sqrt{\frac{4 \times 0.008665}{\pi}} = 0.1050 \text{ m} \quad (105.0 \text{ mm})

\text{Selected Standard Pipe: } \mathbf{\text{DN 100 Schedule 40}} \quad (D_{\text{inner}} = 102.3 \text{ mm}, A_{\text{pipe}} = 0.008219 \text{ m}^2)

\text{Actual HTF Velocity: } v_{\text{actual}} = \frac{0.01473}{0.008219} = 1.79 \text{ m/s} \quad (\text{Ideal Range } 1.5 - 2.0 \text{ m/s})

# Pump TDH & Power Sizing:

Pipe Friction Loss ( $45 \text{ m}$ loop): $3.8 \text{ m}$
Reactor Jacket Drop: $8.5 \text{ m}$ ( $0.80 \text{ bar}$ )
PHE Drop: $5.3 \text{ m}$ ( $0.50 \text{ bar}$ )
3-Way Valve Drop: $4.2 \text{ m}$ ( $0.40 \text{ bar}$ )
Static Elevation Head: $4.0 \text{ m}$

\text{Total Dynamic Head (TDH)} = 3.8 + 8.5 + 5.3 + 4.2 + 4.0 = \mathbf{25.8 \text{ meters}} \quad (2.21 \text{ bar})

P_{\text{hydraulic}} = \frac{0.01473 \times 875 \times 9.81 \times 25.8}{1000} = 3.26 \text{ kW}

P_{\text{brake}} = \frac{3.26}{0.70} = 4.66 \text{ kW}, \qquad P_{\text{motor, HP}} = (4.66 \times 1.34102) \times 1.25 = 7.81 \text{ HP} \implies \mathbf{10 \text{ HP Motor}}

# Step 4: DIN 4754 Expansion Tank Sizing

# System Hold-Up Volume ( $V_{\text{charge}}$ ):

Piping volume ( $45 \text{ m}$ , DN 100): $370 \text{ L}$
Reactor jacket volume ( $5,000 \text{ L}$ GLR jacket): $900 \text{ L}$
PHEs internal volume: $35 \text{ L}$
Skid loop volume: $25 \text{ L}$

V_{\text{charge}} = 370 + 900 + 35 + 25 = 1,330 \text{ Liters}

# Volumetric Thermal Expansion ( $\Delta V$ ):

\Delta T_{\text{max}} = 130 - (-20) = 150^\circ\text{C}

\Delta V = 1,330 \text{ L} \times 0.00095 \text{ K}^{-1} \times 150 \text{ K} = 189.5 \text{ Liters}

# Liquid Seal Reserve ( $V_{\text{seal}}$ ):

V_{\text{seal}} = \max(15\% \times 189.5,\; 5\% \times 1,330) = \max(28.4 \text{ L},\; 66.5 \text{ L}) = 66.5 \text{ Liters}

# DIN 4754 Minimum Tank Volume:

With k_{\text{\exp}} = 1.25 and $30\% \text{ N}_2$ vapor cushion:

V_{\text{tank, DIN 4754}} = \frac{(189.5 \times 1.25) + 66.5}{1 - 0.30} = \frac{236.88 + 66.5}{0.70} = \frac{303.38}{0.70} = \mathbf{433.4 \text{ Liters}}

\mathbf{\text{Recommended Standard Pressure Vessel Size: }} \mathbf{500 \text{ Liters (N2 Cushioned)}}

# Step 5: Secondary PHE Heat Exchanger Surface Areas

Using logarithmic mean temperature difference (LMTD) with multi-pass correction factor $F = 0.95$ :

PHE-1 (Steam Heating, $3.0 \text{ bar g}$ Steam):
- $U_{\text{steam}} = 2,200 \text{ W/m}^2\cdot\text{K}$ , $\text{LMTD}_{\text{steam}} = 32.4^\circ\text{C}$
- $A_{\text{steam}} = \frac{360.94 \times 1000}{2200 \times 32.4 \times 0.95} = \mathbf{5.33 \text{ m}^2}$
PHE-2 (Cooling Water, $30^\circ\text{C} \rightarrow 35^\circ\text{C}$ CW):
- $U_{\text{cw}} = 1,400 \text{ W/m}^2\cdot\text{K}$ , $\text{LMTD}_{\text{cw}} = 22.8^\circ\text{C}$
- $A_{\text{cw}} = \frac{415.63 \times 1000}{1400 \times 22.8 \times 0.95} = \mathbf{13.71 \text{ m}^2}$
PHE-3 (Sub-Zero Chilled Glycol, $-25^\circ\text{C} \rightarrow -20^\circ\text{C}$ Glycol):
- $U_{\text{chill}} = 950 \text{ W/m}^2\cdot\text{K}$ , $\text{LMTD}_{\text{chill}} = 14.2^\circ\text{C}$
- $A_{\text{chill}} = \frac{234.06 \times 1000}{950 \times 14.2 \times 0.95} = \mathbf{18.28 \text{ m}^2}$

# 6. Summary Sizing Data Sheet

Design Parameter	Value	Engineering Units	Notes & Compliance
Peak Heating Duty ( $Q_{\text{heat}}$ )	360.9	kW (310.4 Mcal/h)	$25^\circ\text{C} \rightarrow 130^\circ\text{C}$ in 60 min
Peak CW Cooling Duty ( $Q_{\text{cw}}$ )	415.6	kW (357.4 Mcal/h)	$130^\circ\text{C} \rightarrow 35^\circ\text{C}$ in 45 min (Governing Load)
Peak Chilling Duty ( $Q_{\text{chill}}$ )	234.1	kW (66.6 TR)	$35^\circ\text{C} \rightarrow -20^\circ\text{C}$ in 60 min ( $45 \text{ kW}$ Exotherm)
HTF Circulation Flow Rate	53.0	$\text{m}^3\text{/h}$ (883.8 LPM)	Marlotherm N at $\Delta T_{\text{loop}} = 15^\circ\text{C}$
Header Line DN	DN 100	Sch 40 ( $102.3 \text{ mm}$ ID)	Actual Velocity $1.79 \text{ m/s}$ (Ideal envelope)
Pump Total Dynamic Head	25.8	Meters ( $2.21 \text{ bar}$ )	Includes jacket, fittings, 3-way valves & static head
Pump Motor Power	10	HP ( $7.5 \text{ kW}$ )	Includes $25\%$ hydraulic motor safety factor
Expansion Tank Size	500	Liters	DIN 4754 Standard ( $30\% \text{ N}_2$ space)
Recommended Skid	Option 2	Combined Steam/CW + Chiller	Prevents thermal shock & glycol freezing

# 7. Try the Interactive Sizing Tool

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