Agitated Reactor Calculator

Professional Engineering sizing for multi-impeller agitated reactor and tanks. Evaluates motor power, mixing intensity (P/V), and jacket/limpet heat transfer.

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1. Project Data

2. Vessel & Fluid Properties

Liq. above TL: - | True from bottom: -
Process Fluid Properties

3. Agitator Configuration

Impeller Placement
Impeller 1 (Bottom)
Impeller 2 (Middle)
Impeller 3 (Top)
Bottom Tickler

4. Heat Transfer Configuration

Process Load & Utility Configuration
Sat. Temp: -
Thermophysical Properties

5. Scale-Up Rules

Given a reference (lab/pilot) vessel and the current vessel geometry, compute the required shaft speed under three common scale-up criteria.

Scale-Up Criterion Rule $N_2$ (RPM) Note

6. Solid Suspension — Zwietering Correlation

Minimum just-suspended speed $N_{js}$ for solid particles. Compares $N_{js}$ against the operating speed to indicate suspension status. Leave blank to skip.

$N_{js}$ (min. suspension)
-
Operating $N$
-
Status
-
Reactor Schematic
Hydraulic & Thermal Results
Hydraulic Performance
Required Motor Pwr -
Shaft Power ($P_{sh}$) -
Mix Intensity ($P/V$) -
Agitation Class -
Tip Speed ($v_{tip}$) -
Froude No. ($Fr$) -
Blend Time ($\theta_{95}$) -
Min. Shaft Dia ($d$) * -
Std. Shaft OD -
Selected Motor -
Bulk Velocity ($v_b$) -
Turnover Time ($t_c$) -
Thermal Performance
Est. Batch Time -
LMTD -
Coil Turns / Length -
Inside Film ($h_i$) -
Outside Film ($h_o$) -
Overall HTC ($U$) -
HT Capacity ($Q_{cap}$) -
Heat Flux (kcal/h.m²) -
Agitator Heat In -
Required Util Flow -

* Shaft diameter is a torsion-based estimate using the selected K factor. Bending moment (shaft length / bearing span not entered) and lateral critical speed must be verified separately for the final mechanical design.

Design Tip: Enter geometry and fluid properties to receive intelligent configuration recommendations.
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Engineering Reference & Technical Basis

1. Hydraulic Calculations

Reynolds Number ($Re$) determines flow regime per impeller:

$$Re_i = \frac{\rho \cdot N \cdot D_i^2}{\mu}$$

Power drawn by each impeller ($P_i$) and total mixing intensity ($P/V$):

$$P_i = N_{p,i} \cdot \rho \cdot N^3 \cdot D_i^5 \qquad \frac{P}{V} = \frac{\sum P_i}{V_{liquid}}$$

$N_p$ is regime-corrected using the two-asymptote model (Nagata 1975):

$$N_p(Re) = \max\!\left(\frac{K_p}{Re},\; N_{p,turb}\right)$$

where $K_p$ is the laminar power constant per impeller type (Rushton: 71.5; PBT 45°: 36.5; Hydrofoil: 33.0; Anchor: 220 — from Nagata 1975, Bates et al. 1963). The $K_p/Re$ term dominates in laminar flow ($Re \lesssim K_p/N_{p,turb}$); the turbulent plateau $N_{p,turb}$ dominates above. Accuracy: ≤1% in laminar, ≤15% in transition, 0% in turbulent ($Re \gt 300$).

Interference Factor (IF): When impellers are spaced less than $1.0 D$ apart, their combined power number decreases due to flow interaction.

Geometry convention: All heights ($H$, $C$, $S$) are measured from the bottom tangent line (TL) — the point where the bottom dished head meets the cylindrical shell. The head volume is always fully included in $V_{liquid}$ since the head is submerged whenever any liquid is present. The fill % applies to the straight shell height $H$; the true liquid level from the vessel bottom equals $C_{above TL}$ + head depth $h_{head}$.

Minimum Shaft Diameter ($d$) — equivalent torque method (ASME B106.1M / Shigley's), solid circular cross-section:

$$T_e = K \cdot T_q \qquad d = \left( \frac{16 \cdot T_e}{\pi \cdot \tau_{allow}} \right)^{1/3}$$

where $K$ is the combined loading factor: $K = T_e/T_q = \sqrt{1 + (M_b/T_q)^2}$ (maximum shear stress theory). Since bending moment $M_b$ requires shaft length and bearing span data not entered here, $K$ is used as a conservative proxy. Recommended values: K = 2.0 for standard top-entry agitators (Paul et al. 2004; minimum); K = 3.0 for deep vessels / multiple impellers; K = 1.5 for short shaft with one impeller. The lateral critical speed must be verified separately.

2. Thermal Calculations

Inside film heat transfer coefficient ($h_i$) based on generalized agitated vessel correlation (Uhl & Gray 1966):

$$Nu = \frac{h_i \cdot T}{k} = C \cdot Re^{2/3} \cdot Pr^{1/3} \cdot \left(\frac{\mu_{bulk}}{\mu_{wall}}\right)^{0.14}$$

$C$ = 0.73 (Rushton), 0.53 (PBT), 0.40 (Hydrofoil), 0.36 (Anchor). $Re = \rho N D^2/\mu$; characteristic length = vessel diameter $T$.

Outside film ($h_o$) evaluated at fixed design velocity — decoupled from duty:

Jacket (1.5 m/s, Dittus-Boelter):

$$Nu_o = 0.027 \cdot Re_o^{0.8} \cdot Pr_o^{0.33} \qquad De = 2w$$

Half-pipe limpet (3.0 m/s, Dream 1999):

$$Nu_o = 0.0565 \cdot Re_o^{0.684} \cdot Pr_o^{0.33} \cdot \left(\frac{d}{D}\right)^{0.16} \qquad De = \frac{\pi d}{\pi+2}$$

Internal helical coil (2.0 m/s, Dittus-Boelter + Dean correction):

$$Nu_o = 0.023 \cdot Re_o^{0.8} \cdot Pr_o^{0.33} \cdot \left(1 + 3.5\,\frac{d_t}{D_c}\right)$$

Helical coil active HT area — submerged turns only:

$$n_{active} = \left\lfloor \frac{\min(H_{coil},\,H_{liq})}{p} \right\rfloor \quad A = \pi^2 d_t\, n_{active}\, D_c$$

Overall $U$ and batch time:

$$\frac{1}{U} = \frac{1}{h_i} + R_{f} + \frac{1}{h_o} \qquad t_{batch} = \frac{m C_p}{UA} \ln\!\frac{\Delta T_{init}}{\Delta T_{target}}$$

Condensing steam: $h_o = 5000\ \text{W/m}^2\text{K}$ (heuristic). Antoine equation for steam saturation (valid 0–6 barg).

3. Additional Calculations

Tip speed & Froude number:

$$v_{tip} = \pi D N \qquad Fr = \frac{N^2 D}{g}$$

Vortex risk when $Fr > 0.04$ in unbaffled vessels.

Blend time (Ruszkowski 1994):

$$\theta_{95} = \frac{5.9}{N \cdot N_p^{1/3}} \cdot \left(\frac{T}{D}\right)^2 \cdot \left(\frac{H}{T}\right)^{1/3}$$

Shaft sizing — equivalent torque method (ASME B106.1M):

$$T_e = K \cdot T_q \qquad d = \left(\frac{16\,T_e}{\pi\,\tau_{allow}}\right)^{1/3}$$

$K$ = combined loading factor (default 2.0 for standard top-entry agitators). Lateral critical speed must be verified separately.

Scale-up rules (D₁→D₂):

$$N_2 = N_1\!\left(\frac{D_1}{D_2}\right)^{n} \quad n = \begin{cases} 2/3 & \text{Equal } P/V \text{ or blend time} \\ 1 & \text{Equal tip speed} \\ 2 & \text{Equal } Re \\ 1/2 & \text{Equal } Fr \end{cases}$$

Solid suspension — Zwietering (1958):

$$N_{js} = S \cdot \nu^{0.1} \cdot d_p^{0.2} \cdot \left(\frac{g\,\Delta\rho}{\rho_L}\right)^{0.45} \cdot X^{0.13} \cdot D^{-0.85}$$

$S$ = Zwietering coefficient (impeller/geometry dependent); $d_p$ = particle diameter [m]; $X$ = solid loading [wt%].

References
  • Power Number & Laminar Constants: Nagata, S. (1975). Mixing: Principles and Applications. Halsted Press. | Bates, R.L., Fondy, P.L. & Corpstein, R.R. (1963). Ind. Eng. Chem. Process Des. Dev., 2(4), 310–314.
  • Inside Film (hi): Uhl, V.W. & Gray, J.B. (1966). Mixing: Theory and Practice, Vol. 1. Academic Press.
  • Limpet Coil (ho): Dream, R.F. (1999). Heat Transfer in Agitated Jacketed Vessels. Chemical Engineering, Jan 1999, pp 90–96.
  • Jacket (ho): Sinnott, R.K. & Towler, G. (2009). Chemical Engineering Design, 5th ed. Butterworth-Heinemann.
  • Internal Coil (ho): Perry, R.H. & Green, D.W. (2008). Perry's Chemical Engineers' Handbook, 8th ed. McGraw-Hill. §11-17.
  • Blend Time: Ruszkowski, S. (1994). A rational method for measuring blending performance. IChemE Symp. Series, 136, 283–291.
  • Scale-Up: Paul, E.L., Atiemo-Obeng, V.A. & Kresta, S.M. (2004). Handbook of Industrial Mixing. Wiley-Interscience.
  • Solid Suspension: Zwietering, T.N. (1958). Suspending of solid particles in liquid by agitators. Chemical Engineering Science, 8(3–4), 244–253.
  • Shaft Sizing: ASME B106.1M — Design of Transmission Shafting. | Paul et al. (2004) ibid. | Harland, J.R. (1994). Mechanical Design of Process Equipment.