Real-Time Crystallization Control (PAT)

Batch Controls

Base cooling rate 0.60 °C/min

PAT setpoint S_target 1.15

Seed loading 40 seeds

Inline PAT Probe

S = 1.00 (probe)
T = 40.0 °C

S(t) — ambermean size — blue

Mean crystal size

0.0 µm

Crystal count N

Batch time

0.0 min

Yield

0.0 %

How it works

A cooling batch crystallizer holds a solution above its solubility curve. The driving force is the supersaturation ratio:

S(t) = C(t) / C*(T(t))
C* (T) = C0 + kT · T      (linear solubility)

Two competing rate laws consume that supersaturation — this is the classic nucleation/growth trade-off PAT systems are built to manage:

Growth:      G(S) = kg · max(S−1, 0)^g     (µm/min per crystal)
Nucleation:  B(S) = kb · max(S−1, 0)^b     (new crystals/min)

Every crystal growing consumes solute mass proportional to its surface area × radial growth (dV = 4πr²·dr), which feeds back into C(t) — so growth alone pulls S back down with no controller at all. The risk is nucleation: because b ≫ g, letting S spike creates a burst of tiny new crystals (a wide, hard-to-filter size distribution) instead of growing the seeds you already have.

The inline probe (an FBRM/Raman-style PAT sensor in a real plant) reports S(t) with a little measurement noise. With PAT feedback ON, a proportional controller throttles the cooling ramp itself:

coolRate_eff = coolRate_base · clamp(1 − Kp·(S − Starget), 0, 1.6)

Cooling pauses when S drifts above the setpoint (letting existing crystals grow the supersaturation back down before more nucleation happens) and speeds back up when S falls below it. With feedback OFF the cooling ramp runs open-loop at a constant rate regardless of what the probe reads — watch how much faster the crystal count climbs and how much smaller the mean size ends up for the same batch.

Base cooling rate — the open-loop ramp speed; also the ceiling the controller throttles against in closed loop.
S_target — the supersaturation band the PAT controller tries to hold.
Seed loading — starting crystal count; more seed surface area means less driving force is "wasted" on nucleation.

Growing crystals Inline PAT probe beam

t = 0.0 min

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Real-Time Crystallization Control with Inline PAT