Activity Coefficients
Simulating how NRTL activity coefficients for the ethanol-water system evolve with temperature using PathSim blocks and connections.
The NRTL (Non-Random Two-Liquid) model computes liquid-phase activity coefficients MATHINLINE1ENDMATH that quantify deviations from ideal mixing:
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Here we wire an NRTL block and two Antoine blocks into a simulation to see how activity coefficients and the resulting bubble pressures change with temperature.
System Definition
Set up the blocks: a temperature source, Antoine correlations for both components, and an NRTL activity coefficient model for a 40/60 ethanol-water mixture.
A custom Function block computes the bubble pressure from the activity coefficients and pure-component vapor pressures:
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Wiring and Simulation
Connect the temperature source to NRTL and both Antoine blocks. The NRTL outputs and Antoine outputs feed into the bubble pressure calculation. Scopes record everything.
18:18:27 - INFO - LOGGING (log: True) 18:18:27 - INFO - BLOCKS (total: 7, dynamic: 0, static: 7, eventful: 0) 18:18:27 - INFO - GRAPH (nodes: 7, edges: 10, alg. depth: 3, loop depth: 0, runtime: 0.060ms) 18:18:27 - INFO - STARTING -> TRANSIENT (Duration: 100.00s) 18:18:27 - INFO - -------------------- 1% | 0.0s<0.1s | 3798.4 it/s 18:18:27 - INFO - ####---------------- 20% | 0.0s<0.0s | 18536.8 it/s 18:18:27 - INFO - ########------------ 40% | 0.0s<0.0s | 18993.9 it/s 18:18:27 - INFO - ############-------- 60% | 0.0s<0.0s | 18524.7 it/s 18:18:27 - INFO - ################---- 80% | 0.0s<0.0s | 18866.5 it/s 18:18:27 - INFO - #################### 100% | 0.0s<--:-- | 18440.7 it/s 18:18:27 - INFO - FINISHED -> TRANSIENT (total steps: 200, successful: 200, runtime: 16.90 ms)
Both activity coefficients exceed 1, confirming positive deviation from Raoult's law — a characteristic of the ethanol-water system. The bubble pressure rises steeply with temperature, crossing 1 atm near the expected boiling point of the mixture.