Lab 01 · Master's investigation · VLE and flash

How credible is your predicted phase split?

A 1.00 mol binary feed at 350 K and 90 kPa contains 0.40 mol of component 1. Assume ideal vapor and ideal liquid.

Verify the controlled starting case, then audit the assumptions and test how sensitive the conclusion is to uncertain inputs.

2027 prototype
Review the student workflow

Graduate route. Complete Steps 1–3 to verify the calculation. In Step 4, compare liquid models and run bounded sensitivity scenarios. Finish with three evidence-backed claims about assumptions, sensitivity and model limits. Go to the graduate investigation.

Choose a pressure experimentNamed cases use the synthetic ideal mixture at 350 K and z₁ = 0.40.

Picture a two-phase split

Composition and amount answer different questions

Feed · z₁

Of all feed moles, what fraction is component 1?

Liquid · x₁ and L

x₁ tells its composition. L tells its amount in mol.

Vapor · y₁ and V

y₁ tells its composition. V tells its amount in mol.

β = V/F tells the fraction of feed moles in the vapor. For a 1 mol feed, L + V = 1 mol. The picture shows a two-phase case. Your calculation may instead find liquid only or vapor only.

1. Set the feed and conditions

Basis · 1.00 mol feed

Temperature

Synthetic correlation range 300–390 K.

Pressure

kPa

Calculation range 1–200 kPa.

Component 1 feed mole fraction z₁

mol/mol

Enter a fraction from 0 to 1. For this 1 mol feed, z₁ = 0.40 means 0.40 mol of component 1.

Pure-component saturation pressures

P_i^sat(T) sat = saturation

The pressure at which pure component i has liquid and vapor in equilibrium at temperature T.

One pure component in its own vessel
Pure liquid ⇌ saturated vapor at the same T and P_i^sat(T)

Select a temperature to read the saturation pressures.

Component 1 · AP₁^sat(T): — kPa
Component 2 · BP₂^sat(T): — kPa

Loading the property record…

See the equation, constants and source

Before calculating, what do you think will be present?

Make a prediction, then compare it with the calculated result. You can skip this step. Your choice does not change the calculation.

Add a calculated result to the comparison before changing a condition.

Change the mixture or liquid model

Mixture and property record

Liquid model

The starting problem uses the ideal liquid.

Try the bubble and dew boundaries

Each case loads the synthetic ideal feed at 350 K and z₁ = 0.40. Predict the amount of the phase that is just appearing.

VLE model assumptions

Vapor is ideal. The activity standard state is the pure liquid at the system temperature. The pressure correction and saturated-vapor fugacity correction are set to one. Calculations use a convex liquid model in the supported range.

Open the full Lab 01 for the original temperature diagrams, solver traces and transferred-fit controls.

2. Identify the phases and amounts

Calculate the state to see its phases, compositions and material-balance check.

Name this case

3. Read the pressure–composition diagram

Fixed temperature · P–x–y

Use the operating-pressure line and feed composition to locate the calculated state. Liquid and vapor compositions belong to different curves.

Inspect the numerical curve data

Selected-model equilibrium curve at the calculated temperature.
Liquid x₁	Vapor y₁	Pressure / kPa

4. Investigate the credibility of the prediction

Master's core work

Calculate a state in Step 1 before running either investigation.

A. Audit the assumptions and compare liquid models

Write the equilibrium assumption used here: $y_{i} P = x_{i} γ_{i} P_{i}^{sat} (T)$ .
Identify which terms would change for nonideal vapor or appreciable liquid pressure corrections. All candidates below retain ideal vapor and neglected pressure corrections.
Inspect the interaction parameters recorded with the calculated baseline, compare the four candidates at the same T, P and z₁, and decide what independent data would be needed to select or calibrate them.

Identify the fugacity terms that the current calculation fixes

y_{i} {\hat{φ}}_{i} P = x_{i} γ_{i} f_{i}^{L, *} (T, P)

The vapor-mixture fugacity coefficient represents vapor nonideality. The pure-liquid reference fugacity includes the saturated-vapor and liquid pressure corrections. This Lab sets the vapor coefficient and those pressure corrections to one, giving the simpler equation above. Changing only the liquid activity model does not test those assumptions.

Identify the EOS or virial information and liquid-volume data needed to assess these omitted terms. Explore vapor fugacity in Lab 09.

The table lists the candidate parameter values recorded with the calculated baseline, including default values for unspecified candidates. Edit the model controls and recalculate to change this record. These are hypothetical teaching inputs unless independently calibrated. Model spread is not a confidence interval or proof that one model is correct.

Claim 1 · assumptions and model evidence

B. Examine bounded input and property sensitivity

Enter an assumed half-width for each factor. Start with the illustrative values below and explain why they are useful for this exercise.
Run ten one-at-a-time scenarios and 32 signed joint corner combinations. Read failed and indeterminate scenarios as well as finite results.
Compare the positive and negative one-at-a-time responses. Explain whether their asymmetry supports a local linear approximation.
Repeat near the bubble boundary at 96 kPa. A change in phase branch makes unqualified linear uncertainty propagation unreliable; these finite scenario changes are not automatically local derivatives.

These are deterministic sensitivity assumptions, not measured standard deviations or NIST uncertainty estimates. Each property factor multiplies the complete original saturation-pressure correlation within its stated temperature range. The source constants and baseline property record remain unchanged.

Temperature half-width ±ΔT

Pressure half-width ±ΔP

kPa

Feed half-width ±Δz₁

mol/mol

Component 1 correlation-scale half-width

Component 2 correlation-scale half-width

Sampled joint-corner β range: —
Finite / indeterminate / failed corners: —

The reported range covers only the sampled scenarios. It is not a probability, confidence interval or proven global bound. The factor combinations assume independent variation; no joint error model has been supplied. Zero half-widths can repeat a physical state. An indeterminate vapor amount is not replaced with zero.

Inspect the one-at-a-time scenarios

Scenario	Phase or failure reason	Vapor β	Change in β

Inspect all 32 signed joint corners

Scenario	T / K	P / kPa	z₁	P₁^sat scale	P₂^sat scale	Phase or failure reason	Vapor β

Claim 2 · sensitivity and phase robustness

C. Defend a limited, reproducible conclusion

Evidence linking the model comparison to the sensitivity study Claim 3 · limits and the next evidence needed

For a statistical uncertainty claim, specify input standard uncertainties and their covariances, a justified propagation method and coverage assumptions. The scenario half-widths entered here do not supply these. NIST uncertainty propagation · NIST coverage intervals.

Submission standard: report the baseline and parameter provenance; cite numerical model and sensitivity results; identify retained assumptions, domain failures and phase changes; and propose a discriminating follow-up. The record check only confirms that the sections and calculations are present. Scientific reasoning still needs instructor review.

5. Compare, defend and save

Complete the Step 4 model audit and sensitivity study at 90 kPa, write the graduate claims, and add the result to the comparison.
Load the 96 kPa boundary case, calculate and rerun the same half-widths. Compare phase identity and phase amount with the 90 kPa case, then save it.
Use at least two numerical outputs to defend the graduate claims. The 100 and 75 kPa cases remain available as additional phase-limit checks.
Download the complete study, reopen it, and reproduce a saved case and its investigation record.

Your calculated cases will appear here after you add them.

Optional additional note

The required graduate claims and evidence are recorded in Step 4. Use this field for any extra note; existing notes from older studies are retained here.

Open a saved study