Engineering & Technology · Process Balances, Flowsheets & Design
Measurements, model validation and process documentation
A balance leaves a small unexplained residual. Calling it a leak immediately would skip important questions about time windows, inventory and measurement uncertainty. Calling it zero because it is small would discard evidence. A process record should make both the discrepancy and the limits of its interpretation visible.
Use the earlier material, thermodynamics and fluid-engineering chapters for quantities, energy and flow. Ratios, elementary algebra, units and chemical amount are enough for the constructed calculations here.
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Evaluate process-balance evidence using synchronised measurements, uncertainty, model scope and traceable documentation.
Measurements must describe the same account
Use consistent boundaries, units, composition bases and time intervals. An inlet’s daily average cannot automatically be compared with an outlet’s brief instantaneous reading. Storage can change during a measurement period, including material in connecting lines or intermediate vessels. A steady-state model should be supported by observations appropriate to the variables and interval involved.
Record sensor and sampling locations, measurement methods, calibration information, timestamps and configuration. Composition sampling can add uncertainty and representativeness questions beyond a flow sensor’s reading. If two quantities share a calibration source, calculation input or sampling effect, their uncertainties may be correlated. Treating them as independent without evidence can misstate the uncertainty of a residual.
An original account separates discrepancy from interpretation
Suppose synchronised interval averages are inlet 100 kg/h, outlet 97 kg/h and accumulation 2 kg/h. The residual is 100−97−2=1 kg/h. Supply uncorrelated standard uncertainties of 1, 1 and 0.5 kg/h respectively. With sensitivity coefficients +1, −1 and −1, the residual’s combined standard uncertainty is √(1²+1²+0.5²)=1.5 kg/h.
This calculation uses the supplied correlation assumption and linear account. Standard uncertainty is not a guaranteed error bound, and a residual smaller than one standard uncertainty is not a universal acceptance rule. The result does not prove either a leak or perfect closure. Examine plausible timing, inventory, calibration, sampling and model explanations against the intended decision and its criteria.
Verification and validation answer different questions
Check that the implemented equations, units, conservation relationships and numerical solution represent the intended model. Independently recomputing a worked case or checking a solver’s residual helps verify the calculation. Validation asks whether the model adequately represents the relevant physical behaviour for its intended use, using appropriate observations and their uncertainty. Correct arithmetic alone cannot establish that.
Keep parameter-fitting data and independent evaluation evidence distinguishable. A model adjusted to match one dataset needs further evidence before its predictive performance is claimed for other compositions, flow rates or scales. Preserve the property source and version, assumptions, input records, model revision, residuals and observed range. Document a correction and its consequences rather than silently overwriting the record that explained an earlier decision.
Write a reviewable discrepancy statement
For the supplied interval, report the residual as 1 kg/h with combined standard uncertainty 1.5 kg/h under the stated uncorrelated-input model. Retain all three measured quantities and the method used for the inventory change. Report any known shared influences rather than hiding them inside an unexplained uncertainty total. No probability level or decision threshold was supplied here.
A useful next comparison would align independent records over another documented interval and examine any changing inventory or sampling bias. If the account were used for a different purpose, such as predicting a transient composition, it would need evidence addressing that behaviour. A well-documented balance explains what was checked, what remains uncertain and which claims the evidence can support.
Try the reasoning
Why is the residual not simply inlet minus outlet in this example?
Show the answer and reasoning
Measured inventory is increasing at 2 kg/h, so accumulation must also be subtracted.
When is the root-sum-of-squares result valid here?
Show the answer and reasoning
For the stated linear residual with the supplied uncorrelated standard uncertainties and unit sensitivity magnitudes.
Does fitting the model to these measurements independently validate its predictions?
Show the answer and reasoning
No. Fitting uses those observations; independent, relevant evidence is needed to evaluate prediction for the intended use.
What to carry forward
Keep discrepancies, uncertainty and model scope visible in a record that another reviewer can reconstruct.
References
Teaching resources and research supporting this lesson’s explanations and examples.