Cost estimation and LCA

An assessment computes what a solved flowsheet's equipment costs, what it costs to run, and its life-cycle impact. Each figure is an explicit function y = G(x, d; θ) of the verified state x, the pinned inputs d and the assessment's own data θ (correlation coefficients, prices, unit scores). It is evaluated after the solve and is never part of the compiled problem, so attaching an assessment changes neither the solution, nor its certificate, nor the run's replay identity.

Because G is built by the same compiler as the flowsheet's equations, each output has exact derivatives with respect to the state, the specifications and every input, so a cost or an impact can be a study output or an optimisation objective (see below).

The assessment layer is a Python library layer, openflowsheet.assessment (API). The CLI, HTTP and MCP interfaces do not offer it yet. The cost and climate impact example runs one end to end. The design is ADR 0052 and its design note, docs/derivations/E01-design.md.

Assessment evidence is neither verification nor validation

Every report closes with this statement: "Assessment evidence: an estimate under the stated basis, correlations, data and regimes. It is not numerical verification of the flowsheet and not empirical validation." A cost estimate carries an accuracy class. An impact is only as good as the unit scores behind it.

The assessment document

An assessment is a JSON document validated against schemas/assessment.schema.json:

Section	Holds
basis	currency and year of the estimate; optional location factor, escalation series and exchange rates
operation	operating hours per year, lifetime in years, discount rate
correlation_set, data	the cost correlation set, and any user-supplied sets, index series or LCA tables (each by id and SHA-256)
items	per costed item (named by unit id; P.drive is unit P's motor): its bare-module factor F_BM, an optional correlation choice, a quote, or an exclude with its reason
utilities, materials	each utility's kind, temperatures and price; each raw material or product by connection, with its price; each with optional LCA exchanges
capital, fixed_opex	the capital chain from bare-module costs to total capital; fixed operating cost lines such as maintenance
lca	the unit-score tables, direct-emission factor tables, impact categories, functional unit and allocation
derived, uncertainty	derived ratios of outputs; relative ranges of inputs for the uncertainty propagation

load_assessment validates a document and gives it an identity, its canonical SHA-256. AssessmentProgram.build plans it against a solved flowsheet and returns a program or a typed refusal. program.report(...) writes a report valid against schemas/assessment-report.schema.json.

What is estimated

Sizing. Each unit model maps to a sizing family, which turns the unit into its costable items:

Unit models	Family	Size
thermal.heater, syn001.tp_heater, c1.tp_heater	utility exchanger	area from the duty, U and the mean temperature difference to the selected utility
syn001.heat_exchanger	process exchanger	area from the duty, U and the two streams' temperatures
thermal.flash, syn001.tp_flash, syn001.ph_flash, c1.tp_flash	drum (vertical by default), with its duty exchanger	vessel dimensions and weight
thermal.pump, syn001.liquid_pump	pump, with its electric motor (.drive)	volumetric flow, head, power
thermal.compressor, thermal.turbine	compressor or turbine	power
syn001.column	column shell and trays; condenser and reboiler as utility exchangers	diameter at the controlling tray, height, number of actual trays; the duties
syn001.kinetic_cstr, syn001.conversion_reactor	reactor vessel, with its duty as an exchanger	volume
valves, mixers, splitters, feeds, sinks	no equipment	—

Any other model is refused NO_SIZING_MODEL unless the document gives a quote or excludes it. The mean temperature difference is Underwood's cube-root approximation of the log mean: it is smooth everywhere, including where the two end differences are equal, and departs from the exact log mean by +0.0035 % at an end-difference ratio of 2, +0.38 % at 10 and +2.56 % at 50. An exchanger with a phase change on its process side carries the limitation LMTD_ACROSS_PHASE_CHANGE.

Capital cost. A correlation gives each item's purchased cost at its size. The bare-module cost is the purchased cost times the item's F_BM, which the document states. A capital chain turns the sum of bare-module costs into the total capital. Two chains ship: bare-module-total (the total is the sum) and ebtf-prisma-v1 (EPC = 1.10 · 1.14 · 1.30 · TDC; CAPEX = 1.07 · EPC, after the EBTF method as given in the PrISMa supporting information). A document may also state its own chain. A quote replaces one item's correlation.

Operating cost. Each exchanger is served by a utility selected by a stated rule (the admissible utility by temperature). Its cost is the duty times the utility's price. Electricity is netted across the flowsheet: a turbine that generates more than the motors draw gives a credit (limitation ELECTRICITY_NETTED), and the generator itself is not costed (GENERATOR_NOT_COSTED). Materials are priced by mass (total or of one component): raw materials and waste as costs, products as revenue. Fixed lines are stated amounts or fractions of a capital figure; none is assumed (FIXED_OPEX_UNDECLARED when there are none).

Annual figures. The capital charge is the total capital times the capital recovery factor of the discount rate and the lifetime. The total annualised cost tac is the capital charge plus the operating cost. With a functional unit declared (a stream's mass, a component's mass or moles), the report also gives its annual amount and the levelised cost per unit of it, lcox, besides revenue and profit.

Correlations and their provenance

Correlation forms are code; coefficients are data, and every number has a source. The shipped set is sslw-idaes-v1: the cost correlations of Seider, Seader, Lewin and Widagdo, Product and Process Design Principles: Synthesis, Analysis, and Evaluation, 3rd ed. (Wiley, 2009), ch. 22. The set has eight entries: shell-and-tube exchanger, vertical vessel, horizontal vessel, column trays, pump, electric motor, compressor and turbine.

• Transcribed from the IDAES process modelling framework's SSLW.py (idaes-pse 2.13.0, BSD-3-Clause; the file's SHA-256 is recorded). Every coefficient carries the source line it was read from.
• Checked against the book, number by number, by page and equation. Each validity range cites its page, for example the shell-and-tube exchanger's 150–12,000 ft² (p. 571, Eqs. 22.39–22.42), the electric motor's range (p. 562, Eq. 22.19) and the gas expander's 20–5,000 hp (p. 593, Table 22.32).
• Reported per item: the set, the entry, the form, the citation, the source lines, the ranges, the options and which options were defaulted.

The cost basis of sslw-idaes-v1 is a CEPCI of 500, mapped to the year 2006 for escalation by public indices (limitation INDEX_BASIS_MAPPED).

Turton's correlations are not shipped; a user may register a set of their own. The power-law-v1 form is provided for user data and quotes. CEPCI values are not shipped (they are not openly licensed), but a user may supply them as a series.

Regimes. A correlation has a validity range, and an exchanger may be served by more than one utility. Choices like these are discrete. An assessment never smooths them: it holds a regime (the size piece, the number of parallel units, the utility, the service, the controlling column stage) selected by a stated rule at the solved state. Within its admissible set every regime is the true cost of a realisable design, so its derivatives are exact. Below a correlation's smallest size the item is in its floor regime: the smallest unit is bought, at a constant cost whose derivative is exactly zero. Above the largest size the item is split into parallel units, or refused CORRELATION_OUT_OF_RANGE.

Cost basis and indices

Only public indices ship:

Series	Use	Source
bls-ppi-wpu11-annual-v1	escalation in US dollars	U.S. Bureau of Labor Statistics, PPI WPU11 (machinery and equipment), via FRED
eurostat-ppi-c28-ea-annual-v1	escalation in euros	Eurostat, producer prices NACE Rev. 2 C28, euro area
frb-g5a-annual-v1	exchange rates	Federal Reserve Board, G.5A annual rates, via FRED

A cost is escalated in its source currency, then converted at the target year's exchange rate, then multiplied by the location factor. Each report records the series and the index values used.

Accuracy class and uncertainty

The accuracy class of the estimate is the largest AACE class over the costed items, read from the correlation set's entries or from a quote. An excluded item does not count. An item computed outside its correlation's range (CORRELATION_EXTRAPOLATED) makes the class none. The ranges follow AACE recommended practice 18R-97:

Class	Low	High
5	−20 % to −50 %	+30 % to +100 %
4	−15 % to −30 %	+20 % to +50 %
3	−10 % to −20 %	+10 % to +30 %
2	−5 % to −15 %	+5 % to +20 %
1	−3 % to −10 %	+3 % to +15 %

sslw-idaes-v1 is class 4.

Propagation. Every input with a declared relative range is propagated to first order. Each correlation entry carries its own range, and the document may add ranges, for example on a price. Each output gets two figures, each labelled with its assumption:

• a worst-case interval, with each input at its own adverse bound (conservative for any correlation between inputs);
• a standard deviation, with the inputs independent and uniform on their ranges.

Completeness. A total over an item that was refused is not reported. Every output that depends on the item is null, and the report's status is PARTIAL. An exclude with a reason restores the totals and lists the exclusion. The status values are COMPLETE, PARTIAL and REFUSED.

Life-cycle assessment

The impact is linear in the inventory at the flowsheet's boundary:

h = Q · a(x) + C · b(x)

• a(x) holds the technosphere exchanges. Each utility and material may declare exchanges with background activities, as an amount per unit of its boundary quantity (energy, mass or electricity; generation and substitution are negative).
• b(x) holds the direct emissions: a stream with the role emission maps each component to a biosphere flow.
• Q is a unit-score table: the impact of one unit of each background activity, computed once, offline, and frozen.
• C is a direct-factor table: characterisation factors for the biosphere flows.

The outputs are impact.<category>.rate (per second), .annual and .per_fu (per functional unit, a stream's mass or a component's mass). Allocation may be none, substitution, a constant factor, mass or economic. The unit scores are inputs of the compiled function, so the derivative of an impact with respect to a score is that activity's inventory amount. A contribution analysis therefore comes with every evaluation. Background uncertainty is not propagated (LCA_BACKGROUND_UNCERTAINTY_NOT_PROPAGATED), and capital goods are outside the foreground (LCA_CAPITAL_GOODS_EXCLUDED).

What ships.

Table	Contents	Rights
gwp100-ipcc-ar6-v1	direct factors, climate change, GWP-100 (kg CO2-eq): CO2 fossil 1, CH4 fossil 29.8, CH4 non-fossil 27.0, N2O 273; CO2 non-fossil 0 under the stated cut-off convention for biogenic carbon	five values from IPCC AR6 WG1 (Forster et al., 2021, ch. 7, Table 7.15, p. 1017), with their citation
test-background-v1	a synthetic three-activity background (electricity, heat, a chemical) and its hand-derived unit scores, for tests and examples	Apache-2.0; not the inventory of any real process

What never ships: anything derived from ecoinvent, and the EF 3.1 characterisation factors. No unit-score table of a real background ships today; an open one (USLCI) would ship only with a recorded public-domain or CC0 licence.

Restricted data. A table whose rights forbid redistribution is used where it lies, in the user's own directory. Reports, replay bundles, fixtures and evidence refer to it by id and SHA-256 only, so its scores never leave the user's project. An impact computed from such a table is a result of the user's licensed use. Together with the reported inventory, it may reveal the scores of the activities used. Every such impact therefore carries the limitation LCA_RESTRICTED_DATA_DERIVED(<table_id>); its value is not redacted.

Building a table: the lca extra

pip install "openflowsheet[lca]"

The extra installs Brightway's bw2data and bw2calc; the repository's scripts/build-lca-env.sh builds the audited environment. It adds an offline adapter, openflowsheet.assessment.lca.brightway:

• build_unit_score_table(project, activities, categories, rights, table_id=...) computes the score of one unit of each activity in a Brightway project you have prepared, and records the versions and database metadata.
• build_direct_factor_table(...) takes a method's factors for the biosphere flows you declare.
• foreground_check(...) scores a foreground activity with Brightway, as an independent check.

The adapter never downloads a database. You prepare the project yourself: ecoinvent under your own licence, or USLCI through the Federal LCA Commons. Declare the table you built in the document under data.tables, with its path and SHA-256. Brightway never runs inside a solve, an optimisation or a replay: without the extra, assessments evaluate from their tables as before, and only the adapter's calls return UNSUPPORTED(LCA_ENGINE_UNAVAILABLE).

Cost and impact in studies and optimisation

Sensitivities. assessment_sensitivity gives dy/dp for assessment outputs at a certified solution, by the chain rule through the flowsheet: dy/dp = ∇ₓy · dx/dp + ∂y/∂p. The flowsheet's own sensitivity dx/dp comes from the studies layer, and revision_sensitivity_host builds its host for any solved revision. An output that does not depend on the state (every item at its floor, say) is labelled STATE_INDEPENDENT. An output next to a regime boundary carries REGIME_BOUNDARY_ACTIVE, because its derivative there is one-sided. The example computes the impact's sensitivity to the boiler temperature.

Optimisation. A study names an assessment output as assessment:<output_id> in the objective or the constraints of the general NLP (the nlp extra; see Studies and optimisation):

• The outputs enter the NLP as grey-box outputs with exact derivatives.
• The held regime's admissibility rows become inequalities.
• A candidate is verified only if re-solving it keeps the regime; otherwise it is refused ASSESSMENT_REGIME_CHANGED (check V7).
• An objective far from unit scale is refused ASSESSMENT_OBJECTIVE_UNSCALED, with the scale to divide by. It is never rescaled silently.

The rules:

• The NLP host is the SYN-001 flowsheet; an NLP over a general revision flowsheet is not offered yet.
• Assessment inputs (prices, coefficients) are never decision variables (UNSUPPORTED(ASSESSMENT_PARAMETER_DECISION)).
• A trust-region study cannot take an assessment objective (UNSUPPORTED(ASSESSMENT_OUTPUT_IN_TRF)).
• KKT_POINT_VERIFIED means a KKT point of the held-regime problem. The NLP holds every regime of the program, which is sound but can be more restrictive than an objective needs.