Mass Balance Accounting Rules for Chemical Recycled Polymers

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Co-processing chemical recycling outputs in existing petrochemical infrastructure relies on physically mixing circular intermediate streams with virgin fossil stocks. When mixed plastic waste is converted through pyrolysis, gasification, or depolymerization, the resulting liquid or gaseous hydrocarbons enter multi-stage refining processes where individual circular molecules become physically indistinguishable from fossil-derived naphtha, gas oil, or ethane. Yield losses ruin simple yield ratios.

Steam crackers operating at coil outlet temperatures between 780 degrees Celsius and 875 degrees Celsius break these hydrocarbon inputs into light olefins, aromatics, heavy fuel oils, and methane gas through high-severity thermal cracking. The main challenge in building a verifiable accounting system stems from the physical transformation happening inside these cracking furnaces.

Pyrolysis oil derived from mixed polyolefins carries high concentrations of olefins, dienes, alkanes, aromatics, and heteroatom contaminants such as organic chlorine, nitrogen, silicon, and heavy metals. Injecting untreated pyrolysis oil directly into a steam cracker’s convection section leads to severe tube coking, furnace fouling, and catalyst poisoning in downstream hydrogenation units. Consequently, operators hydrotreat, hydrocrack, or amine-wash raw pyrolysis oil before blending it with straight-run naphtha.

Each purification step creates process losses, volatile off-gases, and heavy residual fractions that never make it to the olefin furnace. Accounting models assuming a one-to-one mass conversion from raw waste plastic to final polymer resin ignore the thermodynamic realities of chemical refining.

Mass balances calculated at the cracker inlet have to include measured losses across pretreatment units. A typical hydrotreater operating at 320 degrees Celsius to 380 degrees Celsius and 5 to 10 megapascals of hydrogen pressure removes organic nitrogen, sulfur, and halogens while hydrogenating dienes to prevent fouling. The mass balance ledger tracks oxygen removal as water, sulfur as hydrogen sulfide, nitrogen as ammonia, and halogens as hydrogen halides.

In addition, light hydrocarbon gases generated during hydrotreating are sent to the refinery fuel gas system ~ a physical loss of carbon from the polymer supply chain. When 100 metric tons of raw post-consumer polyolefin pyrolysis oil enters a pretreatment plant, the hydrotreated oil output typically yields between 82 and 92 metric tons of cracker-ready feedstock, depending on initial contamination levels.

Inside the steam cracker, the hydrotreated circular hydrocarbon cut undergoes endothermic cracking mixed with dilution steam, yielding a varied product slate. A typical naphtha cracker running at moderate severity converts 100 metric tons of hydrocarbon feed into roughly 30 metric tons of ethylene, 15 metric tons of propylene, 5 metric tons of butadiene, 6 metric tons of mixed butylenes, 18 metric tons of pyrolysis gasoline, and 20 metric tons of combined methane, hydrogen, and heavy fuel oil. The furnace itself makes no distinction between inputs.

The mass balance framework allocates circular carbon attributes across this full product slate. If an operator assigns circular status based strictly on total mass output without adjusting for structural carbon yields, high-value ethylene and propylene absorb inflated circular credits while low-value heavy fuel oils are left out.

Yield losses occurring across pretreatment hydrotreaters reduce raw pyrolysis oil circular carbon conversion efficiencies by eight to eighteen percent prior to furnace entry.

Refinery co-processing gets more complicated when pyrolysis oil is introduced upstream of a fluid catalytic cracking unit or crude distillation unit rather than straight into a steam cracker. In crude unit co-processing, circular hydrocarbons split into light straight-run naphtha, heavy naphtha, kerosene, gas oil, and atmospheric residue based on boiling point distributions. Typically, only the naphtha fraction moves on to the olefin cracker.

The rest flows into diesel pools, heating oils, or marine fuel oil. Accounting frameworks must enforce strict stream isolation or apply physical conversion factors that deduct non-chemical fractions from the circular balance before issuing sustainability declarations.

Chemical depolymerization routes like glycolysis, methanolysis, and hydrolysis for polyethylene terephthalate show very different mass balance characteristics. Solvolysis breaks ester bonds to regenerate monomers such as dimethyl terephthalate, purified terephthalic acid, and monoethylene glycol. Unlike thermal pyrolysis of polyolefins, solvolysis produces high-purity monomer streams with stoichiometric material recovery.

Losses happen mainly during filtration, crystallization, and distillation, as residual dyes, additives, barrier polymers, and mechanical impurities separate out. Mass balance accounting here tracks this exact chemical stoichiometry, incorporating added reactant mass like methanol or ethylene glycol while subtracting distillation residues and glycol purge streams.

Circular naphtha co-feeding fails physical yield accounting when an operator calculates circular ethylene allocation on gross liquid intake rather than net furnace conversion. Volatile light hydrocarbons stripped during storage tank nitrogen purging are often classified as internal process fuels, but treating off-gas losses this way distorts mass balances even when these losses fall within standard operational tolerances for petrochemical facilities.

Allocation

Mathematical accounting models convert raw throughput data into certified product claims when physically separating recycled molecules isn’t economically or technically feasible. Selecting an allocation methodology determines how certified circular attributes move through synthesis operations into final polymer resins. International standards, primarily ISO 22095, define chain of custody models ranging from identity-preserved and segregated systems to mass balance models.

In mass balance systems, physical mixing is allowed, but inventory balance transparency must be maintained through explicit mathematical attribution rules.

Three primary allocation methodologies govern mass balance accounting for chemically recycled polymers: proportional allocation, controlled blending, and free allocation. Proportional allocation distributes circular carbon attributes across all output streams strictly by the mass yield of each product leaving the unit. Controlled blending sets maximum thresholds for credit assignment based on verified physical limits within target product lines.

Free allocation permits assigning circular credits to specific high-value streams regardless of physical yield distribution, limited only by total mass conservation across system boundaries.

The choice of allocation model fundamentally shapes the commercial economics of chemical recycling projects. Free allocation lets a cracker operator assign circular credits from an entire cracking run exclusively to the ethylene fraction, maximizing certified polyethylene volumes for premium packaging markets. Proportional allocation, by contrast, forces credits onto low-value co-products like pyrolysis gas, crack C4s, and pyrolysis fuel oil.

When circular attributes get assigned to fuel gas burned in site boilers, those sustainability credits leave the plastics supply chain permanently.

Regulatory frameworks differ widely on free allocation. European Union debates over the Packaging and Packaging Waste Regulation and the Single-Use Plastics Directive focus heavily on restricting free allocation, favoring mandatory proportional or fuel-excluded models. Under fuel exclusion rules, any portion of co-processed circular feedstock converted into heat, power, or transportation fuel must be deducted from the balance before attributing claims to polymer resins.

Attribution rules ultimately dictate commercial value.

Calculating the mass balance attribution factor for a steam cracker taking in hydrotreated pyrolysis oil follows a structured set of steps across each accounting period. The calculation moves through a set procedural sequence:

1. Quantify Raw Circular Mass Input measured via calibrated mass flow meters at the facility battery limit, adjusted for water content and inorganic sediment.
2. Apply Pretreatment Yield Losses by multiplying raw circular intake mass by the verified hydrotreater mass conversion efficiency coefficient.
3. Establish System Energy Deductions by calculating the lower heating value fraction of circular streams consumed internally for process heat or steam generation.
4. Determine Product Conversion Yields for each chemical species exiting the fractionating train using gas chromatography and mass balance flow indicators over the accounting interval.
5. Subtract Fuel Fractions from the total allocatable circular mass ledger when operating under fuel-exclusion regulatory regimes.
6. Distribute Residual Circular Credits to target resin product batches using the designated attribution equation, logging the transaction in the site sustainability registry.

Mathematical modeling of fuel-excluded proportional allocation relies on strict mass conservation. Let Min represent the mass of purified circular feedstock entering the steam cracker over a monthly accounting period. Let Yi represent the physical mass yield fraction of output component i, where species include ethylene, propylene, aromatics, fuel gas, and heavy residues.

Total output mass Mout equals the sum of individual stream masses mi = Min × Yi. Under fuel-excluded proportional allocation, the allocatable circular mass fraction CFk assigned to a specific chemical output stream k in polymer product group P is calculated using this equation:

CFk = Min × left( fracYksumj in P Yj right)

Where j in P represents the set of all non-fuel chemical intermediate streams. This formulation strictly excludes fuel-directed fractions while maintaining linear proportionality across all chemical intermediates. If an operator applies free allocation without regulatory constraints, CFethylene can equal Min × ηmax, where ηmax represents the maximum theoretical stoichiometry allowed under certification boundaries.

Mass balance accounting standards like ISCC PLUS and the Roundtable on Sustainable Biomaterials enforce strict operational boundaries around allocation. Under ISCC PLUS system rule 203-01, conversion factors must be recalculated at least annually ~ or whenever operational shifts alter process yield baselines by more than three percent. Naphtha pricing often drives these operational adjustments.

A sudden shift in furnace severity, executed to optimize margins between light olefins and pyrolysis gasoline, alters the physical yield slate Yi. If an accounting system relies on historical yield factors during a high-severity run, circular attributes assigned to ethylene will misstate actual circular carbon flow, creating audit vulnerabilities during independent reviews.

An allocation system clause explicitly stating “Circular content shall be attributed to designated polymer product lines via free allocation without deduction for internal fuel gas conversion” violates mandatory EU single-use plastics compliance criteria.

Multi-site allocation draws even heavier regulatory scrutiny. Enterprise frameworks attempt to aggregate circular inputs across geographically separated facilities. Under this approach, circular naphtha injected into a cracker at Site A generates credits transferred on paper to virgin polypropylene produced at Site B, hundreds of kilometers away in another jurisdiction.

Regulatory authorities are increasingly rejecting these virtual transfers, demanding a physical connection between where the circular intermediate enters and where the resin declaration is issued.

Physical connection rules require credit allocation to happen strictly within facilities sharing linked logistics infrastructure, like common pipeline networks or integrated industrial parks. When circular inputs enter a centralized olefin unit, credits can be assigned to any polymer plant directly tied to that cracker’s monomer piping. But as soon as monomer is refrigerated, loaded onto vessels, and shipped to an external polymerization unit, the physical chain of custody breaks unless certified mass balance transport documentation travels with the shipment.

Under section 4.3 of the ISO 22095 chain of custody standard, an organization must set clear physical, operational, and time boundaries for its mass balance system. Resin supply contracts need to reference these boundaries explicitly so attribution claims remain legally valid in jurisdictions with strict environmental marketing rules. Missing or ambiguous boundaries expose buyers to enforcement under national green claims laws and packaging tax assessments.

Credit

Temporal and geographical rules dictate how inventory ledgers handle sustainable volume balances across manufacturing networks. Credit management inside mass balance accounting governs how circular surpluses and deficits are rolled forward, transferred across sites, or retired upon product release. Strict ledger integrity prevents double-counting circular attributes across overlapping regulatory regimes and commercial contracts.

The standard balancing period in chemical recycling is three calendar months, with a maximum rolling window of twelve months under schemes like ISCC PLUS. Within this window, a facility can accumulate circular input credits before producing and shipping certified polymer products. If circular feedstock enters inventory in January, the ledger shows a positive credit balance, allowing the operator to sell certified circular resin against that balance throughout the window.

Rollover limits prevent operators from banking circular attributes indefinitely. If a plant does not allocate accrued credits to finished shipments within twelve months, those credits expire and must be written off the site ledger. This rule keeps companies from hoarding historical inputs to create artificial supply surges or manipulate market pricing.

Audits enforce this through physical reconciliation.

Deficit accounting ~ or short-term borrowing ~ allows a facility to ship circular-attributed polymer before physical circular feedstock actually arrives at the plant. It accommodates real-world delays in pretreatment and shipping logistics. But deficit limits are tight.

Under ISCC PLUS, any credit deficit must be cleared within three months or by the end of the certification cycle, whichever is sooner. If the feedstock fails to arrive in time, the facility breaches certification, triggering immediate cancellation of issued sustainability declarations.

Should Credits Transfer across Geographical Manufacturing Boundaries?

Geographical credit transfers remain one of the most contentious topics in sustainability governance. Global chemical producers often want to pool circular feedstock at specialized refining hubs while transferring the resulting credits to regional compounding plants. However, national regulators are increasingly restricting or banning transfers that cross customs borders or separate regulatory regimes.

The United Kingdom Plastic Packaging Tax requires a direct physical link between where circular feedstock is processed and where final resin conversion occurs. Importing circular-attributed resin pellets into the UK under a mass balance claim from an overseas cracker with no physical connection to the imported batch leaves the importer liable for the full tax of 217.85 pounds sterling per metric ton. UK tax authorities treat unlinked geographic transfers as book-and-claim schemes, not valid mass balance systems.

Centralized database registries track credit creation, transfer, and retirement. When a certified supplier ships circular-attributed polyethylene to a converter, it issues a Sustainability Declaration with a unique transaction number. The buyer’s compliance team must confirm that those credits are officially retired in the certifying body’s registry.

Leaving credits active creates double-counting risks where the same volume could be claimed against multiple orders.

System loss adjustments must happen continuously inside the ledger. Evaporation, tank sludge removal, turnaround flaring, and off-spec production all reduce available circular carbon. When a storage tank holding hydrotreated pyrolysis oil is cleaned and five metric tons of insoluble hydrocarbon sludge are removed, the auditor must immediately deduct five tons from the circular credit pool.

Ignoring these losses inflates credit inventories beyond real yield capacity.

Credit rollover windows exceeding twelve calendar months are systematically invalidated during independent annual ISCC PLUS re-certification audits, resulting in immediate ledger balance adjustments.

Trading mass balance credits separate from physical polymer moves the process from mass balance into a book-and-claim system. Certification standards strictly forbid uncoupled credit trading. Circular attributes must move attached to physical shipments of intermediates or finished polymer from the certified plant.

While individual molecules in a container don’t need a fixed percentage of circular carbon, the physical weight shipped must match the credit mass deducted from the site ledger.

Compounding plants running parallel ledgers for bio-based inputs and chemically recycled polyolefins risk severe contract breaches if deficits in post-consumer circular credits are covered by substituting bio-attributed naphtha credits without customer notification. Although the resulting compound remains chemically identical, unapproved credit substitution invalidates declarations of conformity.

Uncertainty remains around how national authorities will align mass balance ledgers with emerging digital product passports and EPR reporting tools. If European repositories demand real-time, batch-level physical mass tracing while private standards allow twelve-month rolling site averages, resin buyers face serious double-entry accounting friction to keep compliance files current.

Purity

Chemical contaminants in post-consumer plastic waste carry over into liquid intermediates, threatening cracker hardware and food-contact compliance. Mixed waste streams contain non-target polymers, flame retardants, plasticizers, organotins, food residues, and metals. Pyrolyzing these complex mixtures transfers volatile organic halides, silicon, nitrogen species, and heavy metals directly into the crude oil fraction.

Chlorine corrodes furnace tubes fast. Organic chlorine ~ mostly from residual PVC and PVDC in polyolefin waste ~ poses severe operational risks. At furnace temperatures, it decomposes into anhydrous hydrogen chloride gas, which causes stress corrosion cracking in stainless steel convection coils, attacks downstream cold-box metallurgy, and poisons precious metal catalysts in acetylene hydrogenation units.

Because of this, olefin plants enforce strict intake limits, often demanding under 10 milligrams of organic chlorine per kilogram of pyrolysis oil.

Silicon causes another set of severe operational failures. It enters pyrolysis oil from silicone adhesives, sealants, anti-foaming agents, and packaging residues in municipal waste. During steam cracking, volatile siloxanes break down into solid silicon dioxide inside distillation column trays and catalyst beds.

These silica deposits blind active sites, cutting catalyst life and triggering emergency shutdowns. Most steam crackers cap silicon tolerance at 1 to 5 milligrams per kilogram.

Heavy metals poison catalysts irreversibly. Trace elements like lead, arsenic, iron, copper, and vanadium wash into crude pyrolysis oil from pigments, stabilizers, and e-waste. They deposit onto hydrotreating catalyst surfaces, blocking nickel-molybdenum and cobalt-molybdenum active sites.

To manage this, refiners run sacrificial alumina guard beds upstream of primary hydrotreaters. Replacement cycles for these guard beds scale directly with heavy metal spikes in incoming feed batches.

Screening for Non-Intentionally Added Substances (NIAS) is central to food-contact compliance. While chemical recycling breaks polymers back down into basic building blocks, high-boiling oligomers, side-reaction byproducts, and persistent contaminants can survive refining and enter the final resin. Operators rely on GC-MS and LC-QTOF-MS to screen for volatile, semi-volatile, and non-volatile NIAS down to microgram-per-kilogram levels.

EU Regulation 10/2011 sets a general specific migration limit of 60 milligrams per kilogram of food simulant, alongside individual limits on the Union List. For chemically recycled polymers used in food packaging, mass balance paperwork alone isn’t enough. The finished polymer batch requires analytical screening to confirm that unlisted substances do not migrate above 10 micrograms per kilogram ~ the threshold requiring formal toxicological evaluation under EFSA guidelines.

The rules governing recycled plastics shifted significantly under EU Regulation 2022/1616, which covers all recycled plastic food-contact materials. It draws a clear line between novel recycling technologies and established processes. Under 2022/1616, chemical recycling that breaks plastic waste down into basic monomers or intermediates before full chemical resynthesis is exempt from individual process authorization rules, as long as the resulting monomers meet the purity standards of Regulation 10/2011.

Proving chemical equivalence between recycled and virgin fossil monomers requires exact batch characterization. Monomers from depolymerization or hydrotreated pyrolysis oil must meet the same physical and chemical specs as fossil streams. Polymer-grade ethylene, for example, requires purity above 99.95 volume percent, with strict limits on contaminants: methane and ethane under 200 microliters per liter, acetylene under 5, carbon monoxide under 2, and total sulfur under 1 milligram per kilogram.

Downstream compounding brings additional purity checks. When circular base resins are mixed with additives, pigments, slip agents, or mineral fillers, compliance teams must evaluate the entire formulation. Secondary additives have to be accounted for separately in the product declaration.

If circular polypropylene resin contains 30 weight percent virgin glass fiber reinforcement, the mass balance claim must explicitly reflect that circular attribution applies only to the base polymer matrix, not the total composite weight.

Food-contact non-compliance often stems from batch-to-batch variation in raw pyrolysis oil. A sudden load of waste containing flame-retarded e-waste can spike polybrominated diphenyl ether levels in crude oil. If fractionation doesn’t strip out these organobromine species, trace bromine passes through into the final polymer, setting off automated flags during customer audits.

When a medical device converter rejects a 60-ton lot of mass-balance polyolefin resin, high-resolution GC-MS analysis often points back to trace organosilicon oligomers at levels as low as 34 micrograms per kilogram, originating from silicone-lubricated bottle caps in the pyrolysis feed. These oligomers alter surface tension on molded drug delivery components, rendering entire batches unusable for pharmaceutical packaging regardless of valid mass balance certificates.

Dossier

Compliance audit trails demand an unbroken record from initial waste collection receipts down to the finished resin invoice. Maintaining a defensible mass balance system means building a dossier that stands up to regulatory inspectors, third-party auditors, and client compliance teams. Paper claims fail at customs ~ having a certificate won’t clear shipment if underlying docs show gaps in material traceability.

The core of any chemical recycling dossier is the Sustainability Declaration, backed by a Certificate of Analysis tied directly to that delivery lot. Schemes like ISCC PLUS, RED II, and the Roundtable on Sustainable Biomaterials define mandatory data fields for valid documentation. Every transaction involving circular-attributed polymers requires exact document mapping.

To evaluate compliance claims, auditors work through a structured inspection sequence. A standard audit covers six core checks:

1. Verify that the supplier’s chain of custody certificate was active and unexpired on the exact date of polymer manufacture.
2. Cross-check the transaction ID on the Sustainability Declaration against the certifying scheme’s central database.
3. Confirm that the declared allocation model matches the regulatory requirements of the destination market.
4. Recalculate the circular mass fraction against net weights on the commercial bill of lading and invoice.
5. Audit the supplier’s site ledger to verify that total credit retirements over the period don’t exceed physical circular feedstock inputs.
6. Review supporting lab reports to confirm that NIAS screening and monomer purity tests were performed on that specific lot family.

Conflicting waste definitions frequently break compliance chains. Under EU framework directives, waste must meet strict “end-of-waste” criteria before reclassification as a chemical feedstock. If a pyrolysis plant processes waste that hasn’t legally achieved end-of-waste status under local permits, the resulting liquid is still legally waste.

Shipping un-cleared waste across borders without proper consent under the Basel Convention or EU Waste Shipment Regulations can trigger immediate criminal prosecution and container seizures.

Distinguishing pre-consumer from post-consumer waste carries heavy financial weight under national recycled content mandates and EPR schemes. Post-consumer waste comes from packaging or goods discarded by households or commercial users; pre-consumer waste is industrial scrap from primary production. Frameworks like ISCC PLUS accept both streams but mandate separate tracking in the ledger.

Claiming post-consumer credits for resin made from industrial off-spec scrap is fraudulent.

Systematic audit discrepancies between certified mass balance input ledgers and physical production outputs trigger immediate suspension of ISCC PLUS chain of custody certificates.

Data governance in mass balance supply chains is moving rapidly toward ERP system integration. Spreadsheet tracking creates unacceptable risks from typos, broken formulas, and manual overrides. Automated mass balance modules inside ERP systems prevent sales teams from issuing circular-attributed orders if the site credit balance hits zero, eliminating accidental overselling.

A simple rule keeps dossiers compliant: every metric ton of circular attribution on an invoice must trace back to an equivalent ton of verified waste input on a certified ledger. Following this plain rule protects compliance officers from liability under consumer protection laws and greenwashing regulations.

Customs authorities in major import markets are tightening scrutiny on circular resin claims. When circular-attributed polyethylene hits a port of entry, inspectors cross-check the invoice, declaration of conformity, and sustainability declaration. If a supplier relies on multi-site transfers with no physical link to the container, inspectors can reject the circular status, reclassifying the shipment as virgin resin subject to local plastic taxes and penalties.

Dispute

Financial and regulatory exposure spikes when corporate claims outpace statutory accounting rules. Sourcing teams signing long-term off-take contracts for mass-balance polymers take on real risk if regulators later reject the chosen allocation methodology. A shift banning free allocation in favor of fuel-excluded proportional models instantly slashes the certified resin output a supplier can generate from a batch of pyrolysis oil, upending contract economics.

Supply contracts for circular polymers need explicit language covering regulatory changes, certification suspensions, and delivery failures. Agreements without remedies for mass balance non-compliance leave buyers exposed to plastic taxes and reputational fallout. Sourcing teams have to build specific performance and compliance clauses directly into purchase agreements.

Contractual terms must explicitly safeguard system integrity. Standard force majeure clauses won’t shield suppliers if certification is revoked during annual audits over accounting errors. Contracts should state that losing certification is a material breach, allowing the buyer to terminate immediately, reject shipments, and recover any resulting tax liabilities or fines.

Penalties for misrepresenting circular content are climbing globally. Under UK Plastic Packaging Tax regulations, applying an incorrect tax rate based on non-compliant mass balance claims triggers heavy sanctions. Authorities impose civil penalties equal to 100 percent of the underpaid tax plus compounding interest, alongside potential criminal charges for tax evasion.

Connecting compliance directly to tax exposure makes document control non-negotiable.

Enforcement of green claims regulations in the EU brings additional exposure. Directive 2024/825 on empowering consumers and the proposed Green Claims Directive require explicit claims ~ including circular percentages ~ to be backed by independently verified accounting methodologies. Marketing a product as “100 percent chemically recycled” based on free allocation when the physical resin holds almost no circular carbon exposes brands to class-action lawsuits and regulatory sanctions.

Gaps between supplier claims and regulatory rules frequently spark commercial litigation between converters and resin producers. If a converter buys certified mass-balance polypropylene to meet a customer’s 30 percent recycled content requirement, and an audit later invalidates the supplier’s allocation model, the converter lands in default. Unable to source replacement material, they risk canceled contracts and damage claims for lost sales.

Mitigating risk requires clear warranty indemnification clauses in purchase specs. Sourcing contracts should require suppliers to maintain active certification under a major chain-of-custody standard, submit to third-party audits on request, and provide written notice within 48 hours of any regulatory inquiry or audit finding. Contracts must also specify which allocation model is authorized for circular calculations.

When resin producers use free allocation to assign circular credits while 22 percent of the underlying pyrolysis oil feed goes into internal refinery fuel gas, tax audits can disqualify the allocation method retroactively under national packaging laws. Regulatory authorities then recalculate circular content using a fuel-excluded proportional model and issue back-tax assessments against the importing converter.

Discrepancies stop production cold. Operations freeze when authorities issue stop-sale orders on non-compliant polymer inventory. Establishing strong internal compliance protocols protects buyers from regulatory default and ensures that every ton of circular-attributed resin arriving at a plant rests on a solid, mathematically defensible mass balance foundation.