NTROPYX and the entropy of combustion.

This note first shows that lowering the fuel’s state entropy at unchanged enthalpy would raise its exergy by only about 2% of its lower heating value, even at the unreachable limit of zero entropy. Fully converted into work, this ceiling corresponds to a fuel-consumption reduction of 3.4 to 6.1% for four pure reference hydrocarbons and a brake efficiency of 30 to 50%, slightly more for a commercial fuel.

It then states the claims of Virgo Global Energy SA on NTROPYX: three of them (A1, A3, A4) in refutable form, the fourth (A2), on the nature of the intervention, without support. Since the claimed effect concerns conversion (A1), the note states A3 and A4 restricted to composition and property analyses, excluding ignition quality.

Finally, it describes the standardised methods and the engine-bench protocol that allow an independent laboratory to confirm or refute them.

The note describes neither the nature of the intervention, nor its implementation, nor its conditions of application: these remain industrial secrets. The references cited cover the physical problem and the method of proof.

Each table, figure and claim carries its status: literature for a published fact, reproducible calculation for a result the reader can recompute from public data, Virgo claim for what the company asserts and this note does not demonstrate, unsupported for a claim this note can neither verify nor refute.

The engine studies in Table 1 rank combustion first among exergy destructions [3–5]; Alkidas ranks it first among irreversibilities after heat transfer [6]. Their methods and bases differ.

At unchanged enthalpy, a drop Δs in state entropy would raise the fuel’s exergy by T₀·|Δs|. The absolute ceiling of this route corresponds to s → 0, a limit out of reach at ambient temperature. Table 2 quantifies this ceiling for four pure reference hydrocarbons, from NIST data [8].

This unreachable ceiling stays of the order of 2% of the LHV, while adiabatic combustion alone destroys 5 to 25% of the reactants’ exergy [1] (Figure 1). A reduction in fuel consumption, however, relates to useful work, not to the LHV.

A drop in the fuel’s state entropy therefore cannot explain a consumption reduction larger than E / (η + E), where η is the brake efficiency measured at the operating point chosen as primary criterion. Chemical energy per kilogram is bounded separately by calorimetry (Methods). The other lever is the conversion itself: the exergy it destroys, T₀·S_gen, and the exergy lost with the exhaust, unburnt fuel and cooling.

ISO 4259-1 defines repeatability r and reproducibility R as limits on the difference between two single, independent results obtained on identical material in the normal and correct operation of the method: a difference due to chance alone exceeds them with a probability of only 5%. r applies under repeatability conditions (same operator, same apparatus, same laboratory, short interval); R applies between laboratories [14]. Both specifications refer to ISO 4259-2 for interpreting results [15].

Two results whose difference stays below r or R are compatible with the same true value at the resolution of the method; they do not prove the samples identical, since the true value is never established exactly [15].

Over N pairs analysed in one laboratory, the mean difference is judged by a paired test. With equal dispersion, this test is finer than r from about four pairs, and clearly finer from about eight. Concluding that there is no difference requires an equivalence margin declared before measurement and an equivalence test; a non-significant result is not enough.

Bomb calorimetry [16] measures the heat of combustion of each batch. Treated and control fuel are compared in the same laboratory, preferably by ASTM D4809, with at least three repeats per batch, through the confidence interval of their difference and a margin m set in advance, expressed as a fraction of the LHV. If this interval lies within the margin, a mass-consumption reduction larger than m / (η + m) cannot be attributed, at the chosen confidence level, to extra chemical energy per kilogram.

Taken together, this bound and the state-entropy bound of the Entropy section exclude, on the fuel side, a mass-consumption reduction larger than (m + E) / (η + m + E). Consumption referred to energy (Protocol) already neutralises a measured LHV difference.

Normative framework.

Engine power and fuel consumption are declared under ISO 3046-1:2002 [18]. The steady-state modes of ISO 8178-4:2020 provide a recognised grid for fixing the measurement points of a laboratory campaign in advance [19]. On vehicles, SAE J1321 measures the change in fuel consumption of a given heavy vehicle after a modification, with a control vehicle running in tandem [20]; SAE J1526 compares vehicles with one another and must not be used to assess a component change [21].

Measurement.

Fuel flow is preferably measured by direct gravimetry, whose regulatory linearity criteria are stricter than those of a flow meter [22]. A comparison between two benches adds their calibration errors to the measured difference; the difference is established by a paired comparison on the same instrumentation, where common calibration errors cancel.

The uncertainty budget follows the GUM [23]. Consumption is referred to energy (MJ per kWh) using the measured LHV of each batch, and the uncertainty of that measurement enters the budget. The exhaust carbon balance [24] checks the paired difference measured by gravimetry, within a tolerance declared in the protocol: it detects a gross error; it does not replace the gravimetric measurement.

Experimental design.

The protocol and the analysis plan are filed before any measurement: operating points, primary criterion, claimed size, equivalence margin, decision thresholds. A homogenised parent batch supplies treated and control batches in equal numbers, at least three of each. Apart from the intervention, treated and control batches are handled identically.

A third party randomly assigns and codes each batch as treated or control; the terms of application of the intervention, witnessed by that third party, are kept in a confidential annex. Operator and analyst remain blind to the code until the data are frozen. The batch is the statistical unit of the primary criterion: the number of batch pairs is sized with Table 4, using σ_d measured in an A-versus-A campaign, between-batch variability included.

Measurements alternate treated and control fuel in a balanced crossover design, for example ABBA, in a randomised order; fuel changeover conditions and the carry-over test are fixed in the protocol. The contrast (B₁ + B₂ − A₁ − A₂)/2 cancels any linear drift of the bench. The engine control unit is frozen, or all its parameters are logged, since an adaptive controller can create or mask a difference. A preliminary A-versus-A campaign, on control batches only, estimates the dispersion of the differences and checks the false-positive rate.

Low coefficients of variation have been obtained on a chassis dynamometer, over a drive cycle, by a laboratory that controlled its noise factors [25]; they do not transfer as such to an engine bench at steady state.

The number of batch pairs is fixed from σ_d measured in an A-versus-A campaign, between-batch variability included: read the ABBA column with c replaced by σ_d, or the AB column with c replaced by σ_d/√2; the per-measurement c only sizes the number of runs per batch. Demonstrating equivalence is sized separately, with n = ((t_1−α/2 + t_1−β/2)·σ/δ)², where δ is the equivalence margin; the protocol keeps the larger of the two numbers.

Diagnostics.

Beyond consumption, the bench measures the quantities the balance requires: indicated work, exhaust, cooling, regulated emissions. At equal heating value, the first law requires the sum of the measured terms to change by as much as the energy of the fuel consumed; the protocol checks this consistency within the closure uncertainty of the balance, declared in advance. The paired exergy balance then splits the change between exergy destroyed and exergy lost (A1).

Refutation criterion.

The claimed size Δ, as a percentage of energy-specific fuel consumption at the point or cycle declared as primary criterion, is handed over in writing when the protocol is filed; the equivalence margin is strictly smaller than Δ. This size is refuted if the upper bound of the 95% confidence interval of the reduction is below Δ; if its lower bound is also positive, an effect exists, smaller than claimed.

Claim A1, in the form declared in the protocol, is refuted if this 95% interval lies entirely within the equivalence margin. An interval containing both zero and Δ leaves the result inconclusive; this case remains possible with the sizing of Table 4 and allows neither a conclusion nor an extension of the campaign not provided for in the protocol.

The supplier accepts in writing, before the campaign, that a result meeting the refutation criterion counts as refutation. The protocol requires a second independent laboratory to reproduce the effect and all data to be published, unfavourable data included.

Precedents.

The US EPA states that its evaluation programme for aftermarket retrofit devices neither approves nor certifies any product [26], and that most of the devices evaluated in previous years had a neutral or negative effect on fuel economy or emissions [27]. The Federal Trade Commission requires scientific substantiation of any fuel-saving claim [28].

US federal regulation (40 CFR Part 610) lists the validity criteria for data submitted by a manufacturer, including disclosure of all results, positive, negative or inconclusive, and the independence of the laboratory [24]. The protocol above adopts these requirements.

A3 and A4 are stated only in restricted form, for composition and property analyses, excluding ignition quality, which belongs to conversion (A1).

This note does not repeat the bench measurements published elsewhere; any attached report must state the methods, the number of batches and pairs, the equivalence margin and the independence of the laboratory.

The exergy-destruction percentages of Table 1 come from different methods (calculation, simulation, experimental data, measurements) and different bases (reactant exergy, fuel exergy, total losses, lost power, and one basis not stated by its source). A complete breakdown of the exergy of a real engine is not given here, for lack of a verified source.