Errors in Boiler Efficiency Standards

This paper presents both criticism and suggested changes to boiler efficiency standards associated with fossil-fired steam generators. These standards include the widely used ASME PTC 4.1 and DIN 1942, and their replacements ASME PTC 4:2008 and the European EN 12952-15. For these standards it is useful to review both old and new. The chief criticism lies with inconsistent application of thermodynamic principles. Conceptual errors are made with reference temperatures and with shaft powers. This paper advocates for the Input/Loss Method. When using computed fuel flow as a touchstone, it becomes obvious that arbitrary use of reference temperatures and/or use of capricious energy credits cannot produce a consistent (absolute) computed fuel flow. Efficiency, calorific value and fuel flow must have fixed definitions concomitant with a system’s useful energy flow. Thermodynamics is not an arbitrary discipline, the computed fuel flow of a system must describe the actual needs. Boiler efficiency requires consistent treatment, producing consistent and absolute fuel and emission flows. Boiler efficiencies and associated calorific values have obvious standing when judging contractual obligations, for thermal performance monitoring, and for confirming carbon emissions. Note that a 0.5 to 1% change in efficiency may well have significant financial consequences when testing a new unit, or the on-going costs associated with fuel and carbon taxes. This paper demonstrates that errors greater than 2% are entirely possible if following the current standards. This paper appeals to the resolution of efficiency at the 0.1% level. The power plant engineer is encouraged to read the Introduction and Summary & Recommendations sections while the thermodynamicist is requested to throughly review and critique the mid-sections. The author hopes such reviews, at a minimum, will advocate for more open discussion. PAPER-80.WPD, Rev 30E. NOMENCLATURE Note that much of the following nomenclature is taken from Exergetic Systems’ Input/Loss Method and its steam generator simulator, EX-FOSS (Lang, 2012a). Molar Quantities Related to Stoichiometrics bA = Moles of water in combustion air, moles/base bZ = Moles of water in-leakage, moles/base bS = Moles of pure sorbent injected, moles/base nj = Moles of product j at boundary, w/o leakage nIdeal-j = Moles of ideal product j, without leakage nS-H2O = Moles of sorbent product hydrate at boundary Nk = Molecular weight of substance k x= Moles of fuel/100 moles dry product (base) zS = Moles of H2O per sorbent product zH = Moles of hydrogen per gaseous fuel "k = Moles of As-Fired fuel constituent k $ = Molar ratio of air leakage to combustion air (S = Moles of excess sorbent per pure sorbent bS. Quantities Related to System Terms CV = Calorific Value HBC = Firing Correction relative to TCAL, )Btu/lbAF HHV = Fuel gross CV at constant volume, Btu/lbmAF HHVP = As-Fired gross CV corr. for constant pressure HNSL = Non-Chemistry & Non-Stack Losses. HPRAct = Enthalpy of Products, actual As-Fired. HPRIdeal-XX = Enthalpy of ideal products at TCAL, see “Subscripts” for XX, Btu/lbmAF. HRXAct = Enthalpy of Reactants, actual As-Fired. 1 Copyright © 2012 by ASME HRXCAL-XX = Enthalpy of generic reactants at TCAL. J = Energy conversion, 778.16926 ft-lbf/Btu LHV = Fuel net CV at constant volume, Btu/lbmAF LHVP = As-Fired net CV corr. for constant pressure mAF = As-Fired fuel mass flow rate, lbmAF/hr QWF = “Useful Energy Flow Developed” to working fluid from combustion gases, Btu/hr R = Gas constant, 1545.325 ft-lbf/lb-mole/R TCAL = Calorimetric temperature, F TRA = Ambient air temp., ref. for PTC 4.1 and 4.4, F TStack = Exit (Stack) boundary temperature, F WID = Fan powers regards outlet streams, Btu/hr 0A = Boiler absorption efficiency, unitless 0B = Boiler efficiency, unitless )HA 0 -CAL-CaSO4 = Heat of Association of CaSO4 hydrates )HD 0 -CAL-Sorb = Heat of Disassociation (e.g., Trona) at TCAL, )Btu/lb-mole. )HF 0 -CAL-k = Heat of Form. of k at TCAL, )btu/lb-mole )Hf-CAL-H2O = Heat of Formation, sat. liquid at TCAL )Hg-CAL-H2O = Heat of Formation, sat. vapor at TCAL )HL/H = Enthalpy correction for net CV, )Btu/lbmAF )HV/P = Enthalpy correction for volume, )Btu/lbmAF )PVL/H = PV energy correction from net to gross CV )UL/H = Internal energy correction from net to gross. Subscripts AF = As-Fired fuel (wet with mineral matter). CAL = Calorimetric, as in calorimetric temperature. CF = Calorimetric Fuel (wet with mineral matter) referenced to dry O2 at TCAL. CM = Calorimetric Fuel with Moist Air (and other reactants) all at TCAL. HHV = Gross calorific value, higher heating value. LHV = Net calorific value, lower heating value. INTRODUCTION TO STANDARDS This section discusses boiler efficiency standards and summarizes their problems. No present boiler efficiency standard addresses calorimetric fundamentals. Although more fully explained in subsequent sections, this statement means that the method of determining the energy content of a fossil fuel dictates the method by which the performance of that fuel is judged when burned to make thermal power. The practical justification for such a statement lies with fuel water plus fuel hydrogen (thus product water). Boiler efficiency as taught by industrial standards using an Input-Output Method is fundamentally: 0B = [Useful Energy Flow Developed] / [Fuel Energy Flow Supplied] (1) Although a simple expression, historically there are any number of interpretations of the terms comprising its numerator and denominator. For example, ASME PTC 4:2008 states (§3-1.2) that one may compute over a dozen different values of boiler efficiency using various interpretations of the same data set! This paper argues there is only one method, a method leading to a consistent and unique computation of fuel and emission flows. Definitions must be explained concerning both a steam generator as a “system” and then its “state”. Applied thermodynamics is defined by a boundary; most boiler efficiency standards err with their boundary assumptions. The boundary of a fossil-fired steam generator being studied for thermal efficiency does not encompass all physical equipment, but rather the constraining volume of its interacting fluids, for example: fuel conveyance, combustion gas confinement, the inside of air ducts and working fluid pipe IDs. This boundary derives from the principle that the thermal efficiency of a steam generator only addresses how the As-Fired fuel interacts with its gas/air/working fluids. Extraneous equipment has no impact on boiler efficiency if not directly affecting the fuel’s interaction with the gas/air/working fluids. This definition is consistent with the concept of the fuel’s calorific value. It immediately excludes such equipment as pulverizers, steam driven pumps, recirculation pumps, and the like. ASME PTC 4 and DIN 1942 would suggest that a higher pulverizer shaft power will increase boiler efficiency. However, pulverizer power has no impact on the interaction of fuel and gas/air/ working fluids (the grinding of coal is emulated during lab preparation of samples). A recirculation pump has no impact on fuel heating the working fluid. The metric boiler efficiency must solely guide the engineer towards reduced fuel flow and CO2 emissions while making adequate steam. Shaft powers are monitored through house load. A system in equilibrium with its medium, from which no power is extracted, defines its dead state (Keenan, 1941). For an active steam generator, having the potential for thermal power, the condition of its dead state is often confused with its “reference state”. The dead state limits how much potential power is possible, an ultimate limit to actual output, the numerator of Eq.(1). For steam generators, the dead state should be taken as the coldest medium associated with the local environment. For an actual steam generator, its thermal power as derived from a given fuel flow are absolutes, established by considering unambiguous differences between reference states (main steam less feedwater, etc.). In engineering, all energy levels are relative to a chosen reference state. Text books will argue that reference states are arbitrary, a simple enough concept when dealing with a single fluid. Water 2 Copyright © 2012 by ASME properties for example, normally referenced to the triple point, could be referenced to the boiling point at 1 atmosphere, resulting in the same Useful Energy Flow Developed of Eq.(1). However, for this discussion we are not concerned with the numerator of Eq.(1), but rather treatment of the denominator. Note that although Eq.(1) expresses an InputOutput approach, conversion to specific values immediately invokes a Heat Loss Method (herein termed the “Energy Balance Method”); but the two must produce identical efficiencies. The argument here is for absolutes in the denominator, that the “arbitrariness” of reference states can not be defined by the casual analyst but, indeed, is established when defining the energy content of the fuel. The technician determining calorific value of natural gas may be required run his/her calculations using a national standard, e.g., 0.0C for France, 15C for Ireland and the U.K., 25C for Germany, 60F (15.56C) for North America, etc. (see ISO 12213-3:2006, ISO 13443:1996 /Cor 1:1997, and AGA Report No. 3), or another yet. For solid and liquid fossil fuels the reference temperature may be viewed by some as arbitrary, but in fact is also set by the technician running the bomb calorimeter, not the casual analyst. For an adiabatic or isoperibol bomb calorimeter, its reference is the “calorimetric temperature” at which the bomb’s water jacket is kept in an equilibrium state. It is well understood that calorific values vary with temperature. Natural gas evaluated at 0.0C is different than that at 25C, a bomb run at 50F will yield a different value for the same coal as one run at 120F. Because AsFired conditions are relative to a reference temperature, boiler efficiency will vary with reference temperature. That said, the objective of this paper and the proposed objective of all efficiency standards is an absolute understanding of a steam generator’s thermal performance, the fuel it consumes, consistent with a defined boundary and actual emission flow. If Eq.(1)’s numerator is an absolute measure of thermal power, we can not allow an arbitrary denominator (implying an arbitrary fuel flow). However, recognizing that boiler efficiency varies with temperature is no justification for standards advocating relative efficiencies, but rather, efficiency equations which properly correct for reference temperature. The test for absolutes is computed fuel flow, a fuel mass flow which justifies the developed output. A temperature dependent CV leads to a temperature dependent boiler efficiency, but corrected to the actual firing conditions and thus producing consistent, and absolute, fuel & emission flows. The act of choosing a calorimetric temperature to either compute (for gaseous fuels) or to measure (for solid and liquid fuels) a calorific value does not give the casual analyst the liberty to then choose another for reference. For any multi-fluid system, only a consistent thermodynamic reference state can be considered or the laws of thermodynamics will not be satisfied. It is not acceptable to assume one energy level for the fuel, another for the working fluid, another for the combustion gases, another for the dry combustion air, and yet another for moisture in the combustion air. As examples: the air’s nitrogen and fuel make combustion products; sorbents, tube leaks and soot blowing add to products; the air’s moisture affects products; and combustion products heat working fluid. ERRORS, WHAT ERRORS ? Addressed are three types of errors and uncertainties involving thermodynamic concepts, procedural problems, and measurements which impact efficiency: 1) System conceptual errors are made when: a) mis-using reference temperatures; b) when treating certain system components, especially shaft powers (i.e., “credit” terms); and c) when not understanding the energy of reactants. 2) Procedural errors are made which impact thermodynamics in a generic manner; e.g., the definition of dry air, use of consistent molecular weights, enthalpic references of fluids which are mixed within the system, thermodynamic properties, etc. 3) Measurement uncertainties such as those found in the lab regards fuel chemistry and CVs, certain loss terms (HNSL), and uncertainties in plant data which affect QWF and thus back-calculated fuel and emission flows. For all of these, the author argues for an accuracy criteria at the ±0.1% )0B level. What this means is that system concepts and procedures affecting a computational efficiency at $ ±0.1% )0B must be included. This is not to say all system concepts and procedures are to be understood at this level, but are to be included given a computational sensitivity thus demonstrated. Although coal analysis between laboratories should lie within ±100 )Btu/lbm (±233 )kJ/kg), modern bomb calorimeters are quoted as having 0.1% )HHV/HHV repeatability. It is this fact which adds imperative. The author’s EX-FOSS program allows for an error calculation based on stoichiometric inconsistencies (as-tested emissions versus assumed fuel chemistry), which if > ±0.1% )0B, and unexplained, results in repeating the test. It is noteworthy that ASME PTC 4 (§5-7.3) expresses this same opinion, that “a convergence limit of 0.1% efficiency is sufficient”. A clear example of the mis-use and capricious nature of current boiler efficiency standards is witnessed by the comments made at a 2009 TAPPI conference. The conference authors appear to be searching for a standard which would produce the highest efficiency to minimize “taxation and legislative problems”; their comments are stunning (Vakkilainen & Ahtila, 2009). 3 Copyright © 2012 by ASME Set out below are errors made in traditional boiler efficiency standards. This list is by no means complete, but concentrates on “credits” and reference temperatures. ASME PTC 4.1 (United States): This code was superseded in 1998 by ASME PTC 4. Although PTC 4.1 is no longer an ASME code nor an ANSI standard, it is included here given its continued use and historic precedence. §1.04.5, shaft powers from pulverizers and circulating pumps are included as energy credits. §7.2.8.1, reference temperature is taken as the air’s ambient temperature (TRA). §7.2.8.1 and Appendix, nitrogen content in dry air is fixed at 76.85% (an assumed weight fraction). §7.3, “heat credits” appear in the numerator and denominator. The FD and ID fans are considered outside the thermodynamic envelope. The standard’s Input-Output and Heat Loss Methods are inconsistent (see the DIN 1942 discussion). This standard applies to any fossil fuel. ASME PTC 4 (United States): The original 1998 release was superseded with a 2008 release to which the following are referenced. §5-5, the defined fuel energy flow ignores the as-fired state (if different from 77F), this would especially destroy any accuracy of gas-fired efficiencies given typical firing from 45F to 60F. §5-7, “fuel efficiency” is PTC 4’s preferred method, fuel energy is not corrected to the as-fired. §5-7.1, “credits” appear only in the numerator. §5-8.1, the conversion from constant volume to constant pressure ignores nitrogen and oxygen bound in the fuel, oxygen is an important term when considering high oxygenated fuels (such as PRB); such PTC 4 conversion is not temperature dependent. §5-9, sorbent energy flows are normalized to the as-fired fuel, which ignores unique sensible energies. §5-9.5.1, §5-9.5.2, §5-11.1, §5-11.4.1, etc., oxygen content in dry air is fixed at 20.95% (Ar and CO2 are not included, molar air/oxygen = 3.7733) . §5-11.2, psychrometric properties should be extended to -40F, as applicable for steam generators found in norther climes; caution should be exercised when using reference psychrometric temperatures; the standard employs a water to dry air ratio of 0.6220 (i.e., textbook), PTC 4 data would suggests 0.6398. §5-13.1, the reference temperature is set constant at 25C. §5-15.5.1 and §5-15.5.2, shaft powers are included as energy credits. §5-19.8, the enthalpy of natural gas should be computed, and is easily done given known properties. §5-19.11 and §5-19.12, “average” combustion gas properties are erroneously employed, such use is hardly justified given the wide applicability this standard is assumed to have; the referenced 1971 JANAF/NASA properties are out-of-date (other citations, appearing political, are quite current). The FD and ID fans are considered outside the thermodynamic envelope. The 2008 release (unlike the 1998 version) relates to coal-, oiland gas-fired steam generators. DIN 1942 (German): This code was superseded by DIN EN 12952-15:2004. The following nomenclature and comments are specific to DIN 1942 (Feb. 1994). §6.2, the reference temperature (tb) is set at 25 C. However, “other temperatures may be agreed upon” by correcting the net calorific value with fuel, air and combustion gas sensible heat terms. §6.3.2.3, so-called “heat credits” (denoted as QZ) includes shaft powers from pulverizers, recirculating gas fans, working fluid circulating pumps and “power from any other motors”. §6.4, DIN 1942 employs the QZ term in both its InputOutput and Heat Loss Methods. In DIN 1942: QN is the useful output (herein QWF); QZB is the fuel energy (mAFLHVP); and QVtot is the loss term. 0B-LHV = QN (DIN-144) QZB + QZ 0B-LHV = 1.0 QVtot (DIN-147) QZB + QZ For Eq.(DIN-147) an increase in QZ will always increase 0B-LHV provided QVtot > 0.0. However, the same increase in QZ will always decrease the Input-Output efficiency of Eq.(DIN-144), thus guaranteeing inconsistent computed fuel flows. This same conundrum exists with PTC 4.1, with PTC 4 and its “gross efficiency” definition, and with other standards. §6.3.4.1, oxygen content in dry air is fixed at 20.938% (Ar is not included, air/oxygen = 3.7760). Draft European Standard: The following comments reference prEN 12952-15 of Nov. 1999, which is now issued as EN 12952-15. The draft and the new closely follow DIN 1942, employing its nomenclature and general methods. §7.2, the reference temperature (tb) is set at 25 C, but “other temperatures may be agreed upon” which corrects heat credits as done in DIN 1942. §7.3.4.1, oxygen content in dry air is fixed at 20.938% (Ar is not included but apparently CO2 is included, 4 Copyright © 2012 by ASME air/oxygen = 3.7760). §7.4.3.2, energy credits appear only in the denominator. The ID fan is considered outside the envelope; the FD fan may be considered inside the envelope. This standard applies to any fossil fuel. BS 2885 (British): The following comments reference BS 2885:1974; which has been superseded by the British Standards Institute (BSI) issue of BS EN 12952-15:2003 (basically the revised DIN 1942). §2 (bottom), all fuels shall use a “calorimetric temperature” of 25C. Section E and Section F, Item 434, the standard expects that flue gas nitrogen is to be measured, thus dry air is not specified. Items 708, 804 and 907 (and Notes), the reference temperature for sensible heats in the dry flue gas, moisture in the combustion air and fuel is the combustion air temperature (per ASME PTC 4.1), not 25C as its stated “calorimetric temperature”. Item 901 (and Notes) regards “Method A” (InputOutput) it does not consider energy credits; it invokes a simple “fuel efficiency” in which the CV bears no Firing Correction. However Item 902, invoking the Heat Loss Method (“Method B”) considers the “heat equivalent of auxiliary power” as a loss, carrying the same sign as the radiation & convection loss. Such inconsistencies will result in impossible differences in computed fuel flows. Energy credits (shaft powers) appear only in the denominator of its Heat Loss Method. This standard applies to any fossil fuel. Standard for Recovery Boilers Used in the Pulp & Paper Industry (United States): This standard was prepared by the Technical Association of the Pulp and Paper Industry (TAPPI,1996) and was based on a 1993 draft of ASME PTC 4 using its energy balance method; however there appears to be some controversy in Europe when applying this standard (Vakkilainen & Ahtila,2009). §0 (page 4), the reference temperature is set at 77F. §7.1.4.1 and §7.1.4.3, oxygen content in dry air is fixed at 23.14% (a carry-over from ASME PTC 4.1, but used as a molar ratio and is not correct) . For recovery boilers, burning black liquor fuel, is it common industrial practice to correct the measured heating value for Heats of Formation for the reduction of Na2SO4. Such corrections address the difference between ideal combustion products associated with a bomb calorimeter versus actual products associated with further reduction of certain black liquor compounds. Such corrections are thermodynamically inconsistent, as the calorific value is corrected with a computed )HR term: (HHVP )HR + HBC). This standard applies only to recovery boilers burning sodium-laced black liquor. CONCEPTUAL AND PROCEDURAL ERRORS Standards have no monopoly on conceptual errors. Previous versions of the Input/Loss Method did not properly recognize energies of reactants; it used a complicated set of corrections which now appear frenetic. The present approach (this Rev. 30) greatly simplifies when developing Eqs.(3) thru (4C). They demonstrate that gross and net reactant and product terms are identical. Most observed conceptual errors are associated with product water, formed from the fuel’s entrained water and from bound hydrogen. Thus, conceptual errors associated with the calorimetric temperature for highly energetic fuels, with low product water, are slight and typically do not meet the 0.1% )0B criteria. However, conceptual errors associated with fuels producing 10% or more product water (such as high volatile B bituminous (hvBb), to PRB coal, to the lignites and peat) are appreciable, ranging from 0.2% to the 0.8% )0B level assuming a 18 )F (10 )C) change in calorimetric temperature. Such errors derive from assuming a reference temperature for boiler efficiency calculations, while the calorific value was determined at another. For example, a 0.5% )0B error is made for Powder River Basin (PRB) coal when 25C is the assumed reference, while the CV was determined at 35C. Conceptual errors may also exist when not recognizing the sensitivity of the ratio of ambient oxygen to dry air. A change of ambient oxygen from 21% to 20.5% represents a decrease of 0.253% )0B-HHV for a typical PRB fired unit assuming a constant Stack O2; a 1.128% )0B-HHV decrease for 19% ambient. Of the steam generators tested by the author, typically 1 in 10 were found to have degraded ambient oxygen levels typically caused either by a weather inversion, still air or flue gas leakage into FD Fans. The NASA (1976) standard ambient oxygen is 20.9476% at sea level. Conceptual errors are also made when following the current standards (low water fuels aside) which involve the treatment of shaft powers, discussed in the next section. Procedural errors are made by not adhering to the latest thermodynamic standards. The author finds it rare that any two standards use the same molecular weights. Inconsistency is present in air psychrometric properties (see ASHRAE procedures, discussed below). One would expect to use the same fundamental methods when evaluating a combustion turbine versus a conventional steam generator (ASME PTC 22 assumes 60F as a base, conversion is allowed per its §4.12, versus ASME PTC 4). Precise methods offer little comfort if laboratories 5 Copyright © 2012 by ASME cannot record CVs with at least repeatability, if not also with accuracy. Although the 0.1% )0B criteria is meet in repeatability when using the modern bomb calorimeter, we must remember that variability found in CVs (say from grab sampling) may, indeed, be quite real. Standards must present a practical statistical treatment of multiple lab chemistries and CVs, as would be associated with testing a coal-fired unit. It is noteworthy that ASME PTC 4 devotes its Section 7 to uncertainty analysis. Although Section 7 is clearly amenable for academic pursuits, it is not something most power plant engineers are going to place under their pillows. The coal-fired industry needs procedures, fully integrated within the standards for evaluating a test: 1) Consistency of individual as-tested fuel chemistries, rejecting any CV given an outlying chemistry [one solution is to apply techniques afforded in the OxyHydrocarbon model (see Lang & Canning, 2007)]; 2) Define a steady state period by examining time plots of feedwater and fuel flows (over at least 15 min.), the averaged data resulting in QWF [although such plots have been used by the author and his colleagues for years, the precedence for this is 125 years old! (Kent, 1884)]; 3) Tolerance on a proper Energy Balance Method efficiency, as based on items only affecting calorific value (i.e., sampling) and QWF; and 4) A consistent boiler efficiency, allowing the calculation of an absolute fuel flow. CONSISTENT BOILER EFFICIENCY The temperature used to operate a bomb calorimeter, or to compute a gaseous CV, is the beginning point for developing consistent thermodynamics. Calorific values for solid or liquid fuels are obtained either by adiabatic or isoperibol bomb calorimetry following ASTM D5865 or ISO 1928:1995(E). An adiabatic bomb calorimeter detects the gross energy liberated from ideal combustion, burned in pure O2, by maintaining a constant water bath temperature about the bomb, which defines the calorimetric temperature, TCAL. An isoperibol bomb calorimeter detects the net energy liberated by accurately monitoring the water bath temperature, its resultant average value being TCAL. Many modern bomb calorimeters are automated to run at a programmable TCAL. The author has found various labs in North America and Europe using 27C (80.6F), 28.5C (83.3F), 30C (86F) and, commonly, 35C (95F). Up thru 2007 the author could not find any laboratory in North America or in Europe determining coal CVs at 25C, the reference for most standards! Boiler efficiency should be a simple reflection of what the technician, determining CV by either calculation or measurement, has produced. The calorimetric process begins with reactants, the combustion event, and ends with ideal products of CO2, SO2 and H2O. This process is path dependent, the traditional path is to maintain an essentially constant temperature of the calorimeter’s heat sink. When mimicking this calorimetric process when applied to a steam generator, the thermodynamicist need only account for: losses associated with actual product streams; all reactants (moist air, sorbents, leakages, etc.); and sensible heats accounting for the fact that reactants may not be fired at the calorimetric temperature. This then is the conversion efficiency of burning fuel, delivering a “Useful Energy Flow Developed” from combustion; i.e., its interaction with gas/air/working fluid. If consistent fuel and emiussion flows are to be computed from boiler efficiency, QWF must only reflect heating from combustion gases. The execution of these concepts is a bit more involved. The definition of gross calorific value (higher heating value) as based on a bomb calorimeter is the energy liberated from products formed relative to the calorimetric temperature, this includes, of course, the water produced as reduced to the liquid state. We do not measure net values (lower heating values). The internal energy liberated from a constant volume bomb is relative to the equilibrium temperature at which the bomb functioned, as described by the following: Š MQT-Cal = HHV = HHVP + )HV/P (2) Note that Eq.(2) is path dependent, for a traditional bomb calorimeter, industrial practice sets this path as one having a constant bath temperature. By correcting for PV work, via )HV/P, conversion is made from a constant volume internal energy (HHV) to an enthalpy base (HHVP). A fuel’s calorific value, after conversion, is the difference between the enthalpy of ideal combustion products (HPRIdeal-CF-HHV) and the enthalpy of the reactants (HRXCal-CF-HHV) as ideally oxidized in bone-dry O2, and both evaluated at that temperature at which these quantities were formed, at TCAL. From First Law conservation, Eq.(2) results in the following expressions, descriptive of a “calorimetric system” (i.e., measured or computed). The net CV base of Eq.(3B) is justified below. HHVP = HPRIdeal-CF-HHV + HRXCAL-CF-HHV (3A) LHVP = HPRIdeal-CF-LHV + HRXCAL-CF-LHV (3B) However, there is additional complexity. When we either measure or compute a CV, we employ dry O2 to produce idea products, thus there are no compound formations, reactants or products, not directly associated with the pure fuel; i.e., a calorimetric system. Of course, since all streams are at TCAL there is no sensible heat. In a calorimetric system, there is no product water formed which does not derive from the fuel; it being condensed (a 6 Copyright © 2012 by ASME gross CV), or not (a net CV). However, when analyzing a system using moist combustion air, the Heat of Formation of the air’s water must be accounted when evaluating the actual Heat of Reactants. We must track separately that water associated with the fuel, verus ambient moisture ... and all other reactants. For example, consider 1.0 mole of moist methane being burnt in moist oxygen. The following suggests how HRXCAL-CF must be computed: For a gross CV base, all at TCAL: {0.9[CH4] + 0.1[H2O]}As-Fired + 1.8[O2] + 0.3[H2O]Vap => 0.9[CO2] + 1.9[H2O]Liq + 0.3[H2O]Vap For a net CV base, all at TCAL: {0.9[CH4] + 0.1[H2O]}As-Fired + 1.8[O2] + 0.3[H2O]Vap => 0.9[CO2] + 2.2[H2O]Vap As an example of the molar nomenclature used below, in these reactions: x = 1.0; "CO2 = 0.9; bA = 0.3; nCO2 = 0.9; etc. In all systems, the gross CV reflects the condensation of product water derived only from the As-Fired fuel (at TCAL). Also, as a fine point, it is not credible to suggest that, for example, if a gaseous fuel contains CO2 or water, or coal contains water with a leakage of working fluid, or combustion air bears moisture, that ideal combustion products cannot be defined consistent with Eq.(3). Thus by adding the Heats of Formation of non-fuel reactants to HRXCAL-CF of Eq.(3), we form an energy of combined fuel and non-fuel reactants, all at TCAL, termed HRXCAL-CM. To balance Eq.(3), such treatment implies that the energy of ideal combustion products now reflects non-fuel reactants, termed HPRIdeal-CM; thus: HHVP = HPRIdeal-CM-HHV + HRXCAL-CM-HHV (4A1) LHVP = HPRIdeal-CM-LHV + HRXCAL-CM-LHV (4A2) where: HRXCAL-CM-HHV = HRXCAL-CF-HHV + [Non-Fuel )HF 0 -CAL-k] (4B1) = HHVP + HPRIdeal-CF-HHV + [Non-Fuel )HF 0 -CAL-k] (4B2) = HHVP + [(nIdeal-CO2 )HF 0 -CAL-CO2) + (nIdeal-SO2 )HF 0 -CAL-SO2) + (nIdeal-H2O)H 0 f-CAL-H2O) + bA(1.0 + $))H 0 g-CAL-H2O + bZ)H 0 f-CAL-H2O + bS(1.0 + (S)()HF 0 -CAL-Sorb )HD 0 -CAL-Sorb)]/(xNAF) (4B3) HRXCAL-CM-LHV = HRXCAL-CF-LHV + [Non-Fuel )HF 0 -CAL-k] (4C1) = LHVP + HPRIdeal-CF-LHV + [Non-Fuel )HF 0 -CAL-k] (4C2) = LHVP + [(nIdeal-CO2 )HF 0 -CAL-CO2) + (nIdeal-SO2 )HF 0 -CAL-SO2) + (nIdeal-H2O)H 0 g-CAL-H2O) + bA(1.0 + $))H 0 g-CAL-H2O + bZ)H 0 f-CAL-H2O + bS(1.0 + (S)()HF 0 -CAL-Sorb )HD 0 -CAL-Sorb)]/(xNAF) (4C3) As observed, Eq.(3) is substituted into Eq.(4A) for HRXCAL-CF allowing HRXCAL-CM to be computed using Eq.(4B3) or Eq.(4C3). In summary, since the thermal efficiency of an ideal system described by Eqs.(3) or (4A) is unity, it follows that either Eqs.(3) or (4A) must serve as the basis for all boiler efficiency standards. FIRING CORRECTIONS When developing an expression for boiler efficiency, the As-Fired fuel’s energy content must be corrected for sensible heat relative to TCAL. Note that firing fuel at 10 C or 100C cannot affect its interaction with the gas/air/working fluids, if properly referenced to TCAL. As analysts we should be able to run calorimeters at any temperature, fire the fuel at any other temperature, without bias to the concept of ideal combustion, without affecting thermodynamic principles, and still compute an absolute fuel flow. Thus by simply adding a “Firing Correction” term (HBC) to each side of Eq.(4A), we bring the reactants term to the As-Fired, maintaining unity 0B: HHVP + HBC = HPRIdeal-CM-HHV + HRXCAL-CM-HHV + HBC (5A) LHVP + HBC = HPRIdeal-CM-LHV + HRXCAL-CM-LHV + HBC (5B) Note that the signs associated with Eqs.(3), (4) & (5) yield to the convention of a positive calorific value (note that the numeric value of HPRIdeal is always < 0.0, and HRXCAL is typically < 0.0). The efficiency of a system described by Eq.(5) is unity. Eq.(5) is interesting in that no condition of any reactant stream will cause departure from unity efficiency given all are at TCAL. Bone dry or fogged combustion air, nor size of FD Fan, nor steam-air heating, nor sorbent flow, nor water leakage, etc. will affect boiler efficiency per se. Such situations only affect inlet streams. Although entering the system not at TCAL, and so corrected by HBC, under ideal conditions all products exit at TCAL. The next developmental step is to degrade from the ideal by accounting for losses. How thermodynamic losses are grouped may be treated in any number of ways. For this work, they are based on specific energy terms (Btu/lbm), and are described by 3Losses/mAF. If just subtracting losses from HPRIdeal-CM, Eq.(5) becomes unbalanced without an efficiency term. Thus use of either gross efficiency (0B-HHV) or net efficiency (0B-LHV) to achieve conservation. The HPRIdeal-CM term being at TCAL. 7 Copyright © 2012 by ASME 0B-HHV (HHVP + HBC) = [HPRIdeal-CM-HHV 3Losses/mAF] + HRXCAL-CM-HHV + HBC (6A) 0B-LHV (LHVP + HBC) = [HPRIdeal-CM-LHV 3Losses/mAF] + HRXCAL-CM-LHV + HBC (6B) The computed boiler efficiencies follow directly, noting that in Eq.(7) the actual Enthalpy of Reactants (HRXAct) was substituted for [HRXCAL-CM + HBC]: