biogas plasticization coupled anaerobic digestion: the anaerobic pump stoichiometry

Biogas Plasticization Coupled Anaerobic Digestion:The Anaerobic Pump Stoichiometry

Keith A. Schimel

Received: 15 May 2013 /Accepted: 27 September 2013 /Published online: 19 December 2013# Springer Science+Business Media New York 2013

Abstract This paper presents the stoichiometry section of a bioenergetics investigation into thebiogas plasticization of wastewater sludge using the Anaerobic Pump (TAP). Three residuesamples, an input substrate and two residual products, were collected from two side by sideoperated AD systems, a conventional continuous flow and stirred reactor, and TAP, andsubmitted for elemental and calorimetric analyses. The elemental compositions of the residueswere fitted to a heterotrophic metabolism model [1] for both systems. To facilitate balancedstoichiometric models, a simple “cell” correction computation separates measured residualcomposites into “real” residual composition and cell growth (C5H7NO2) components. Theelemental data and model results show that the TAP stage II residual composition(C1H0.065O0.0027N0.036) was nearly devoid of hydrogen and oxygen, leaving only fixed carbonand cells grown as the composition of the remaining mass. This quantitative evidence supportsprior measurements of very high methane yields from TAP stage II reactor during steady-stateexperiments [2]. All performance parameters derived from the stoichiometric model(s) showedgood agreement with measured steady-state averaged values. These findings are strong evi-dence that plasticization–disruption (TAP) cycle is the mechanism responsible for the observedincreases in methane yield. The accuracy achieved by the stoichiometry models qualifies themfor thermodynamic analysis to obtain potentials and bioconversion efficiencies. How appliedpressure causes matrix conformation changes triggered by a functional consequence (plastici-zation and disruption) is this study’s essential focus.

Keywords Advancedanaerobicbioconversion .Biogas .Biomass .Continuous flow.Pressurecycle . Plasticization . Renewable energy .Waste

Nomenclature

AE Available electrons transferrable during the biological oxidationof organic material

GW Global warmingGWP Global warming potentialCHP Combined heat and power

Appl Biochem Biotechnol (2014) 172:2227–2252DOI 10.1007/s12010-013-0558-7

Electronic supplementary material The online version of this article (doi:10.1007/s12010-013-0558-7)contains supplementary material, which is available to authorized users.

K. A. Schimel (*)Technology Matrix Corporation, 330 Apple St, Syracuse, NY 13204, USAe-mail: [email protected]

http://dx.doi.org/10.1007/s12010-013-0558-7

B1 AD performance parameter liters CH4 per gram of VS addedto the system

B AD performance parameter liters CH4 per gram of COD addedto the system

ICUCF Ion-containing, unit-carbon formulaICUCFW Ion-containing unit carbon formula weightC-mol Carbon mol mass (C1)ICC-mol Ion-containing carbon mol massDa Dalton unit or universal mass unit (grams per mole—

replaces amu.)s′ n-fw which is fraction of Cn converted to CO2 in the

particulate pCOD calculationr 0.5 (a-fx-(3(c-fz))) which is 1/2 hydrogen mass balance in the

particulate pCOD calculationRf Refractory coefficient that represents the fraction of particulate

COD (pCOD) that is non-biodegradable at infinite digestiontime; computed using Eq. 2

So The initial biodegradable COD (or pCOD) concentration attime t=0 (grams COD liter−1)

St Total COD (or pCOD) concentration at any time t(grams COD liter−1)

SBo Biologically available COD (or pCOD) concentration(grams COD liter−1)

STo Total chemical oxygen demand (TCOD or pCOD) concentrationin (grams COD liter−1)

S Effluent biodegradable TCOD (or pCOD) concentration out(grams COD liter−1)

Tp Cycle period time (hours)Tg Glass transition temperature (°C), temperature at which an

organic substance transitions from the amorphous (glassy)to a rubbery state

Q The flow rate into an AD reactorSi concentration of solid pCOD of recycle+influent mixtureQr Recycle rate for TAP=40 l/day for the project (all TAP steady states)α Qr/Q=the recycle ratioX In reactor cell concentration (grams per liter) with an assumed

composition of C5H7NO2

L Ligand (substrate) concentration (grams per liter) of elementalcomposition CnHaObNc (s)

V Reactor volume (liters)P Pressure (force/unit area)Y Cell yield (grams of organisms grown per gram of substrate

COD consumed)‘ Superscript indicating a biological process taking place in an

aqueous environment under non-standard conditions at298.15 K and 1 atm (1 atm=101.325 kPa)

ΔGA GAo−GA, change in Gibbs free energy pure absorbent

(A) and absorbent in equilibrium with sorbed solvent(calories or kilojoules per gram of absorbent)

2228 Appl Biochem Biotechnol (2014) 172:2227–2252

ΔfGo ΔfH

o ΔfSo Gibbs free energy, enthalpy, or entropy of formation, respectively,

of a specified quantity of a pure substance in its standard stateat 298.15 K and 1 atm

ΔfG′ ΔfH′ ΔfS′ Free energy, enthalpy, or entropy of formation, respectively, ofa specified quantity of an impure substance in aqueous solutionor suspension, not at a standard state at 298.15 K and 1 atm.An example of this would be living cells, a biological processor dissolved substances at a concentration of other than 1 M

VS Volatile solids concentration, direct measurement, grams liter−1

VS (percentremaining)

Volatile solids remaining expressed as a percentage ofthe initial So, calculated as 100(VS/VSo)

TCOD Total oxygen demand (grams oxygen per liter−1 or mole substrate−1)sCOD Soluble oxygen demand (grams oxygen per liter−1 or mole substrate−1)pCOD Particulate oxygen demand (grams oxygen per liter−1 or

mole substrate−1)T Temperature (degree Celsius)

Introduction

Anaerobic digestion (AD) is a natural microbial process that is commonly used to produce energy(methane) from wet organic wastes like municipal sludges, MSW RDF, animal and cropresiduals, and many more organic materials. Collectively, these wastes represent a large sourceof low-cost, carbon neutral fuel. However, current mesophilic AD technology bioconversion isincomplete, slow, and considerable residue remains requiring post-processing and disposal. Thekey constraints leading to poor AD performance are substrate degradation resistance caused byresistant intermolecular bond interactions complicated by less than optimum enzyme-particlegeometry and a highly variable rheology caused by natural moisture sorption. There has beennumerous research efforts focused on improving the digestability of biomass substrates [3–13].The general approach has been to add large amounts of energy, usually in the form of heat (steam,etc.), to condition the substrate prior to conventional AD. This strategy negates the mesophilicAD advantage of net positive energy efficiency and in some cases, produces toxic by-products.

This author [14, 15] introduced a low energy input, high efficiency, advanced AD designcalled The Anaerobic Pump (TAP). The process apparatus, substrate characteristics, andperformance pertaining to TAP and a continuous flow stirred reactor (CFSTR, control) havebeen given in prior publications [2, 14–20]. TAP drives the anaerobic reactions to nearcompletion via biogas plasticization–disruption. This design strategy utilizes the auto-generative production of biogas to extend the softening (plasticization) of the organic solidsubstrate beyond natural moisture sorption. Continuous cycling through pressure sorption–lowpressure desorption (a repetitive hysteresis loop) drives relaxation of the biomass polymers,exposing the substrate organic-resistant fraction (Rf) to enzymatic hydrolysis. The low pressuredisruption period resets the hysteresis, the solution chemistry, and reduces digesting particlesize. The work (W) needed to drive polymer relaxation is provided for free, since the gasplasticizer (biogas) is continuously regenerated. A comparison of experimental steady-stateperformance data (see Table 2) for both side by side prototypes, CFSTR and TAP, digesting a50:50 wastewater sludge mixture showed that TAP drove AD reactions to near completion, farbeyond levels attainable by conventional (CFSTR) digestion system [2]. An overall ∼3×improvement in bioconversion was partially explained by a large increase in kinetics. But tofully explain the observed large gain, it was hypothesized that substantial improvement insubstrate biodegradability (1−Rf>1) must have occurred in TAP stage II. To test this

Appl Biochem Biotechnol (2014) 172:2227–2252 2229

hypothesis, a study of TAP and CFSTR biological thermodynamics (bioenergetics) was neededto explain the effect plasticization–disruption has on increasing the hydrolysis rate of substrateresistance fraction (Rf).

In review, we first note that the thermodynamics of primary anaerobic reactions canaccurately represent substantial pathway complexities without explicitly accounting forsecondary factors [21]. The thermodynamic properties of organic solids undergoing complexAD reactions are controlled either thermodynamically or kinetically [22]. Empircical ADkinetics follows thermodynamic laws [23, 24]. If the rate of substrate utilization controls theproduct formation pathway(s) where all of the reactions are thermodynamically favorable,the reactions are considered kinetically controlled [21, 25–33]. If, however, the second lawof thermodynamics is blocked by strong chemical bonds, then the extent of productformation is thermodynamically controlled. This control is what limits AD in nature whereit takes many repetitive exposure to outside forces like rain, freezing, thawing, drying, wind,earthquakes, and volcanic activity, moisture sorption–desorption to break and disentanglepolymers along weak bond lines, causing cracks, freeing particles, and reducing particle sizeso that polymers are free to follow the thermodynamic second law and fall to a lower energylevel. The consequences of these repetitive forces found in nature do not occur in aconventional anaerobic digester. Energy in some form must be supplied to break anddisentangle bond networks that defy the second law of thermodynamics. If cross-linkedbond strength is sufficiently diminished and enough moisture is supplied, then extremelyefficient catabolic reactions are poised to proceed uninhibited very close to thermodynamicequilibrium (ΔG→0) [34].

Organic solids are composed of a wide variety of hydrophilic and hydrophobic carbohydrates,lipids, and proteins tightly bound in a complex network of fibrous materials. Some materials areeasily attacked by facultative anaerobic flora, and others are very resistant. Depending on thedegree of intermolecular complexity, heterogeneous organic polymer mixtures naturally absorbwater into their amorphous carbohydrate intercellular regions resulting in a highly variablerheology [35, 36] as evidenced by thixotropic reograms [35] and isotherm swelling loops [37].This makes processing (mixing and separation) organic slurry mixtures difficult. In addition,much of the particle biodegradable fraction is “buried” beneath the surface, reducing polymerbioavailability. Large particle size limits bioavailability. Solid organic substrate particles(ligands—L) are irregular three-dimensional shaped objects, whereas microbial floras (X) areattached to surface areas (two dimensional). It generally requires energy input to reduce theparticle size so that the exposed surface area can geometrically increase to support cell growth.Depending on the particle size distribution, as much as 90 % of biodegradable organics can be“buried” beneath the substrate surface, out of reach (beyond diffusion distance) of the highlyefficient syntrophic microbial enzyme systems rapidly growing on their surface(s). An underly-ing polymer may be biodegradable, but it may not be readily bioavailable.

Natural moisture sorption by solid organic materials is believed to occur in response to atendency to disperse (dissolve in solution). It involves two transport processes, first solventdiffusion (Fickian) into void “free” volume space between networked bonds followed bychain disentanglement (non-Fickian) [38, 39]. In the transition, the adsorbent’s free energy islowered because of the “natural” expansion (swelling) via solvent uptake against theabsorbent’s network bond stress. The Gibbs free energy (ΔGA) loss due to moisture sorptioncan be written according to Eq. 1 as follows;

ΔGA ¼ GAo−GA ¼ F∑−W ð1Þ


where ΔGA is the Gibbs free energy lost by the absorbent (A), GAo Gibbs free energy of the

dry absorbent (A), GA is the Gibbs free energy of absorbent in equilibrium with sorbedsolvent (kilojoules per gram absorbent), F is the Helmholtz free energy per unit surface area,∑ surface area per gram of absorbent which is not a constant once sorption begins, and W(kilojoules per gram absorbent) is the work done by the moisture sorption expansion andseparation (unraveling) of the absorbent into structural subunits. Note that the magnitude ofΔGA loss (Eq. 1) is dependent on surface area (∑) and work (W) or pressure times volume(P*V=W). For example, absorbents (A) like dried sludges and manures exposed to highhumidity have a high differential heat of adsorption (∼1.0 kJ/g water), reflecting a highnatural affinity for moisture. The amount absorbed depends largely on the availability ofmoisture from the surroundings and the amount of available free volume [40] in the polymermatrix. The matrix “swells” as it absorbs water into the free volume in cell cavities and cellwalls. Water is highly effective at penetrating amorphous carbohydrates [40] but notcrystalline (cellulose) regions. Highly ordered crystalline and semi-crystalline regions hinderdiffusion. This is generally referred to as the two-phase model, the impermeable crystallineor semi-crystalline phase and the more permeable amorphous phase. For example, crystal-line cellulose microfibrils are surrounded by amorphous (glassy) materials like hemicellu-loses and lignin (occupying space between fibrils). Primary wastewater sludges, on the otherhand, contain very low crystalline content, <3 % of the volatile solids due to the presence ofcellulose paper products. The other component of the 50:50 sludge mixture, waste activatedsludge has much lower crystalline cellulose content, ∼1/2 % of the volatile solids that isprimarily due to resistant polymers in bacterial cell walls. In contrast, wood and cottoncontain 50 % and 90 % cellulose, respectively. Penetrants in general expand the averagecapillary in the amorphous phase by a combination of two effects. First, they tend to clusterin small free volume space in the amorphous (glassy) regions of the network. Secondly, thepenetrants interfere or disrupt the intermolecular hydrogen bonding of carbohydrates,increasing the number of degrees of freedom of the carbohydrate chains that leads to a“cold” relaxation of the structure. The cross-linkages between lignin and hemicellulose mustbe relaxed before cell wall crystalline materials can be effectively attacked by anaerobiccellulolytic bacteria (cellulases/cellulosomes) and fungi. A threshold relaxation coincideswith reaching critical volume dilation, a critical point where plasticization [41] is observed.At the threshold relaxation point (∼20w/w% water content for wastewater sludges) polymerstransition from a glassy to a rubbery state [42]. This cause and effect is not confined to justcellulosic materials or sludges, but has been observed in starches, gelatins, dried foods, andmany other hygroscopic organic materials. The sorbed water is closely associated with theamorphous carbohydrate polymer and not with itself [40]. Inside cells, water is part of thefluid matrix, not bound waters of hydration. Cell cavities contain approximately five timesmoremoisture than the cell walls where crystalline materials can be the main component. At theplasticization threshold, the absorbents’ (A) structural and physical properties rapidly changedue to molecular relaxation. The approach to a new equilibrium is generally slow with a longequilibration time (>1month) [40]. From the relaxation threshold point forward, all measures ofmechanical strength rapidly diminish. Restoring structure integrity of plasticized material (i.e.,drying) is always incomplete. In addition, smaller molecules such as CO2 and ammonia gasesand volatile organic acids and alcohols can have sufficient diffusional mobility to diffuse intoamorphous matrix areas. Carbon dioxide gas (CO2), a major constituent of digestion biogas(∼40–50 %v/v), is well known to be capable of plasticizing cross-linked elastomers, copoly-mers, and polymer blends, even at low pressures [43–47]. CO2 is much more condensable than


CH4, so both diffusivity and solubility favor CO2 transport in anaerobic environments. Becauseof the “natural” hydroscopic character of AD substrates like sludges and manures, they areusually delivered in a “water-logged” or a moisture relaxed quasi-equilibrium state. But not allof the cross-linked network bond tension has been relaxed. The solid still remains intact,teetering on the verge of hydrolysis (soggy and deformed). This is where TAP biogas plasti-cization can play a significant role. A completely flooded AD reactor (TAP) can be designed tofacilitate CO2 gas sorption–desorption needed to overcome the remaining bond resistance. Thesorption of multiple solvent components is additive toward the plasticization threshold. Eachcontributes to the total overall work W (Eq. 1) needed to achieve bond relaxation and particlesize reduction to the point where all substrate volatile mass becomes bioavailable.

Methanogenesis is a dehydration reaction. The hydrogen and oxygen from sorbed watercontribute to the formation of hydrocarbon and oxygenated products of AD fermentationreactions. Moisture sorption to approximately 50w/w% total moisture content (free+parti-cle+capillary+floc) is requisite for sustaining uninhibited AD of a sludge biodegradablefraction. When moisture content falls below ∼50w/w%, AD gas production suffers andbelow ∼40w/w%, it ceases. Low moisture availability at the cellular level corresponding tohigh solid concentrations has a negative effect [48]. The overall decomposition rate de-creases, higher concentrations of inhibiting compounds increase because of low masstransfer rates, poor diffusion and distribution, and insufficient mixing of substrate withinoculum. Higher viscosities require longer periods to adequately mix substrate, inoculums,and moisture. It is very important that the rate of moisture diffusion into the substrate cellularregions exceeds the dehydration rate of AD reactions.

Sorbed moisture improves the binding potential for enzymatic hydrolysis. Specific enzyme–protein groups (binding modules) have a great affinity for insoluble non-crystalline(amorphous) polymers. For example, the breakage of matrix cross-linked bonds in amorphousmaterials can expose underlying crystalline biopolymers like cellulose to depolymerization bythe synergistic activity of specialized fungi and anaerobic cellulolytic bacteria (i.e.,Clostridiumsp.) yielding glucose (saccrification). Effective cellulose hydrolysis requires the synergisticwork of several different kinds of cellulases that tend to group into binding modules.Carbohydrate-binding modules (CBM) bind to insoluble non-crystalline cellulose with anaffinity approximately 10–20 times greater than their affinity for cello-oligosaccharides and/orsoluble polysaccharides [49]. The presence of sorbed water at these binding interfaces signif-icantly improves CBM binding affinity (ΔGbinding gain). The process of receptor binding isdriven by diffusion: that is, the binding process needs no energy input other than naturallyoccurring heat from the environment (surroundings). The structure of the enzyme–protein (X)substrate–ligand (L) complex is not rigid but dynamic which keeps the molecules in a state ofperpetual thermal motion, while the substrate–ligand (L) molecules are being continuouslyshuttled into and out of enzyme–protein (X) docking sites. Eventually, a state of dynamicequilibrium is reached where on average a constant fraction of substrate–ligand (L) is dockedonto or complexed with the enzyme–proteins (X), a situation described by classic empiricalenzyme–substrate kinetic expressions [31]. However, access to docking sites can be preventedby extensive lignin–hemicellulose cross-linking. The critical mechanism that drives a success-ful degradative pathway must involve an improvement in the conformational distributionon substrate–ligand (L) surfaces. Thus, to drive uninhibited toward hydrolysis, a conformationmodification must enable binding modules to diffuse, recognize, dock, bind, and unbind withthermodynamic favorability and virtually no impedance. This sequence requires the sorption ofwater at the cellular level.


The combination of constraints that defines the extent of thermodynamic control corre-lates to the substrate refractory coefficient Rf. Rf is that fraction of the organic particulatesubstrate that is bioconversion resistant, left by a particular process (i.e., conventional AD)or series of processes after being held for infinite time [50]. For convenience, the particulatechemical oxygen demand (pCOD) is the organic fraction measurement (S). Some researchershave used volatile solids (VS) or total COD (TCOD) instead. 1−Rf is that proportion of theresidue pCOD that is biodegradable. Rf (or 1−Rf) values can be used to rank substrate–process biodegradability. Equations 2 and 3, the simple product of only two ratios, can beused to calculate the refractory (Rf) pCOD fraction or biodegradable (1−Rf) pCOD fractionfor a particular substrate and process combination as follows;

Non−biodegradable fraction ¼ R f ¼ Bo=Bt St=STo−1h i

þ 1 ð2Þ

and

Biodegradable fraction ¼ 1−R f ¼ Bo=Bt STo−Stð Þ=SToh i

ð3Þ

where STo is the measured input feed particulate chemical oxygen demand (pCOD) concen-tration, St is the measured particulate chemical oxygen demand concentration (pCOD) in theeffluent matched with Bt, the measured methane yield, for a given steady-state hydraulicretention time t, respectively. Bo is the maximum methane yield possible (liters CH4) pergram of COD) obtained by extrapolating methane yield to infinite hydraulic retention time(HRT). The use of Eq. 2 and 3 assumes that the degree of bioconversion of the biodegradablefraction (1−Rf) is directly proportional to the solids’ retention time and inversely propor-tional to the non-biodegradable mass fraction (Rf). Most importantly, both independentvariables (B and S) are AD process dependent. By definition [50], the St and Sto measure-ments are usually composite residue pCODs. Estimating Rf (Eq. 2) for a conventionaldigestion (CFSTR) units results in only small error because cell growth is so small.However, for more advanced processes like TAP, where most of the substrate is convertedto biogas, the accumulated cell growth is a significant proportion of the measured pCODremaining and (Eqs. 1 and 2) results in significant error. In this case, “true” substrate residuepCOD (w/o cell growth) should be used for Eq. 2 St and Sto measurements since 1−Rf→1.Using conventional CFSTR Rf as a reference, if a particular process is observed to improvethe substrate biodegradability, then the decline in the refractory coefficient (ΔRf) should beproportional to a corresponding gain in binding free energy (ΔΔGbinding).

This study was designed to test of the hypothesis that the TAP methane yield (and otherperformance parameters) gainwas due in large part to a significant improvement in bioconversionof the substrate refractory fraction (Rf). Elemental analyses of the process residues showedprogressive loss in composition integrity as AD bioconversion proceeds. This paper is the firstof a two-part series. It compares the CFSTR and the Anaerobic Pump (TAP) elemental andstoichiometric analyses. McCarty’s heterotrophic metabolism (stoichiometry) models [1, 51–54]were built on the elemental analysis of three 15-day hydraulic residence time (HRT) residues; onefeed sludge biomass and two degraded residues; one each from the anaerobic CFSTR and TAPprototype systems. Average performance parameters are derived from stoichiometry reactions byregressing elemental data against the average measured steady-state performance parametervalues provided by the Boone TAP investigation [2, 16]. The measured performance valuesand calculated values from each stoichiometric reaction model (CFSTR and TAP) are then


compared. A companion paper will present the thermodynamic extensive properties and analysisof the stoichiometric reactions (both TAP and CFSTR) presented in this paper. How appliedpressure causes a substrate conformational change triggered by a functional consequence,plasticization and disruption, is this study’s essential focus.

Materials and Methods

The determination of anaerobic stoichiometric reactions requires both proximate and ele-mental data. The paired proximate data were collected during the Boone TAP investigation[16]. All applicable analytical methods for solids and gas analysis were done in accordancewith Standard Methods for the Examination of Water and Wastewater [55]. In addition, threeresidue samples from the 15-day HRT steady-state were collected, dried, and provided forthis study’s elemental, ionic, and calorimetric analyses. The residue samples were collectedat TAP and CFSTR sampling port locations identified in previous publications [2, 16]. Thethree residue samples were (1) sample port 1—input substrate 50:50 wastewater sludgemixture common to both CFSTR and TAP systems, (2) sampling port 2—CFSTR HRT 15-day output residue, and (3) sampling TAP port 5—TAP Stage II bottom digested sludgeresidue. All three samples were dried at 103±1 °C, cooled in a dessicator, sealed, and storedat 4 °C.

Sample Preparation

Prior to elemental and calorimetric analyses, each residue sample was rechecked formoisture content. Percent moisture was measured by a Sartorius electronic moistureanalyzer (model MA40). If needed, the samples were dried again at 103 °C, stabilizedin a dessicator, weighed until the weight change remained below 0.1 % for 2 min.The stable dried residue samples were then split into three analytical aliquot streamsfor analysis; one for ultimate elemental analysis, one for ionic series, and one forbomb calorimetry. Preparation of samples for elemental analysis followed ASTME1757, standard practice for preparation of biomass for compositional analysis. Thesample preparation and results of the residue calorimetric analyses will be presentedin the companion thermodynamic manuscript.

Laboratory Analytical Methods

Quadruplicates of all three residue samples were submitted to ultimate elementalcomposition analysis via flash dynamic combustion followed by gas chromatographyand ash content analysis (CEN 14775 ASH and ISO 1171). The elemental analysis forcarbon, hydrogen, oxygen, nitrogen, and sulfur (CHONS) followed ASTM D3176-89.Total phosphorus analysis followed EPA/600/R-93/100, Method 365.1. The standardapproach to elemental oxygen measurement by difference consistently underestimatedthe percentage of oxygen (O) in all three residues. Hence, the determination ofoxygen (O) via pyrolysis with platinum–carbon catalyst method was necessary. Theoxygen is then measured as CO2 (g) via gas chromatography. Sulfur was measuredseparately according to ASTM E775. Selected ionic elements (K, Mg, and Ca) weredetermined by digestion/atomic absorption spectrophotometry following EPA method


7000B. All analyses were standardized against pure (analytical grade) compounds withknown compositions and blanks.

Stoichiometric Growth Models

Resolving anaerobic metabolic networks normally requires considerable data to constructgrowth process equations [56]. This is especially challenging for heterogeneous solidsubstrates being consumed by a mixed consortium of anaerobes. Models are necessarilycomplex if all product intermediates are included [21, 25, 57]. However, there is an approachthat can simplify the problem. It involves combining overall theoretical reactions withsimplifying assumptions that allow for minimal analytical data. In this study, the stoichio-metric elemental compositions obtained from residue elemental analysis and the observedaverage experimental yields from proximate analysis are least square (OLS) adjusted to yieldaveraged stoichiometric molar coefficients for McCarty’s [1] heterotrophic anaerobic me-tabolism model Eq 4;

CnHaObNc sð Þ þ 2nþ c−b− 9ds=20ð Þ− de=4ð Þð ÞH2O lð Þ→ n−c− ds=5ð Þ− de=8ð Þð ÞCO2 gð Þ

þ de=8ð ÞCH4 gð Þ þ de=8ð ÞCH4 gð Þ þ ds=20ð ÞC5H7NO2 sð Þ

þ c−ds=20ð ÞNH4þ þ c−ds=20ð ÞHCO3

−

ð4Þ

where d (=4n+a−2b−3c) is the total available electron (AE) transferable from the substratebiomass CnHaObNc (s), s=molar fraction of d synthesized to organism cell mass C5H7NO2

(s), and e (1−s) is fraction of d transferred to the production of methane. Equation 4 must becorrected for the reaction residue that remains after a bioconversion process. A residueelemental composition is actually a composite of cell growth plus the remaining “true”residue. Accordingly, the microbial cell growth on the “true” substrate is the compositionC5H7NO2 (s) [58]. This model treats the mixed culture as a single virtual microorganism(C5H7NO2) catalyzing all fermentative pathways. The cell growth correction can be com-puted by a simple indirect method, termed a “composite cell correction” that separates the“true” residual from the virtual cells grown. This correction is particularly important whencell growth significantly advances beyond mere “stabilization” as experienced with theAnaerobic Pump. Since the cell mass has a known virtual composition C5H7O2N, thenreaction equations can be solved simultaneously to yield values for the “true moles ofsubstrate residual” (fc) and correct molar cell growth (m) per Eq. 5 as follows;

fCnHaObNc s; compositeð Þ−mC5H7O2N1 s; cellsð Þ→fcC1Hac=fcObc=fcNcc=fc s; real residualð Þ ð5Þ

When multiple reactions occur in an AD system, such as methanogenesis and denitrifi-cation, an overall stoichiometric equation can be written as a linear combination of thesestoichiometric reactions. Fortunately, denitrification intermediates, such as nitrite (NO2

−),nitric (NO) and nitrous (N20) oxides, rarely appear in digester effluents and do not accu-mulate in anaerobic digesters.


Finally, combining the three corrections to the McCarty model Eq. 4, denitrification, ADresidual, and cell composite correction (Eq. 5), results in a “realistic working” AD processequation Eq. 6 as follows:

CnHaObNc s; substrateð Þ þ f nde=5ð Þ= 1þ f nð Þð ÞNO3− þ f nde=5ð Þ= 1þ f nð Þð ÞHþ

þ 2nþ c−b− 9ds=20ð Þð Þð − de=4ð ÞÞ

− f n 9ds=20þ 12de=20ð Þ−2n−cþ bð Þð ÞÞ= 1þ f nð ÞÞ

−fc 2nþ c−b− 9ds=20ð Þ− de=4ð Þð ÞÞH2O lð Þ→fcCnHaObNc s; residualð Þ

þ n−c− ds=5ð Þ− de=8ð Þð Þ þ f n n−c−ds=5ð Þ= 1þ f nð Þð Þ

−fc n−c− ds=5ð Þ− de=8ð Þð ÞÞCO2 gð Þ

þ de=8ð Þ= 1þ f nð Þð Þ−fc de=8ð Þð ÞCH4 gð Þ

þ f n de=10ð Þ= 1þ f nð ÞÞN2 gð Þ þ f n ds=20þ ds=20ð Þ= 1þ f nð Þð Þ

–fc ds=20ð ÞÞC5H7NO2 sð Þ þ c−ds=20ð Þ þ fn c−ds=20ð Þ= 1þ f nð Þð Þ

−fc c−ds=20ð ÞÞNH4þ þ c−ds=20ð Þð

þ f n c−ð ds=20Þ= 1þ f nð ÞÞ−fc c−ds=20ð ÞÞHCO3−

ð6Þ

where fn refers to moles of substrate needed for NO3− denitrification per mole of substrate input.

All stoichiometry components in the Eq. 6 reaction are given on a C-mole basis except cell massgrown, which is given in the classic empirical N-mole basis (C5H7NO2). If the AD systemproduces two residues, such as the TAP process, then Eq. 6 must be further modified to includeboth residues. Similarly, if an AD system has two stages, then Eq. 6 must be further modified tocompute the actual “net” biogas production, gas compositions, and residue compositions perstage. The molar coefficients in Eq. 6 can be easily determined by ordinary least squares (OLS)regression included in most common spreadsheet programs [59].

Stoichiometric COD Model

The theoretical chemical oxygen demand (COD) of each residue composition can be estimatedusing Eq. 7. The COD parameter is often used as the primary organic concentration measure-ment in AD substrate utilization studies because it can be conveniently calculated in materialand energy balances (0.35 l CH4/g COD). Similarly, the microbial cell COD can be conve-niently calculated as 1.414 times the cell weight, which is based on the amount of oxygentheoretically required to completely oxidize the virtual cell formula C5H7NO2 [60].

CnHaObNc þ 0:5 fyþ 2s0 þ r−bð ÞO2→fCwHxOyNz þ s0CO2 þ rH2Oþ c−fzð ÞNH3 ð7Þ

where: s′=n−fw which is fraction of Cn converted to CO2=n if f=0r=0.5 (a−fx−(3(c−fz))) which is 1/2 hydrogen mass balancepCOD (grams O/mole particulate residue)=0.5 (fy+2s′+r−b)×32 g (O/mole O2).Because the COD reflux test [55] reaction is assumed complete for all possible residue

compositions, the f CwHxOyNz residual in Eq. 7 is set to zero (f=0) leaving Eq. 7 with the


reaction products CO2, water, and ammonia. The use of Eq. 7 assumes that there is enoughresidue hydrogen (a) to form the c moles of the ammonia (NH3) product. However, whenthere is not enough hydrogen to form the reactant ammonia c NH3, the case where a<3c,H2O must be supplied to the reactant side of the equation in the amount of r=0.5(a−3c) toresolve values with the COD reflux procedure that provides the excess water in the form ofdilution of dichromate and sulfuric acid reagents.

Simplifying Assumptions, Approximations, and Experimental Errors

This is a thermodynamic study of mixed anaerobic microbial growth consuming a time-varyingheterogeneous substrate. Hence, thermodynamicists cannot expect the same level of accuracyobtainable with pure cultures consuming pure, small molecular weight substances. These analyt-ical estimates are the result ofmany assumptions, approximations of a theoretical metabolicmodel[1] regressed to time averaged pseudo-steady-state performance parameters.

The “real world” 50:50 sludge mixture substrate, fed to both systems, was assumed to containnegligible active anaerobic cells (non active or lyophilized cells). Lyophilized cells are not livingcells contributing to the acetogenesis or methanogenesis processes. Conventional AD producesvery little cell mass. This assumption is normally acceptable for microbial cell yields (Y) frommethane fermentation and denitrification. Literature reported cell yield values are typically on theorder of 0.05 g (VS) cells grown per gram COD fed to a conventional anaerobic digester [61].This is the baseline cell yield value assumed for conventional digestion (CFSTR) in this study.

The model ignores the fact that AD volatile acid and alcohol CODwash out with the effluentof both systems. The washout amount represents a loss in potential methane production.Volatile acids measured as soluble COD (sCOD) production is ignored in Eqs. 4 and 6 andall subsequent reactions presented in this paper. The presence of sCOD concentrations in theprocess influent and/or effluent is assumed to be relatively small compared to the inputparticulate mass (pCOD) or the mass converted to methane. Similarly, the balanced stoichio-metric model ignores quantities of dissolved gases such as nitrogen (N2) entering and exitingeither system. Adopting these assumptions will cause the accumulation of small but consistentsystematic errors in estimates of the corresponding performance parameters.

There are well-known precision and accuracy problems associated with total and solublechemical oxygen demand (TCOD and sCOD) and total solids (TS) and volatile solids (VS)determinations [55]. With the COD test in particular, the difficulty arises with the error inobtaining a representative sample from organic waste slurries and compounding it with astandard laboratory COD reflux test [55] that often requires 100× dilution. This sampling andanalysis train is nearly impossible to duplicate by one technician let alone several techniciansparticipating in a steady-state experiment. The statistical error around COD and VS data is themain source of error in AD performance parameter estimates. Measurement faults are difficultto isolate. In addition, TCOD, sCOD, TS, and VS values are often biased. Because of theseknown sources of experimental errors, differences between measured and stoichiometriccomputed parameters such as yields (i.e., B liters per gram COD) were expected in this study.

An elemental analysis of the TAP fugitive residue (TAP sampling port #3) was not done.Because of the fugitive nature of the TAP port #3 effluent stream, the amount and compo-sition were expected to be variable. The total biogas production from TAP stage I and theCFSTR units were similar; hence, it was assumed that the TAP stage I fugitive residuestream composition was equivalent to the average CFSTR output residue composition,C1H0.889O0.28N0.028 (residue 2 in Table 1). This assumption limited elemental analyses toonly two product residues and the input substrate residue, thus significantly reducing thescope of this project.


Analytical Results

Chemical and Structural Elemental Analysis Results

Table 1 presents the results of the chemical and structural elemental analysis for the threeresidue samples collected from the two systems studied (TAP and CFSTR).

CFSTR Stoichiometric Process Model

Elemental analysis data (Table 1) for the raw substrate (1) and conventional residue C-res (2)were used to construct the AD stoichiometric process model Eq. 6 for the continuous flowstirred tank reactor (CFSTR). The substrate decomposition reaction is formed by subtractingcomposite CFSTR residual (f C-res) from methane formation reaction Eq. 4 (ignoring denitri-fication of the moment) which results in Eq. 8 as follows:

C1H1:474O0:403 N0:076 sð Þ þ 0:17H2O lð Þ→0:465C1H0:889O0:28N0:028 þ 0:14CO2 gð Þþ0:26CH4 gð Þ þ 0:26CH4 gð Þ þ 0:019C5H7NO2 sð Þþ0:044NH4

þ þ 0:044HCO3−

ð8Þ

Then, adding denitrification side reaction for the average 33 mg/l NO3–N influent concen-tration to Eq. 8 results in Eq. 9 as follows:

C1H1:474O0:403 N0:076 sð Þ þ 0:045NO3− þ 0:045 Hþ

þ0:092H2O lð Þ→0:465C1H0:889O0:28N0:028 sð Þ þ 0:165CO2 gð Þþ0:235CH4 gð Þ þ 0:023N2 þ 0:018C5H7NO2 sð Þ þ 0:044NH4

þ þ 0:044HCO3−

ð9Þ

Applying the growth correction with nitrogen conservation to the CFSTR compositeresidual (f=0.465) in Eq. 9 results in a corrected C-mole composition for the C-residual anda corrected molar value fc=0.354, a 24 % molar coefficient decline according to Eq. 10:

0:465C1H0:889O0:28N0:028 sð Þ−0:0221C5H7O2N1 sð Þ→0:354C1H0:73O0:24N0:037 sð Þ ð10Þ

Substituting the “corrected” residual stoichiometry (Eq. 10) into Eq. 9 results in the workingCFSTR stoichiometric model corrected for both growth and denitrification Eq. 11 as follows:

C1H1:474O0:403 N0:076 sð Þ þ 0:045NO3− þ 0:045 Hþ

þ0:126H2O lð Þ→0:354C1H0:73O0:24N0:037 sð Þ þ 0:21CO2 gð Þþ0:29 CH4 gð Þ þ 0:023N2 þ 0:022C5H7NO2 sð Þ þ 0:04NH4

þ þ 0:04HCO3−

ð11Þ

The Anaerobic Pump Stoichiometric Overall Process Model and Analysis

TAP has two output residues, fugitive solids in stage I overflow stream and a plasticizedresidual exiting the bottom of stage II at port 5 and recycled back to stage I. The TAP recyclingloop helps to maintain populations of the slower growing methanogenic organisms in bothreactors. The ultimate elemental analysis data for the (1) raw substrate, (2) fugitive residue, and(3) the stage II bottom sample, as given in Table 1 were used to construct the balanced


Table 1 Ionic and structural analysis for the three AD process residues

1. Common Raw Substrate Feed Sludge—Structural Elements a

Elements g % of dry weight VS Avg. (g % TS) Avg. (g %) of ash

Carbonb 56.3, 56.37, 56.72, 57.01 40.42

Hydrogenb 7.02, 7.0, 7.01, 6.97 5.00

Oxygenb 30.45, 30.65, 30.1, 30.4 21.71

Nitrogenb 4.91, 5.13, 5.01, 4.95 3.57

Phosphorousb 1.27, 1.44, 1.41, 1.39 3.13 7.17

Sulfurc As K2SO4 & P4O10 0.71 3.88

Subtotal residue structural elements: 74.534

% volatile solids = 71.407

1a. Raw Substrate Feed Sludge—Ionic Elements:

Potassiumd K2SO4 1.74

Potassium K2O 2.26 2.72

Magnesiumd MgO 0.82 1.36

Calciumd CaO 0.40 0.57

Subtotal residue ionic elements: 5.22 –

Total Structural+Ionic %: 79.75 15.69

C H O N P S K Mg Ca

3.365 4.959 1.357 0.255 0.101 0.022 0.102 0.034 0.010

1.000 1.474 0.403 0.076 0.030 0.0066 0.030 0.010 0.003

2. 15-day CFSTR Conventional Residue C-Res Sludge—Structural Elementsa

Elements g % dry weight of VS Avg. (g % TS) g % as ash

Carbonb 67.37, 66.78, 66.72, 67.13 44.42

Hydrogenb 5.02, 5.0, 5.01, 4.97 3.32

Oxygenb 25.1, 25.61, 25.2, 24.1 16.58

Nitrogenb 2.08, 2.3, 2.4, 2.0 1.46

Phosphorousb As P4O10 3.38 7.754

Sulfurc As K2SO4 0.83 4.514

Subtotal residue structural elements: 69.98

% volatile solids= 66.60

2a. 15-day Conventional C-Res Sludge—Ionic Elements:

Potassiumd As K2SO4 2.03

Potassium As K2O 2.57 3.10

Magnesiumd As MgO 0.89 1.47

Calciumd CaO 0.44 0.61

Subtotal residue ion elements: 5.92 –


C H O N P S K Mg Ca

3.698 3.289 1.036 0.104 0.109 0.022 0.102 0.034 0.010

1.000 0.889 0.280 0.028 0.030 0.0066 0.030 0.010 0.003

3. 15-day TAP Stage II Bottom Residue R-Res Sludge—Structural Elementsa

Elements g % dry weight of VS Avg. (g TS %) g % as ash

Carbonb 63.36, 61.53, 62.55, 63.12 44.98

Hydrogenb 6.48, 6.79, 5.87, 7.1 4.71

Oxygenb 29.5, 29.9, 29.62, 30.18 21.4


stoichiometric process equation. The process stoichiometry that generates the fugitive residual(fug-res) (ignoring denitrification) results in Eq. 12:

C1H1:474O0:403 N0:076 sð Þ þ 0:277H2O lð Þ→0:265C1H0:889O0:28N0:028 sð Þþ0:213CO2 gð Þ þ 0:213CO2 gð Þ þ 0:349CH4 gð Þþ0:026C5H7NO2 sð Þ þ 0:0423NH4

þ þ 0:0423HCO3−

ð12Þ

The fugitive composite residual (fug-res) 0.265C1H0.889O0.28N0.028(s) in Eq. 12 is theresidual that escapes in stage I effluent. The process stoichiometry that leaves the stage IIcomposite residual (R-res) (ignoring denitrification) results in Eq. 13 as follows:

C1H1:474O0:403 N0:076 sð Þ þ 0:347H2O lð Þ→0:19C1H1:248O0:357N0:012 sð Þþ0:245CO2 gð Þ þ 0:377CH4 gð Þ þ 0:029C5H7NO2 sð Þþ0:045NH4

þ þ 0:045HCO3−

ð13Þ

The difference between the raw substrate C1H1.474O0.403 N0.076 (s) and composite stage II residual0.19C1H1.248O0.357N0.012 is representative of “advanced” biological conversion due to biogas plas-ticization–disruption. Combining Eqs. 12 and 13 results in the stoichiometry process equation Eq. 14with denitrification for 33 mg/l NO3–N but is uncorrected for composite cell growth as follows:

C1H1:474O0:403 N0:076 sð Þ þ 0:045NO3− þ 0:045Hþ þ 0:127H2O lð Þ→0:19C1H1:248O0:357N0:012 sð Þ

þ0:265C1H0:889O0:28N0:028 sð Þ þ 0:172CO2 gð Þ þ 0:233CH4 gð Þþ0:023N2 gð Þ þ 0:019C5H7NO2 sð Þ þ 0:047NH4

þ þ 0:047HCO3−

ð14Þ

Table 1 (continued)

Nitrogenb 0.88, 0.85, 0.97, 0.90 0.65

Phosphorousb As P4O10 3.65 8.37

Sulfurc As K2SO4 0.40 2.20

Subtotal structural elements: 75.79

% volatile solids= 72.13

3a. TAP Stage II Bottom R-Res Sludge—Ionic Elements:

Potassiumd As K2SO4 0.99

Potassium As K2O 2.62 3.15

Magnesiumd As MgO 0.96 1.59

Calciumd As CaO 0.47 0.66

Subtotal residue ion elements: 5.03 -


C H O N P S K Mg Ca

3.744 4.637 1.337 0.046 0.118 0.013 0.092 0.039 0.012

1.000 1.248 0.357 0.012 0.031 0.0034 0.025 0.011 0.003

a Elemental analysis of 100 g dry wt (15 day HRT) residue samplesb Ultimate elemental analysis via combustion chromatography-thermo-conductivity detector, oxygen beingdetermined by pyrolysis tube-carbon monoxide methodc Sulfur analysis via combustion to sulfur dioxide method, total phosphorus via (EPA/600/R-93/100, Method365.1)d Total K+ , Mg++ , and Ca++ via atomic absorption spectrophotometry EPA method 6010B


Applying Eq. 5 composite growth correction to Eqs. 12 and 13with nitrogen conservation resultsin a corrected molar compositions for both the TAP residuals according to Eqs. 15 and 16,respectively;

TAP Stage I Fugitive Residual (58 % molar coefficient decline);

0:265 C1H0:889O0:28N0:028−0:031 C5H7NO2→0:11175 C1H0:189O0:116N0:067 ð15Þ

and TAP Stage II Residual (89 % molar decline);

0:19 C1H1:248O0:357N0:012−0:0339 C5H7NO2→0:0206 C1H0:00067O0:0056N0:1134 ð16Þ

Substituting these “real” residual compositions (Eqs. 15 and 16) plus the denitrificationreaction for 33 mg/l NO3–N into Eq. 6 results in the working TAP Eq. 17 as follows:

C1H1:474O0:403 N0:076 sð Þ þ 0:045NO3− þ 0:045Hþ þ 0:266H2O lð Þ

→0:0206C1H0:00067O0:0056N0:1134 sð Þ þ 0:11175C1H0:189O0:116N0:067 sð Þþ0:292CO2 gð Þ þ 0:390CH4 gð Þ þ 0:023N2 gð Þþ0:0299C5H7NO2 sð Þ þ 0:036NH4

þ þ 0:036HCO3−

ð17Þ

Equations 11 and 17 were evaluated for six performance parameters, specific methaneyield (B1, VS mass), specific methane yield (B, pCOD), moles biogas/mole substrate,cell mass yield, and biogas compositions CO2 and CH4 at STP. They were selected togenerate the residual(s) best fit molar coefficients by ordinary least square (OLS).Table 2 compares results of measured performance parameters [16] with those frompredicted by OLS analyses for both these AD systems (CFSTR and TAP). Table 2performance parameter comparison includes estimates with and without denitrificationand with and without composite cell mass correction. The need for both corrections isvery noticeable.

The Anaerobic Pump Stoichiometric Stage Process Models

The stoichiometric models for each stage of the Anaerobic Pump (TAP) can be obtained byreverse engineering the port #4 recycle residue composition from the overall process model(Eq. 17). Substituting these “real” residual compositions for stage II recycle and stage Ifugitive stream, solving for a port#4 recycle residual (0.623C1 H1.03 O0.143N00.059), andadding a proportional denitrification reaction result in a TAP stage I net working equation(Eq. 18) and stage II net working equation (Eq. 19) as follows:

TAP net stage I:

C1H1:474O0:403 N0:076 s : inputð Þ þ 0:021C1H0:00067O0:0056N0:1134 s : recycleð Þþ0:0145 NO3

− þ 0:0145Hþ→0:11175C1H0:189O0:116N0:067 s−fugitiveð Þþ0:623C1H1:03O0:143N00:059 s : port#4ð Þ þ 0:09CO2 gð Þ þ 0:123CH4 gð Þþ0:0073N2 gð Þ þ 0:0098C5H7NO2 sð Þ þ 0:024NH4

þ þ 0:024HCO3−

þ0:074H2O lð Þ

ð18Þ


TAP net stage II:

0:623C1H1:03O0:143N00:059 s : port#4ð Þ þ 0:042NO3− þ 0:042Hþ þ 0:302H2O lð Þ

→0:021C1H0:00067O0:0056N0:1134 s : bottom recycleð Þ þ 0:217CO2 gð Þþ0:268CH4 gð Þ þ 0:021N2 gð Þ þ 0:021C5H7NO2 sð Þþ0:0142NH4

þ þ 0:0142HCO3−

ð19Þ

Table 2 Comparison of CFSTR and TAP performance parameters

Performance parameter Average for CFSTRa

Average for TAP combinedb

1. 15day B1 = liters CH4/gram substrate VS addedObserved from kinetic analysis : methane @STP 0.264 0.390Uncorrected stoichiometry : w/o denitrification: 0.266 0.353Uncorrected stoichiometry : w/ denitrification: 0.238 0.236Corrected True Stoichiometry : w/ denitrification: 0.292 0.3952. Process % pCOD reduction in 15-day HRTObserved from kinetic analysis (% pCOD reduction) 57.65 % 82.48 %Uncorrected stoichiometry % pCOD w/o denitrification 56.03 % 56.45 %Uncorrected stoichiometry % pCOD w/ denitrification 52.48 % 52.17 %Corrected true stoichiometry % pCOD w/ denitrification 61.28 % 80.46 %3. 15-day B = liters CH4/gram substrate pCOD addedObserved from kinetic analysis : methane @STP 0.202 0.303Uncorrected stoichiometry : w/o denitrification: 0.166 0.224Uncorrected stoichiometry : w/ denitrification: 0.148 0.147Corrected true stoichiometry : w/ denitrification: 0.182 0.2464. Cell yield (Y, gm cell VS /gram sub pCOD added)Observed cell yield (Y) from literature (60) 0.050 0.100*

Uncorrected stoichiometry : w/o denitrification cell yield 0.051 0.052

Uncorrected stoichiometry : w/ denitrification cell yield 0.058 0.059

Corrected true stoichiometry : w/ denitrification cell yield 0.070 0.0965. Average % biogas composition @STPAverage measured methane (%CH4) 54.6 % 54.2 %Average measured carbon dioxide (%CO 2) 41.2 % 42.0 %

Average measured nitrogen (%N 2) 4.2 % 3.8 %

Uncorrected stoichiometry : %CH4 w/o denitrification 65.7 % 61.8 %

Uncorrected stoichiometry : %CO 2 w/o denitrification 34.3 % 38.2 %

Uncorrected stoichiometry : %N2 w/o denitrification - -

Uncorrected stoichiometry : %CH4 w/ denitrification 55.6 % 54.5 %

Uncorrected stoichiometry : %CO2 w/ denitrification 39.1 % 40.2 %

Uncorrected stoichiometry : %N2 w/ denitrification 5.3 % 5.3 %

Corrected true stoichiometry %CH 4 w/ denitrification 55.8 % 55.4 %Corrected true stoichiometry %CO2 w/ denitrification 39.9 % 41.4 %Corrected true stoichiometry %N2 w/ denitrification 4.3 % 3.2 %

Black font means averaged measured or calculated values from Dave Boone’s kinetic investigation data, based on measured VS, COD, and biogas composition–gas chromatography. Green font means value is

cell growth uncorrected and without denitrification reaction. Blue font means value is cell growth

uncorrected with denitrification reaction. Red font means value is cell growth corrected with

denitrification reactionaAverage CFSTR green means applying Eq. 8; blue means Eq. 9; red means Eq. 11 bAverage TAP combined means stage I + stage II values, green color means combining Eq. 12+13; blue

color applying Eq. 14; red color means applying Eq.17 c TAP observed cell yield (Y) is estimated for complete mineralization of the substrate


Once the port #4 recycle composition was determined, Eqs. 18 and 19 can be used to computethe biogas production and composition for each TAP reactor stage. A good correlation betweenstoichiometric predicted values and measured values is achieved with an OLS-derived Port #4recycle of 0.623C1 H1.03 O0.143N00.059 as shown in Table 3. To reconcile the stoichiometric(predicted) port #4 recycle volatile solids concentrations with the average measured recycle VSsteady-state values, simply add additional port #4 residual (pass through recycle) to both sides ofeach equation (Eq. 18 and Eq. 19) until the flow-through VS concentration values match.

Discussion

The topics requiring discussion are: (1) a summary quantitative view of AD degradationprogress, (2) the residue pCOD calculation via Eq. 7 overestimates the measured pCODvalues, (3) statistical errors using simple OLS regression, (4) cell yields are greater for TAPbecause bioconversion is much greater, (5) molar biogas production is considerably greaterfor TAP than CFSTR, (6) denitrification must be included in the analysis to approximate thebiogas composition (%CH4, %CO2, and %N2), (7) both denitrification and cell correctionmust be included in the OLS regression to achieve a reasonable correlation with measuredperformance parameters, and (8) to approximate the TAP stage biogas production andcomposition, the port #4 recycle residue must be defined via OLS.

Biodegradation Progress

Table 1 exhibits a summary of the elemental analysis for the three residuals. A comparison ofmolar residual compositions shows the progress of anaerobic digestion. By inspection, goingfrom substrate IFUCF (#1) to the CFSTR residual IFUCF (#2) and Eq. 8 shows the AD transitionfrom the feed substrate to the point approaching “stabilization.”Amole of 50:50 sludge substratestarts out relatively rich in hydrogen, oxygen, and nitrogen as C1H1.474O0.403N0.076(s). Over the15-day digestion period, the cell growth consumes the easily degradable substrate materialleaving a more difficult to degrade composite residual of 0.465C1H0.889O0.28N0.028 to dispose(CFSTR). Relative to carbon, a substantial amount of hydrogen, oxygen, and nitrogen has beendepleted during substrate stabilization. Four hydrogens are removed in the formation of everyCH4 molecule produced, and two oxygens are removed in the formation of every CO2 molecule

Table 3 Comparison of measured and predicted TAP stage biogas compositions

Stage performance parameter TAP Stage I Eq. #18 TAP Stage II Eq. #19

1. Average total biogas production (total moles biogas/molesubstrate input)

Measured average steady-state value (mole/mole) 0.220189 0.510645

Corrected true stoichiometry average 0.220186 0.506032

2. Average stage biogas composition (%) @STP

Average steady-state measured methane %CH4 55.67 % 53.27 %

Average steady-state measured carbon dioxide %CO2 41.03 % 42.63 %

Average steady-state measured nitrogen %N2 3.30 % 4.10 %

Corrected true stoichiometry %CH4 w/ denitrification 55.67 % 53.06 %

Corrected true stoichiometry %CO2 w/ denitrification 41.03 % 42.81 %

Corrected true stoichiometry %N2 w/ denitrification 3.3 % 4.14 %


produced. Hidden in the composite residual composition (IFUCF [2]) is a non-trivial amount ofhydrogen, oxygen, and nitrogen sequestered as cell growth 0.02C5H7NO2 (s). Subtracting cellgrowth (cell correction) from the composite by applying Eq. 5 leaves significantly less molaramount for the “true” residual 0.354C1H0.73O0.24N0.037 (s). This residual is composed of notice-ably less hydrogen, oxygen, and nitrogen relative to carbon per Eqs. 10 and 11. According toEq. 11, the CFSTR “true” residual reaction consumes approximately 10 % w/wH2O (grams H2Oper gram of dry biomass represented as CHON) to complete partial stabilization reaction of themixed sludge substrate. This is approximately half (1/2) the moisture content needed to induce amatrix transition from a glassy (amorphous) to a rubbery state (∼20%w/wH2O). This leads to theconclusion that moisture sorption must continue during active AD, not only to maintain thesubstrate polymer transition from glassy to the rubbery state at the cellular level but also toprovide moisture needed for the AD reaction(s).

The need for moisture continues as the AD reactions progress beyond “stabilization.”By inspection of Table 1 (TAP), going from the raw substrate IFUCF [1] to the TAPresidual IFUCF [3] shows that the cell growth continues to increase as substrate conver-sion continues beyond stabilization, but now substantially more hydrogen and oxygenremain in the composite residual C1H1.248O0.357N0.012 (s), while more nitrogen is lostwhen compared to the C1H0.889O0.28N0.028 CFSTR stabilized residual. A residue hydrogenand oxygen increase with greater decomposition is counterintuitive. However, applyingthe cell correction Eq. 5, the reason for the hydrogen, oxygen, increase becomes clear. Thecells grown fraction of the composite is no longer a minor constituent. In fact, the cellcorrection Eq. 16 reveals a true stage II residue that is actually a minor substrate residueconstituent nearly devoid of hydrogen and oxygen plus 87 % fixed carbon (% CHON)C1H0.00067O0.0057N0.1134, and the major constituent is now the cells grown (attached to thedepleted substrate). The stage II bottom composite residue is composed of approximately93 % (w/w) bacterial cells (C5H7NO2) and only 7 % (w/w) remaining substrate residue(mainly fixed carbon). In reality, the cell growth fraction is an amalgam of cells formedduring log growth (active cells) and decayed cell by-products as a result of death,maintenance, and predation (endogenous metabolism). The depleted composite residuerecycled from stage II provides TAP stage I with continuous inoculum (seeding) and asupport medium for immobilization of new cell growth and retention. According to Eq. 17,the overall TAP reaction needs ∼21.6 % w/w moisture to nearly complete the anaerobicbioconversion reaction. Note this is nearly equivalent to the threshold moisture content(∼20 % w/w) needed to induce a matrix transition from a glassy to a rubbery state. Amoisture content range of 50 % is typically reported for uninhibited AD. The sum of theobserved sorption+reaction moisture consumed to complete bioconversion agrees wellwith the published range. Again, to maintain the substrate polymer transition from glassyto the rubbery state at the cellular level, it appears that moisture sorption must continueduring active AD.

Statistical Error Comparisons

As shown in Table 1, the elemental analysis (CHONPS+K, Mg, Ca) accounts for nearly 80,78, and 79 % total solids dry weight for each of the three residues, respectively. Table 4shows elemental mean values and standard deviation (σ) for the important five volatileelements (CHONS) and molecular weight (IFUCFW) for all three residues.

Summing the elemental molecular weights results in the residue(s) ion-free unit carbonformula weights (Table 4). These formula weights (IFUCFW) appear to have a goodaccuracy with a coefficient of variation of only 1.3 % for the raw heterogeneous substrate


50:50 substrate mixture, 1.4 % for the CFSTR residue, and 1.4 % for the TAP bottomresidue. Therefore, the accuracy for stoichiometric molecular structures shown in Eqs. 11and 17 and Table 4 is acceptable. Note that initially the molecular weight decreases forconventional (stabilization) digestion residue and then increases for the full (TAP) digestionresidue. The explanation for the increase in molecular weight is the depleted substrate(IFUCFW) and cell growth given in the “Biodegradation Progress” section.

The selection of performance parameters for ordinary least square (OLS) adjustment canhelp minimize the effect of measurement errors on predicting stoichiometric model coeffi-cients. The parameter list should include both VS and COD (two measures of organiccontent)-based parameters to help offset experimental bias. Similarly, more accuratelymeasured parameters can be used to offset less accurately measured parameters. Data faultsand systematic experimental bias usually appear as poor correlation coefficients betweendata series. If it is apparent that the dataset has outliers, a good alternative regression ismethod may be Least Absolute Deviation regression (LAD) [62]. If, on the other hand, bothCOD and VS data should prove to be confounded, then reduced major axis (RMA,geometric mean) regression may be a good alternative [63]. A reasonably good method ofvalidating a regression model (OLS, RMA, or LAD) is by applying either of two commonresampling methods, jackknifing and bootstrapping [64].

A good AD stoichiometric growth model must accurately predict not only the gas phasecomposition and total gas production but also the amount of residual remaining and amountorganisms grown on the substrate during a steady-state period. Six parameters, methaneyields B and B1, biogas composition %CH4, %CO2, and %N2, organism cell yield (Y), andthe total molar biogas production were selected with this in mind. All regression parametersare conveniently in the 0 to 1 range. The difficulty that arises in determining modelcoefficients and performance values is due to measurement errors typically surroundingsteady-state average values. Steady-state mean values typically have coefficient of variationsin the double digits. In addition, OLS regression theory assumes the independent X vari-able(s) is measured with no error. This is not the case as shown in Table 3; the formulaweights show a coefficient of variation around the mean value of ∼1.4 %, though small whencompared to double digit steady-state errors. This validates using simple OLS regression todetermine the mean coefficients for the performance parameters estimates from equationsEq. 11 and Eq. 17. Figures 1 and 2 show the regression variables compared to a perfect fit foreach regression parameter on the 0 to 1 interval for both processes.

Table 4 Residues’ volatile (CHONS) elemental statistics

Raw 50:50 substrate (%TS) CFSTR residue (%TS) TAP bottom residue (%TS)

Elementa Mean σ Mean σ Mean σ

Carbon 40.4 0.21 44.4 0.20 44.9 0.58

Hydrogen 5.0 0.02 3.3 0.01 4.71 0.38

Oxygen 21.7 0.16 16.6 0.42 21.4 0.22

Nitrogen 3.6 0.07 1.5 0.12 0.65 0.04

Sulfur 0.71 0.01 0.53 0.01 0.07 0.01

IFUCFW 22.15 0.29 18.84 0.27 20.15 0.28

IFUCFW ion-free unit carbon formula weight for the residue volatile fraction (CHONS), σ the standarddeviation around the mean value assuming a normal distribution of errorsa Based on 10-g quadruplicates (n=4) for each residue; units % total solids dry weight


According to Table 2 and Figs. 1 and 2, all six model regression performance parametersshow good agreement with measured steady-state performance parameters. The meanagreement between the calculated and the experimentally determined values for theCFSTR was 100.34±2.2 % with a correlation coefficient (r) of 0.99. The mean agreementbetween the calculated and experimentally determined values for TAP was 0.976±2.6 %with a correlation coefficient (r) of 0.94. The mean agreement for CFSTR is slightly betterthan for TAP. To achieve this level of correlation with measured steady-state biogascomposition values, the model process equations must include the denitrification reactionand cell correction.

As shown in Figs. 1 and 2 and discussed earlier in the “Stoichiometric CODModel” section,errors in calculating methane yields (B1 and B in Table 2) are artifacts of experimental errors(sampling+analytical) associated with COD andVS determinations. This inaccuracy appears inthe OLS regression (Figs. 1 and 2 above). The deviation from the “perfect fit line” isconsiderable for those performance parameters that use COD (B) and VS (B1). Equation 7overestimates pCOD which then underestimates methane yield (B=liters CH4/gram COD

Fig. 1 CFSTR measured vs. predicted performance values via simple regression analysis

Fig. 2 TAP measured vs. predicted performance values via multiple regression analysis


input). Ignoring the soluble COD (sCOD) in Eq. 11 (CFSTR) and Eq. 17 (TAP) is a systematicerror as described in the “Stoichiometric CODModel” section. The continuous loss of sCOD inprocess effluents reduces the methane yield observed. The net effect is the methane yield (B)calculations based on pCOD is noticeably smaller than those based on measured values asshown in Figs. 1 and 2 (range of 0.2 and 0.3). As bioconversion improves beyond merestabilization (TAP Fig. 2), the effect of this error becomes more pronounced. The bulk of theerror in estimating COD containing parameter values is the direct result of using Eq. 7 toestimate particulate COD (pCOD) without a correction for sCOD. To remedy this inaccuracy,the McCarty stoichiometry equation (Eq. 4) would have to include a product soluble COD(sCOD included in Eq 11 and 17), and a corresponding correction for Eq. 7 that would greatlyincrease the degree of complexity of this analysis.

TAP: Correlation Between Each Stage Residue and Gas Production

TAP experimental prototype was designed with two reactors, two residuals, and twomeasured biogas outputs [65]. A primary purpose of this design was to separate the biogasproduced under each stage pressure environment. The critical operations of substrate seedingand solids capture/liquid separation in stage I produced the least biogas. The measuredsteady-state biogas production record showed that 30 % of the total biogas was produced byTAP stage I and the remaining 70 % by stage II. Overall, TAP removed approximately 73 %of the refractory fraction (Rf) within the nominal 15-day hydraulic retention time. Some ofthe refractory fraction solids escaped via port #3 with the fugitive volatile solids. The resultis outstanding conversion efficiency for an all “natural” mixed culture microbial process.Since the vast majority of the substrate bioconversion occurred in TAP stage II, it must haveproduced the majority of cell growth (Eq. 16). Therefore, TAP stage II controls both theextent of digestion (thermodynamics) and digestion kinetics. To exactly match stoichiomet-ric output for each stage to the measured gas output requires the determination of the stage Irecycle residual(s) compositions. A rather simple reverse engineering of the stage biogasoutput yields the port #4 recycle composition (0.623C1 H1.03 O0.143N00.059) as shown inEq. 18 and Eq. 19.

Cell yield (Y) Holds Constant

A common key assumption in AD growth theory is that cell yield remains constant over awide range of substrate concentrations (S) in an AD reactor [53]. This long establishedaxiom is upheld by the results of this stoichiometry (Table 2 CFSTR) study. The extent ofdigestion is consistently limited to “stabilization” by the presence of refractory fraction (Rf)substrate polymers; therefore, YRf=(1−Rf)Ymax: YRf∼0.05 grams cell VS/gram substrateCOD according to the literature [61]. Ymax the theoretical maximum cell yield calculatesto approximately 0.1 g cell VS/gram substrate COD indicating complete bioconversion.Classically, this assumes that S (Eqs. 1 and 2) is the total COD (TCOD) measurement whichis actually the composite of both the biodegradable+nonbiodegradable COD fractions. Interms of cell growth, the denitrification reaction is essentially irrelevant. As the substratedegradation proceeds beyond the conventional stabilization or “biodegradability limit,”according to Table 2 TAP data, cell growth continues and accumulates, and the cell yieldincreases to approximately 0.1 g cell VS/gram substrate COD input. Therefore, as Rf→0,Y→Ymax:Ymax→0.1 g cell VS/gram substrate COD input. The overall TAP cell yielddetermined by OLS regression was 0.0952 g cell VS/gram substrate pCOD. This is remark-ably a good agreement between theory and fitted results. These analytical results leave little


doubt that advanced substrate conditioning via biogas plasticization increases cell yields aspredicted by theory.

Conclusions and Recommendations

This 50:50 heterogeneous sludge substrate is composed of two gross fractions: conventionalAD biodegradable (1−Rf) and conventional AD non-biodegradable (Rf) fractions. As asludge(s) ages, the polymers that remain and accumulate have greater molecular weightand are progressively more resistant to degradation. Hence, substrate biodegradability andresistance are at least partially a function of its history. The two fractions are about 50:50 forDurham mixed sludge. The Durham sludge is composed of approximately 50 % primary and50 % waste activated sludge, the former is comparably biodegradable and the latter iscomparably resistant. The crystalline weight fraction is most likely in the single digits anda constituent of the primary sludge fraction. Hence, comparing CFSTR Eq. 11 to TAPEq. 17–19 suggests that conventional stabilization fails to fully unwind the substrate bondnetwork leaving a considerable refractory residual for handling and disposal. In contrast,TAP biogas plasticization/disruption succeeds in nearly completing polymer bond breakageand unraveling. Therefore, the biodegradability of a substrate (Rf) is not a fixed property.Instead, bio-resistance is a variable that is dependent on the work (W) done on it by aparticular process (i.e., CFSTR vs. TAP) or a series of processes. We believe that this is thefirst time this has been adequately demonstrated.

Even though wastewater sludges are typically delivered in a moisture-saturated pre-plasticizedstate, at or near equilibrium, the plasticization of the amorphous polymer mass is clearlyincomplete, and crystalline regions are not penetrated at all. This is the barrier that limits theanaerobic digestion potential of most organic solid substrates. However, solvents like H2O, biogasCO2 and intermediates like alcohols, volatile acids, and ammonia can penetrate and help toplasticize resistant polymers. The combination reduces the substrate enthalpy binding resistance.This strategy was shown to be successful for this 50:50 wastewater sludge mixture (Durhamsludge).

The long held belief that pressure has no effect on anaerobic digestion (AD) is negated bythese research findings. AD is affected by pressure, not just temperature. ThermodynamicEq. 1 predicts this outcome. A mixture of moisture, biogas (mainly CO2), and other ADintermediate solvents (ammonia, alcohols, and volatile acids) under pressure can beabsorbed, diffuse and plasticize both substrate fractions, relaxing the bond stress of theresistant substrate polymers so they may undergo anaerobic kinetic reactions. This suggeststhat the extent AD bioconversion is only limited by the degree of substrate plasticization–disruption achievable under a particular set of environmental conditions.

These results are strong quantitative evidence that a consortium of ordinary anaerobicmicroorganisms is capable of completing bioconversion of both the conventional biode-gradable (1−Rf) and the resistant (Rf) fractions. This quantitative evidence supports priormeasurements of very high methane yields from TAP stage II reactor during steady-stateexperiments [2]. The most likely mechanism responsible for modifying polymer conforma-tions and distributions is the plasticization effect. The plasticization–disruption pressurecycle (stage II) is the only substantive difference between the two systems studied. TAPstage II results (Tables 2 and 3) show evidence of rapid, unimpeded, and near complete ADbioconversion to biogas. Using AD produced biogas (mainly CO2) to co-penetrate (with moisture)the substrate polymers thus enhancing sorption/diffusion is a viable approach to improvingbioconversion. These stoichiometric results confirm that biogas plasticization improves AD [2].


These results show that residue elemental compositions (Table 1) plus the denitrificationreaction can be successfully fitted to the McCarty theoretical heterotrophic metabolismmodel framework [1]. In order to further improve the accuracy of this stoichiometricanalysis, the modified stoichiometry equation would have to be further corrected for solubleCOD (sCOD) production, further modifying working equations, Eqs. 11, 17, 18, and 19.However, a more complex and comprehensive mathematical model [21] would require muchmore extensive experimental and analytical work.

The process reactions derived using this simplified data reconciliation method represent areasonably accurate quantitative description of anaerobic digestion (AD) for both the CFSTRandAnaerobic Pump (TAP). The stoichiometric equations (CFSTR Eq. 11 and TAP Eqs. 17 to 19)provide good estimates of the mean steady-state performance parameters for both prototype units.The “corrected” stoichiometric process equations demonstrate an internal consistency that yieldsestimated average performance parameter accuracies well within the limits of steady-state exper-imental error. This is fortuitous given the numerous approximations and assumptionsmade in theseanalyses (“Stoichiometric CODModel” section). The simplifying assumptions significantly reducethe amount of analytical work and data reconciliation [56] needed to create the models. The goodagreement qualifies these two stoichiometric models for further thermodynamic analysis. Thethermodynamic changes that accompany advanced TAP reactions are quantifiable including thecontribution made by the phenomenon of “plasticization” toward advanced bioconversion.

The simplified computational treatment developed herein may be used to evaluate andcompare efficiencies with other biomass conditioning and/or disruptive methods that purportto improve energy recovery from organic solid wastes. Processes that utilize natural micro-bial enzyme systems like TAP may prove to be operationally more efficient and less capitalintensive than thermochemical methods such as pyrolysis and gasification.

In retrospect, adopting an experimental control temperature of 25 °C (rather than 20 °C)would conveniently match thermodynamic standard state 25 °C (298.15°K) and 1 atmpressure, though neither entropy nor enthalpy varies greatly with temperature.Temperature control at a slightly higher temperature (25 °C instead of 20 °C) would havea minor effect on kinetic and thermodynamic results.

There may be a significant payoff for AD designs that correct the key constraints involved insubstrate degradation resistance and non-bioavailability. Removal of the biodegradabilitybarriers will improve the process kinetics as well as the bioconversion efficiency. As loadingrates increase, requiring faster and faster bioconversion rates, the need to eliminate the masstransfer resistance becomes acute. One way of doing this is to design AD reactors to saturate thesolution with moisture and CO2 (from biogas), much like it is accomplished in rumen. Thepayoff will be an overall improvement of 40 to 50 % in bioavailability followed by biocon-version at maximum utilization rates [2]. Maximizing energy recovery and minimization ofresidual mass requiring disposal (landfilling) or composting (handling) will improve ADeconomics. Maximizing energy yields in the form of methane (for example CHP) at full-scale waste treatment facilities can, in most cases, exceed facility electricity demand by ordersof magnitude [66], the implied specter of self-sustainable waste treatment completely off-grid.

There is still much work to be done. There is a need to establish a universally accepted datareconciliation method for ADmetabolic processes that is rapid and fully integrates changes in thesolid substrate at the molecular and elemental levels with cell population growth in anaerobicsystems. The simplified approach developed herein may be a good candidate. Closer attentionmust be given to the diffusion-controlled nature of the anaerobic processes occurring on solidsurfaces, particularly those involving the phenomenon of “plasticization” and its relationship tocellulolytic and proteolytic pathways. This phenomenon’s effect on the digestion of naturalpolymers has been ignored for far too long. Surface processes play a major role in rheological


changes to digesting substrates. For instance, changes in these surface properties significantlychange the surface mass and heat transfer characteristics. In addition, more biogas plasticizationresearch dealing with resistant residues such as animal and crop residues would be helpful.Integration of kinetic analysis and bioenergetic analysis can provide useful insights to guide thefuture research design efforts [1]. Ultimately, the combination may provide AD biotechnologywith a unified analytical framework based on first principles that can be expressed quantitativelyfor comparison and verification purposes.

Glossary

Elements:

C CarbonH HydrogenO OxygenN NitrogenP PhosphorusS Sulphur

Elemental Subscripts:

n Moles of carbona Moles of hydrogenb Moles of oxygenc Moles of nitrogend Moles of sulfur

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