EVIDENCE OF CARBOXY ESTER MECHANISMS IN NITRIFICATION FROM THE DYNAMIC REACTION KINETICS AT NATURAL CONCENTRATIONS. Part III. The Oxidation of Ammonia in Nitrification Follows Pseudo Half Order Kinetics Compatible with a Carboxy Ester Mechanism where Hydroxamic Acid is an Intermediate not Hydroxylamine.

EVIDENCE OF CARBOXY ESTER MECHANISMS IN NITRIFICATION FROM THE DYNAMIC REACTION KINETICS AT NATURAL CONCENTRATIONS. Part III. The Oxidation of Ammonia in Nitrification Follows Pseudo Half Order Kinetics Compatible with a Carboxy Ester Mechanism where Hydroxamic Acid is an Intermediate not Hydroxylamine. Andrew P. G. Newton1 1) newton.carboxy[email protected] Abstract Ammonia pulse test experiments at different pHs were conducted on a submerged biofilter with fast recirculation acting as a batch reactor. The steadystate ammonia concentrations in an organic carbon substrate-free environment were similar to natural water courses and the introduced pulses were less than 1 mg / l of total ammonia nitrogen. At pH levels of 7.2 to 9.0 ammonia concentrations returned to the steady state values within 30 minutes, while a significant lag with a slower reaction was noted at a pH of 6.2. Integrated half-order plots have better correlations than the integrated Michaelis-Menten plots. Half-order reaction kinetics differs from Michaelis-Menten type kinetics in a subtle way, with a second molecule leaving in the equilibrium-binding step. At very low ammonia concentrations, as found in natural water courses, half-order kinetics results in faster reaction rates. Half-order kinetics is compatible with the theory that the reactions proceed via a carboxylic ester route, using ATP in a cyclic fashion, with iron-stabilized hydroxamic acid as the true intermediate in ammonia oxidation. The intermediate undergoes a hydrolysis reaction to nitrite and the ester is recycled. The mechanisms include features which allow efficient dynamic control and optimisation as demanded by evolution without extremely toxic hydroxylamine as an intermediate. Design equations are provided for the optimisation of nitrification filters at low and medium TAN concentrations, based upon half-order kinetics and liquid film diffusion. Similar experiments at very high ammonia concentrations, such as those in wastewater treatment, described in the literature indicate that the reaction kinetics, with pre-oxygenated water and favourable temperature conditions, then follows second-order kinetics compatible with a dimer reaction as given in the carboxy ester mechanisms. Data from the literature that examined nitrification in soils using high concentrations of urea indicate that under these conditions, the toxicity of nitrite and ammonia forces the production of nitrous oxides or given time to optimise the diffusion resistance is increased in the form of an intercellular gel. Key words: Nitrification, Pulse testing, Reaction kinetics, Carboxy ester, Theorised mechanisms 1. Introduction Investigations into the mechanisms of nitrification have generally been conducted in a biochemistry laboratory setting, whereby the bacteria are grown in the presence of various molecules of interest. This type of experiment precludes reaction dynamics and thus predetermines the results. Kinetic studies from wastewater plants or aquaculture often report correlation coefficients of grouped data, but they give little insight into the mechanisms. The total concentrations of ammonia nitrogen (TAN) in water treatment and also growth studies in a biochemistry setting are generally very high, and the dissolved oxygen can be limiting. Ammonia levels in a smolt recirculating aquaculture system (RAS) and natural water courses are, however, very low. Kinetic data[1] from submerged RAS nitrifying biofilters, where the flow rate was altered every 24 hours, have established that the reactions can be influenced by liquid film diffusion. In such a case, the reaction is dependent upon the biofilm active area and the liquid film diffusion coefficient as well as the reaction kinetics. To fit the kinetic data, the active area had to be half of the actual area or the film diffusion coefficient for ammonia oxidation would at best, be 60% of the figure for ammonia in pure water. Indeed, excellent fits are obtained with a diffusion coefficient more in line with that of the salt ammonium bicarbonate. Furthermore, the data spread was much larger than would be expected from an RAS with a constant nitrogen load. The numbers of such slow-growing bacteria cannot be expected to have continuously varied. In turn, the evidence suggests that these bacteria were optimising the nitrification reaction rate. Failure to account for the influence of liquid film diffusion on kinetic data can mask the underlying reaction kinetics, and thus also the corresponding mechanisms. In the case of experimental procedures designed to minimise liquid film diffusion, as outlined in the previous paper [2], the reaction kinetics can be examined in a pH-controlled but not predetermined manner based on observing the natural response to disturbances. These initial pulse-testing experiments, involving large impulses, confirmed that, at higher TAN concentrations, the oxidation reaction follows zero-order kinetics before switching to half-order or first-order kinetics. Michaelis-Menten kinetics was not supported. It was also found that the reactions could be autocatalytic in nature, depending on the filter history. The experiments provided evidence that the ammonia oxidation reaction was subject to the use of an activator and that bicarbonate ions were probably involved in the reactions; in this case not only as buffers. The pulse experiments described here involved modest impulses and were designed to observe the dynamic nitrification reactions, particularly at low concentrations. Nitrification at the concentrations found in aquaculture or in water courses, in which liquid film diffusion is influencing, raises very serious questions regarding energy management of the bacteria. Nitrifying bacteria are at least 2.5 billion years old [3], whereby older archaea mostly share the same metabolic pathways as bacteria. The bacteria exist despite living on the most frugal of energy sources in competition with heterotrophic bacteria, which have more energy to obtain fixed nitrogen. Evolution will have rejected mechanisms which 1 Parameter Units Aquaculture R2 Experimental dp(mm) 12.2 6 a of filter (m2/m3) 271 550 z (m) 2 x 1.80 1 x 1.02 Re(superficial) 13-187 194 DHCO− 3/OH−(m2/s ×109) 1.12/2.18 1.48/2.88 h (m/min ×103) 0.36-2.22 1.62/2.52 Table 1: Liquid Film Mass Transfer Parameters. Diffusivity for Ammonium Cation with Given Anion do not support very efficient control and optimisation strategies. In addition, it would be expected that the process of nitrification would avoid the use of extremely toxic intermediate chemicals. 2. Experimental The bacteria for the experiment were a mix of pure culture Nitrosomonas europea and Nitrobacter europea living on a Skinner and Walker type medium lacking organic carbon. The details of the experimental rig, with its horizontal submerged biofilters forming a fast recirculating system, have already been described [2]. It was also shown that nitrite oxidation proceeds at a very fast rate, so that nitrite is not expected to inhibit the ammonia oxidation reactions. The pulse tests here were conducted at less than 1 mg/l TAN, with the pH of the rig being altered a few days prior to the tests. As previously, samples were taken after allowing the substrate pulse to circulate in order to avoid any transient effects. The aim of the experimental design was to reduce the effect of liquid film diffusion on the reaction kinetics observed at low, environmentally-relevant ammonia concentrations. Halving of the particle diameter and increasing the temperature both result in higher liquid film mass transfer coefficients. Table 1 compares the experimental pulse test design with the recirculating aquaculture system (RAS) data as calculated using the recommended equation of Dwivedi and Upadhyay [4]. The system liquid volume was 31.2 l, of which 7 l was contained in the filter (the filter void fraction being 0.45). 3. Results The pH was successfully maintained at the stated pH by means of the control system adding aqueous sodium carbonate. The first samples were taken 5 minutes after the pulse addition. The TAN versus time data from the pulse test experiments are given in Fig. 1. As in the pre-test experiments, integrated kinetic plots were carried out to distinguish between the two kinetic types. Half-order kinetics, in which the origin is zero and the slope yields the 2 kinetic constant, are provided in Fig.2. The plots for Michaelis-Menten kinetics, in which the slope and a negative intercept yield the kinetic constants, are provided in Fig. 3. The resulting correlation ratios and the apparent kinetic constants are provided in Table. 2 and Table. 3. 0 0.2 0.4 0.6 0.8 1 1.2 −20 0 20 40 60 80 pH 6.2 0 0.1 0.2 0.3 0.4 0.5 0.6 0 5 10 15 20 25 30 35 pH 7.2 0 0.1 0.2 0.3 0.4 0.5 0.6 0 5 10 15 20 25 30 35 pH 8.0 0 0.1 0.2 0.3 0.4 0.5 0.6 0 5 10 15 20 25 30 35 pH 9.0 TAN (mg/l) Time from End of Lag (min) TAN (mg/l) Time After First Sample (min) TAN (mg/l) Time After First Sample (min) TAN (mg/l) Time After First Sample (min) Figure 1: Pulse TAN Tests at Different pHs. Fits based upon the chi-square fitted plots for a pH of 7.2, 8.0 and 9.0, first-order kinetics ( ) can be rejected in favour of half-order ( ) or Michaelis-Menten kinetics ( ). At a pH of 6.2, where ammonia gas is in short supply, it is observed that the TAN concentration does not drop for a significant period of time. The ammoniaoxidising bacteria require time to utilise the sudden increase in ammonia. That is, a molecule, such as ATP, is required to respond that was readily available for ammonia oxidation in the experiments at higher pHs, but is in short supply or harder to produce at a pH of 6.2, through proton pumping for example. There would appear to be an accelerated reaction rate after the lag before it stabilises at a more constant rate. Despite the good fits, a closer examination of residuals to the fits is warranted. Data on residuals to the best fits are provided in Figure 4, with curves drawn through the points. A simulation of the experimental dynamics after the pulse input is also provided in Fig. 5. Within the scope of the experiment, the biofilm area was not determined, but was taken to cover all the available area. The extent to which this area is then "activated" is unknown. It will be assumed that two thirds of the 3 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0 10 20 30 40 50 60 70 80 pH 6.2 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0 5 10 15 20 25 30 35 pH 7.2 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0 5 10 15 20 25 30 35 pH 8.0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0 5 10 15 20 25 30 35 pH 9.0 √Ci−√C t(min) √Ci−√C t(min) √Ci−√C t(min) √Ci−√C t(min) Figure 2: Half-Order Kinetics irregular particle-specific area is covered with active ammonia-oxidising bacteria, corresponding to the area of a spherical particle. As in Figure.7 the data at pH 7.2 can be fitted with a pseudo-rate constant k of 9.1×10−5mg1/2l1/2/min. The pseudo-rate constant to liquid film diffusion coefficient ratio is zero or close to it. 4. Discussion The pulse experiments described here were conducted at low ammonia concentrations, more in line with those in aquaculture and natural water courses. They were all conducted a few days apart, and, unlike the pre-testing experiments, the pulse concentrations were moderate and short-lived. A very signifiPulse Testing Data at Re 194 pH R2kIa 7.2 0.994 0.035 8.0 0.996 0.045 9.0 0.992 0.042 Table 2: Apparent Half-Order Kinetic Constant 4 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 0 50 100 150 200 pH 6.2 0 1 2 3 4 5 6 7 8 0 20 40 60 80 100 120 pH 7.2 0 1 2 3 4 5 6 7 8 0 20 40 60 80 100 120 pH 8.0 0 1 2 3 4 5 6 7 8 0 20 40 60 80 100 120 pH 9.0 ln(Ci/C)/(Ci−C) t/(Ci−C) ln(Ci/C)/(Ci−C) t/(Ci−C) ln(Ci/C)/(Ci−C) t/(Ci−C) ln(Ci/C)/(Ci−C) t/(Ci−C) Figure 3: Michaelis-Menten Kinetics cant difference to the pre-testing experiments is that the time required to reduce the pulse from 1 mg/l to 0.03 mg/l, not 0.35 mg/l TAN, was only 35 minutes. The half-order rate constants are provided in Table. 2. When operating the experimental rig at low steady-state concentrations, the bacteria reacted much faster to obtain the energy contained in the substrates. In common with the repeat experiment in the previous paper, the bacteria optimise the process and, in this case, do so on a very short time scale. Grouping data, in which the bacteria can optimise between runs, complicates analysis of the reaction kinetics. The emphasis should be on data quality, as is the case for pulse testing in the process industries. Reactions occur in a short period of time and the main experimental deficiency was that a continuous TAN trend is desirable for pulse testing. Pulse Testing Data at Re 194 pH R2kIa kII 7.2 0.264 0.079 0.881 8.0 0.852 0.173 3.01 9.0 0.067 -0.015 -3.94 Table 3: Apparent Michaelis-Menten Kinetics Constants 5 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 0 5 10 15 20 25 30 35 Michaelis-Menten −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 0 5 10 15 20 25 30 35 Half Order Residuals (tfit/t −1) Time After First Sample (min) pH 7.2 pH 8.0 pH 9.0 Residuals (tfit/t −1) Time After First Sample (min) pH 7.2 pH 8.0 pH 9.0 Figure 4: Michaelis-Menten Kinetic and Half-Order Plot Residuals Recirculating Aquaculture System u>16 m/h Biofilter R2kIa R1 0.964 0.037 R2 0.955 0.044 Table 4: RAS Apparent Half-Order Kinetic Constants An examination of the residuals from the chi-square fits indicates that they are significantly worse at the beginning of the tests. The residual plots appear similar to an underdamped second-order system returning to its set point after a disturbance. Such behaviour is typically caused by some feedback control mechanism. As the residuals are pH-dependent, this suggests that feedback control using protons from the products of the process to control the feed-rate (substrate binding) occurs. The repeat experiment [2] also suggests that rapid autocatalytic optimisation can occur, but the mechanisms discussed in current literature do not envisage the use of activators. Any postulated mechanism must address the issue of process control and optimization, as demanded by evolution. The integrated Michaelis-Menten kinetic plots do not obey the expected tight linear relationship with a negative intercept. Conversely, the integrated half6 0 0.5 1 1.5 2 0 1 2 3 4 5 0 0.005 0.01 0.015 0.02 0 0.2 0.4 0.6 0.8 1 TAN (mg/l) Time (min) NA(mg/min) k×103(m3/m2)(mg/l)0.5/min Figure 5: Left: Simulated behaviour after a pulseis added to the tank ( ) and then exits the biofilter ( ). Right: The effect of increased activator concentrations for liquid film diffusion coefficient h= 0.36 ×103m/min with C = 1 ( ), 0.5 ( ), 0.2 ( ) and 0.1 ( ) mg/l. order plots, with the origin as the intercept, do. Based upon the integrated rate equation plots, half-order kinetics enjoys better correlations and less variation in the determined kinetic constants compared to Michaelis-Menten kinetics as given in Table. 3. In addition, the pre-pulse testing experiment [2] at higher TAN concentrations, but less than 2 mg/l TAN, also correlates to a half-order integrated plot. The integrated Michaelis-Menten plots do not correlate. The recirculating aquaculture system data [1] were complicated by liquid film diffusion, but the apparent rate constants in this case were also more consistent for half-order kinetics. The spread in the RAS data can be attributed to bacterial process optimisation. Limiting the data to superficial velocities over 16 m/h as in Fig. 6 gives a more linear plot with a large data spread. All three data sets thus indicate that the oxidation of ammonia proceeds according to half-order kinetics. This contradicts the often assumed MichaelisMenten kinetics, in which ammonia is in equilibrium, binding with the enzyme ammonia monoxygenase and then reacting with a peroxide to hydroxylamine. The rate equations are based upon the bulk total ammonia nitrogen rather than the bulk fluid ammonia gas concentration. The apparent half-order kinetic constants do not vary significantly with pH, implying that the concentration in the cells of the substrate is relatively constant and independent of the bulk fluid 7 0 0.05 0.1 0.15 0.2 0.25 0.3 0 5 10 15 20 R1 0 0.05 0.1 0.15 0.2 0.25 0.3 0 5 10 15 20 R2 √Ci−√C Residence Time (min) √Ci−√C Residence Time (min) Figure 6: RAS Half-Order Kinetics pH. This could be a result of binding and/or transport molecules supplying the oxygenase enzyme. 4.1. Initial Reaction Rates and Control Within the scope of the pulse experiments the first sample, taken after 5 minutes to allow for complete mixing, was taken as the initial concentration. This approach is the same as that taken in chemical engineering and therefore deviates from many Michaelis-Menten derived plots in biochemistry. which use initial reaction rates. The problem in an intact biocell setting is that optimisation and control response must be anticipated. The initial reaction rate will be influenced by this behaviour. If we are to examine steady-state reaction kinetics using integrated reaction plots, then the initial concentrations of importance are those which occur after the immediate peak control response. It is suggested that the initial concentration should be chosen in such a manner that the resulting integrated plots will conform to some known steady-state kinetics. For example, in the pre-test experiment [2] the bacteria are seen to switch the kinetics. In the pulse tests here it is anticipated that the initial reaction rate is adjusted by pH and ATP control. To fit the immediate initial rate data, the relevant concentrations in the cells would be required. By biochemical standards the ammonia oxidation reaction is very slow and yields insights into the mechanisms and control behaviour. Any attempt to 8 the bacteria numbers, rather than activator concentrations, are responsible for the spread in the plots. In this case, the kinetic constants for the more typical pH ranges are similar, which would suggest that the reaction was, to a large extent, decoupled from the bulk pH in the typical operating ranges. It is easier to maintain the internal pH at a high pH as the reaction produces protons, with the concentration of bicarbonate ions also playing a role. The non-linear half-order plot for a pH of 6.2 suggests that changes in the carboxy phosphate concentration occurred in a pH environment which was challenging. 4.5. Nitrifying to Very Low Ammonia Concentrations Without any mass transfer influence, the ammonia oxidation rate, and thus nitrification, is governed by the bulk TAN concentration to the power of a half 4. This also yields the fastest reaction rates. At very low concentrations, where the mass transfer driving force diminishes, diffusion becomes a possible limiting factor and needs to be minimised. The reaction rate is then equal to the mass transfer rate. N=h(C−C∗) = kC∗1/2(5) C∗=(k/h)2+ 2C−k/hq(k/h)2+ 4C 2(6) When k/h is equal to zero, the equation represents the case of no diffusion resistance. Figure 5 shows that increasing the rate constant using an activator for strong liquid film diffusion at low substrate concentrations has limited benefits. Maintaining high activator concentrations at low substrate concentrations can be expected to require more energy. A better strategy would be to increase the use of the activator in a ratio to the liquid film transfer coefficient. N=h(C−C∗)=kC∗1/2 AT P C∗1/2(7) Based on this scenario, with a constant liquid film coefficient, the reaction order appears to be first order. N=k′C∗=1 1 k′+1 h C(8) In the case of sustained higher substrate concentrations, with reduced diffusion resistance, increasing the bacteria concentrations at lower activator concentrations is deemed to be more advantageous. The mixing regime in combination with the hydraulics plays a central role in achieving low ammonia concentrations. Table. 5 indicates the flow regimes of different biofilter types. The liquid film correlation of Dwivedi and Upadhyay[4] used previously [1] for submerged packed bed biofilters is also valid for fluidised biofilters (mixed flow). The following outlines the design considerations for a recirculating aquaculture system (RAS) nitrification filter but the same principles also apply to 15 0 0.1 0.2 0.3 0.4 0.5 0.6 0 5 10 15 20 25 30 35 pH 7.2 0 0.1 0.2 0.3 0.4 0.5 0.6 0 5 10 15 20 25 30 35 pH 7.2 TAN (mg/l) Time After First Sample (min) √Ci−√C t(min) Figure 7: Half-order kinetics with no liquid film diffusion k/h = 0 ( ) and weak liquid film diffusion k/h = 0.25 ( ). Regime Biofilter Type Natural Water Course Plug Submerged crushed rock Fast flowing stream with small pebbles Mixed Fluidised sand Fast flowing river with sediment Mixed Fluidised plastic (MBBR) Table 5: Flow Regimes natural water courses. It is assumed that solid waste, as a high ammonia/BOD concentration source, is removed and treated separately from the recirculated water. Nitrifying bacteria are sensitive to light, so the biofilter design should exclude light and, in the case of fast flowing streams, shade from trees should be provided (in addition to the shade provided by the reverse side of stones). Particles with intricate internal structures can be expected to predominately form a biofilm on the external area, as the concentrations at the biofilm interface are extremely low. Eqn.9 shows that the biofilter media specific area is clearly a major variable, but its advantages can be reduced at low ammonia concentrations in a mixed flow design. −rA=aN (9) 16 τ=V/q =CAi −CAo −rA (10) τ=V/q =zAx/q = CAi Z CAo dCA −rA (11) 0 50 100 150 200 250 300 0 0.2 0.4 0.6 0.8 1 MM Kinetics 0 50 100 150 200 250 300 0 0.2 0.4 0.6 0.8 1 Half Order 0 200 400 600 800 1000 0 0.2 0.4 0.6 0.8 1 Half + LFD k= 0.02 k h= 4 0 200 400 600 800 1000 0 0.2 0.4 0.6 0.8 1 Half + LFD k= 0.047 k h= 4 1/−rA(lmin/mg) TAN (mg/l) 1/−rA(lmin/mg) TAN (mg/l) 1/−rA(lmin/mg) TAN (mg/l) 1/−rA(lmin/mg) TAN (mg/l) Figure 8: Top. Inverse rate plot using fitted constants for pH 7.2 data. Half-order and Michaelis-Menten kinetics for different fluid mixing scenarios. Bottom. Influence of liquid film diffusion. Prehn’s Test Group 4.5 and 40 m/h. The design equation for mixed flow is provided by Eqn.10 and for plug flow by Eqn.11. Both batch reactors and also plug flow reactors in fast recirculation systems as used here, follow Eqn.11, where only the elapsed time rather than the residence time is used. Residence times, and thus the volumetric requirements, are illustrated in Fig. 8, using the experimental fits with an inlet TAN of 0.5 mg/l reduced to 0.05 mg/l. In order to distinguish between half-order kinetics and Michaelis-Menten kinetics experiments are best conducted at very low TAN concentrations. Where ammonia outlet concentrations are low, plug flow has the lower residence time requirements (area under curve). Where outlet ammonia concentrations are higher, the requirements for mixed flow (rectangular area at inlet concentration) are close to plug flow for a specific particle size, although a fluidised biofilter will have a higher voidage. Poor liquid film diffusion results in 17 increased residence time requirements and thus, assuming a superficial velocity, forms the basis of the iterative design steps in which the filter type and particle characteristics are examined. Reducing particle size increases the specific area, but in the case of a submerged biofilter, the size should not be too small as this may cause blockages and bypassing. On the other hand, fluidised systems may suffer from hydraulic instability and erosion issues. The moving bed biofilm reactor (MBBR) design originates from wastewater treatment applications at high ammonia and BOD concentrations. It is a mixed flow design. In such a system aeration should be conducted in order to yield water velocities which minimise diffusion limitation. Low ammonia concentration systems also have low dissolved oxygen requirements for the nitrification step. In general, a design choice must be made between the use of moving plastic particles with their large specific areas, and, in such cases, how much they should move, or whether a stationary packed bed design is better. 4.6. Autocatalytic Kinetics Following the peroxide reaction the intermediate is transported to an enzyme which conducts the hydrolysis reaction to nitrite, generating energy in the process. This can be used to produce more of the ester or for growth. Production of more of the ester results in autocatalytic kinetics [2]. Z+WGGGAN + Energy([B]) (12) The ammonia oxidation rate depends on the concentration of [B], but only to the half order. Conversely, growth (active area) is first order. Thus, in situations with sustained high ammonia concentrations the bacteria can be expected to switch from producing the ester to producing proteins for growth. 4.7. Strong Liquid Film Diffusion Liquid film diffusion reduces concentrations in the area around the biofilm and, at low TAN concentrations, lowers the reaction rate. Prehn’s [22] experimental biofilter setup, operated at a similar superficial velocity to that used here, took over 300 minutes to lower the TAN from 1 mg/l to 0.05 mg/l at best, as opposed to 40 min. Prehn estimated the average biofilm thickness in their filter to be only 14 µm, which is entirely in line with the bacteria avoiding mass biofilm transfer limitations. The filter media was propriety tubular mesh of 55 mm diameter and had a correspondingly low specific area. In the case of a pipe with no biofilm the large mesh diameter would suggest laminar flow and thus a constant liquid film coefficient independent of velocity [23]. Integrated plots for various kinetics are provided in Figure 9. Based on the correlation coefficients provided in Table. 6, half-order kinetics is equally as valid as first-order kinetics with deviations generally occurring at low concentrations. Acceptable correlations for zero-order kinetics are found at lower velocities where the final TAN concentrations were approximately 0.4 mg/l. 18 Michaelis-Menten kinetics yields poor correlation coefficients with positive intercepts and is thus rejected. Importantly, unlike Michaelis-Menten kinetics, there is no continuous change over the experiments with high impulse concentrations displaying zero-order kinetics to those indicating first-order kinetics at low impulse concentrations. Their experimental data, especially at low concentrations, thus supports strong liquid film diffusion where the activator concentration varies with superficial velocity as in equation 5. Since liquid film transfer coefficient behaviour is unknown, further conclusions cannot be drawn. Either the mesh filter media lowers film transfer resistance or, although based upon the mesh diameter laminar flow, the biofilm itself prevails. As illustrated in Figure 8, increasing the superficial velocity from 4.5 to 40 m/h reduces the TAN concentration to 0.2 mg/l rather than 0.3 mg/l. 0 0.2 0.4 0.6 0.8 1 1.2 0 50 100 150 200 250 300 Zero Order 0 0.5 1 1.5 2 0 50 100 150 200 250 300 First Order 0 0.5 1 1.5 2 2.5 0 100 200 300 400 500 M-M 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0 50 100 150 200 250 300 Half Order C t(min) ln(Ci/C) t(min) ln(Ci/C)/(Ci−C) t/(Ci−C) √Ci−√C t(min) Figure 9: Integrated kinetic plots for Prehn et al’s data for the test group at 4.5 m/h The grouped data is derived from 2 or 3 repeat experiments using different filter elements from the same biofilter (elements were in parallel) in the RAS. It can be observed that each filter element had similar reaction rate constants up until the lowest concentrations. Newton [1] analysed very low TAN concentration RAS data and tested for goodness of fit using chi-square probabilities. The analysis revealed that multiple molecule reaction mechanisms, such as half-order kinetics, produced similar kinetic constants for the two biofilters which were in parallel. First-order, zero-order and Michaelis-Menten kinetcs fits required 2to 3-fold differences in the kinetic constants for the two filters. Prehn’s data con19 Test Group m/h 2.5 4.5 9 18 40 Re (superficial) 34 60 121 241 536 zero-order 0.937 0.919 0.93 0.834 0.839 First order 0.976 0.954 0.987 0.94 0.988 Michaelis-Menten 0.229 0.143 0.534 0.472 0.787 half-order 0.979 0.971 0.985 0.954 0.97 Table 6: Correlation coefficients R2derived from Prehn et al’s data for simple integrated reaction kinetics. Test Group m/h 2.5 4.5 9 18 40 Ci1.35 1.25 1.11 1.0 1.02 k×a0.0163 0.0205 0.0282 0.033 0.0466 hm/s ×1050.34 0.42 0.58 0.68 0.96 Table 7: Prehn et al’s data fitted for half-order kinetics with strong liquid film diffusion assuming k/h = 4 curs with half-order kinetics along with the use of activators, as in the theorised carboxy ester mechanisms, yielding apparent first-order kinetics in the case of strong liquid film diffusion. A more suitable setup to investigate the effects of flow velocities employs a plug flow design yielding short residence times through the use of a filter medium whose liquid film transfer characteristics have been typified. TAN concentrations below 0.6 mg/l using a Skinner and Walker medium [1], in which data from any filters in parallel is not grouped, would seem most appropriate. 4.8. High Ammonia Concentrations Result in Second-Order Kinetics Associated with Dimer Reactions The kinetic experiments were conducted at low (natural) inlet ammonia concentrations, mostly below 0.6 mg/l TAN, resulting in extremely thin biofilms. Zero-order kinetics in a partially penetrated thick biofilm leading to half-order kinetics [24] [25] at low TAN concentrations can be dismissed [22] in the experiments here. The observed half-order reaction kinetics is due to the ammonia oxidation reactions themselves. Haug and McCarty [26] examined nitrification at much higher concentrations using synthetic wastewater containing no carbon source. The inlet concentrations to their biofilter were approximately 10 mg/l TAN, with the treated water exiting at 1 mg/l TAN. Importantly their experiments used preoxygenated water to avoid the dissolved oxygen limitations typically experienced at high ammonia concentrations. In all other respects, the experimental setup and the submerged filter size were similar to that used here. The observed ammonia oxidation reaction order in their concentration ranges at 25◦C was 1.5 and not 0.5 as found here at more natural concentrations. Higher ammonia concentrations are more toxic, and in addition to this, when using carboxy ester mechanisms the probability that an undesired substrate es20 0 0.5 1 1.5 2 2.5 3 3.5 4 0 6 12 18 24 30 36 0 0.5 1 1.5 2 0 6 12 18 24 30 (C(1−nobs) i−C(1−nobs))/(1 −nobs) Filter Height Inches 1.5 0.75 0.5 (C(1−1.5) i−C(1−1.5))/(1 −1.5) Filter residence time, min 8.7 8.1 8.3 8.6 10 13.9 Figure 10: Left:Data from Haug and McCarty Figure 2. Integrated kinetic plot confirming the observed reaction order at high ammonia concentrations as in wastewater treatment to be 1.5. n= 2nobs −1Right:Haug and McCarty Table V 24◦C. Increase in inlet concentrations drops reaction rate, possibly due to increased toxicity and inadequate biofilm thickness developed in time. ter will be formed increases. Because of the production of intercellular gel and the resulting internal diffusion, concentrations can be lowered at the cell walls. This comes with an energy cost and a time delay in reacting to large step disturbances. The amounts produced can be expected to match the concentrations, with biofilm thickness varying along the filter length but not necessarily the cell density within it. The kinetics of ammonia oxidation at high concentrations is similar to that of internal diffusion in catalyst pellets. In fact, equation 6 can be equated with those for catalyst pellets, where the observed reaction order differs from the true reaction order [27][28]. The relationship is provided by nobs = (n+1)/2. Haug and McCarty’s experiments at higher temperatures, with an observed reaction order of 1.5, are thus compatible with internal diffusion and a true reaction order of 2. Zero-order and half-order kinetics are rejected as shown in Fig.10. The data implies that the rate-limiting reaction step changes at higher ammonia concentrations, yielding entirely different reaction kinetics. A second-order reaction implies that two ammonia-bound molecules react with each other. This is much like the formation of double-stranded DNA from single-stranded DNA, which also yields second-order reaction kinetics. Such a dimer mechanism has been provided in the carboxy ester mechanisms involving 21 an iron-peroxide enzyme. Rather than being a random event of two ammonia molecules meeting at a metal enzyme site, the reaction is probably being choreographed by charge-based, iron-binding mechanisms. It is concluded that at higher concentrations, the ester equilibrium binding step is no longer limiting, presumably because there are excess amounts of ATP. At lower temperatures, Haug and McCarty’s data indicate that the rate order drops to 1, presumable due to ATP/energy constraints. The oxidation of ammonia is thus being conducted in an efficient way over a large concentration range through the use of intercellular gel and changes in the reaction kinetics. The product of ammonia oxidation, nitrite, is extremely toxic and this, in turn, implies that the nitrite-oxidising bacteria are separated from the ammonia oxidisers by intercellular gel. The toxic nature of the substrates and the binding properties of the carboxy esters can form the basis of symbiotic relationships. It can be speculated that step changes to higher concentrations with an inadequate biofilm thickness can lead to a decrease in the reaction rate. In wastewater treatment plants, dissolved oxygen concentrations will often limit the reactions, with other bacteria breaking down proteins generating ammonia. However, because the ammonia is toxic to those bacteria, this will allow for more symbiotic relationships regarding the intercellular gel. 4.9. Iron-Based Cytrochrome c-554s Reconstituted systems of membranes containing ammonia mono-oxygenase with purified "hydroxylamine" oxidoreductase have only converted ammonia to nitrite in the presence of cytochrome c-554 [29] [30]. This indicates that cytochrome c-554 is essential in the oxidation of ammonia. Andersson et al. [31] carried out a very extensive investigation into this ferric cytochrome. Their studies were "consistent with either an electron transport role or an enzymatic function" for cytochrome c-554. Ammonia and hydroxylamine had no effect on the optical or EPR spectrum of ferric cytochrome c-554. In addition, "no oxygen uptake was observed with ammonia or hydroxylamine in the presence or absence of reducing agents". They showed that cytochrome c-554 has four ferric haems and that unique magnetic interactions exist. These complex magnetic interactions were indicated to be pH-dependent. Although "the role of cytochrome c-554 in ammonia metabolism by Nitrosomonas remains unknown" [31], they suspected that the role of cytochrome-554 is two-fold and reflects either an oxygen or ammonia binding/enzymatic function as well as an electron transport function. 4.10. Theorised Mechanism for the Oxidation of Hydroxamic Acid The hydrolysis reaction occurs at a different enzyme and needs to be transported there in a stabilized form, such as by producing an iron complex. This oxidation is fully reversible and is catalysed by the enzyme named "hydroxylamine" oxidoreductase. The reaction may proceed with one hydroxamic acid molecule being hydrolysed to nitrite and the starting phosphate ester. The oxidation of ammonia is sensitive to light and this would suggest that alternatively 22 a nitroso mechanism might be involved. This then implies that two hydroxamic acid molecules are involved in a symmetric reaction which results in two different oxidation states. The theorised general mechanism for this reaction is provided below:- E O C O N H OH E O C O N H OH H2O E O C O ONO E O C O N O 4H++ 4e− E O C O N O 2H++ 2e− E O C O N H OH E O C O ONO E O C O OPO2− 3 HPO2− 4NO− 2+H+ The electrons are assumed to be transferred between cytochrome c-554 and cytochrome c-552. The electrons then pass along the cytochrome chain to form NADH. The NADH could undergo oxidative phosphorylation, yielding 3 ATP 23 molecules. ATP could also be produced by the protomotive force. This ATP can then be used to produce more carboxy phosphate ester, and/or for growth. Suzuki and Kwok [29] noted in their reconstituted experiments that ammonia oxidation was affected by the phosphate concentration, which would strengthen the half-order kinetic mechanism interpretation of the data presented here, and MgCl2in combination with cytochrome c-554. Newton [9] proposed the use of iron-stabilised hydroxylamic acid to confirm that it is a substrate for the hydrolysis enzyme, but it could be argued that it is broken down to hydroxylamine. Reaction kinetics are therefore the best method to establish the true intermediate reaction mechanisms. 4.11. Soils, Substrate Toxicity and Symbiosis In the chemical process industries, the main process objective might be considered to be an economic one, such as maximising feedstock processing. This is indeed mostly the case, but it comes after honouring operator safety, plant integrity, and product specifications. Multi-variable controllers with predictive abilities are often used, with process disturbances being handled before the economic variables are pushed. Growth studies with bacteria may be interpreted in terms of determining maximum substrate processing rates, but there are other process objectives. In agriculture, ammonium nitrate and urea, which are granular solids with a high fixed nitrogen content, are used as fertilisers. Both are made from synthesis gas, whose feedstock is methane gas (a potent green-house gas) yielding carbon dioxide. Urea is broken down by organisms that contain the hydrolysis enzyme urease, yielding two ammonium ions, a bicarbonate ion and a hydroxide ion. Urea itself is relatively non-toxic, as is nitrate, but ammonia is toxic and the nitrification intermediate nitrite is very toxic. In soils, where the moisture content determines the concentrations, it is clearly a significant factor. Ardakani et al. [32] examined the kinetics of nitrification in artificial soil using urea rather than ammonia itself. The experiments involved percolating water containing 100 ppm N urea through the soil. After 17 days it was judged, based upon the concentration profiles, that a steady-state had been established. The experiment was continued for a further 14 days and the substrate concentration profiles again determined. The use of urea introduces more complexity, but their repeated experiment reveals the objectives of the bacterial processes. The results for both days, down to a depth of 20 cm, are presented in figure 11, with the non-toxic and toxic substrates plotted separately. The urea hydrolysis rate is higher on the 17th, as are the resulting nitrate levels. After a further 14 days, with the potential for further optimisation, the rate of urea conversion has decreased and the concentration of toxic ammonia increases. The observed 40 ppm ammonia-N concentration represents a concentration 100 times higher than the natural water course concentrations examined earlier. On day 31, nitrite levels are lower, but less nitrous oxide / dinitrogen has been produced from nitrite. If the numbers of ammonia and nitrite oxidisers had increased in the 14 days, then the ammonia concentrations would be expected to be lower and 24 [8] J. March, et al., Advanced organic chemistry, McGraw-Hill, 1985. [9] A. P. G. Newton, Investigations into the kinetics of nitrification, Ph.D. thesis, Department of Chemical and Process Engineering, Heriot-Watt University, Edinburgh, Scotland (9 1990). [10] J. Loveless, H. Painter, The influence of metal ion concentrations and ph value on the growth of a nitrosomonas strain isolated from activated sludge, Microbiology 52 (1) (1968) 1–14. [11] P. Wood, Nitrification as a bacterial energy source, Special Publications of the Society of General Microbiology, Vol. 20: Nitrification (1986) 39–67. [12] J. H. Shears, P. Wood, Spectroscopic evidence for a photosensitive oxygenated state of ammonia mono-oxygenase, Biochemical Journal 226 (2) (1985) 499–507. [13] T. Hollocher, M. Tate, D. Nicholas, Oxidation of ammonia by nitrosomonas europaea. definite 18o-tracer evidence that hydroxylamine formation involves a monooxygenase., Journal of Biological chemistry 256 (21) (1981) 10834–10836. [14] R. Dua, B. Bhandari, D. Nicholas, Stable isotope studies on the oxidation of ammonia to hydroxylamine by nitrosomonas europaea, FEBS letters 106 (2) (1979) 401–404. [15] K. Anderson, A. Hooper, O2 and h2o are each the source of one o in no2-. 15n-nmr evidence, Febs. Lett 164 (1983) 236–239. [16] J. A. Zahn, D. M. Arciero, A. B. Hooper, A. A. DiSpirito, Evidence for an iron center in the ammonia monooxygenase from nitrosomonas europaea, FEBS letters 397 (1) (1996) 35–38. [17] T. Yoshida, M. Alexander, Hydroxylamine formation by nitrosomonas europaea, Canadian journal of microbiology 10 (6) (1964) 923–926. [18] M. T. Von Breymann, Studies of hydroxylamine in the marine environment, Master’s thesis, Oregon State University, United States of America (1982). [19] G. Bengtsson, S. Fronæus, L. Bengtsson-Kloo, The kinetics and mechanism of oxidation of hydroxylamine by iron (iii), Journal of the Chemical Society, Dalton Transactions (12) (2002) 2548–2552. [20] A. Kock, H. W. Bange, Nitrite removal improves hydroxylamine analysis in aqueous solution by conversion with iron (iii), Environmental Chemistry 10 (1) (2013) 64–71. [21] S. Gebhardt, S. Walter, G. Nausch, H. Bange, Hydroxylamine (nh2oh) in the baltic sea, Biogeosciences Discussions 1 (1) (2004) 709–724. 31 [22] J. Prehn, C. K. Waul, L.-F. Pedersen, E. Arvin, Impact of water boundary layer diffusion on the nitrification rate of submerged biofilter elements from a recirculating aquaculture system, Water research 46 (11) (2012) 3516– 3524. [23] A. Skelland, Diffusional mass transfer, Wiley, 1974. [24] WEF, Design of Municipal Wastewater Treatment Plants: WEF Manual of Practice No. 8 ASCE Manuals and Reports on Engineering Practice No. 76, Fifth Edition, McGraw-Hill Education, 2010. [25] P. Harremoës, Biofilm Kinetics, Vol. 2, John Wiley and Sons Ltd, 1978, pp. 71–109. [26] R. T. Haug, P. L. McCarty, Nitrification with submerged filters, Journal (Water Pollution Control Federation) (1972) 2086–2102. [27] J. Coulson, J. Richardson, Chemical Engineering, Vol. 3, Pergamon, 1979. [28] G. Froment, K. Bischoff, Chemical reactor analysis and design, Wiley, 1990. [29] I. Suzuki, S.-C. Kwok, A partial resolution and reconstitution of the ammonia-oxidizing system of nitrosomonas europaea: role of cytochrome c 554, Canadian Journal of Biochemistry 59 (7) (1981) 484–488. [30] D. C. Y. Tsang, Mechanism of ammonia oxidation in nitrosomonas europaea: role of cytochrome c-554, Master’s thesis, University of Manitoba, Canada (1982). [31] K. K. Andersson, J. D. Lipscomb, M. Valentine, E. Münck, A. B. Hooper, Tetraheme cytochrome c-554 from nitrosomonas europaea. heme-heme interactions and ligand binding., Journal of Biological Chemistry 261 (3) (1986) 1126–1138. [32] M. Ardakani, M. Volz, A. McLaren, Consecutive steady state reactions of urea, ammonium and nitrite nitrogen in soil, Canadian Journal of Soil Science 55 (2) (1975) 83–91. [33] T. Hofman, H. Lees, The biochemistry of the nitrifying organisms. 4. the respiration and intermediary metabolism of nitrosomonas, Biochemical Journal 54 (4) (1953) 579–583. [34] M. Engel, M. Alexander, Enzymatic activity of nitrosomonas extracts, Journal of bacteriology 78 (6) (1959) 796. [35] H. Lees, Hydroxylamine as an intermediate in nitrification, Nature 169 (4291) (1952) 156–157. [36] W. O. Kermack, H. Lees, The chemosynthetic micro-organisms, Science Progress 40 (157) (1952) 44–53. 32