Anaerobic digestion (AD), as one of the oldest human biotechnology, has attracted revived research focus on the underpinning biological principle in recent years due to its potential in renewable green energy. With the assistance of the latest 454 deep sequencing technology, two independent studies were conducted with a shared goal to understand the operational influences on the AD microbiology from the unprecedented depth and breadth of genetic information. The first study aimed to decipher the contribution of a newly-devised waste sludge pretreatment method, which promised significant improvement in downstream biogas production. The first application of whole genome metagenomic approach on this topic revealed extensive shifts in both microbial and functional consortia towards higher biodegradation after pretreatment; meanwhile dominant acetoclastic and hydrogenotrophic methanogenesis pathways were identified concurrently with an alternative enzymology in Methanosaeta. The second study focused on the temporal dynamics of bacteria residing in production-scale biogas bioreactor coupled with multiple-sampling strategy for a realistic description of the actual microbial structure. Both bacterial fingerprint marked by feedstock and evolutionary drive towards biodegradation were revealed by 16S rDNA amplicon multiplex pyrosequencing, where clustering analyses further delineated the taxonomic plasticity and functional resilience of the bacterial communities over time. Phylogeny coverage of the highly diverse population was also improved by the adopted strategy, providing insights for sampling and sequencing standards. Altogether, the combined results garnered knowledge enrichment to the relationship between AD microbiology and operational parameters, which will assist the design of more efficient bioenergy platform in future. / published_or_final_version / Biological Sciences / Master / Master of Philosophy

The Continuously fed Stirred Tank Reactor (CSTR) is a popular design for anaerobic treatment of wastewater. This reactor type is simple in design and operation, independent of biomass type and low in capital costs. The CSTR has, however, to be operated at long Hydraulic Retention Times (HRT) of the order of 16 to 30 days since biomass is continuously lost with the effluent. Various alternate concepts of reactor design have, therefore, been developed to allow more rapid treatment. Treatment can be enhanced by retaining biomass within the digester so that the HRT is decoupled from solid biomass retention time (SRT). Unlike in continuous stirred tank digesters where the SRT is equal to HRT, the SRT in other designs are much greater than the HRT. This allows the wastewater to be treated at high throughputs while retaining the biocatalyst (or biomass) mediating the treatment within the digester. In this study the operation of a CSTR was intensified by separating SRT from HRT while taking into account the economical aspects. The intensification of operation is defined as increasing wastewater throughput or organic loading rate while at the same time maintaining efficiency of treatment and robustness to reject disturbances (changes in wastewater concentration and flow rate). The operation of existing CSTR was intensified by addition of carriers. It is hypothesized that by providing surfaces (or carriers) for bacterial attachment within the continuous stirred tank digester, biomass will be better retained and the wastewater throughput can be increased. The carriers or surfaces employed in this study were light carrier elements (shredded granular rubber tire having a density of 0.96 g/cm3) that move gently with the water in the reactor. This carrier material is much cheaper compared with other commercial carrier materials. This reactor type, called an Anaerobic Moving Bed Reactor (AMBR), was applied in this study to treat high strength synthetic wastewater, containing molasses as the main substrate. The improvement of reactor performance was clearly shown by the capability of the system to be operated without any difficulties at HRT of 6 days at an OLR of 5.8 g COD/l/d or at HRT of 1 day at an OLR of 4 g COD/l/d. The carriers were shown to be effective in retaining biomass aggregates. The AMBR was further intensified by changing the feeding strategy. It was shown that in stirred tank digester without carriers an intermittent feeding strategy resulted in better microbial capacity to degrade higher chain volatile fatty acids like propionic and butyric acids than the continuous feeding mode. An increase in degrading capacity of the intermittently fed digester was shown via degradation rates of pulse additions of propionic and butyric acids and by its capability of handling all changes in loading rates imposed. The continuously fed digester, receiving constant feed, on the other hand, suffered more when loading rates were changed, and the degradation rates of propionic and butyric acids were slower. The intermittent feeding mode was then implemented on the AMBR, and it was operated as a sequencing batch reactor with a fill, react, settle and decant period in each cycle. The sequencing batch mode when applied to the AMBR (now called an Anaerobic Moving Bed Sequencing Batch Reactor or AMBSBR) could increase capability of the digester to handle higher shock loads. At 3.8 d HRT the AMBSBR could handle an OLR of 10.8 g COD/l/d as opposed to 7.4 g COD/l/d by the AMBR. At 2.5 d HRT the AMBSBR could handle an OLR of 6.4 g COD/l/d while the AMBR could only be loaded at an OLR of 4.2 g COD/l/d. The ratio of SRT to HRT was at least 15 for this reactor. The reactor was able to handle concentrated feed flow rates at longer cycles or more dilute feed flow rates at frequent shorter cycles. The proposed operational strategies were verified by using a structured mathematical model which was developed based on the IWA ADM1 model. Several modifications were implemented to the model to obtain better predictions. The modified model was capable in predicting all the trends of the operating variables from both continuously and intermittently fed reactors. None of the two model versions (ADM1 and modified models) was, however, able to predict the increased propionate degradation capacity in intermittently fed digesters. The reason for this was the assumption of fixed stoichiometry of fermentative reactions for glucose mineralisation. By modifying the fractions of glucose mineralisation a better fit between experimental results and the model could be obtained.

Human consumption of water contaminated with faecal polIutants is the source of most sanitation related diseases. Excreta related diseases can be controlIed by improvements in excreta disposal. The primary consideration is to remove contact between the people and the faecal matter. The conventional waterborne sewage system is not an achievable minimum standard in dense peri-urban areas in the short term, due to its high cost. A need for a cost effective system that is easily maintained and does not require electricity or highly skilled labour for developing communities in South Africa was identified. The objective of this investigation was to assess the suitability of the Anaerobic Baffled reactor (ABR) as a primary onsite treatment system for low-income communities. The ABR is a high-rate compartmentalised anaerobic bioreactor, the design of which promotes the spatial separation of microorganisms. The trials were conducted on a 3200 L pilot-scale reactor placed at Kingsburgh wastewater treatment works, which receives only domestic wastewater. The ABR proved to be stable and consistent in its performance. Operating at a hydraulic retention time of 22.5 h, the reactor effiuent was ca. 200 mgCODIL. The 0,45flm filtered (soluble) COD was 100 mgIL, indicating there was approximately 100 mgIL of COD in the effluent that was in particulate form. The ABR achieved 60%VSS and 50%TSS removal with effiuent TSS content of about 225 mgIL. The system was hydraulicalIy overloaded and organicalIy under loaded. The Biochemical Methane Potential tests showed that 60% of the COD in the effiuent was biodegradable, and the effluent COD could be reduced to less than 100 mgCODIL if the HRT is increased giving a possible removal of 80%. The analytical campaign revealed that we were sampling at peak flow, when COD was high. The average COD fed to the reactor was much lower than that showed by routine analysis and the ABR had a "true" COD removal of 42%. The reactor was able to handle the daily variation ofthe wastewater. Settling tests were done to measure how much of the suspended solids in the ABR are retained at the operating upflow velocity. The method selected was shown to have an error that ranged from 5 to 42%, and the ABR was retaining between 60 and 90% ofsolids in the reactor at an upflow velocity of O.5m/h. The preliminary work with the fabric membrane showed great potential benefits that can be gained if it had to be included. It showed good ability to remove indicator organism and solids that contributed a lot to the effiuent COD. The membrane had 5 log removal of indicator organism and 80% reduction of COD. The membrane was operated for a short time before clogging; its operational lifespan needs to be greatly extended before it can be used with the reactor in a community. Since there is no nutrient removal in the AER, the effiuent can be used for food production provided sufficient pathogens removal is achieved. Provided that the first compartment can be modified and the concentration of pathogens in the effluent is sufficiently reduced, the ABR can be considered for use in a community. / Thesis (M.Sc.Eng.)-University of KwaZulu-Natal, Durban, 2005.

Providing water and proper sanitation to poor communities by 2015 is one of the United Nations targets for this millennium. In South Africa many communities aspire to waterborne sanitation. However, there is a technology gap for decentralized and sustainable waterborne sanitation systems capable of treating domestic wastewater (Foxon et al., 2006). Although domestic wastewater is more commonly treated using aerobic processes, anaerobic processes may be more appropriate for decentralized applications since they do not require aeration. Research is currently being undertaken to understand the behavior of a combined ABR-MBR unit for treating domestic wastewater. In this study, the anaerobic baffled reactor (ABR) was investigated by analyzing physico-chemical and biochemical data from experiments on a laboratory-scale ABR. This anaerobic reactor was treating complex particulate wastewater made up of sludge from the ventilated improved pit latrine toilets (known as VIP sludge). The main focus of this study was to establish the relationship between the increasing organic loading rates and the effluent characteristics (such as chemical oxygen demand: COD and extrapolymeric substances: EPS). The present work was structured in two parts; in the first part the reactor was operated at constant hydraulic retention time (HRT) without controlling feed characteristics. In the second part, the ABR was operated with step increases in organic loading rates. It was logistically not possible to provide a feed of real domestic wastewater to the laboratory-scale equipment. Consequently, a pit latrine sludge diluted with tap water was used to feed the ABR. This feed was found to have different biodegradability characteristics compared to domestic wastewater. However, the results still give insight into the performance of the ABR and into the treatability of VIP sludge. COD removal ranged from 52 to 80 % depending on the inlet COD. Some COD removal was due to solids retention in compartments, while it was estimated that only 28% of COD removal was due to biological degradation. Soluble extrapolymeric substances (proteins and carbohydrates) which are usually a by -product of anaerobic degradation were higher in the feed than in the effluent despite the increasing organic loading rates. However, more than 50 % of soluble extrapolymeric substances from the influent remained in the effluent and were found (in a parallel project) to influence membrane fouling in the membrane section of the experimental set-up (ABR-MBR unit). Parameters such as pH, conductivity, alkalinity, total and volatile solids were also investigated in this study. The pH decreased slightly from the inlet to the outlet during all runs even though the loading rates were increased. Conductivity increased significantly from influent to effluent with the increasing organic loading rates. Large amounts of total solids were retained in the reactor during the treatment process. Low alkalinity production was recorded during the operation of the reactor. In most cases, the data recorded in this study showed a low biological activity taking place while the reactor was working at room temperatures. Overall, up to 80% of removal efficiencies in terms of total COD and solids were recorded with increasing organic loading rates at constant hydraulic retention time. While these results do not allow the prediction of ABR-MBR performance during the treatment of real wastewater, it was concluded that: Most solids retention occurred in the feed tank. Most COD removal occurred as a result of solids retention and digestion. Loading characteristics did not strongly influence effluent EPS, pH or alkalinity, but did influence COD and conductivity. The relatively low biodegradability of the feedstock indicates that anaerobic digestion is not the most appropriate treatment for VIP sludge. / Thesis (M.Sc.Eng.)-University of KwaZulu-Natal, Durban, 2010.

This thesis presents a chemical, microbiological and mathematical analysis of an anaerobic baffled reactor (ABR) treating domestic wastewater. The purpose of this study was to gain an understanding of the mechanisms of treatment of domestic wastewater in an ABR at pilot-scale, and to use this understanding to develop some guidelines for the design of ABR technology for the anaerobic treatment or pre-treatment of domestic wastewater. Previous research has been undertaken on ABR technology, but no detailed studies of the performance of an ABR on domestic wastewater at pilot-scale have been reported. In this thesis, operating data from a 3 000 ℓ pilot-scale ABR are presented and analysed. Two hypotheses were proposed: that (i) the baffled design of the reactor would facilitate phase separation whereby acidogenic and methanogenic processes predominate in different physical locations in the reactor; and (ii) the critical design parameter is the applied hydraulic retention time. The principle findings of this research were: • The pilot-scale ABR functioned as a solids retention device. Particulate material was retained through settling in the first compartment, forming a gel-like matrix. Reduction of solids occurred through anaerobic conversion to CH4 and CO2. • Partial phase separation of acidogenic and methanogenic communities was observed. • The major factor that controlled biomass washout rate and therefore reactor performance was upflow velocity in each compartment. At higher upflow velocities, slow growing microorganisms failed to establish, resulting in increased solids accumulation rates, while at lower upflow velocities, stable digestion proceeded. • Relatively poor treatment rates were obtained due to the low inherent alkalinity of waters in eThekwini municipality resulting in low operating pH values. • Insufficient pathogen reduction was observed indicating that post-treatment of effluent would be required. It was concluded that the benefit of the baffled design was related to the system’s solids retention characteristics and that the critical design parameters for an ABR domestic wastewater treatment unit were compartment upflow velocity and applied hydraulic retention time. / Thesis (Ph.D.)-University of KwaZulu-Natal, Durban, 2009.

The sugar industry processes sugar cane and sugar beet to manufacture edible sugar. A high rate anaerobic system followed by an activated sludge process to 'polish' the effluent is presently the best available technology not entailing excessive costs for the treatment of wastewater from sugar processing factories. Upflow anaerobic sludge blanket (UASB) reactor systems are the most commonly implemented, with the higher loaded expanded granular sludge bed (EGSB) type systems gradually replacing at least some of the UASB applications. This higher loading carries with it a greater risk of process instability, especially given the irregular quantity and composition of sugar processing wastes. Control actions are required for process efficiency, preferably with appropriate control parameters monitored on-line. The need to balance economics (with regards to quantities of chemicals dosed) with the safety/stability of the process further exacerbates the need for close control. There are a limited number of control actions available e.g. bicarbonate alkalinity (BA) dosing, temporary diversion of load by feed rate variation, or dilution with final effluent. Monitoring of conventional anaerobic digester systems typically consists of a combination of intermittent manual sampling followed by off-line analysis coupled with qualitative observations. Hence a decline in reactor performance could go unnoticed for a significant period of time. A simple yet reliable control system could not only minimise labour, but could also react to any changes in reactor conditions as soon as they occurred, leading to more efficient process operation, higher quality treatment and ultimately greater economic gain. The industrially recognised 'bottleneck' in the quest for automatic control is the availability of reliable and cheap on-line analysers. In the work presented here a series of experiments have been carried out on a simulated sugar processing wastewater using an on-line BA monitor in conjunction with an adaptive control strategy developed in a parallel PhD project. The possibility of achieving successful automatic control of an EGSB reactor through its start up phase and also during steady state operation (including some degree of process optimisation) and a series of organic step-change experiments was investigated. Two different control actions to maintain a BA set-point in the reactor, organic loading rate (OLR) variation and BA dosing, were compared. Research was carried out on a 30 1 EGSB reactor rig operating at 37 °C, fitted with on-line sensors to measure temperature, gas production, carbon dioxide percentage and pH. All sensors were interfaced with a PC configured to scan the sensors at one minute intervals. Five attempts to automatically start-up the EGSB reactor were made (Experiments 1-5), using OLR variation as a control action at a constant hydraulic retention time (HRT) of 23.3 hours, with various improvements and adjustments made to the reactor and control system after each. It was concluded that it was not possible to automatically control start-up to steady state using OLR as a control action using the BA monitor and controller in their present forms. Main reasons for this were the susceptibility of the laboratory-scale BA monitor to blockage by biomass washed out of the reactor (a common occurrence during the start-up phase) and the severity of loading rate oscillations. For Experiment 6 BA was dosed according to the relationship of the on-line BA monitor output to the BA setpoint, and OLR was changed approximately weekly according to operator expertise based on on- and off-line data and visual observations. HRT was maintained at 22 hours. A successful, sustainable startup was achieved, with mean % COD removal during the first 10 weeks being 78 % at a mean OLR of 9 kgCOD/m3 /day. After the successful start-up period, the reactor's HRT was approximately halved to 11.2 hours, and two OLR stepchange experiments (from 10.0 kgCOD/m 3/day to 28.1 kgCOD/m3 /day, and from 11.8 kgCOD/m3/day to 32.4 kgCOD/mVday) of twelve hour duration were carried out, followed by a removal of the control system and a similar organic step-change experiment (13.0 kgCOD/m 3/day to 32.9 kgCOD/m 3/day). It was found that approximately halving the HRT had no significant effect on the biomass or biomass activity. The HRT change did however adversely affect the smoothness of control, although control was not lost, as the on-line BA was always kept between 1500 and 2000 mgCaCO3/l. All parameters measured (pH, BA TVFA, effluent COD, carbon dioxide percentage, off-line methane percentage) indicated that conditions were less severe during and after organic step-changes when control was present. The controller also minimised the time spent at pH values potentially damaging to the bacteria (time spent at pH less than 6.0 in the two OLR step-change experiments where control was present (Experiments 6.3 and 6.4) was no greater than one hour, and in the experiment with no control (Experiment 6.5) was 8 hours) and returned the reactor to conditions conducive to efficient waste water treatment faster than when no control was present. Throughout all experiments controller oscillations remained severe. In this case, BA dosing as a control action was preferable, as the destructive effect of severe oscillations in the volume of BA dosed was considerably less than the effect of severe oscillations in the OLR, which repeatedly led to washout. Although it was possible to control the reactor subjected to OLR step-changes using the BA monitor based control system, control of the start-up phase was problematic. The BA monitor was not reliable or robust enough to provide the requisite data for use in the automatic control of the start-up of a high rate anaerobic digester. A thorough professional re-engineering of the B A monitor to deal with a greater sample flow rate, deliverable by a full-scale reactor (using wider bore tubing and larger flows, a more precise pumping system, and possibly with a suitable low maintenance sample filtration unit) could provide a suitably reliable and robust instrument.

Integrated algae pond systems (IAPS) combine the use of anaerobic and aerobic bioprocesses to effect wastewater treatment. Although, IAPS as a technology process offers many advantages including efficient and simultaneous N and P removal, no requirement for additional chemicals, O2 generation, CO2 mitigation, and a biomass with potential for valorization, a lack of technological advancement and the need for large land area, has limited the reach of this technology at industrial scale. In mitigation, peroxonation was introduced as a tertiary treatment unit and its effect on COD and TSS of IAPS treated water investigated. An effort was made to characterize the soluble but persistent COD in IAPS treated water and, productivity of the HRAOP mixed liquor was investigated to gain insight into the potential use of this biomass. Results show that peroxone treatment effectively reduced COD, TSS, and nutrient load of IAPS water without any significant impact on land area requirement. Indeed, summary data describing the effect of peroxone on quality of IAPS-treated water confirmed that it complies with the general limit values for either irrigation or discharge into a water resource that is not a listed water resource for volumes up to 2 ML of treated wastewater on any given day. Extraction followed by FT-IR spectroscopy was used to confirm albeit tentatively, the identity of the soluble but persistent COD in IAPS treated water as MaB-floc EPS. Results show that MaB-flocs from HRAOPs are assemblages of microorganisms produced as discrete aggregates as a result of microbial EPS production. A relationship between photosynthesis and EPS production was established by quantification of the EPS following exposure of MaB-flocs to either continuous light or darkness. Several novel strains of bacteria were isolated from HRAOP mixed liquor and 16S ribosomal genomic sequence analysis resulted in the molecular characterization of Planococcus maitriensis strain ECCN 45b. This is the first report of Planococcus maitriensis from a wastewater treatment process. Productivity and change in MaB-flocs concentration, measured as mixed liquor suspended solids (MLSS) between morning and evening were monitored and revealed that MLSS is composed of microalgae and bacteria but not fungi. Concentration varied from 77 mg L-1 in September (winter) to 285 mg L-1 in November (spring); pond productivity increased from 5.8 g m-2 d-1 (winter) to 21.5 g m-2 d-1 (spring); and, irrespective of MLSS concentration in late afternoon, approximately 39% was lost overnight, which presumably occurred due to passive removal by the algae settling pond. The outcomes of this research are discussed in terms of the quality of treated water, and the further development of IAPS as a platform technology for establishing a biorefinery within the wastewater treatment sector.

Inadequate sanitation is one of the leading causes of water pollution and consequently illness in many underdeveloped countries, including South Africa and, specifically, the Eastern Cape Province, where cholera has become endemic. As modern wastewater treatment processes are often energy intensive and expensive, they are not suitable for use in these areas. There is thus a need to develop more sustainable wastewater treatment technologies for application in smaller communities. The integrated algal ponding system (IAPS) was identified as a possible solution to this wastewater management problem and was investigated for adaptation to local conditions, at the Rhodes University Environmental Experimental Field Station in Grahamstown, South Africa. The system was monitored over a period of nine years, with various configuration adjustments of the high rate algal pond (HRAP) unit operation investigated. Under standard operating conditions, the system was able to achieve levels of nutrient and organic removal comparable with conventional wastewater treatment works. The mean nitrate level achieved in the effluent was below the 15mg.l-1 South African discharge standard, however, nitrate removal in the IAPS was found to be inconsistent. Although the system was unable to sustain chemical oxygen demand (COD) removal to below the 75mg.l-1 South African discharge standard, a removal rate of 87% was recorded, with the residual COD remaining in the form of algal biomass. Previous studies in the Eastern Cape Province have shown that few small wastewater treatment works produce effluent that meets the microbial count specification. Therefore, in addition to the collation of IAPS data from the entire nine year monitoring period, this study also investigated the use of the HRAP as an independent unit operation for disinfection of effluent from small sewage plants. It was demonstrated that the independent high rate algal pond (IHRAP) as a free standing unit operation could consistently produce water with Escherichia coli counts of 0cfu.100ml-1. The observed effect was related to a number of possible conditions prevailing in the system, including elevated pH, sunlight and dissolved oxygen. It was also found that the IHRAP greatly enhanced the nutrient removal capabilities of the conventional IAPS, making it possible to reliably and consistently maintain phosphate and ammonium levels in the final effluent to below 5mg.l-1 and 2mg.l-1 respectively (South African discharge standards are 10mg.l-1 and 3mg.l-1 in each case). The quality of the final effluent produced by the optimisation of the IAPS would allow it to be used for irrigation, thereby providing an alternative water source in water stressed areas. The system also proved to be exceptionally robust and data collected during periods of intensive and low management regimes were broadly comparable. Results of the 9 year study have demonstrated reliable performance of the IAPS and its use an appropriate, sustainable wastewater treatment option for small communities.

Endoglucanases play an important function in cellulose hydrolysis and catalyse the initial attack on the polymer by randomly hydrolysing the β-1,4 glucosidic bonds within the amorphous regions of cellulose chains. Cellulolytic bacteria have been isolated and characterised from the sewage sludge and the activation of several hydrolytic enzymes under biosulphidogenic conditions of sewage hydrolysis has been reported. The aims of this study were to: identify, induce production, locate and isolate, characterise (physicochemical and kinetic) and purify endoglucanases from anaerobic biosulphidogenic sludge. The endoglucanase activities were shown to be associated with the pellet particulate matter and exhibited a pH optimum of 6 and temperature optimum of 50 °C. The enzymes were thermally more stable when immobilised to the floc matrix of the sludge than when they were released into the aqueous solution via sonication. For both immobilised and released enzymes, sulphate was slightly inhibitory; activity was reduced to 84 % and 77.5 % of the initial activity at sulphate concentrations between 200 and 1000 mg/l, respectively. Sulphite was stimulatory to the immobilised enzymes between 200 and 1000 mg/l. Sulphide stimulated the activities of the immobilised endoglucanases, but inhibited activities of the soluble enzymes above 200 mg/l. The enzyme fraction did not hydrolyse avicel (a crystalline substrate), indicating the absence of any exocellulase activity. For CMC (carboxymethylcellulose) and HEC (hydroxylethylcellulose) the enzyme had K_m,app_ values of 4 and 5.1 mg/ml respectively and V_max,app_ values of 0.297 and 0.185 μmol/min/ml respectively. Divalent ions (Cu²⁺, Ni²⁺ and Zn²⁺) proved to be inhibitory while Fe²⁺, Mg²⁺ and Ca²⁺ stimulated the enzyme at concentrations between 200 and 1000 mg/l. All the volatile fatty acids studied (acetic acid, butyric acid, propionic acid and valeric acid) inhibited the enzymes, with acetic acid eliciting the highest degree of inhibition. Sonication released ~74.9 % of the total enzyme activities into solution and this was partially purified by PEG 20 000 concentration followed by DEAE-Cellulose ion exchange chromatography, which resulted in an appreciable purity as measured by the purification factor, 25.4 fold.

The influence of Al 3+ on the anaerobic treatment of a poultry slaughterhouse wastewater was studied in this work. The soluble COD (SCOD), volatile acid (VA) concentrations, and methane yield values were measured and compared for zero, 15, and 40 ppm Al 3+ runs. Methane yields of 55.4, 144.2, and 215.4 ml CH4/g. COD for zero, 15, and 40 ppm Al 3+ concentrations, respectively, were observed. Furthermore, SCOD and VAs were not detectable in the reactor that was seeded with 40 ppm Al 3+. It was concluded that inhibitory effects of long chain fatty acids (LCFAs) on aceticlastic methanogens were reduced by aluminum ion. This conclusion was also corroborated by a new mathematical model for estimating the Monod parameters developed in this work. The main characteristic of this new model is that estimated parameters must satisfy some restrictions, which provides consistency for the estimated parameters.