Bias error in each of the models for the given dataset was quantified with the Mean Error (ME) and Percentage Bias (PBIAS) criteria. On the basis that measures of error in these criteria are defined as observed variable less predicted variable, a negative outcome reflects a systematic over-prediction and a positive outcome reflects a systematic under-prediction. AD-FTRW2 under-predicts all of the measured variables except Mixed Liquor Suspended Solids (MLSS) which is marginally over-predicted. Due to the very low percentage bias outcomes for both pH and MLSS in AD-FTRW2, it can be said that the model displays negligible bias error for these variables. Bias error can be said to be significant in AD-FTRW2 for the variables Alkalinity, Biogas Flow Rate and VFAe. Notably bias error for pH and Alkalinity shifts from systematic over-prediction in AD-FTRW1 to systematic under-prediction in AD-FTRW2. This indicates a marked change in the underlying models governing these variables. These variables would be most significantly influenced by the ionic speciation modelling in AD-FTRW1 and AD-FTRW2 which is the area that this study has changed most markedly.
Finally the co-efficient of efficiency (CE1,2) gives a means of directly comparing the performance of each of the models on the given dataset with a value of 1 indicating perfect performance (with respect to AD- FTRW2), zero indicating no improvement in performance from the reference model and negative values indicating negative improvement with respect to the reference model. The reference model in this instance was taken as AD-FTRW1. The co-efficient of efficiency highlights that AD-FTRW2 presented an improved performance on all of the measured variables except VFAe with the greatest area of improvement being in the area of pH prediction.
Table 14: Hypothesis Test Parameters
Hypothesis Testing
Statisitcal Index Degrees of Freedom Sum of Squared Residuals Measure of Variance
Output Unit AD-FTRW1&2 AD-FTRW1 AD-FTRW2 AD-FTRW1 AD-FTRW2
pH - 26 3.25 1.15 0.13 0.04
Alkalinity - 14 15244100.60 11967520.50 1088864.33 854822.89
Biogas Flow Rate - 26 131161.07 75241.52 5044.66 2893.90
VFAe - 14 1812185.57 1897193.05 129441.83 135513.79
MLSS - 26 205.19 172.21 7.89 6.62
With reference to the methodology outlined in Section 3.8.2, a hypothesis test was carried out by means of an F-test to establish whether the improvements seen in the predictive capacity of AD-FTRW2 were significant as compared to the predictions of AD-FTRW1. The test hinges on a ratio of two variances which were calculated as the quotient of the sum of squared residuals over degrees of freedom. All of these measures are depicted in Table 14 above. Two important notes are the differing degrees of freedom between the modelled variables and the fact that the sum of squared residuals is reduced from AD- FTRW1 to AD-FTRW2 for all variables except VFAe. The implication of the latter was that the F-test was not performed on VFAe due to the fact that there was clearly no improvement on the predictability of this variable. The degrees of freedom are calculated as the difference between the number of data points
and the number of free parameters in each model ( ). The reason for the fact that this quantity alternates between 26 and 14 for the different variables is that the dataset used for model validation had 12 days of data missing for alkalinity and effluent volatile fatty acid concentration.
Table 15: Hypothesis Test Conclusions
Hypothesis Testing
Statisitcal Index F-test statistic Critical F Value F-test conclusion
Output Unit AD-FTRW1 vs 2 AD-FTRW1 vs 2 AD-FTRW1 vs 2
pH - 2.83 1.93 significantly_different
Alkalinity - 1.27 2.48 not_significantly_different
Biogas Flow Rate - 1.74 1.93 not_significantly_different
VFAe -
MLSS - 1.19 1.93 not_significantly_different
Table 15 above depicts the results of the hypothesis test on each target constituent. It was carried out at a significance level of . The F-test, which takes into account model complexity together with model accuracy, reveals that AD-FTRW2 is only significantly better in predicting pH. Under the assumptions highlighted in the section on Model Evaluation Approach, the statistical analysis supports the research hypothesis that “The pH prediction in Sasol Technology’s existing AD model (AD- FTRW1) will be improved through the incorporation of a more comprehensive ionic speciation model (AD-FTRW2).”
5 DISCUSSION
Anaerobic digestion, as a treatment option, has significant operational and cost benefits when compared to an activated sludge unit treating a similar effluent. These include reduced energy input, energy recovery from biogas and low sludge production.
Reduced energy input (as compared to activated sludge systems) is as a consequence of the fact that anaerobic digestors do not require aeration. Aeration is coupled with a significant energy cost due to the fact that it requires blowers to force air into the system. In the Sasol wastewater treatment processes it is also speculated that aeration results in volatilization of many of the organics in the wastewater. This is an environmental concern as it implies a displacement of the contaminants in the wastewater whereby water pollution becomes air pollution with no intermediate treatment.
Lower sludge production is a consequence of the fact that biomass yield co-efficients are lower in anaerobic systems. Further to this, anaerobic membrane bioreactors (the reactor technology for which AD-FTRW1 and AD-FTRW2 were specifically developed), have an increased advantage in that they have a significantly reduced land footprint. This stems from the fact that the membrane systems enable increased sludge retention times resulting in better acclimated biomass that is more efficient in digesting the organics typically present in that system’s feedstock. This increase in digestion efficiency leads to a reduction in the required hydraulic retention times and therefore smaller reactors. As was mentioned previously the drawbacks to anaerobic digestors are that they are difficult to control, prone to system failure and they lack disturbance rejection ability. The solution to these drawbacks is seen to lie in accurate mathematical modelling of these systems that will lead to advanced model-based process control. It is in light of this philosophy that this research was undertaken and the implications of the steps taken in this research are discussed in greater detail in this section.
The enhanced modelling depicted by the comparative results of AD-FTRW1 versus AD-FTRW2 has industrial implications in the realms of research and development, process design, operation and control.
- Coupled modeling and experimentation in the context of optimal experimental design has the potential to speed the technological development process in this field.
- The enhanced process model (AD-FTRW2) could assist in the design of new anaerobic digestion of Fischer-Tropsch reaction water facilities.
- From an operation and control perspective, AD-FTRW2 could assist in advanced model-based control to improve process disturbance rejection. Further to this, the model could be used to optimize alkalinity and nutrient dosage, which has proven to be the major operating cost in anaerobic digestion of Fischer-Tropsch reaction water.
The significance of this work from a research perspective in the anaerobic digestion modelling field is that the developed model (AD-FTRW2) addresses limitations identified in preceding AD models and
specifically in ADM1. The enhanced physico-chemical modelling achieved by integrating a comprehensive ionic speciation subroutine introduces the modelling of non-ideality through ion activity corrections and ion pairing; both model features that were lacking in ADM1 (Batstone et al., 2012). The validation of AD-FTRW2 on experimental data sourced from a lab-scale digester treating industrial effluent of a pH of approximately 3.77 shows that the method of physico-chemical modelling applied in this research gives indications of representing low pH systems well. This should improve the capability of the model for simulating digester failure; a limitation identified in ADM1 whose pH system is only valid for dilute systems (Batstone et al., 2012). While the better modelling of digester failure is indicated, this needs to be validated with appropriate reactor failure experimental data that was not available in this research. AD-FTRW2 is also significant in that it shows a strong interaction between gas transfer (carbon dioxide expulsion and dissolution), ionic speciation and consequently pH in its modelling results. The interaction of these systems is known to be significant (Batstone et al. 2012) but is not always modelled as such. Finally, AD-FTRW2 handles the modelling of the phosphorous weak acid-base system; another limitation identified in ADM1.