A probabilistic approach to modeling struvite precipitation with uncertain equilibrium parameters

Significance Statement

Precipitation as well as accumulation of struvite within sludge digestion and post-digestion processes has been identified as costly and enigmatic problems for wastewater structures. Normally, struvite form on the surfaces of pipes, submerged fittings and equipment, and mixers, therefore, limiting their efficacy and necessitating regular repairs. Fouling, which may occur extensively, may render the entire system and operation inoperable and the whole piping system may have to be replaced.

However, the conditions of struvite super saturation within wastewater can be suitable for the extraction of struvite for the recovery of phosphorus irrespective of the same conditions promoting fouling. This process can be of commercial importance where the ammonia and phosphate rich crystals have been indicated to be effective slow-release fertilizer.

Estimating the precipitation potential of struvite is paramount for cost-effective and efficient design and operation of wastewater treatment plants. It is of outmost importance to develop an effective model of struvite solubility, which can be adopted to the highly variable conditions within a wastewater stream. In addition, the same considerations should be made while intentionally precipitating struvite for agricultural and other environmental purposes. The efficacy of a deterministic model for struvite solubility is diminished by certain sources of uncertainty. Unfortunately, this problem has not been resolved. These sources of uncertainty, which include measurement errors, equilibrium parameters, and wastewater composition, affect struvite prediction in varying ways.

Nathaniel Barnes and Alan Bowers at Vanderbilt University developed a struvite solubility model where the equilibrium constants were considered as empirically distributed variables within a Monte Carlo simulation. This was in a bid to understand the effects of uncertainty on precipitation potential over a varying pH of 6-8.5, ionic strength of 0-1M, and temperature range of 0-60 °C. Implementing field conditions measured at a struvite-afflicted treatment plant as input parameters, the uncertainty observed in the struvite super saturation ratio was noted to be highly consequential. Their research work is published in Chemical Engineering Science.

The authors developed a struvite solubility model in which they treated equilibrium constants with uncertainty (Monte Carlo variables) in a bid to understand the effects of uncertainty on struvite precipitation estimation. Above all, the authors performed a sensitivity analysis to pinpoint which uncertainties had more effects on equilibrium solubility predictions.

Equilibrium parameters used in struvite precipitation have not been strictly known, while their literature values variability results in significant uncertainty in equilibrium predictions. The Monte Carlo simulations done by the authors indicated that deterministic models are insufficient for the precise prediction of solubility irrespective of their prevalence in contemporary studies. Owing to this uncertainty of inputs, there exists an inherent limit to the predictive power of struvite precipitation models as indicated by a 90% confidence interval. This uncertainty was identified to be dependent on the orthophosphate and struvite solubility product.

The results of the Monte Carlo model developed by Barnes and Bowers indicated that despite the underlying uncertainty, precipitation could be modeled precisely within a range of values. A representative field data, struvite-heavy wastewater environment confirmed this conclusion and offered an example of the utility of uncertainty modeling. The use of deterministic models as well as single equilibrium constants without taking into account uncertainty was proven to be inadequate for struvite precipitation prediction.

A probabilistic approach to modeling struvite precipitation with uncertain equilibrium parameters.. Advances in Engineering

About the author

Alan Bowers, Associate Professor at Vanderbilt University, Nashville, TN in the Department of Civil & Environmental Engineering.  BCE, MCE and PhD degrees from the University of Delaware.  Research interests include Environmental Chemistry and modeling of physical/chemical and biological processes for Water and Wastewater Treatment, and the role of uncertainty in process modeling and decision making.

Technological challenges, such as fracking to develop natural gas deposits, the discovery of   non-biodegradable micro-pollutants in the environment and the necessity to recycle resources challenge the limits of knowledge.  Our research strives to understand the basic chemistry and biology involved and to develop new technologies for water and wastewater treatment.  This includes evaluating novel chemistries to recycle critical resources, such as struvite, MgNH4PO4, to recover high-grade phosphorus (a declining resource) from wastewater. In addition, novel uses of magnesium oxide/hydroxide for pH and Alkalinity control in water and wastewater processes is under investigation.

About the author

Nathaniel Barnes,

Graduate Research Assistant at Vanderbilt University, Nashville, TN in the Environmental Engineering Program.  He has an undergraduate degree in Civil Engineering from the University of Minnesota.  His research includes the Role of Uncertainty in Environmental Modeling, Struvite Management in Wastewater Processes, and Magnesium Hydroxide in Water and Wastewater Treatment.


N.J. Barnes and A.R. Bowers. A probabilistic approach to modeling struvite precipitation with uncertain equilibrium parameters. Chemical Engineering Science, volume 161 (2017), pages 178–186.


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