A generic reverse osmosis model for full-scale operation

This short article is a digest of a recently published research paper by Dorien Gaublomme in the journal Desalination. You can find the full article here if you want to read more details. In this paper, a generic steady-state model for reverse osmosis (RO) was set-up and applied to a unique three-year data set from a full-scale RO process operated by FARYS at Tereos Starch and Sweeteners Belgium.

Why a generic RO model?

The decline in fresh water resources has led to the use of reverse osmosis (RO) in different water treatment applications, such as sea and brackish water desalination, drinking water production as well as water reuse. In these applications, the quality of the feed water often varies in time, e.g. seasonally in case of drinking water derived from surface water. Such dynamic variations in feed water quality make the operation of RO facilities challenging as regards the aim for a high recovery while protecting the membranes.

Mathematical models can be a powerful tool in the operation of these RO facilities. Industry mainly depends on practical experience and commercial software tools from membrane manufacturers for whom design is the main purpose. These tools only apply to a particular brand of membranes and the computer code is not disclosed, which makes them inflexible and even cumbersome to use for operation. In parallel, a number of researchers developed mathematical models for model-based optimization of RO. Most models, however, do not consider both full-scale and good modeling practice, which makes them less suited in practice. Other factors that hamper their applicability in industry, are the lack of an uncertainty range in the model outputs and the possibility to use online data from sensors as input for simulations.

In this work, a generic (applicable to any RO membrane, hence, manufacturer-independent) steady-state model for RO is set-up and applied to a full-scale case study. The one-dimensional model is based on the solution-diffusion model and predicts the performance of the RO process with the feed flow rate, the applied feed pressure, and the feed conductivity as model inputs. The model development was done based on a unique three-year data set from a full-scale RO installation operated by FARYS. Specific attention was paid to each step in the modeling procedure as specified by the good modeling practice protocol in order to quantify and interpret the model's short and longer-term predictive power.

Step1: Global sensitivity analysis (GSA)

As a first step, a global sensitivity analysis is performed for the model structure in order to screen the model for its most sensitive parameters. Parameter sensitivity is a property of the model structure and reveals important information with respect to choices in a good modelling practice procedure. For example to choose those parameters to use for the calibration. It was found that the model outputs (i.e. the variables of interest, chosen as pressure drop, recovery and permeate solute concentration) are most sensitive towards the water and the solute permeability, and the feed spacer channel height, and therefore, only these parameters were used in the calibrated. Often, too many (correlated) parameters are used for calibration which induces identifiability problems (i.e. multiple solutions exist) and reduced predictive power (i.e. predictions will be unreliable). This demonstrates the importance of this GSA step in deciding on the right parameters to calibrate.

Step2: Calibration

Next, a calibration procedure was set-up, based on the results of the global sensitivity analysis, as presented in Figure 1.

Figure 1: Schematic representation of the modeling procedure, where SSE is the sum of squared errors, and N the number of data points.

The model was calibrated for its most sensitive parameters, being the water and solute permeability, and the feed spacer channel height. The result of the calibration of the water permeability, also calculated as the membrane resistance, is shown in Figure 2. The initial membrane resistance of the installation was compared to the resistance at test conditions reported by the membrane manufacturer. The latter was found to be 30% lower. This highlights the importance of calibration since the manufacturer's test results do not always reflect the full-scale situation.

Figure 2: Calibrated water permeability and membrane resistance are shown since the start-up of the full-scale RO process in 2015. The horizontal line represents the membrane resistance at the start-up. The dashed horizontal line represents the membrane resistance as reported by the manufacturer. The vertical lines show when a cleaning-in-place (CIP) was performed. The ? and ? marks represent the dates of the calibration and validation samples, respectively.

The membrane resistance increases (or the water permeability decreases) over time which confirms the presence of fouling. Since the influence of fouling is not yet included in the current model structure, the model is not able to perform a long-term prediction of the water permeability. The general trend is captured, but not the build-up of reversible fouling on the short term and irreversible fouling on the long term.

Step3: Validation

In a last step, the model was validated using online sensors as a model input. Model validation is a crucial step in model building and often overlooked or ignored. Yet, it is important to evaluate how the model behaves in situations it has not seen before (i.e. different from the calibration step, where a match is being made between model and data).

A validation of the generic model was performed and also a comparison was made with the commercial software Winflows. Despite the lack of long-term predictive power since fouling was not included, the model with online conductivity data as input showed satisfactory results, i.e. an average deviation from the data of 2.7%, 12.7%, 34.1% and 18.7% for respectively the recovery, the concentrate pressure, the permeate and concentrate solute concentration (Figure 3).

Figure 3: Average deviation between the models and the data of the model outputs (a) recovery and feed pressure (Winflows*) (b) concentrate pressure, (c) concentrate solute concentration and (d) permeate solute concentration for the validation dataset. The error bars show the result of the uncertainty analysis of the generic model with online conductivity as input.

Finally, an uncertainty analysis on the model output was performed. Such an analysis allows to quantify the uncertainty of the model output in relation to sources of uncertainty of the model. In this case, the model is fed with online sensor data which comes with a measurement error. The power of such an analysis is that one can get an idea how much of the deviations found in the validation could be accounted for by uncertainty propagation. Here, we quantified the uncertainties related to the online sensors and observe that they can partially explain the observed deviations.

Take homes

?       A generic RO model is proposed and applied to a unique 3-year data set from a full-scale process.

?       Water and solute permeability, and feed spacer channel height are calibrated.

?       Manufacturer's tests do not always reflect full-scale situation: value of calibration.

?       The model with online data as input can predict the performance of an RO process.