# On Operating a Nanofiltration Membrane for Olive Mill Wastewater Purification at Sub- and Super-Boundary Conditions

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. The Boundary Flux Model

_{b}, in case of constant feedstock characteristics and operating conditions, the following equations may be written [11]:

_{p}(t) ≤ J

_{b}

_{p}(t) − J

_{b}); J

_{p}(t) > J

_{b}

^{−1}m

^{−2}bar

^{−1}), and J

_{p}and J

_{b}are the permeate and boundary flux (L h

^{−2}m

^{−2}), respectively. Moreover:

- α, expressed in (L h
^{−2}m^{−2}bar^{−1}), represents the constant permeability reduction rate suffered by the system and will be hereafter be called the subboundary fouling rate index; α is a constant, valid for all flux values. - β, expressed in (h
^{−1}bar^{−1}), represents the fouling behavior in the exponential fouling regime of the system, and will be hereafter called superboundary fouling rate index; β appears not to be a constant, and changes with TMP. The chosen fitting equation used for β is equal to [11]:

_{b})

_{b}(bar) the applied transmembrane pressure at the boundary point.

_{p}* from a known initial value of the permeate flux J

_{p}(t

_{1}) at time t

_{1}and same TMP value as [12]:

^{−1}) is the chemical oxygen demand of the feedstock and taken as the key parameter for its characterization; m and w (L h

^{−1}m

^{−2}bar

^{−1}) are the permeability and the pure water permeability of the membrane, respectively. The terms ρ

_{1}(bar L mg

^{−1}), m

_{1}(L

^{2}h

^{−1}m

^{−2}bar

^{−1}mg

^{−1}), and γ (bar) are fitting parameters, t (h) is the operating time, σ (–) is the reflection coefficient of the membrane, R the rejection, π the osmotic pressure, and P

_{0}the applied pressure at start of operation (t = 0). A is the membrane area (m

^{2}), F is a flow rate (L h

^{−1}), and the suffixes f, c, and p stand for feed, concentrate, and permeate, respectively.

_{p}as a function of time is evaluated by Equation (7). Due to the presence of β ≠ 0, this latter value is surely lower than that calculated for the same t

_{2}value by Equation (6). The difference between the permeate flux values J

_{p}by Equations (6) and (7) is given by the additional formation of irreversible fouling on top of the reversible one. As a consequence, this difference is given by an irreversible reduction of the membrane permeability; that is, a corresponding and definitive change in the pure water membrane permeability as evaluated by Equation (15).

## 3. The Experimental Setup

^{−1}. The membrane (model DK2540F) is characterized by a mean pore size value of 0.5 nm, and was used for more than 1000 h of operation time. The active membrane area of the module is equal to 2.51 m

^{2}, and the maximum allowable operating pressure is equal to 32 bar. Acting on the regulation valves V1 and V2, it is possible to set the desired operating pressure P over the membrane maintaining the feed flow rate constant with a precision of 0.5 bar.

## 4. Results and Discussion

_{b}and TMP

_{b}were found to be 12.18 L h

^{−1}and 8 bar, respectively. In order to run the simulation, an operating pressure value must be fixed and was set equal to TMP

_{b}less a safety margin of 1 bar—that is, 7 bar. The obtained output by the model is reported below (Figure 2).

_{b}appears not to be a safe choice, since at a certain point a kink appears in the plot, corresponding to the appearance of a β value in the relevant calculations, and therefore the appearance of irreversible fouling. The simulation predicts that a transition from sub-boundary to super-boundary operating conditions will occur after 16.9 min of operation.

_{b}values by the model were plotted as well (dotted line). It is possible to observe how the kink appears as soon as the permeate profile crosses the relevant J

_{b}line. Since J

_{b}is not constant, but a function of time and operation (TMP, COD, R), this evaluation is only possible by proper model software application: indeed, J

_{b}reduces as a function of time not only due to the α value, but also due to the increase in COD given by the batch concentration effect following the increasing recovery values. As a consequence, the relevant J

_{b}values (calculated by Equation (5)) are reducing faster than J

_{p}, which is function of α only (Equation (6)). As soon as J

_{b}becomes lower than J

_{p}, Equation (6) is substituted by Equation (7). In this second part of the operation, β is no longer equal to zero, and consequently, the almost linear flux profile of J

_{p}during the first part of operation starts to assume exponential characteristics. The same applies to J

_{b}, since the value of w(t) in Equation (5) is sensibly reducing as well, due to the irreversible fouling formation: this latter value can be calculated by Equation (15), with a permeate flux value equal to that resulting from Equation (7).

## 5. Conclusions

## Author Contributions

## Conflicts of Interest

## References

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**Figure 1.**Schematic of the pilot plant. E: heat exchanger; FT: feed tank; M: membrane housing; P: pressure; V: valve.

Parameter (Units) | Value | Parameter (Units) | Value |
---|---|---|---|

m_{1} (L^{2} h^{−1} m^{−2} bar^{−1} mg^{−1}) | 11 × 10^{−6} | α (L h^{−2} m^{−2} bar^{−1}) | 130 × 10^{−3} |

ρ_{1} (bar L mg^{−1}) | 0.0 | ζ (h^{−1} bar^{−2}) | 27 × 10^{−3} |

w(0) (L h^{−1} m^{−2} bar^{−1}) | 1.07 | COD (mg L^{−1}) | 17,400 |

σ (–) | 36.80 | γ (bar) | 0 |

TMP_{b} (bar) | 8 |

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**MDPI and ACS Style**

Stoller, M.; Ochando-Pulido, J.M.; Field, R.
On Operating a Nanofiltration Membrane for Olive Mill Wastewater Purification at Sub- and Super-Boundary Conditions. *Membranes* **2017**, *7*, 36.
https://doi.org/10.3390/membranes7030036

**AMA Style**

Stoller M, Ochando-Pulido JM, Field R.
On Operating a Nanofiltration Membrane for Olive Mill Wastewater Purification at Sub- and Super-Boundary Conditions. *Membranes*. 2017; 7(3):36.
https://doi.org/10.3390/membranes7030036

**Chicago/Turabian Style**

Stoller, Marco, Javier Miguel Ochando-Pulido, and Robert Field.
2017. "On Operating a Nanofiltration Membrane for Olive Mill Wastewater Purification at Sub- and Super-Boundary Conditions" *Membranes* 7, no. 3: 36.
https://doi.org/10.3390/membranes7030036