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Passive membrane systems for small communities Oka, Patricia Ayuningtyas 2015

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  Passive Membrane Systems for Small Communities by Patricia Ayuningtyas Oka  B.A.Sc, Mining and Mineral Processing Engineering, The University of British Columbia, 2009  A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF  MASTER OF APPLIED SCIENCE in THE FACULTY OF GRADUATE AND POSTDOCTORAL STUDIES (Civil Engineering) THE UNIVERSITY OF BRITISH COLUMBIA (Vancouver) January 2015  © Patricia Ayuningtyas Oka, 2015     ii  Abstract Submerged hollow fibre ultrafiltration (SHFUF) is an established drinking water treatment technology viable for community-scale use. It can effectively treat surface water up to 4-log removal of colloids, pathogenic bacteria, and viruses. However, current use of SHFUF in small/ remote communities is hindered by the system’s complexity and high construction and operating costs. The present study focuses on the development of a novel and simple SHFUF system that can operate passively and with limited mechanical complexity for the production of drinking water in small/ remote communities. The experimental program was divided into four main stages; each stage was instrumental in eliminating component of a SHFUF system that contributes to its complexity (ie. backwash, permeate pump, aeration and recovery cleaning) and achieving an optimized state feasible for a small community use. Surface water containing 6-7 ppm dissolved organic carbon (DOC) was used for the pilot-scale experiments.  In Stage 1, the contributions of periodic backwash in SHFUF were assessed through a comparative study of with and without backwash systems at sub-critical fluxes of 10, 20 and 30 L/m2h. While the benefits of backwash were clearly observed at 30 L/m2h, backwash was less necessary at lower permeate fluxes. At 10 L/m2h, flux was successfully maintained over the 2-month operation without backwash, indicating that backwash can be eliminated when operating at a low flux. Elimination of backwash reduces power requirements, increases throughput, and simplifies the system. In Stage 2, further simplification to the system was achieved through gravity permeation at a constant hydrostatic pressure. Gravity permeation at 10 L/m2h could be maintained with a head of 37 mbar. In stage 3, further reduction in energy consumption was achieved through operations under reduced air sparging conditions. Although reduced aeration decreased the permeate flux that could be maintained, this decrease can be compensated by proportionally increasing the number of membrane modules.  In stage 4, recovery cleaning was confirmed to recover all of the permeability loss during the 2-month operation. Results from the present study confirm that technical complexity and energy requirements of SHFUF can be substantially reduced and made feasible for use in small/ remote communities.   iii  Preface This dissertation is original, unpublished, independent work by the author, Patricia Oka.   iv  Table of Contents Abstract  ....................................................................................................................................................... ii Preface  ...................................................................................................................................................... iii Table of Contents ......................................................................................................................................... iv List of Tables .............................................................................................................................................. viii List of Figures ............................................................................................................................................... ix Nomenclature ............................................................................................................................................. xii Acknowledgements ..................................................................................................................................... xvi Dedication .................................................................................................................................................. xvii 1. Introduction ................................................................................................................................... 1 1.1 Aims and Objectives ...................................................................................................................... 1 1.2 Thesis Structure ............................................................................................................................. 2 2 Literature Review .......................................................................................................................... 3 2.1 Membrane Filtration in Drinking Water Treatment ...................................................................... 3 2.2 Submerged Hollow Fibre Ultrafiltration Membrane (SHFUF) ....................................................... 5 2.3 Membrane Fouling in SHFUF systems ........................................................................................... 7 2.4 Fouling Constituents in Surface Water Sources Affecting UF Performance and Permeate Quality  ……………………………………………………………………………………………………………………………………………….10 2.5 Fouling Control ............................................................................................................................ 11 2.5.1 Periodic Backwash .................................................................................................................... 12 2.5.2 Air Scour .................................................................................................................................... 12 2.5.3 Sub-Critical Flux Operation ....................................................................................................... 13 2.6 Passive Membrane Filtration ....................................................................................................... 14 3 Knowledge Gap and Objectives of Present Study ....................................................................... 16 4 Material and Methods ................................................................................................................. 18 4.1 Experimental Program ................................................................................................................. 18 v  4.2 Pilot-scale Submerged Hollow-Fibre Membrane System ............................................................ 19 4.3 Source Water ............................................................................................................................... 24 4.4 Experimental Setup ..................................................................................................................... 25 4.4.1 Stage 1: Contributions of Periodic Backwash in Long-Term SHFUF Operations under Sub-Critical Flux Conditions.............................................................................................................. 25 4.4.2 Stage 2: Contributions of Constant-Pressure Permeation in Long-Term SHFUF Operations under Sub-Critical Flux Conditions ............................................................................................ 27 4.4.3 Stage 3: Contributions of Air Sparging in Long-Term SHFUF Operations under Sub-Critical Flux Conditions ................................................................................................................................. 28 4.4.4 Stage 4: Contributions of Membrane Recovery Cleaning in Long-Term SHFUF Operations under Sub-Critical Flux Conditions ............................................................................................ 29 4.5 Quality Control ............................................................................................................................ 29 4.5.1 Membrane Integrity Testing ..................................................................................................... 29 4.5.2 Membrane Cleaning .................................................................................................................. 30 4.5.3 Clean Water Tests ..................................................................................................................... 30 4.5.4 Transmembrane Pressure ......................................................................................................... 30 4.5.5 Sampling .................................................................................................................................... 31 4.6 Analytical Methods ...................................................................................................................... 31 4.6.1 Total and Dissolved Organic Carbon (TOC and DOC) ................................................................ 31 4.6.2 High Performance Liquid Chromatography (HPLC) .................................................................. 32 4.7 Data Analysis Methods ................................................................................................................ 33 4.7.1 Quantification of Fouling Effects on Membrane Performance ................................................ 33 4.7.2 Determination of the Pre-dominant Fouling Mechanisms ....................................................... 33 4.7.3 NOM Characterization and Quantification ............................................................................... 34 4.7.4 Mass Balance of NOM throughout the Passive Membrane System ......................................... 36 5 Results, Data Analysis and Discussion ......................................................................................... 39 vi  5.1 Long Term Fouling Mitigation in SHFUF systems ........................................................................ 39 5.1.1 Contributions of Backwash to Fouling Control in Long-term SHFUF operation under Sub-Critical Flux Conditions.............................................................................................................. 39 5.1.2 Contributions of Constant-Pressure Permeation in Long-Term SHFUF Operations under Sub-Critical Flux Conditions.............................................................................................................. 41 5.1.3 Contributions of Air Sparging in Long-Term SHFUF Operations under Sub-Critical Flux Conditions ................................................................................................................................. 43 5.1.4 Contributions of Recovery Cleaning on Membrane Modules and Operation .......................... 47 5.1.5 Fouling Mechanisms in Passive Membrane Operations ........................................................... 49 5.2 Natural Organic Material (NOM) in Passive Membrane Operations .......................................... 54 5.2.1 Accumulation of NOM in System Reactor ................................................................................ 54 5.2.2 Removal of NOM during Treatment ......................................................................................... 58 5.2.3 Degradation of NOM in System Reactor ................................................................................... 62 6 Prototype Design of Passive Membrane Filtration...................................................................... 64 7 Conclusions .................................................................................................................................. 66 References .................................................................................................................................................. 68 Appendix A : Clean Water Fluxes and Initial Membrane Resistances ........................................................ 72 Appendix B:  Excel Visual Basic for Applications (VBA) Commands ............................................................ 77 Appendix C : Instrument Calibration Curves ............................................................................................... 81 Appendix D: Complete Resistance Data for Stage 2 ................................................................................... 83 Appendix E: Flux Reduction in Stage 4 ........................................................................................................ 84 Appendix F: Statistical Reports of the Fouling Models for Continuous Aeration ....................................... 85 Appendix G: Statistical Reports of the 5 Best-Fit Fouling Models for 25 Minutes Off – 5 Minutes On ...... 96 Appendix H: Statistical Reports of the 5 Best-Fit Fouling Models for 4 Hours Off – 30 Minutes On ....... 116 Appendix I: Statistical Reports of the 5 Best-Fit Fouling Models for 4 Hours Off – 5 Minutes On ........... 127 Appendix J: Statistical Reports of the 5 Best-Fit Fouling Models for No Aeration ................................... 138 vii  Appendix K: Mass Balance of NOM in a Wasting Passive Membrane System under Continuous Aeration ................................................................................................................................................... 149 Appendix L : Mass Balance of NOM in a Wasting Passive Membrane System under Intermittent Aeration of 25 Minutes off – 5 Minutes On .............................................................................................. 151 Appendix M : Mass Balance of NOM in a Wasting Passive Membrane System under Intermittent Aeration of 4 Hours off – 30 Minutes On ................................................................................... 153 Appendix N: Mass Balance of NOM in a Wasting Passive Membrane System under Intermittent Aeration of 4 Hours off – 5 Minutes On.................................................................................................... 155 Appendix O: Mass Balance of NOM in a Wasting Passive Membrane System under No Aeration .......... 157 Appendix P: Mass Balance of NOM in a Non-Wasting Passive Membrane System without Backwash ... 159 Appendix Q: Mass Balance of NOM in a Non-Wasting Passive Membrane System with Backwash ........ 161  viii  List of Tables Table 1 Summary of the Four Constant Pressure Individual Fouling Models ............................................... 9 Table 2 Summary of the Four Constant Pressure Combined Fouling Models .............................................. 9 Table 3 Operational Conditions of the Three-stage Experimental Program .............................................. 18 Table 4 Membrane Module Properties of the Present Study ..................................................................... 21 Table 5 TOC and DOC of Jericho Pond Water ............................................................................................. 25 Table 6 Ranges of Retention Time for the Different NOM Types in the Water Samples ........................... 35 Table 7 Fitted Values of the Exponential Regression Model for Each of the Reduced Aeration Condition ..................................................................................................................................................... 46 Table 8 Fitted Values of the Exponential Regression Model for Before and After Recovery ..................... 49 Table 9 Fitted Parameters for the Single and Combined Fouling Models .................................................. 51 Table 10 Averaged Concentrations of High Molecular Weight, Humic Substances and Low Molecular Weight Neutrals Contents in Feed Water ................................................................................... 54 Table 11 Summary of the Pairwise Comparison between the Feed Water, System Reactor, Permeates to Determine Consistency of Raw Water Feed and Overall NOM Removal .................................... 61 Table 12 Proposed Designs and Capacity for Prototype ............................................................................. 65    ix  List of Figures Figure 1 Membrane Filtration Spectrum (USEPA, 2005) .............................................................................. 4 Figure 2 Typical Membrane System Configurations ( a). External Membrane Configuration; b). Submerged Membrane Configuration) ......................................................................................... 5 Figure 3 Process Diagram of a Typical Submerged Membrane System ....................................................... 6 Figure 4 Typical hydrodynamic conditions in SHFUF operation ................................................................... 6 Figure 5 Typical Fouling Mechanisms in Membrane Treatment (a) Adsorption, b) Pore Blocking, c) Cake Deposition,  d) Gel Formation) ...................................................................................................... 8 Figure 6 Illustration of the Effect of Biofilm formation on Permeate Quality during an Ultra-low Gravity Permeation by Derlon et al. in 2014: a). Case of membrane system without biofilm, b) Case of young and thin biofilm developed on a membrane, c). Case of an old and thick biofilm on a membrane (Derlon et al., 2014). ................................................................................................. 11 Figure 7 Fouling coefficient across different flux indexes (Bérubé et al., 2008) ........................................ 14 Figure 8 Schematic presentation of the dead-end UF system (Peter-Varbanets et al., 2010) ................... 15 Figure 9 Simplification of the complex SHFUF into a simple system over the span of the research ......... 19 Figure 10 System Reactor Configuration .................................................................................................... 20 Figure 11 Membrane Potting Configuration ............................................................................................... 21 Figure 12 Membrane Stand Design and Installation................................................................................... 22 Figure 13 Configuration of the System Aeration ........................................................................................ 23 Figure 14 Establishment of constant hydrostatic pressure in SHUFUF System Stages 2 through 4 ........... 24 Figure 15 Schematic of the Pilot-scale Submerged Membrane System Assessing the Benefits Backwash under Constant Low-Flux Operation ........................................................................................... 26 Figure 16 Range of Flux Index Investigated in the Present Study ............................................................... 26 Figure 17 Schematic of the Pilot-scale Submerged Membrane System Operating as Passive Membrane System at 10, 13 and 16 LMH ...................................................................................................... 27 x  Figure 18 Schematic of the Pilot-scale Submerged Membrane System Operating as Passive Membrane System with Intermittent Aeration ............................................................................................. 28 Figure 19 Membrane Integrity Testing ....................................................................................................... 29 Figure 20 Chromatogram of a typical surface water with responses for organic carbon detection (OCD), UV-detection at 254 nm (UVD) and organic nitrogen detection (OND). Source: Huber et al., 2011 ............................................................................................................................................. 34 Figure 21 Typical Linear Correlation found between the measured DOC in ppm and calculated AUC from HPLC analyses on the feed and system reactor samples ............................................................ 36 Figure 22 Schematic Diagram ..................................................................................................................... 37 Figure 23 Reduced Membrane Permeability over Volume Filtered for both With and Without Backwash Operations(a). 30 LMH without Backwash, b). 30 LMH with backwash, c). 20 LMH without Backwash, d). 20 LMH with Backwash, e). 30 LMH without Backwash, and f). 30 LMH with Backwash………………..........………………………………………………………………………………….………………….40 Figure 24 Normalized Membrane Permeability of Gravity Permeation at 10, 13, and 16 LMH Post-Acclimatization Period ................................................................................................................. 42 Figure 25 Reduced Normalized Membrane Permeability over Time( a). 25 Minutes off – 5 Minutes on; b). 4 Hours off – 30 Minutes on; c). 4 Hours off – 5 Minutes on; and d). No Air Sparging…………….44 Figure 26 Effect of Reduced Air Sparging Conditions on Membrane Permeability .................................... 46 Figure 27 Reducing Fouling Rate with Increasing Air Sparging Frequencies .............................................. 47 Figure 28 Reduced Permeability over Volume Filtered for the 25 Minutes off – 5 Minutes on Modules After Recovery Cleaning (a). Module 1, b) Module 2, c). Module 3) .......................................... 48 Figure 29 Top Ranked Models Fitted to the Measured Data for the Different Air Sparging Conditions (a). infinity Air ON/OFF ratio, b).  0.2 Air ON/OFF Ratio, c). 0.13 Air ON/OFF Ratio, d). 0.02 Air ON/OFF Ratio, e). 0 Air ON/OFF Ratio, f). 0.2 Air ON/OFF Ratio After Recovery Cleaning)………53 Figure 30 Typical NOM Profile of the Feed Water (a). Fall 2013, b). Winter 2013, c). Spring 2014, d). Summer 2014) ………………………………………………………………………………………………………………………55 xi  Figure 31 Differences in Organic Content between System Reactor and Feed Tank under Different Operation Conditions: with and without wasting, backwash and different on/off frequencies of air sparging  (a). HMW, b). HS, c). LMN)………………………………………………………………………………….57 Figure 32 Typical NOM Profile at the Different Stages of Treatment (a). With Wasting and b). Without Wasting)……………………………………………………………………………………………………………………………...…58 Figure 33 Mean Removal of Organics under Different Operating Conditions: with and without wasting, backwash and different on/off frequencies of air sparging (a). HWM, b). HS, c). LMN)…….......60 Figure 34 Typical Trends of Measured and Theoretical NOM over Time for the Wasting and Non-Wasting Reactors (a). HMW in a Wasting Reactor, b). HMW in a Non-Wasting Reactor, c). HS in a Wasting Reactor, d) HS in a Non-Wasting Reactor, e). LMN in a Wasting Reactor, f). LMN in a Non-Wasting Reactor .................................................................................................................. 63 Figure 35 Prototype Diagram with 135 lpcd capacity and an option to be gravity-fed ………………..…………65   xii  Nomenclature θ Angle between liquid surface and the capillary wall [xx] Concentration of xx ∆P Transmembrane pressure µ Dynamic viscosity of water µ20 Dynamic viscosity of water at 20oC  µT Dynamic viscosity of water at ToC  ∞ Infinity AUC Area under the curve B Membrane permeability B/Bi Normalized membrane permeability Bi Initial membrane permeability normalized to 1 Bs Normalized membrane permeability at steady state CF Particles concentration in bulk liquid CM Particles concentration at membrane surface Cp Particles concentration in the permeate CPWDU Community potable water dispensing units  d Diameter of the pore Da Dalton DI De-ionized water Dia. Diameter DOC Dissolved organic carbon F Feed Ft Total mass of NOM in feed at time t GE General Electric H Hydrostatic head HCl Hydrochloric acid HMW High molecular weight HPLC High performance liquid chromatography HS Humic substances xiii  ID Inner diameter J Flux Jo Initial operating flux JOP Operating flux k Membrane integrity constant K Fouling coefficient Kb Complete blocking fouling coefficient Kc Cake fouling coefficient Ki  Intermediate fouling coefficient Ks  Standard fouling coefficient Ktot Total fouling coefficient LMA Low molecular weight acid LMH Litre per m2 per hour LMN Low molecular weight neutrals lpcd Litres per capita per day lpd Litre per day MBR Membrane biological reactor MCF Macrofiltration MF Microfiltration MW Molecular weight MWCO Molecular weight cut-off n Number of data points NaClO Sodium Hypochlorite NF Nanofiltration NOM Natural organic matter NTU Nephelometric Turbidity Units  Ø Diameter OCD Organic carbon detection OD Outter diameter ON/OFF On/Off aeration cycle ratio P Permeate xiv  PEG Polyethylene glycol pF Pressure at the feed side of the membrane POE Point-of-entry POU Point-of-use pp Pressure at the lumen side of the membrane PSS Polystyrene sulfonate PT  Pressure transducer PT  Transmembrane pressure at temperature ToC Pt  Total mass of NOM in permeates at time t Q Flow Qfeed Flow into the pressurized-vessel Qin Influent flow Qout Effluent flow R Total resistance R2 Coefficient of determination  Ri Initial concentration of a NOM in system reactor RIR Irreversible fouling resistance coefficient Rm Membrane resistance coefficient RO Reverse Osmosis RR Reversible fouling resistance coefficient Rt/R0 Relative membrane resistance RTH Theoretical concentration of a NOM in system reactor s Standard error s/m2 Seconds per square meter SHFUF Submerged Hollow Fibre Ultrafiltration SRT Solid retention time SSR Residual sum of squares  St HPLC signal response at time t t Time T.AUC Total area under the curve TMP Transmembrane pressure xv  TOC Total organic carbon UF Ultrafiltration USB Universal serial bus UV254 Ultraviolet absorption at 254 nm V Volume   Total volume fed to the system reactor between two sampling dates VP Total volume filtered  VW Total volume wasted VBA Visual Basic for Application W Waste Wt Total mass of NOM in waste at time t ZW-1000 ZeeWeed®-1000 membrane ZW-500 ZeeWeed®-500 membrane    xvi  Acknowledgements The completion of this thesis would not be possible without the contributions of many people that I truly respect and care about. For that, I would like to take the opportunity to express my sincere gratitude to them. I would like to thank my supervisor, Dr. Pierre Bérubé, for the intellectual support and guidance throughout my research. I am grateful for his passion in teaching and strong belief in the ability of his students. His attendance and patience in all stages of my learning curve and research experience is very much appreciated. I would also like to thank my second reviewer, Dr. Victor Lo, whose comments and technical inputs have further enhanced the quality of this thesis. I would like to thank Paula Parkinson and Tim Ma for their valuable training in the lab. Their tireless assistance and amicable friendships gave incredible values to my laboratory experience.  I would also like to thank Bill Leung for his handiwork, which enabled this research project, and his admiring stories of his life, loving family and love for literature, that brightened my research days. I would also like to thank for the sincere friendships and support from all of my cohort in the graduate student office (Room M107). I appreciate all the coffee breaks we took, which were sometimes too many in a day, and the delicious potlucks we had, which always ended up serving as a competitive cooking ground. Special thank you is forwarded to Jason Leong, who was always there for me in countless rainy and cold days for the sampling of 2 m3 Jericho pond water, which was used in this research. I am also grateful for the assistance of a GRA student, Nesar Kadem, during my research who periodically helped me with water analyses and sampling. I am thankful for my lab mate, Roman Vortisch, who brought laughter into my day-to-day lab routine. I especially thank him for showing his support from Germany by sending one joke a day throughout the last revision week of this thesis. For the editing of this thesis, I’d like to thank fellow engineer Patrick Davies, PhD. candidates Shona Robinson and Jörg Winter, Postdoctoral fellows Heather Wrey and Zaki Sayed, fellow MASc. candidates Christina Starke and Samuel Stime, who were very kind to contribute their time and expertise. Lastly, but most importantly, I would like to express my gratefulness to my partner in crime, Patrick Davies, for his presence in every single day of my graduate life. I would like to especially thank him for the psychedelic stories of Achilles and the Tortoise from Gödel, Escher, Bach that he read for me on my most uninspiring days and for his newfound love for bartending, which came very handy during the final stages of this project.   xvii  Dedication   This thesis is dedicated to my mother, to whom I gratefully owe my love and fascination for engineering. This thesis is also dedicated to my father, who envisioned my future and devoted his life and prayers to it.  1  1. Introduction Submerged hollow fibre ultrafiltration (SHFUF) is an established drinking water treatment technology viable for community-scale use. It is capable of removing colloids, pathogenic bacteria, and viruses in water up to a log removal value (LRV) of four. However, the adoption of SHFUF for small-scale water treatment in small communities or rural areas is currently hindered by the complexity and costs of the system. As stated by USEPA in their Drinking Water Treatment for Small Communities report, the most significant requirements of small systems are low construction and operating costs, simple operation, high adaptability to part-time operations and low maintenance (States, 1994). While the context of a membrane treatment gives a promising outcome of steady high quality drinking water production, its operation requires the availability of skilled operators, a large capital expenditure and a high energy input that rural areas may not have.  Fortunately, in the recent decade, research studies have collectively discovered the potential of membrane systems to operate and self-maintain for an extended period through operations under sub-critical flux conditions. Under sub-critical flux conditions flux has been reported to remain constant and fouling was not observed (Howell, 1995; Wang et al., 2008a). Furthermore, cake layer that forms on the membrane surface under these conditions tends to grow in thickness rather than density (Akhondi et al., 2014) due to the development of cavities, channel networks, and heterogeneous structures that decreases the resistance of the fouling layer and stabilizes the operating flux (Peter-Varbanets et al., 2011).  The first attempt in developing a simple membrane system has only been recently explored through the development of a completely self-sustained, ultra-low pressure flat-sheet membrane system (Boulestreau et al., 2012; Peter-Varbanets et al., 2010). Similar attempts toward system simplification and energy reduction in SHFUF have not been done due to their susceptibility to fouling in the absence of fouling controls, such as backwash and aeration.  1.1 Aims and Objectives The objectives of the present research was to develop a novel and simple SHFUF system that can operate passively and with limited mechanical complexity for the production of drinking water in small/ remote communities.  In meeting the objectives, performance examination on the novel system 2  was done with respect to the effects of operating flux, backwashing, air sparging, as well as, recovery cleaning on the long term operation of the system under sub-critical flux conditions. In conjunction to this, the study attempted to shed some light on the fouling and biological mechanisms governing the operation of the system. 1.2  Thesis Structure The discussion of the relevant studies by others is compiled in Chapter 2. Chapter 3 outlines the research questions that drive the direction of the study. Chapter 4 describes in detail the materials and methods adopted to conduct and answer the proposed research questions. The obtained data and analyses are presented and discussed comprehensively in Chapter 5. The engineering application of the present study is further discussed in Chapter 6. Finally, the conclusions from the present study are presented in Chapter 7.   3  2 Literature Review 2.1 Membrane Filtration in Drinking Water Treatment Although the first membrane manufacturing and industrial application was started in the 1920s in Germany, the use of membrane filtration in drinking water treatment did not gain popularity until more than 70 years later. During this time, the use of membranes in water treatment had only been considered in some European countries, such as France and Netherlands, who pioneered its use in water treatment in the 1970s. The widespread adoption of membrane treatment was hampered by the high capital and operating costs of the systems. In addition, the extent of treatment by the membrane was viewed to be excessive for the drinking water standard at the time, thereby presenting a poor business case for the use of membranes in water treatment projects.  In the 1990s, a series of serious Cryptosporidium outbreaks occurred in major cities throughout the world. One outbreak in 1993 which affected 403,000 people in Milwaukee, US, became the catalyst to the development of a more stringent drinking water legislation. The new legislation mandated membrane treatment for high risk sources. This created volume and competitiveness in the membrane market in the late 1990s, making membrane technologies more economical in the following years  (Pearce, 2011).  Today, the use of membranes in drinking water treatment includes a range of applications from the removal of solutes through reverse osmosis (RO) and nanofiltration (NF) to the removal of fine particles through ultrafiltration (UF) and microfiltration (MF). For fresh water treatment applications, membrane filtration is usually performed using either UF or MF treatment, where contaminants are removed through size exclusion. Therefore, it is essential to properly select the pore-size specification for effective treatment. Figure 1 displays the operating spectrums of the different types of membrane treatment. Aside from pore-size, the success of the treatment itself is dependent on the operability of other variables, including membrane permeability and process stability (Pearce, 2011), which vary depending on the type and configuration of the system.  Unless indicated otherwise, the following discussion focuses on membranes used for fresh water treatment (ie. MF and UF).  4   *MCF = Macrofiltration Membrane Figure 1 Membrane Filtration Spectrum (USEPA, 2005)  There are three categories of membrane geometries used in water treatment: tubular, flat sheet and hollow fibre. Hollow-fibre membranes are the most commonly used type, largely due to its high packing density and backwash ability.  Applications of flat-sheet membranes as a single layer or spiral-wound, are more challenging compared to hollow fibre because of the propensity of these membranes for pore-clogging and limited backwash ability. Whereas, applications of tubular membranes are common in small systems with highly turbid waters due to its low packing density and niche on high tolerance of high cross-flow velocity (MWH, 2005).  In water treatment, membrane modules can be configured as either external or internal. An external membrane system uses pressurized vessels to house the membrane. A positive pressure is applied to the feed side of the membrane to provide the driving force for the liquid to permeate through the membrane. High pumping capacity and piping complexity are usually associated with an external membrane system. On the other hand, an internal membrane system (also known as submerged system, as addressed from this point on) combines both the raw feed and membrane modules in one tank. A negative pressure or suction is applied to the permeate side of the membrane to provide the driving force for the liquid to permeate through the membrane (MWH, 2005; Pearce, 2011). External and submerged membrane configurations are illustrated in Figure 2.   5   Figure 2 Typical Membrane System Configurations  ( a). External Membrane Configuration; b). Submerged Membrane Configuration) 2.2 Submerged Hollow Fibre Ultrafiltration Membrane (SHFUF) Submerged systems consists of membrane modules immersed in an open raw water tank. Hollow fibre membrane modules are commonly used in submerged systems because of their high surface area and backwash ability (Peinemann and Nunes, 2010). Permeate is generally extracted out of the tank from the top of the modules using a negative pressure generated by a permeate pump. Particles greater than the membrane pore-size are retained at the surface, while permeate is collected on the other side (lumen) of the membrane. A portion of the permeate collected is pumped back to backwash the modules and the remainder is collected for drinking use. Figure 3 depicts a typical schematic diagram of a submerged hollow fibre membrane system.  Unless indicated otherwise, the following discussion focuses on SHFUF membranes.  a). b). 6   Figure 3 Process Diagram of a Typical Submerged Membrane System Generally, air is added at the base of the membranes to generate turbulent air and liquid two-phase flow at the surface of the membrane. This turbulence creates shear forces between the bulk liquid and the retained particles at the membrane surface, eroding and preventing further build-up of retained material (ie. foulants). Figure 4 illustrates the eroding of the foulants by aeration in a submerged system.  Figure 4 Typical hydrodynamic conditions in SHFUF operation  The application of SHFUF in water treatment has become increasingly popular for both operational and economic reasons. For example, the submerged configuration of the system allows it to operate with a relatively low energy consumption and low system complexity compared to its predecessor, the external membrane systems (Pearce, 2011). Furthermore, the high surface area and Turbulent Flow Membrane  Turbulent Flow Permeate Flow Air  7  packing density of the hollow fibres allows for higher productivity compared to other types of membranes given the overall footprint.   SHFUF systems can be operated under constant flux or constant pressure (MWH, 2005; Pearce, 2011). Over time, particle accumulation at the membrane surface under constant pressure increases the resistance to the permeate flow, resulting in the reduction of permeate flux. Whereas under constant flux operation, particle accumulation increases the resistance to the permeate flow, resulting in the increase of trans-membrane pressure (TMP). To prevent excessive accumulation of retained material at the membrane surface, SHFUF units are equipped with various fouling prevention features and maintenance programs, such as air scour, periodic backwash and recovery cleaning. Although effective, these fouling controls substantially increase the complexity and cost of membrane systems.  2.3 Membrane Fouling in SHFUF systems Fouling is the accumulation of particles or solutes at the membrane surface (Field, 2010). It largely results from particle size exclusion by the pores and chemical/electrical attractions that may exist between retained material and the membrane (Cho J., 1999; Jermann, Pronk, Meylan, & Boller, 2007; Pearce, 2011). In SHFUF systems, fouling tendency is often affected by the high fibre packing density, which limits two-phase flow at the membranes surface (Yeo et al., 2006). Furthermore, operating conditions and feed characteristics also play a significant role in SHFUF fouling (Aimar and Bacchin, 2010; Tang et al., 2011). The presence of fouling is commonly manifested by an increase in resistance to permeate through a membrane. The relationship between permeate and resistance is presented in Equation 1. Equation 1      =  ∆	 ()                                                                where,  J is volumetric water flux through the membrane, L/m2.h  ∆P is the transmembrane pressure (TMP), bar  µ is dynamic viscosity of water, kg/m.s RM is membrane resistance coefficient, m-1  RIR is irreversible fouling resistance coefficient, m-1 8  RR is reversible fouling resistance coefficient, m-1 Another indicator of fouling is the reduction in membrane permeability, which is inversely proportional to the total increase in membrane resistance as expressed in Equation 2.  Equation 2        = ∆ =  ()  where, B is membrane permeability, meters. Fouling forms through different mechanisms as illustrated in Figure 5.  Adsorption can occur with and without the presence of permeate flux. It is typically driven by specific interactions between the membrane and the solute/ particles in the bulk feed.  Pore blocking (intermediate or complete) occurs as a result of the migration of particles towards the membrane via permeate flux and their entrapment in the membrane pores. The migration of particles towards the membrane by permeate flux may also result in foulant accumulation at the surface of the membrane, known as cake deposition. The degree of accumulation, however, depends on the balance between convective transport of solutes towards the membrane and back-diffusion transport, which is discussed in Section 2.5.    Figure 5 Typical Fouling Mechanisms in Membrane Treatment (a) Adsorption, b) Pore Blocking, c) Cake Deposition,  d) Gel Formation) In some cases, fouling may occur from a combination of different mechanisms depending on system conditions and presence of specific foulant constituents (Bolton et al., 2006). Many studies have attempted to identify different fouling mechanisms, individually and in combinations, for the purposes of understanding the effects of different operating conditions and/or foulant constituents on membranes performance (Bolton et al., 2006). Table 1 and Table 2 summarize the individual and combined fouling models for constant pressure operation as derived by Bolton et.al. (2006).  a) b) c) d) 9  Table 1 Summary of the Four Constant Pressure Individual Fouling Models Single Fouling Mechanism Equation Fitted Parameter Reference Standard  =  1 + 2  Ks (L/m2) Equation 3 Intermediate Blocking  = 1 + ln (1 + ) Ki (L/m2) Equation 4 Complete Blocking  = " + (1 − exp(−")) Kb (hr-1) Equation 5 Cake  = 1'  ()1 + 2*+ − 1, Kc (m4hr/L2) Equation 6  Table 2 Summary of the Four Constant Pressure Combined Fouling Models Combined Fouling Mechanisms Equation Fitted Parameters Reference Cake – Complete  = " -1 − exp .−"*+ ()1 + 2'+ − 1,/0 Kc (m4hr/L2) Kb  (hr-1) Equation 7 Cake - Intermediate  = 1 ln .1 + *  1(1 + 2*+) +2 − 13/ Kc (m4hr/L2) Ki (L/m2) Equation 8  Complete - Standard  = "  1 − exp  −2"2 +   Kb (hr-1)     Ks (L/m2) Equation 9  Intermediate -        Standard  =  1 ln 1 + 22 +  Ki (L/m2)    Ks (L/m2) Equation 10 Cake - Standard  = 2 (4 567 (283 − 13 :;5567(<), + 13, Where, < =  8274? + 434?* − 4+34?* 4 =  A49 + 43* + 2 + 3*  Kc (m4hr/L2) Ks (L/m2) Equation 11   Equation 12  Equation 13     10  Whatever the driving mechanism may be, all fouling leads to a rise in the membrane’s hydraulic resistance, which may or may not be reversible. Over time, foulants may transform physically through compression and/or chemically through biodegradation, leading to further fouling (Field, 2010; Pearce, 2011; Rodríguez et al., 2012). The following section introduces different fouling constituents commonly found in source waters and their effects on membrane fouling.   2.4 Fouling Constituents in Surface Water Sources Affecting UF Performance and Permeate Quality There are four broad categories of raw water constituents that have been documented to cause fouling : particulates, inorganic, organic, and micro-biological organisms (Field, 2010; Pearce, 2011). Particulate foulants are defined as undissolved organic and/or inorganic matter that have the ability to block or blind the membrane surface. Inorganic foulants in water sources are typically dissolved materials, which tend to precipitate on the membrane surface under certain conditions. In water treatment, inorganic foulants may be present as coagulant residuals from the upstream processes in the treatment plants (Pearce, 2011). Organic foulants, also known as natural organic matter (NOM), include both undissolved and dissolved materials (MWH, 2005). However, it is the dissolved components of organic foulants that have been widely known to cause rapid membrane fouling.  Fouling by NOM is usually through adsorption and pore blocking, which can be irreversible through regular hydrodynamic fouling control, such as air scour and backwash (Aoustin et al., 2001; Fan et al., 2001; Kimura et al., 2006).  In a typical natural surface water, NOM consists of 60-90% of hydrophobic humic substances (HS), 10-15% of hydrophilic high molecular weight (HMW) substances and 25-40% of hydrophilic low molecular weight (LMW) substances (Peter-Varbanets et al., 2011; Thurman, 1985; Y. Choi, 2003). Any NOM constituents can be responsible for membrane fouling and flux decline. However, recent studies have confirmed that the hydrophilic portion of the NOM is responsible for most of the fouling (Jarusutthirak, 2002; Jermann et al., 2007; Kimura et al., 2004; Lin et al., 2000). Within this portion of the NOM, both the high and the low molecular weight substances of the hydrophilic group play a role in the fouling of UF membranes. The HMW materials (ie. polysaccharides and protein) often foul membranes through cake deposition and pore blocking at the membrane surface, whereas, low molecular neutrals tend to adsorb onto the membrane pores (Jarusutthirak et al., 2002; Speth et al., 2000). Overtime, 11  microbial communities in the system excrete extracellular material and establish colonies, forming a biofilm. This is known as biological fouling (MWH, 2005; Pearce, 2011; Qu et al., 2013; Wang et al., 2008b).  Several studies have reported that the presence of young and thin biofilm can act as pre-coat to the membrane surface, which minimizes further fouling and enables long-term membrane operation (Peter-Varbanets et al., 2010; Ye et al., 2011). However, the long-term presence and accumulation of biofilm is also known to compromise permeate quality as the biofilm hydrolyzes into soluble material that is permeable through the membrane. The rate at which hydrolysis occurs is proportional to the mass of volatile solids in the biofilm (Derlon et al., 2014). Nonetheless, biofilm is easily removable through recovery cleaning using chemical agents, such as chlorine (MWH, 2005). Figure 6 was adopted from Derlon et al.’s study to illustrate the contribution of biofilm to permeate quality.   Figure 6 Illustration of the Effect of Biofilm formation on Permeate Quality during an Ultra-low Gravity Permeation by Derlon et al. in 2014: a). Case of membrane system without biofilm, b) Case of young and thin biofilm developed on a membrane, c). Case of an old and thick biofilm on a membrane (Derlon et al., 2014). 2.5 Fouling Control The degree of fouling in submerged systems is a complex function of feed characteristics, membrane properties and operating conditions (Aimar and Bacchin, 2010; Raffin et al., 2012; Tang et al., 2011). Due to the many variables affecting fouling, fouling controls can be implemented in many ways, both directly or indirectly. Direct methods may include adding turbulence promoters, implementing pulsed or reverse flow, rotating/ vibrating membranes, air scour, periodic cleaning and backwash. Indirect methods include pre-treatment of feed water, membrane surface treatment/ modification, and 12  selection of appropriate operating mode (Akhondi et al., 2014). The following sections discuss the three most common fouling controls used in a submerged hollow fibre system. 2.5.1 Periodic Backwash Backwash is an operational approach that reduces foulant deposition by the reversal of permeation flow, going outwardly from the membrane’s lumen to the feed wall side. The cyclical outward direction of the flow dislodges foulants inside the pores and detaches deposition at the membrane’s surface. Detaching and dislodging foulants from the membrane surface not only reduces the resistance to the permeate flow, but also the effect of the concentration polarization mechanism on the membrane, which would otherwise enhance mass flux toward the membranes in the reactor (Pearce, 2011).  Backwash cycles are usually programmed to occur 1 to 4 times per hour (Pearce, 2011), but can vary over a greater range depending to the membrane product. Every cycle of backwash allows both detachment and reorganization of the foulant structure to maintain a sustainable flux, which is a flux at which fouling rate is operationally and economically acceptable (Guglielmi et al., 2007; Ognier et al., 2004). The implementation of backwash is proven to improve and prolong the usability of membranes (Akhondi et al., 2014). However, the efficiency of backwash may decrease over time due to the inability of the reversed flow to dislodge or displace all foulants.  The efficiency of backwash is limited by both the amount of product loss and the energy required to reverse the flow (Psoch and Schiewer, 2005). A study by Akhondi et al. in 2014 demonstrated that for a given volume, higher backwash flux provides greater cleaning efficiency than longer backwash duration (Akhondi et al., 2014). A study led by Chua in 2003 demonstrated that optimum backwash flux was approximately twice the flux of the permeate flow, beyond which no further improvement was observed (Chua et al., 2003).  2.5.2 Air Scour Air scour or sparging is an operational approach that reduces foulant deposition by increasing air/water turbulent at the surface of the membrane, hence enhancing hydrodynamic conditions around the membrane surface. The introduction of air bubbles at the bottom of the reactor, directly below the membranes, produces sub-turbulent or turbulent conditions near and at the membrane’s surface. The rising bubbles generate secondary flows in their wake and entrain bulk liquid that results in fiber sway, resulting shear forces and eroding foulant layers at the membrane’s surface (Cabassud et al., 1997; Wu 13  et al., 1999; Zularisam et al., 2006).  Inducing air scour during backwash is also a common practice that has been confirmed beneficial to enhance fouling removal and backwash efficiency. It is understood that while backwash detaches the particles from the membrane, air scour removes these particles away from the membrane into the bulk feed (Bessiere et al., 2009; Serra et al., 1999).   The benefits of air scouring application in membrane systems have been comprehensively studied. A comparison study conducted by Judd et al. in 2001 confirmed that dual-phase cross-flow brought by the introduction of air results in a significantly higher pseudo-state permeate flux than a single-phase cross-flow filtration under constant-pressure operation (Judd et al., 2001). The higher steady-state flux  achieved indicates that there is less foulant deposition on the membrane under dual-phase cross-flow (Ducom et al., 2002). Berubé and Lei (2006) observed an optimum point beyond which an increase in bulk cross-flow through air scour above 0.3 m/s will not give further improvement to the system performance. 2.5.3 Sub-Critical Flux Operation  Another approach for fouling controls in membrane systems is to operate below critical flux (Psoch and Schiewer, 2005). Critical flux is an operating flux below which increase in TMP over time does not occur (ie. no fouling) and above which the opposite is observed (Wang et al., 2008b). The concept of critical flux was first introduced by Field et al. in 1995 for MBR applications, where sub-critical flux conditions in MBR operations were achieved with the assistance of air sparging alone. As a result, a 12-month continuous operation was achieved without backwashing and chemical cleaning (H. Ishida, Y. Yamada, 1993).  The application of critical-flux by means of hydrodynamic modifications in drinking water treatment has since been studied and confirmed to have benefits in fouling prevention. Bérubé and Lei (2006) reported the significant reduction of fouling occurrences as the flux index is lowered to less than zero (Figure 7). Flux index is the difference between the operating flux and the critical flux. Sub-critical conditions can be achieved by operating under a constant low flux or pressure, where the mass transport of foulants in the direction of the membrane through the convective flow of permeate is minimized. The lower mass transport also reduces compaction of foulants on the membrane surface, allowing the foulant layer to grow in thickness and porosity rather than density while a steady transmembrane pressure is maintained (Akhondi et al., 2014; Rodríguez et al., 2012).   14   Figure 7 Fouling coefficient across different flux indexes (Bérubé et al., 2008) 2.6 Passive Membrane Filtration The definition of passive filtration comes from the biomedical field, which defines the self-sustained physical transport process of biochemical and other atomic substances across the cell membranes of an organism (Pont and Bonting, 1981). The self-sustained characteristic enables the system to operate without any additional driving force other than the mechanical properties of the system, such as the growth of entropy in the system. In the case of membrane application, the enabling properties would be the given hydrostatic head, the membrane’s surface characteristics, and the resulting vacuum from the pressure difference across the membrane. The application of this passive filtration concept in an actual membrane operation is intended to reduce the system’s dependency on additional driving forces (e.g. pumps) and user maintenance (e.g. monitoring and cleaning).  Coupling the passive filtration concept with the concept of sub-critical flux operation is understood to have complementary effects in the reduction of both energy consumption and user maintenance requirements that has historically made conventional SHFUF systems complex and expensive.  A way of combining the two concepts is by operating membrane permeation under a constant, ultra-low hydrostatic pressure driven by gravity. Over time, the system is expected to reach a steady-state at a very low operating flux, at which point the system will become stable and self-sustained, such as observed by P.H. Hodgson (1994), Howell (1995) and Wu et al. (1999). This particular phenomena was confirmed in a pilot study by Peter-Varbanets et al. in 2010, which investigated the 15  potential suitability of a gravity-driven, flat-sheet membrane operation for decentralized drinking water treatment. In their research, a 40-cm hydrostatic pressure was applied to induce continuous permeation on a dead-end operated UF flat-sheet membrane. No additional control features, such as air sparging, backwash or chemical cleaning, were added to maintain the stability of the system.  Under this ultra-low pressure, the growth in fouling thickness was observed to be counteracted by biological activity. This activity makes the fouling structure porous, maintaining a low fouling resistance and a steady-state permeate flux (Peter-Varbanets et al., 2011). The system proposed by Peter-Varbanets et al. (2010) was field tested in Annet-sur-Marne, France and Ogunjini, South Africa to provide sufficient drinking water for 100-200 people.  Their results produced insights on other aspects affecting the system’s operation, such as pre-treatment of high turbid waters (>100 NTU) and daily wastage for a better flux stabilization (Boulestreau et al., 2012). . Figure 8 illustrates the process diagram of the gravity system developed by Peter-Varbanets in 2010.  Figure 8 Schematic presentation of the dead-end UF system (Peter-Varbanets et al., 2010)     16  3 Knowledge Gap and Objectives of Present Study The idea to simplify and develop a more affordable membrane system has only been explored recently with the development of a completely self-sustained, ultra-low pressure flat-sheet membrane system (Boulestreau et al., 2012; Peter-Varbanets et al., 2010). Similar attempts toward system simplification and energy reduction in SHFUF have not been done due to their susceptibility to fouling in the absence of fouling controls, such as backwash and aeration. Therefore, the main objective of the present study is to develop a novel and simple SHFUF system that can operate passively and with limited mechanical complexity for the production of drinking water in small/ remote communities. In meeting the objective, the present study will attempt to address the following research questions: I. Can process complexity of the conventional SHFUF system be simplified without compromising the operational stability? A. Is it possible to eliminate periodic backwash? i. What are the contributions of periodic backwash in SHFUF operation under sub-critical flux condition? ii. Can backwash be completely eliminated under sub-critical flux condition? B. Is it possible to eliminate the use of permeate pump using passive membrane filtration (ie. gravity-driven) and still achieve a steady flux? i. Does fouling behave similarly in sub-critical flux operations under constant flux (ie. pumped flow) and constant pressure (ie. gravity driven)? ii. What is the magnitude of permeate flux that can be sustained? C. Is it possible to eliminate air sparging in passive membrane filtration used in I-B for further system simplification? i. What are the contributions of air sparging in passive membrane filtration under sub-critical flux conditions? ii. Can air sparging be completely eliminated in passive membrane filtration?  II. What are the impacts of recovery cleaning on hollow-fibre modules and their performance? A. Is recovery cleaning capable to recover all of the loss permeability from a long-term operation?  B. Does acclimatization help to improve membrane performance? 17  III. What are the mechanisms that govern the performance of the passive membrane system used in I-B?  IV. What are the predominant fouling mechanism(s) in passive membrane system? A. Does air sparging frequency affect the predominant fouling mechanism?  V. What are the contributions of biological communities in passive membrane filtration? i. Is there evidence that biomass accumulation occurs during passive permeation?  ii. Does this biomass accumulation in the system reactor help the removal of organics?       18  4 Material and Methods 4.1 Experimental Program The experimental program was divided into four main stages that investigated the contributions of: 1). periodic backwash, 2). constant-pressure permeation, 3). air sparging, and 4). recovery cleaning in SHFUF operations under sub-critical flux conditions. Each stage was instrumental in eliminating one complex aspect of SHFUF system and bringing it closer to an optimized state that is feasible for a small community use. Table 3 summarizes the complete experimental program of the present study and Figure 9 illustrates the evolution of the system from each stage to the next. Table 3 Operational Conditions of the Three-stage Experimental Program Parameter of Interest Reactor Flux (LMH) Operation Type Aeration Backwash Daily Wasting 1. Periodic Backwashing A 10 Constant Flux 3.8 L/min Continuous 10-min/ 4-hr filtration  20 none 30  B 10 Constant Flux 3.8 L/min Continuous none  20 none 30  2. Constant-Pressure Permeation  10 *Constant Pressure 3.8 L/min Continuous none  C 13 10 %V  16  3. Air Sparging   D1 10 *Constant Pressure 3.8 L/min 25mins off/ 5 mins on none 10 %V E 10 *Constant Pressure 3.8 L/min 4hrs off/ 5 mins on none 10 %V F 10 *Constant Pressure 3.8 L/min 4hrs off/ 30 mins on none 10 %V G 10 *Constant Pressure No Aeration none 10 %V 4. Recovery Cleaning D2 10 *Constant Pressure 3.8 L/min 25 mins off/ 5 mins on none 10 %V *vacuum pressure provided by gravity  19   Figure 9 Simplification of the complex SHFUF into a simple system over the span of the research For all of the experimental stages, laboratory data such as temperature, production volume and transmembrane pressure were recorded daily. Water samples were collected every 2 to 5 days from all components of the treatment, including feed tank, system reactor and permeate flasks. Each sample was analyzed for its carbon content using total and dissolved organic carbon (TOC-DOC) analysis and its size exclusion chromatography using high performance liquid chromatography (HPLC) analysis.   4.2 Pilot-scale Submerged Hollow-Fibre Membrane System The pilot-scale submerged hollow-fibre membrane systems used in the present study are illustrated in Figure 15, Figure 17, and Figure 18. In general, the systems consisted of a feed water tank, a system reactor, membrane modules and a permeate collection unit. Depending on the investigated conditions, the systems would be equipped to conduct periodic backwash, pump permeate, and aerate. This section discusses in detail each component that made up the pilot-scale systems used in Stages 1 through 4. The feed water system of the pilot-scale consisted of one peristaltic pump (Masterflex) and an enclosed feed tank of 450 mm ID by 570 mm tall with a removable lid.  Throughout the study, the liquid level in the reservoir was maintained at an elevation that is sufficient to continuously provide feed to 20  the system reactor for a period of three days. The feed flow to the system reactor was supplied at a rate that was close to the permeation rate to maintain constant operating level.   The system reactor was an open cylindrical tank with an inside diameter of 155 mm and a total reactor height of 1,270 mm. A working depth of 1,000 mm was adopted to create sufficient freeboard. The total operating volume of the system reactor was approximately 19 litres. Water temperature inside the system reactor was measured daily using an alcohol based thermometer (Fisher Scientific 15-030 or CanLab D67412), which was installed inside the reactor. The system reactor was also equipped with a discharge valve at the bottom of the tank for daily wasting, which was started in Stage 2. Also added in Stage 2 was an overflow line to maintain a consistent head for a stable siphon flow of permeate. Figure 10 illustrates details of the design of the system reactor.  Figure 10 System Reactor Configuration Inside the system reactor was a set of membrane modules made with ZeeWeed® 500 hollow-fibres (GE Water and Process Technologies, Oakville, Canada), which are non-ionic and hydrophilic UF membranes. Their physical properties are summarized in Table 4. Each membrane module consisted of three 510 mm-long membrane fibres that were potted together into bulkheads. The bulkheads were 50 mm-long ¼” OD rigid tubing. One of bulkheads was open to allow permeate flow, whereas the other was sealed with epoxy glue. A total effective fibre length between the bulkheads was 430 mm, creating a total effective membrane surface area of 0.00717 m2 per bundle.  Figure 13 details the configuration of the membrane module.  21  Table 4 Membrane Module Properties of the Present Study Membrane Properties Unit Value Outside Dia. mm 1.77 Nominal pore Dia. um 0.04 Typical TMP psi 1-8 Number of Strands unit 3 Length mm 430 Total Filtration Area m2/ module 0.00717            For each experiment, a total of three membrane modules were made and mounted on a three-legged membrane stand. Depending on the operation conditions, the three modules may or may not operate as triplicates. Each module was secured with an adjustable membrane holder on either ends with a pot-to-pot distance of 420 mm, or 98% of membrane looseness, to allow sufficient freedom for fibre movement and avoid membrane agglutination. Figure 12 details the installment of the modules onto the membrane stand. Permeate Figure 11 Membrane Potting Configuration 22   Figure 12 Membrane Stand Design and Installation  (a) Membrane Modules Arrangement, b). Design Criteria of the Adjustable Membrane Holder) Permeation in Stage 1 was generated with a Masterflex pump (series 7520-35 and 7528-30 for Reactor A and B, respectively) with four Masterflex head pumps, specifically configured to produce the fluxes of interest. The configuration was as follows: one size-13 head pump (7013-21 ) to create 10 LMH, two size-13 head pumps (7013-21) to create 20 LMH, and one size-14 head pump (7014-21) to create 30 LMH. Within each of the permeate lines,  resistance to permeate flow was measured using Omega Engineering Inc. pressure transducer (Model PX243A-15BG5V) and recorded by HOBOware U12 data logger every 3 minutes. Permeation in Stages 2 through 4 was driven by a constant hydrostatic pressure and resistance to permeate was stable.  Fouling control through periodic backwashing (ie. in Stage 1) was performed by reversed flow of the permeate pump every 4 hours for 10 minutes at the same permeating fluxes, such that backwash flow was equal to the permeate flow. Fouling control through air sparging was provided by a sparger with three 1/8”-diameter orifices, located below the membrane modules. A normally-closed solenoid valve and a timer was added into the system in Stages 3 and 4 to conduct intermittent aeration in the system reactor. Figure 13 depicts the configuration of the system aeration. b). a). 60 mm Ø 5 mm  23   Figure 13 Configuration of the System Aeration Permeate collection generally consisted of a 5-litre flask per permeate line and an electronic balance (Denver Instrument MXX-10). In stages 2 through 4, a graduated cylinder with an overflow line into the permeate flask was added to maintain the hydrostatic head difference (refer to Figure 14). The weight of the produced permeate was taken once a day. Total volume filtered given time was calculated from multiplying the permeate weight by the density of water. Permeate flux was calculated daily using Equation 14. Equation 14   =  CD E F G  where, J is operating flux, L/m2.h  Vp is volume of permeate, litres  t is filtration time, hours  A is total filtration time, m2. 24   Figure 14 Establishment of constant hydrostatic pressure in SHUFUF System Stages 2 through 4 4.3 Source Water  Raw water used in this study was surface water from Jericho pond, located approximately 1 km south of the Jericho beach. Jericho pond is a typical run-off water pond that also serves as a natural habitat for ducks, blackbirds and fish. Its subjection to quality change due to seasonal changes and biological activities makes it an ideal representation of a typical surface water source. Raw water was collected once every 3 weeks. Approximately 2 m3 of water was collected in total over the one-year research period.  Immediately after the collection, water was transported back to UBC Environmental Engineering Lab and filtered through a 100 µm screen. Pre-treated water was then analyzed for total organic carbon (TOC) and dissolved organic carbon (DOC) contents as per Section 4.6.1, after which they were stored in a refrigerator at 4oC until the time to use. Prior to use, the water was warmed to room temperature, diluted with tap water to a DOC concentration of approximately 6-7 ppm, and tested for DOC and TOC. Table 5 summarizes the dissolved and total organic content in the raw Jericho Pond water.   25  Table 5 TOC and DOC of Raw Jericho Pond Water Sampling Date Volume (L) DOC (ppm) TOC (ppm) 03-Sep-13 90 22.9 32.0 30-Sep-13 113 17.0 28.3 05-Nov-13 90 14.5 23.8 04-Dec-13 113 13.1 18.5 23-Dec-13 113 12.5 18.6 10-Jan-13 158 10.6 16.3 23-Jan-14 135 9.5 14.2 06-Feb-14 158 8.6 11.3 20-Feb-14 158 9.0 12.6 06-Mar-14 158 7.9 9.6 14-Mar-14 113 8.7 10.5 27-Mar-14 158 7.2 10.6 17-Apr-14 135 11.1 16.6 29-Apr-14 158 12.4 18.5 09-May-14 113 12.5 18.2 Total 1,958 11.3 16.4 4.4 Experimental Setup 4.4.1 Stage 1: Contributions of Periodic Backwash in Long-Term SHFUF Operations under Sub-Critical Flux Conditions Two parallel experiments, with and without backwash, were conducted at constant low-fluxes. Each reactor contained three independent modules operating at fluxes of 10, 20 and 30 LMH for an extended period of 2 months. Backwash was controlled with a timer to occur every 4 hours for a duration of 10 minutes at the applied permeating fluxes. A continuous aeration at 3.8 L/min was adopted throughout the stage. Daily wasting was not incorporated in this stage. Figure 15 depicts the process diagram of Stage 1.  Given that the system reactor and membrane module configuration were directly adopted from a previous study by Bérubé & Lei (2006), the system was assumed to inherit the same estimated critical flux of 98.1 ± 2.8 LMH with the presence of a continuous aeration at 3.8 L/min. The fluxes of 10, 20 and 30 LMH considered in the present study were therefore sub-critical. Figure 16 was directly adopted from Bérubé & Lei (2006) to highlight the sub-critical zone that was considered in the present study.  26   Figure 15 Schematic of the Pilot-scale Submerged Membrane System Assessing the Benefits Backwash under Constant Low-Flux Operation   Figure 16 Range of Flux Index Investigated in the Present Study    Region considered in present study 27  4.4.2 Stage 2: Contributions of Constant-Pressure Permeation in Long-Term SHFUF Operations under Sub-Critical Flux Conditions Stage 2 was conducted with the understanding that backwash did not provide any significant improvement to SHFUF performance under constant low flux of 10 LMH in Stage 1 and thus, can be eliminated. The pilot-scale system used in Stage 2 was an identical setup to that in Stage 1, without the presence of periodic backwash, pressure transducers and permeate pump. A hydrostatic head was adopted to provide a continuous siphon flow of permeate by means of pressure difference. In order to maintain a constant hydrostatic head, an overflow line was added to the system reactor to recycle any excess feed to the reservoir tank. Three independent membrane modules were installed in the reactor to operate independently at constant heads (H) equivalent to 10, 13 and 16 LMH. Note that because the intrinsic membrane resistance varied from membrane module to membrane module, the relationship between flux and applied hydrostatic head was not linear. The hydrostatic head needed to generate fluxes of 10, 13, and 16 LMH were determined to be 37, 73 and 73 mBar (or 38, 74 and 74 cm), respectively. A continuous aeration at 3.8 L/min was adopted throughout the experiment.  A solid retention time (SRT) of 10 days was adopted by wasting 10% of the system reactor’s operating volume each day. Figure 17 depicts the process diagram of Stage 2. Items identified in grey are those removed from the setup used during Stage 1.  Figure 17 Schematic of the Pilot-scale Submerged Membrane System Operating as Passive Membrane System at 10, 13 and 16 LMH  Hydrostatic Head (H) 28  Prior to applying the experimental conditions, the membrane modules were acclimatized with continuous aeration for 20 days, which consisted of 10 days of priming at a constant flux of 10 LMH and 10 days of gravity permeation at a constant head of 76 cm or approximately 25 LMH. The priming period was meant to establish a consistent pressure difference for siphon (ie. gravity) flow, and the high-flux permeation period was meant to ensure the presence of biofilm at the membrane surface. Biofilm is believed to help the establishment of steady-state conditions in the system reactor.  4.4.3 Stage 3: Contributions of Air Sparging in Long-Term SHFUF Operations under Sub-Critical Flux Conditions Stage 3 was conducted with the understanding that in Stage 2, 1). a continuous and stable passive permeation was achievable through siphon mechanism and 2). 10 LMH operating flux was maintainable through an extended operation of passive permeation. The pilot-scale system used in Stage 3 were made identical to Stage 2, except for the addition of a timer and a solenoid valve to control the different aeration conditions in the system reactor. Four aeration conditions were investigated: no aeration, intermittent aeration cycles of 25 minutes off – 5 minutes on, 4 hours off – 30 minutes on and 4 hours off – 5 minutes. Experiments for each condition investigated were performed with three identical membrane modules (ie. triplicates) operating at a constant head (H) equivalent to 10 LMH. A 10%-volume daily wasting was conducted during aeration, except for conditions with no aeration. Prior to each experimental condition, membrane modules were acclimatized as in Stage 2 with continuous aeration. Figure 18 depicts the process diagram of Stage 3. Items identified in grey are those removed from the setup used during Stage 2.  Figure 18 Schematic of the Pilot-scale Submerged Membrane System Operating as Passive Membrane System with Intermittent Aeration   Hydrostatic Head (H) 29  4.4.4 Stage 4: Contributions of Membrane Recovery Cleaning in Long-Term SHFUF Operations under Sub-Critical Flux Conditions The pilot-scale system used in Stage 4 was identical to that used in Stage 3 (refer to Figure 18). Stage 4 was conducted to investigate the effectiveness of recovery cleaning on modules after an extended operation.  Recovery cleaning was performed on three membrane modules from Stage 3’s 25 minutes on – 5 minutes off at the end of its 2-month operation. Membrane recovery cleaning was conducted through a complete drainage of the system reactor, which was then refilled with a solution containing 500-ppm NaClO. NaClO permeation was conducted for 4 hours by gravity, after which the tank was drained and refilled with new raw water feed. The membranes were directly put back into operation without acclimatization.   4.5 Quality Control 4.5.1 Membrane Integrity Testing Membrane integrity tests were conducted prior to starting each experiment. Membrane integrity tests were done by submerging and pressurizing each module to 10 psi with air while submerged in de-ionized (DI) water. Pressure was monitored in the air line using a pressure transducer connected to a data logger and a standby computer.  Any observable bubbles released from the module would indicate that the module was breached, in which case the module would have to be repaired or completely replaced with a new one. Figure 19 illustrates the laboratory set-up for membrane integrity test.   Figure 19 Membrane Integrity Testing  30  4.5.2 Membrane Cleaning A new membrane module was used for each experiment, except for the experiments performed in Stage 4. Each new membrane module was chemically cleaned before the start of each experiment to ensure complete removal of any preservatives. Sodium hypochlorite solution (NaClO) was used as follows. 1. A new membrane module is placed in an enclosed container filled with a 750-ppm NaClO solution (25 ml NaClO at 6% and 1,975 ml distilled water) for 16 hours. 2. This solution is then filtered through the module at -4.1 psi for 20 minutes. 3. The container is then drained and a fresh 50-ppm NaClO solution (1.7ml NaClO at 6% and 1,998.3 ml distilled water) is added and then filtered through the module for 20 minutes at -4.1 psi. 4. The cleaned membrane module is stored in a 50-ppm NaClO solution until used. Prior to using, each module was rinsed three times and filtered at -4.1 psi for 20 minutes with DI water. 4.5.3 Clean Water Tests An overnight clean water test (approximately 20 hours) was conducted before the start of each experiment using DI water at the operating flux of interest. Throughout the test, transmembrane pressure was measured and recorded by a data logger. The long duration of clean water flux was adopted to ensure the achievement of a steady-state TMP by the modules. The filtered water was circulated back into the feed container to maintain a constant water level throughout the experiment.  The initial membrane resistance was back-calculated with Equation 1 using the known permeate flux and the obtained steady-state clean water TMP as inputs. Since fouling does not occur when filtering DI water, membrane resistance (Rm) is equivalent to the total filtration resistance (R). The complete data obtained from the clean water tests is available in Appendix A. 4.5.4 Transmembrane Pressure Measured transmembrane pressures were collected and updated daily from the data logger using a visual basic for applications (VBA) algorithm (Appendix B). Upon using the data, TMP values were normalized to a temperature of 20oC using Equation 15 to account for slight daily temperature fluctuation in the room.  31  Equation 15 H+I' = HJK+I'KJ  where, H+I' is the normalized TMP at 20oC, N/m2 PT is the obtained TMP at temperature ToC, N/m2 μ+MN is water viscosity at 20oC, Ns/m2 µT is water viscosity at ToC, Ns/m2. Water viscosity value at ToC was estimated using the three regression models listed below over the range of temperatures observed during the present study (17 to 28oC).  Equation 16 KJOPQRSIT = −2.76x10XT + 1.55x10? Equation 17 KJRSQRPIT =  −2.17x10XT + 1.44x10? Equation 18 KJRPQ[SIT = −2.00x10XT  + 1.40x10?   4.5.5 Sampling Operating samples were collected from feed tank, system reactor and permeate flasks every 3 to 5 days throughout the duration of each experiment. The feed tank was sampled at mid-depth after fully-stirring the contents of the tank. System reactors without daily wasting (Stages 1 and 2) were sampled at approximately 25 cm below the height of the liquid level. System reactors with daily wasting (Stages 2 through 4) were sampled at the discharge point during daily wasting. Permeate samples were taken directly from the permeate flask. All samples were collected in a beaker that that had previously been rinsed with the sample. 4.6 Analytical Methods  4.6.1 Total and Dissolved Organic Carbon (TOC and DOC) TOC and DOC samples were analyzed in a batch every 7 to 10 days. For dissolved organics quantification, each sample was filtered with a 0.45 µm nylon filter prior to the analysis and preserved with one drop of 10% hydrochloric acid (HCl) solution. Quantification of organic carbon was conducted 32  with instrument IL 550 TOC-TN by Hach and run by software OmniTOC4.5, according to their user manuals.  Three blanks and six different concentration standard solutions at 1, 2, 10, 20, 40 and 50 ppm were included in each batch of the DOC/TOC analyses. The standards were made from diluting a 1,000-ppm stock solution of 0.5312 grams of potassium hydrogen phthalate in 250 ml of H3PO4 to the concentrations of interest with DI water. During the analysis, a total volume of 0.25 ml was extracted from each sample vial for carbon detection.  The presence of carbon in each sample was reported in total integrated area (arbitrary unit) by the instrument. The linear relationship that occurs between the integrated area and organic carbon concentration in the standards was used to normalize the measurement variability among the samples within each run. A typical linear relationship between the areas and organic concentrations are projected in Appendix C.  4.6.2 High Performance Liquid Chromatography (HPLC) Size exclusion chromatography was performed on a batch of samples every 3 weeks. Prior to the analyses, each sample was filtered with a 0.45 um nylon filter. Size exclusion was conducted with a 20 mm ID x 250 mm stainless steel TSKgel column of 30-µm silica-based resin and a series of instruments, including: Waters 717plus autosampler, Waters 600 controller, Waters 2410 refractive index detector, Waters 486 tunable absorbance detector (programed to operate at 254 nm), Sievers 900 portable TOC analyzer and Sievers inorganic carbon remover.  Two blanks and six at 10-ppm calibration standards (four polyethylene glycol (PEG) solutions of 600, 1500, 3300, 6000 Da in molecular weight and two polystyrene sulfonate (PSS) solutions of 15000 and 41000 Da) were included in each batch of samples analyzed. An aqueous buffer (5.0 KH2PO4 and 4.5 Na2HPO4.7H2O in 2 litres of DI water) was used in isocratic mode at 1 ml/minute. Run time was 100 minutes to accommodate TOC analyzer cycles, during which time a total volume of 1 ml was extracted from each sample vial for analysis.   Presence of total organic materials and organic materials absorbing UV254 were identified by the peaks produced in the analysis. The retention times at which the peaks occur are linearly correlated with the Log10 of their molecular weights. A typical calibration curve obtained from the analyzed standards in each batch was available in Appendix C. 33  4.7 Data Analysis Methods 4.7.1 Quantification of Fouling Effects on Membrane Performance The occurrence and progress of fouling was confirmed by the reduction in membrane permeability over time. System performance for each of the investigated conditions was presented through the plotting of relative membrane permeability (B/Bi) over volume filtered and time. Equation 2 was used to calculate the membrane permeability given flux and constant hydrostatic head.   Comparison of system performances between conditions was conducted through a pairwise comparison. The difference between the two compared targets was calculated for each obtained data point (governed by time or volume filtered), from which an overall mean difference was then calculated. The variant of the mean was presented with 95% confidence interval using the standard equation below. Equation 19 ±95% = ∝ +2  x √^ where, t is the t distribution α is the degree of freedom  s is standard error n is number of data points. 4.7.2 Determination of the Pre-dominant Fouling Mechanisms The pre-dominant fouling mechanism(s) was determined through data modelling using the individual and combined fouling models developed by Bolton, Lacasse, & Kuriyel (2006) for a constant-pressure system, as presented in Table 1 and Table 2. Throughout the analysis, volume was represented in litres, flux was in LMH and time was in hours. The fit the models in each data set was analyzed using a statistical software package of SigmaPlot 12 by Systat Software Inc.  Essential parameters, such as residual sum of squares (SSR), coefficient of determination (R2) of the model, as well as the fitted parameters’ standard errors (s), t-statistics and p-values, were evaluated to determine the validity of the analysis. For comparison, all models considered were ranked based on how well they could be fitted to the measured data (ie. lowest to highest SSR values). The complete statistical reports of the top 5 models are available in Appendices F through J.  34  4.7.3 NOM Characterization and Quantification Responses from both the UV254-detection (UVD) and organic carbon detection (OCD) were compiled and synchronized using a VBA algorithms for Excel, which is available in Appendix B. Profiles obtained from HPLC were characterized according to a study by Huber et al. in 2011, as illustrated in Figure 20. The detectable peaks of A to E mark the typical surface water characteristics, which include the presence of biopolymers, humic substances (HS), building blocks, low molecular-weight acid (LMA), and low molecular-weight neutrals (LMN), respectively. The signal response in the y-axis signifies the strength of the corresponding NOM constituent, which was identifiable by the ith minute of travel time (retention time) defined in x-axis.   Figure 20 Chromatogram of a typical surface water with responses for organic carbon detection (OCD), UV-detection at 254 nm (UVD) and organic nitrogen detection (OND). Source: Huber et al., 2011 NOM quantification was, conducted via integration of the area under the curve. Equation 20 was used to integrate the total area under the curve over the 100-minute total retention time. Equation 20 _6:` a;b: cdeb; _ℎb gh;ib (_. acg) = j kEl − kElmOnd (kEl − kElmO)  o (  −  )Ep  where, T.AUC quantifies the total signal received for NOM in a water sample, unitless ti is the ith measurement of time in minutes during the 100-minute retention time,  St is the signal response at the corresponding time, unitless. 35  Estimations on the contribution of each NOM type in T.AUC can be done by truncating the integrated water profile according to the time range during which each peak was received. Table 6 summarizes the time windows for each NOM in the investigated waters.   The intermediate peaks of humic substances, building blocks and LMA were combined into a single HS peak. Table 6 Ranges of Retention Time for the Different NOM Types in the Water Samples Natural Organic Matters Retention Time (mins) High Molecular Weight (HMW) 19 ≤ x ≤ 36 Humic Substances (HS)  36 < x ≤ 59 Low Molecular Neutrals (LMN) x > 59   Using the defined time boundary, the total response received for each NOM type was calculated using Equation 21 to Equation 23. Equation 21 acg qrs = j kEl − kElmOnd (kEl − kElmO)  o (  −  )?tpu  Equation 22 acg  qk = j kEl − kElmOnd (kEl − kElmO)  o (  −  )Xup?v  Equation 23 acg nrw = j kEl − kElmOnd (kEl − kElmO)  o (  −   )pt  where, the summation of these AUC’s is also equal to T.AUC. NOM quantification was calculated using the linear relationship that exists between the total area under the curve (T.AUC) and the measured DOC in ppm from Section 4.6.1, as also displayed by Figure 21. The concentration of any NOM type can be calculated using Equation 24 given the availability of DOC measurements, such as in the case of feed tank and system reactor samples.  36   Figure 21 Typical Linear Correlation found between the measured DOC in ppm and calculated AUC from HPLC analyses on the feed and system reactor samples Equation 24 [NOM Type] in feed or reactor = Gx' yz{ J|}~J.Gx'  o €g‚ƒ}„~  where, [NOM Type] is the concentration of a specific NOM type of interest, ppm and DOCsample is the measured DOC concentration of the sample in question, ppm.  In the case of permeates, where DOC measurements were not conducted, NOM concentrations were estimated from the calculated NOM concentrations of the corresponding system reactor on the day of interest. Equation 25 was used to estimate the NOM concentration in permeates. Equation 25  [NOM Type] in Permeate = Gx' yz{ J|}~ ^ ~…ƒ~‚E~Gx' yz{ J|}~ ^ ~‚*E†…  x [NOM Type] in Reactor 4.7.4 Mass Balance of NOM throughout the Passive Membrane System A mass balance calculation was conducted to estimate the theoretical concentrations of NOM in the system reactor in the absence of biological activity. The difference between the theoretical and the measured values indicate the contributions of biological activities during the extended operation passive membrane system. Throughout the analysis, the system reactor was assumed to be fully mixed. Figure 22 illustrates the input-output flows of the system reactor. 37      Figure 22 Schematic Diagram  The total mass of NOM fed to the system reactor was estimated by summing the products of each measured NOM concentration in feed and the corresponding total volume discharged over the span of the experiment (ie. 60 days), as expressed in Equation 26 and Equation 27. Equation 26        F  =  ∑  ( [‰E]t ‹‚|Ep  o E )   Where, F is the estimated cumulative mass of NOM in feed over the span of the experiment, milligrams  t is nth sampling day [Ft] is NOM concentration in feed at time t, ppm E is the total volume fed to the system reactor between two sampling dates, litres.  Equation 27 E  =  .j EE + Œ/ Where, VP is the total volume filtered, litres and Vw  is the total volume wasted, litres. The mass of NOM permeated through the membrane between sampling intervals was estimated by accounting the permeate production from all modules used in the experiment using Equation 28.   Equation 28          P =  ∑ ( ∑ ( [HE]^p  ot ‹‚|Ep  ∆ ∑ tE )) 38  Where, P is the estimated cumulative mass of NOM permeated through the membrane over the span of the experiment, mg n is the total number of membrane modules in an experiment and [Pt] is the NOM concentration in permeates at time t, ppm. The mass of NOM wasted was estimated similarly as both the feed and permeates. Equation 29 was used to estimate the total mass of NOM wasted throughout an operation, where [Rt] is the reactor concentration at time t. Equation 29          W =  ∑ ( [E] ot ‹‚|Ep  ∆ ∑ ŒtE ) Where, W is the estimated cumulative mass of NOM wasted over the span of the experiment, mg   [Rt] is the NOM concentration in waste at time t, ppm.  Therefore, the theoretical cumulative NOM mass (RTH) in system reactor at any time during the operation can be calculated using Equation 30. RTH should only be used as a trend indicator of biological activity in the system reactor rather than an exact quantification. Equation 30   JŽ = ∑ (‰E − HE + sE) + Et ‹‚|Ep            ,    RTH ≥ 0 Where, RTH is constrained to be equal or greater than zero, mg Ft is total mass of NOM in feed at time t, mg Pt is total mass of NOM in permeates at time t, mg Wt is total mass of NOM in waste at time t, mg Rt-1 at t = 1 is the mass of NOM in system reactor at initial time.  39  5 Results, Data Analysis and Discussion Chapter 5 presents and discusses the experimental results obtained from the SHFUF pilot-scale trials. The chapter is divided into two sections, 1). long-term fouling mitigations in in SHFUF systems and 2). presence of organic material in passive membrane operations.  Together, the two sections will attempt to comprehensively answer the research questions proposed in Chapter 3. 5.1 Long Term Fouling Mitigation in SHFUF systems 5.1.1 Contributions of Backwash to Fouling Control in Long-term SHFUF operation under Sub-Critical Flux Conditions The benefits of backwash in long-term, constant low-flux operations were assessed through a comparative study of two parallel pilot-scale SHFUF systems operating with (Reactor A) and without (Reactor B) periodic backwash. Both systems were operated until either the membrane’s maximum operable transmembrane pressure (8 psi) was reached or a maximum of 2 operating months was reached. The objective of Stage 1 of the present study was to determine whether the elimination of periodic backwash is possible in a low-flux SHFUF operation. The elimination of periodic backwash is expected to simplify the system and significantly reduce the system’s energy requirements and operating costs. The performances of the two pilot systems at different operating fluxes (10, 20 and 30 LMH) were evaluated by comparing the rate at which membrane permeability was lost with respect to volume filtered. Figure 23 present the declining normalized permeability over volume filtered for the two pilot systems operating at sub-critical fluxes. At 30 LMH, a gradual decline in the normalized permeability with respect to volume filtered was observed in both of the reactors, with and without backwash. The continuous decline over time observed in both Figure 23a and Figure 23b suggest a growing fouling rate even with the presence of periodic backwash. However, the total filtration volume that could be achieved by the reactor with backwash was five times that of the reactor without backwash. The higher permeability observed in the reactor with backwash resulted from the partial removal of foulants by the periodic backwash. As expected, the periodic backwash was able to improve hydrodynamic conditions within the reactor by dislodging foulants from the membrane surface and pores. 40  c). cd). f). e). b). a). Figure 23 Reduced Membrane Permeability over Volume Filtered for both With and Without Backwash Operations  (a). 30 LMH without Backwash, b). 30 LMH with backwash, c). 20 LMH without Backwash, d). 20 LMH with Backwash, e). 30 LMH without Backwash, and f). 30 LMH with Backwash) 41    At 20 LMH, a gradual decline in the normalized permeability with respect to volume filtered was again observed for reactors with and without backwash. The rate at which permeability declined, as illustrated by Figure 23c and Figure 23d, was lower than that observed at 30 LMH. Moreover, a steady state was reached in the reactor with backwash at a normalized permeability (B/Bi) of 0.75. Consequently, the 8 psi termination point was never reached in the reactor with backwash. Over the 2-month period the reactor with backwash produced approximately 70 L of filtered water, while the reactor without backwash produced 45 L of filtered water. The steady-state condition that was reached indicated that at this operating flux, backwash was still instrumental in enhancing the system’s hydrodynamic conditions through the establishment of a critical-flux condition, where fouling ceased to occur. Subsequently, the impacts of backwash on membrane permeability was not as prominent as was observed at 30 LMH. At 10 LMH, an initial decline in the normalized permeability with respect to volume filtered was observed in reactors with and without backwash prior to reaching a similar steady state at a normalized permeability (B/Bi) of 0.6. Consequently, the 8 PSI termination point was also never reached by either reactor (refer to Figure 23e and Figure 23f).  Over the 2-month period, both reactors produced 40 L of filtered water. The short stabilization period during the first 8 L of production indicated that fouling still occurred even during an extremely low-flux filtration. A number of studies have suggested that some initial fouling does occur under low-flux filtration and is largely the cause of concentration polarization development (Marshall et al., 1996; Miller et al., 2013). Nonetheless, the low operating flux significantly limited the rate and amount of particle mass travelling toward the membrane (Pearce, 2011), which enabled the system to reach steady-state conditions without backwash. The normalized permeability after backwash was observed to be exactly the same as that of prior backwash. The results from Stage 1 indicate that at 10 LMH periodic backwash can be safely eliminated without any significant impact on membrane’s fouling rate.  5.1.2 Contributions of Constant-Pressure Permeation in Long-Term SHFUF Operations under Sub-Critical Flux Conditions  Fouling during constant-pressure SHFUF operation without backwash was assessed by operation using gravity-driven permeation (ie. siphoning) at a constant hydrostatic head. The alteration of the system to a gravity flow without backwash reduces system’s complexity and costs, making it more suitable for remote applications. The objectives of this stage were 1). to assess if fouling was similar under constant-pressure and constant-flux operation, and therefore allowing gravity to be used to 42  provide the driving force for permeation through the membrane and 2). to closely investigate the magnitude of permeate flux that can be sustained in passive membrane filtration, which was previously identified between 10 and 20 LMH in Stage 1.  Three hydrostatic heads that generate fluxes of 10, 13 and 16 LMH were considered in Stage 2. Prior to operation at the fluxes of interest, all three modules were acclimatized through 10 days of priming and 10 days of 75mBar gravity-permeation.  Figure 24 illustrates the progression of normalized membrane permeability over volume treated for 10, 13 and 16 LMH post acclimatization period. The complete permeability data obtained in Stage 2 can be found in Appendix D.  Figure 24 Normalized Membrane Permeability of Gravity Permeation at 10, 13, and 16 LMH Post-Acclimatization Period After the acclimatization period, the 10 LMH module had completely reached steady-state conditions, normalized membrane permeability was constant at B/Bi of approximately 1 for the 2-month operation. The steady-state permeability observed under gravity permeation (ie. constant-pressure) was similar to that achieved under constant-flux conditions observed in Stage 1. Miller et al. (2013) reported that below a threshold flux, fouling is similar for both constant-pressure and constant-flux operations. This confirms the similar fouling behaviour observed in both constant-flux (Stage 1) and constant-pressure (Stage 2) operations at 10 LMH, which was a sub-critical flux.  At the intermediate fluxes of 13 and 16 LMH, a steady-state conditions were not immediately observed after the acclimatization period as the normalized permeability (B/Bi) continued to decline to a steady-state value of 0.8. These results indicate that at 13 and 16 LMH, the steady-state permeability that can be sustained is lower than that which can be sustained at 10 LMH.  43  Overall, the results from Stage 2 indicate that 1). fouling behaviour in constant-pressure system is similar to that in constant-flux under sub-critical flux conditions, 2). gravity force is sufficient to sustain a continuous SHFUF operation, thus can be used for permeation, and 3). 10 LMH was observed to be the optimum flux that can immediately establish steady-state conditions at a high normalized permeability.   5.1.3 Contributions of Air Sparging in Long-Term SHFUF Operations under Sub-Critical Flux Conditions The contributions of air sparging in passive membrane filtration was assessed through a comparative study of four parallel pilot-scale gravity driven systems operating at 10 LMH under intermittent air sparging cycles of 25 minutes off – 5 minutes on in Reactor D, 4 hours off – 30 minutes on in Reactor E, and 4 hours off – 5 minutes on in Reactor F and under no air sparging in Reactor G. The elimination of air sparging in passive membrane system is expected to further reduce cost and complexity. The objective of Stage 3 of the present study was to assess 1). the contributions of air sparging in passive membrane filtration as a fouling control and 2). the feasibility of operating passive membrane filtration with complete absence of air sparging. All experiments were conducted in triplicate, except for one of the conditions investigated for which the experiment was conducted in duplicate. Each reactor was acclimatized as in Stage 2 prior to operating at a hydrostatic pressure equivalent to 10 LMH and under reduced aeration. Figure 25 illustrates the progression of normalized membrane permeability over volume post-acclimatization under different air sparging conditions. The complete permeability data obtained in Stage 3 can be found in Appendix E.  After the acclimatization period, the normalized membrane permeability was observed to decline with respect to the volume filtered for the four conditions investigated in this stage. The extent of the decline increased as air sparging was decreased. Following the initial rapid decline, the rate at which the normalized membrane permeability (B/Bi) decreased reduced.  For all conditions investigated, the normalized membrane permeability either reached or trended towards a steady state of approximately 0.2. A reduction in the rate of decline to a steady state was also reported by Miller at al. (2014). For all conditions investigated, the decline in the normalized permeability with respect to the volume filtered could be modeled using the exponential relationship presented in Equation 31. The fit of the model to the obtained data is also presented in Figure 25. 44   Figure 25 Reduced Normalized Membrane Permeability over Time ( a). 25 Minutes off – 5 Minutes on; b). 4 Hours off – 30 Minutes on; c). 4 Hours off – 5 Minutes on; and d). No Air Sparging)a). b). d). e). 45  Equation 31  =  + ∆    bo‘C where,  ’’l  is normalized permeability at a given volume, unitless Bs is normalized membrane permeability at steady state, m ∆ ’’l  is change in normalized membrane permeability prior to reaching steady state, unitless K is fouling coefficient, L-1 V is volume filtered, L. For the two conditions with the least air sparging (ie. no air sparging and intermittent cycle of 4 hours off – 5 minutes on), steady-state conditions appeared to have been reached after filtering approximately 20 and 30 L, respectively. For these conditions, the normalized membrane permeabilities at steady state were estimated to be 0.22±0.004 and 0.26±0.003, respectively, by fitting Equation 31 to the measured data. These Bs values were equivalent to 2 and 2.7 LMH, respectively, and are lower than the steady-state flux of 4 LMH that was obtained by Boulestreau et al. (2012) and Peter-Varbanets, Margot, Traber, & Pronk (2011) in their similar gravity-operated flat-sheet membrane system with no aeration.  The difference in result from the present study and those reported by others is likely due to differences in organic content of the waters investigated, which ranged between 2.0 to 2.7 ppm DOC in Peter-Varbanets et al.’s and Boulestreau et al.’s study and 6.0 to 7.0 ppm DOC in the present study.  For the other two conditions with higher air sparging (ie. 25 minutes off – 5 minutes on and 4 hours off – 30 minutes on), steady state conditions were not reached during the two-month operation. As a result, Equation 31 alone was not able to estimate the normalized membrane permeability at steady state without an assumed constraint. Since the normalized permeability of the two conditions appeared to trend towards a steady state value similar to that observed for the previous conditions with the least air sparging, a constraint of Bs equalled to the averaged normalized permeabilities of the two conditions with the least air sparging (0.24±0.007) was applied to produce a representative model for the two higher air sparging conditions. The fit of the assumed model to the measured data was close to that of the model without the constraint, supporting the validity of the assumption (refer to Figure 25a and Figure 25b). The four fitted models representing the different extent of reduced air sparging are presented in Figure 26 with respect to the system with continuous air sparging for a direct performance comparison. Their fitted parameters and errors are summarized in Table 7.  46   Figure 26 Effect of Reduced Air Sparging Conditions on Membrane Permeability Table 7 Fitted Values of the Exponential Regression Model for Each of the Reduced Air Sparging Conditions   Bs ∆ ’’l  -K Reactor Conditions ON/OFF Ratio Mean ±95% Mean ±95% Mean ±95% C Continuous ∞ 1.04  0.01 0.02 0.01 2.96x10-18 0.003  D1 25min off/ 5 mins on 0.20 0.24*  N/A 0.84 0.004 0.023 0.0013 E 4hrs off/ 30 mins on 0.13 0.24*  N/A 0.78 0.005 0.043 0.0003 F 4hrs off/ 5 mins on 0.02 0.26  0.003 0.74 0.003 0.109 0.002 G No Air Sparging 0.00 0.22  0.004 0.78 0.004 0.544 0.0178 *assumed normalized permeability at steady-state   The above results suggest that the extent of total permeability drop with aeration that is less than continuous is the same regardless the on/off ratio, as all of the reduced aeration conditions eventually reached the same steady-state permeability that was approximately 24% of the initial permeability. This residual permeability, nonetheless, allows long-term operation of a passive membrane filtration at a lower, but steady flux. The contributions of aeration were clearly observed in the rate at which steady state conditions were reached (ie. fouling coefficient) by the different aeration conditions. Figure 27 illustrates the correlation between fouling coefficient and ON/OFF ratio of the aeration. Providing a small amount of aeration, such as 5 minutes every 4 hours, was enough to decrease the fouling rate by over 80%. Any reduction in fouling positively impacts the capacity of the system in terms of volumetric throughput.  4Hrs off-5Mins on G 25 Mins off-5 Mins on 4Hrs off-30 Mins on No Air Sparging D1 E F C C Continuous D1 G E F 47   Figure 27 Reducing Fouling Rate with Increasing Air Sparging Frequencies 5.1.4 Contributions of Recovery Cleaning on Membrane Modules and Operation The final stage of the present study was conducted to investigate the contributions of 1). recovery cleaning on the restoration of membrane permeability and 2). acclimatization on the long-term operation of passive membrane systems. Modules from the system with reduced aeration of 25 Minutes off – 5 Minutes on were cleaned (see Section 4.4.4) and returned to operation without acclimatization. Figure 28 presents the change in the normalized membrane permeability before and after recovery cleaning. The efficiency of cleaning was demonstrated by the complete recovery of membrane permeability after cleaning. Without the acclimatization, the initial permeability of the cleaned membrane modules was 45% greater than that observed following acclimatization. The difference in the membrane permeability was expected, likely due to the contribution of foulants pre-coating the membrane during the acclimatization period. At this higher permeability, the system was fouling at a proportionally higher rate. Equation 31 was fitted to the measured data to determine the steady-state permeability and the fouling rate before and after-recovery cleaning. Table 8 compares the fitted values of the three modules operated with recovery cleaning. The fouling rate (-K) was observed to be greater following recovery cleaning and without acclimatization. Also, the normalized membrane permeability at steady state was greater following recovery cleaning and without acclimatization. Despite the difference in fouling rates and system stability, both pre- and post-recovery operations produced the same throughput over the 2-month span.  48    Figure 28 Reduced Permeability over Volume Filtered for the 25 Minutes off – 5 Minutes on Modules After Recovery Cleaning (a). Module 1, b) Module 2, c). Module 3)   a). b). c). 49  Overall, results indicated that acclimatization did not improve membrane performance as was claimed by Ye et al. (2011). In fact, acclimatization appeared to hinder the occurrence of sustainable conditions, leading to a lower steady-state permeability. It should, however, be noted that different acclimatization approaches were not considered in the present study. It is possible that other acclimatization methods (e.g. lower fluxes/gravity pressure and shorter periods) may be beneficial to membrane performance. Table 8 Fitted Values of the Exponential Regression Model for Before and After Recovery Parameters 9.8LMH 10.2 LMH 10.8 LMH Before After Before After Before After ““”   0.24±N/A* 0.50±0.003 0.24±N/A* 0.50±0.006 0.24±N/A* 0.34±0.002 ∆ ““”   0.96±0.006 1.16±0.022  0.84±0.004 0.99±0.015 0.88±0.004 0.81±0.007 -K 0.02±0.0002 0.15±0.004  0.02±0.001 0.07±0.002 0.02±0.0002 0.07±0.001 *assumed 5.1.5 Fouling Mechanisms in Passive Membrane Operations An analysis to determine the predominant fouling mechanisms governing passive membrane filtration was conducted by fitting the individual (Table 1) and combined (Table 2) fouling models defined by Bolton et al. (2011) to the measured data. The predominant fouling mechanisms were assumed to be the ones for which the corresponding fouling model best-fit the measured data. The best fit was determined by the coefficient of determination (R2) and residual sum of squares (SSR) of the fitted models, while also considering the resulting statistic indicators, such as standard errors (s), t-statistics and p-value. The complete statistical reports are provided in Appendices F through J. According to the analysis, all the investigated conditions were predominately governed by the same models. Four possible models, cake-complete, cake, cake-intermediate, and cake-standard, were identified to share the same likelihood to govern the system under different air sparging conditions. Figure 29 presents the fit of these models with the obtained data.  However, the negative complete-blocking coefficients (Kb) obtained from fitting cake-complete model in the data sets suggest an impossible hypothesis of de-blocking of the pores during the operation of passive membrane filtration.  Furthermore, the statistical analysis of both the cake-intermediate and cake-standard models revealed high standard errors, low t-statistics and p-values of 1 on the fitted intermediate- (Ki) and standard-blocking (Ks) coefficients. This implies uncertainties to the actual contributions of the intermediate- or standard-blocking mechanisms in membrane fouling during passive filtration. On the other hand, cake 50  coefficient (Kc) consistently fit the data with low standard errors, high t-statistics and p-value of <0.0001 for both the individual and combined model analyses. From this examination, cake formation was determined to be the predominant mechanism governing the fouling of passive membrane filtration in all of the investigated operating conditions. Thus, it can be concluded that fouling predominantly occurs at the membrane surface despite the air sparging conditions. Table 9 summarizes the results of the individual and combined model analyses.51  Table 9 Fitted Parameters for the Single and Combined Fouling Models    Air ON/OFF Ratios   0 0.02 0.13 Rank Model R2 SSR Fitted Parameters R2 SSR Fitted Parameters R2 SSR Fitted Parameters 1 Cake 0.96 35 Kc = 8.50±0.14 0.96 171 Kc = 1.73±0.02 0.96 359 Kc = 1.29±0.01 2 Cake- Intermediate 0.96 35 Ki = 2.90x10-9±3.00x10-2 Kc = 8.25±0.26 0.96 173 Ki = 2.41x10-10±4.03 x10-4 Kc = 1.70±0.01 0.96 362 Ki =5.64x10-10±3.51x10-4 Kc = 1.27±0.02 3 Cake- Standard 0.96 35 Ks =5.02x10-6±3.87x1010 Kc = 8.93±0.15 0.96 173 Ks = 1.04x103±9.88 x104 Kb = 1.82±0.02 0.96 365 Ks = 4.52x106±2.94x1010 Kc = 1.36±0.01 4 Intermediate 0.53 440 Ki = 0.94±0.03 0.52 2002 Ki = 0.29±0.01 0.53 4051 Ki =0.21±3.10x10-3 5 Intermediate - Standard 0.53 440 Ki = 0.94±0.07 Ks = 1.39x10-18±2.0810-4 0.52 2002 Ki = 0.29±0.02                   Ks = 7.01x10-19±1.01x10-4 0.53 4051 Ki =0.21±0.01                    Ks = 8.66x10-20±5.84x10-5 6 Standard 0.14 812 Ks = 0.29±0.01 0.16 3540 Ks= 0.08±2.00x10-3 0.16 7277 Ks = 0.06±1.05x10-3 7 Complete - Standard 0.14 812 Kb=  4.00x10-4±4.24 x103 Ks = 0.29±4.24x102 0.16 3540 Kb = 1.00x10-4±2.42x103    Ks = 0.08±2.43x102     0.25 6511 Kb= 4.57x10-16±7.98x104        Ks = 0.061±0.00 8 Complete 0.06 887 Kb = 1.57±0.08 0.11 3700 Kb = 0.42±0.01 0.12 7617 Kb = 0.31±0.01 9* Cake-       Complete 1.00 1 Kb = -1.34±0.27 Kc = 23.49±0.35 1.00 8 Kb = -0.38±0.01 Kc = 3.89±0.04 0.99 67 Kb = -0.28±0.01 Kc = 2.80±0.05 *Invalid results due to the negative fitted Kb 52  Table 9 Fitted Parameters for the Single and Combined Fouling Models (Continued)   Air ON/OFF Ratios   0.2 0.2** Infinity Rank Model R2 SSR Fitted Parameters R2 SSR Fitted Parameters R2 SSR Fitted Parameters 1 Cake 0.94 134 Kc = 0.71±0.01 0.94 714 Kc = 0.79±0.01 0.86 5735 Kc = 0.36±0.01 2 Cake- Intermediate 0.94 1359 Ki = 1.61x10-10±2.20x10-4  Kc = 0.70±0.01 0.94 722 Ki = 2.16x10-11±2.12x10-4 Kc =0.78±1.97x10-3 0.86 5779 Ki = 1.20x10-10±5.27x10-4 Kc = 0.35±0.01 3 Cake- Standard 0.94 1369 Ks = 5.02x103±1.34x106  Kc = 0.75±0.01 0.94 727 Ks = 923.17±9.49x104        Kc = 0.84±0.01 0.85 5807 Ks = 1.27x107±3.29 x1011 Kc = 0.38±0.01 4 Intermediate 0.50 11602 Ki = 0.16±2.58x10-3 0.51 6284 Ki = 0.18±3.08x10-3 0.46 21426 Ki = 0.11±2.48x10-3 5 Intermediate- Standard 0.50 11602 Ki =0.16±0.01                    Ks = 1.39x10-19±5.49x10-5 0.51 6284 Ki =0.18±0.01                      Ks = 2.21x10-19±6.05x10-5 0.46 21426 Ki = 0.11±0.01                 Ks = 1.77x10-19±9.30x10-5 6 Standard 0.11 20410 Ks = 0.05±9.61x10-4 0.14 10883 Ks = 0.05±1.09x10-3 0.15 34061 Ks = 0.03±8.99 x10-4 7 Complete- Standard 0.11 20410 Kb= 8.72x10-5±2.29x103  Ks = 0.05±2.29x102 0.14 10883 Kb= 1.22x10-5±3.68x102 Ks = 0.05±3.68x101 0.15 34061 Kb= 2.67x10-5±1.63x103 Ks = 0.03±1.63x102 8 Complete 0.06 21603 Kb = 0.25±0.01 0.09 11581 Kb = 0.27±0.01 0.08 36798 Kb = 0.18±0.01 9* Cake - Complete 0.99 152 Kb = -0.29±0.01                Kc = 1.98±0.03 1.00 21.6 Kb = -0.29±3.48x10-3 Kc = 1.98±0.02 0.99 90 Kb = -0.75±0.01 Kc = 3.03±0.05 *Invalid results due to the negative fitted Kb **After Cleaning (Reactor D2)53   Figure 29 Top Ranked Models Fitted to the Measured Data for the Different Air Sparging Conditions (a). infinity Air ON/OFF ratio, b).  0.2 Air ON/OFF Ratio, c). 0.13 Air ON/OFF Ratio, d). 0.02 Air ON/OFF Ratio,  e). 0 Air ON/OFF Ratio, f). 0.2 Air ON/OFF Ratio After Recovery Cleaning) a. b. d. c. f. e. 54  5.2 Natural Organic Material (NOM) in Passive Membrane Operations 5.2.1 Accumulation of NOM in System Reactor Dissolved organic carbon (DOC) and total organic carbon (TOC) analyses were conducted to quantify the proportion of particulate and dissolved organic component in the feed water. Size exclusion chromatography analyses using high performance liquid chromatography (HPLC) were conducted to characterize the composition of the soluble natural organic matter (NOM) in the feed. The objective was to determine the stability of the different NOM constituents within the system during long-term operation.  The DOC and TOC of the feed water was 6.31±0.54 ppm and 11.47±2.39 ppm, respectively. The NOM was categorized into three major soluble fractions consisting of 1). biopolymers or high molecular weight substances (HMW), 2). humic substances (HS) and 3). low molecular weight neutrals (LMN). Figure 30 illustrates the typical size exclusion chromatograms of the raw feed water during different seasons.   The NOM concentration in the feed water was highest during high rainfall seasons (i.e. spring and winter), where high runoff tends to increase the mobilization of humic substances (Uyak et al., 2008) into the pond, from which the raw feed water was collected. The HS accounted for approximately 70 to 86% of the total NOM, whereas HMW and LMN accounted for 20% and 13% of the total NOM, respectively. These proportions are consistent with those reported by others for typical natural surface waters (Peter-Varbanets et al., 2011; Thurman, 1985; Y. Choi, 2003).  Table 10 summarizes the concentration and percent contribution of each NOM fraction to the DOC content. Table 10 Averaged Concentrations of High Molecular Weight, Humic Substances and Low Molecular Weight Neutrals Contents in Feed Water Season Concentration (ppm) Percent Contribution (%) HMW HS LMN  Total  HMW HS LMN Fall 2013 0.94 3.72 0.72 5.38 17% 69% 13% Winter 2013 0.50 5.29 0.35 6.14 8% 86% 6% Spring 2014 1.67 5.02 0.59 7.29 23% 69% 8% Summer 2014 0.76 4.92 0.43 6.10 12% 81% 7%  55   Figure 30 Typical NOM Profile of the Feed Water  (a). Fall 2013, b). Winter 2013, c). Spring 2014, d). Summer 2014)  Response signals from both the 254 nm ultraviolet (UVD254) and organic carbon detections (OCD) are reported in arbitrary units.    UVD OCD    UVD OCD    UVD OCD a). b). c). d).    UVD OCD 56  For the reactors with no wasting (ie. SRT of infinity), the NOM concentration increased over time, especially with respect to HMW and HS. UF membranes can effectively retain HMW and some of the larger HS. Therefore the accumulation of HMW and some HS was expected in the system. A total HMW accumulation of 2.37±1.11 ppm and 1.69±0.54 ppm, as well as HS of 3.40±1.31 ppm and 2.98±1.13 ppm were observed with and without backwash, respectively. For the reactors with daily wasting (ie. SRT of 10 days), the NOM concentration in the system reactors was similar to that of the concentration of the feed, and therefore NOM did not accumulate. This results indicate that the daily wasting of 10% of the operating volume was sufficient to prevent the accumulation of NOM in the system reactor. The differences between the feed water and system reactor concentrations for HMW, HS, and LMN are summarized in Figure 31a, b and c. 57   Figure 31 Differences in Organic Content between System Reactor and Feed Tank under Different Operation Conditions: with and without wasting, backwash and different on/off frequencies of air sparging  (a). HMW, b). HS, c). LMN)   b). a). c). 58  5.2.2 Removal of NOM during Treatment  NOM characterization and quantification was done on the permeates for each condition investigated to determine the overall NOM removal during treatment. As previously discussed, an increase in the concentration of HMW and HS occurred in the system reactors without daily wasting. This increase had an effect on the overall NOM removal. With wasting, the NOM concentration in permeates was equal or less than then concentration in the feed water, which was similar to the concentration in the system reactor. Whereas without wasting, the NOM concentration in the permeate was higher than the concentration in the feed water especially with respect to HS. Figure 32 illustrates typical NOM profiles observed with and without wasting.  Figure 32 Typical NOM Profile at the Different Stages of Treatment (a). With Wasting and b). Without Wasting)   a). b). 59  The differences between the feed and permeate concentrations for HMW, HS and LMN are summarized in Figure 33. Overall, HMW were effectively removed both with and without wasting. This was expected because UF membranes can effectively retain HMW. With wasting, the concentration of HS and LMN in the feed and permeate were generally the same, indicating that these NOM components were not effectively removed with wasting, which is consistent with results presented in Section 5.1.2. However, without wasting, the concentration of HS in the permeate was greater than that in the feed. The overall increase in HS during treatment likely resulted from the hydrolysis of material retained by the UF membranes (ie. particulate organic material, HMW and larger HS) into smaller material with a molecular weight similar to that of HS (Derlon et al., 2014; Niaounakis, 2014). The concentration of LMN in the feed and permeate were generally the same, indicating that LMN were not effectively removed without wasting. This is consistent with the results presented in Section 5.1.2. Although the dissolved NOM components were not all effectively removed to an appreciable extent, the total concentration of organic matter decreased substantially during treatment from 11.47±2.39 ppm to 5.23±0.79 ppm and 6.84±0.02 ppm, with and without wasting, respectively. Table 11 summarizes the observed removal of the different NOM components for the different operating conditions investigated.  60   Figure 33 Mean Removal of Organics under Different Operating Conditions: with and without wasting, backwash and different on/off frequencies of air sparging (a). HWM, b). HS, c). LMN) a). b). c). 61   Table 11 Summary of the Pairwise Comparison between the Feed Water, System Reactor, Permeates to Determine Consistency of Raw Water Feed and Overall NOM Removal   With Wasting Without Wasting  Without Backwash With Backwash Air (ON/OFF) 0 0.02 0.13 0.2 Continuous Continuous Continuous ∆ in Reactor mean ±95% mean ±95% mean ±95% mean ±95% mean ±95% mean ±95% mean ±95% HMW (ppm) -0.25 0.56 0.10 0.37 -0.05 0.21 -0.38 0.21 0.42 0.34 1.69 0.54 2.37 1.11 HS (ppm) -0.02 0.86 -0.20 0.69 1.82 1.00 0.04 0.81 1.03 0.48 2.98 1.13 3.40 1.31 LMN (ppm) 0.16 0.35 0.16 0.59 -1.65 2.16 0.75 0.82 -0.34 0.54 -0.07 1.24 2.56 3.17 NOM Removal mean ±95% mean ±95% mean ±95% mean ±95% mean ±95% mean ±95% mean ±95% HMW (ppm) 1.50 0.396771 0.43 0.27 0.16 0.10 0.70 0.15 0.31 0.24 0.60 0.18 0.59 0.21 HS (ppm) 2.45 1.267199 0.63 0.78 -1.46 1.23 0.82 0.82 -1.17 1.19 -2.12 1.30 -2.27 1.26 LMN (ppm) 0.26 0.165882 -0.01 0.46 0.55 2.12 -0.27 0.38 0.23 0.56 1.68 1.19 1.62 1.10 %NOM Removal mean ±95% mean ±95% mean ±95% mean ±95% mean ±95% mean ±95% mean ±95% HMW 88% 8% 84% 26% 35% 12% 90% 6% 86% 283% 59% 11% 58% 16% HS 5% 22% 27% 17% 13% 59% 35% 18% 13% 21% -60% 43% -67% 41% LMN -54% 149% 66% 97% 61% 167% 53% 221% 52% 89% -22% 147% -30% 149% 62  5.2.3 Degradation of NOM in System Reactor A mass balance was performed to determine if NOM degradation occurred during treatment. The extent of the degradation was quantified based on the difference between the measured and the theoretical NOM concentrations in the system over time. The theoretical NOM concentration in the system was estimated based on the difference between the mass input of NOM into the system through the feed and the mass output of NOM out of the system through the permeate and daily wasting. The results from the mass balance analysis are presented in Figure 34. The complete mass balance calculations are available in Appendices K through Q for all of the conditions investigated. Figure 34a and Figure 34b illustrate the increasing trend of the HMW’s theoretical concentration over time that was projected for all conditions investigated, while the HMW’s measured concentration remained relatively constant. The greater theoretical concentration than the measured indicates that degradation of HMW occurred during treatment. Peter-Varbanets et al. (2010) also claimed that cavities within the foulant layer are formed by biological activity during passive membrane filtration. The observed HMW degradation is, therefore, likely to result from biological activity.  Figure 34c and Figure 34d illustrate the declining trend of the HS’ theoretical concentration over time that was projected for all conditions investigated, while the HS’ measured concentration remained relatively constant. The lower theoretical than measured concentration indicates that HS were generated over time. These results are consistent with those presented in Section 5.2.2 that indicated the increase in the permeate’s HS concentration due to the hydrolysis of material retained by the UF membranes into smaller material with a molecular weight similar to that of HS.  Figure 34e and Figure 34f illustrate the increasing trend of the LMN’s theoretical concentration over time projected for conditions investigated, while the LMN’s measured concentration remained low and constant. The higher theoretical concentration than measured indicates that degradation of LMN occurred during treatment. Overall, the mass balance analysis confirmed the biodegradation of NOM during treatment.63   Figure 34 Typical Trends of Measured and Theoretical NOM over Time for the Wasting and Non-Wasting Reactors (a). HMW in a Wasting Reactor, b). HMW in a Non-Wasting Reactor, c). HS in a Wasting Reactor, d) HS in a Non-Wasting Reactor, e). LMN in a Wasting Reactor,    f). LMN in a Non-Wasting Reactor)a). b). c). d). e). f). 64  6 Prototype Design of Passive Membrane Filtration The results from the present study were used to develop preliminary prototype designs of passive membrane treatment systems suitable for remote communities. Three prototype sizes were considered to provide potable water to 1). single households, 2). a group of five household and 3). a community of 20 household. An illustration of the prototype is provided in Figure 35. The proposed design considers a hollow fibre module submerged within a cylindrical casing. The cylindrical casing is approximately 81 cm in height and 0.8 cm in diameter. The module is made of made of 70-cm long strands of ZW-1000 hollow fibres (GE Water and Process Technologies, Oakville, Canada) potted into cylindrical bulkheads at both ends, which will be installed with 98% looseness (or 27 cm installment length). A gravity head of approximately 40 cm is applied to provide the driving force for permeation through the membranes, giving an initial flux of approximately 10 LMH. A controlled raw feed rate is provided by either a pump or a gravity-fed system.  An air inlet located at the bottom of the reactor is used for sparging. For the initial prototype development, continuous aeration is considered for fouling control. As determined in the present study, continuous air sparging at 0.009 m3/m2/s is sufficient to enable sustainable operation at the flux of 10 LMH. Without continuous aeration, the steady-state flux would lower to approximately 2.5 LMH (Section 5.1.3). Therefore, operation without air sparging would be possible but would require that the membrane fibres be quadrupled to compensate for the lower sustainable flux.  Ten percent of the system reactor’s volume is to be manually wasted every day to avoid NOM accumulation in the system, which could lead to a reduced treatment efficiency (Section 5.2.2). A permeate collection tank is connected at the bottom of the system to store the filtered water. The proposed design provides 40, 600 and 4000 litres per day (lpd) of filtered water for 1, 5 and 20 households, respectively. These estimations were made based on the assumption of 4 people per household at 10 litres per capita per day (lpcd) of drinking and cooking water (for the single household system) and 50 lpcd of drinking, cooking and sanitary water (for the 5 and 20 household systems). A summary of the design assumptions and capacity for the prototypes is presented in Table 12. 65   Figure 35 Prototype Diagram with 135 lpcd capacity and an option to be gravity-fed  Table 12 Proposed Designs and Capacity for Prototype   66  7 Conclusions 1. The permeate flux had a significant effect on the efficacy of backwashing. As the permeate flux decreased the need for backwashing to minimize fouling diminished. At a permeate flux of 10 LMH, long term operation could be achieved without backwash.   2. At a hydrostatic head producing an equivalent to 10 LMH, fouling during constant-pressure operations was similar to that for constant-flux operations. Constant-pressure, gravity operations with a hydrostatic head of 37mbar could be used to sustain operation at 10 LMH.   3. Continuous air sparging was required to maintain a permeate flux of 10 LMH. Reducing the extent of air sparging reduced the permeate flux that could be maintained. For all reduced air sparging conditions investigated, the permeate flux that could be maintained was approximately 2.5 LMH.   4. The complexity of a SHFUF can be simplified by eliminating backwash (conclusion 1), operating with gravity flow (conclusion 2), and eliminating/reducing the need of air sparging (conclusion 3) without compromising the long-term operational stability of the system.  5. Recovery cleaning could effectively recover the decrease in permeability which occurred during long-term operations.   6. Acclimatization method adopted in the present study did not help to improve membrane performance. Its adoption hindered the occurrence of sustainable conditions, leading to a lower steady-state permeability.  7. Modeling suggested that fouling was predominantly governed by cake formation for all conditions investigated.    8. A mass balance analysis indicated that NOM degradation occurred during treatment and that the degradation resulted from biological activity.   67  9. NOM accumulation in the system without wasting negatively affected the overall treatment efficiency. The total NOM removal achieved by the reactors with wasting was 4.63±2.41 ppm, while that without wasting was 6.25±3.18 ppm.    68  References Aimar, P., Bacchin, P., 2010. Slow colloidal aggregation and membrane fouling. Journal of Membrane Science 360, 70–76. doi:10.1016/j.memsci.2010.05.001 Akhondi, E., Wicaksana, F., Fane, A.G., 2014. Evaluation of fouling deposition, fouling reversibility and energy consumption of submerged hollow fiber membrane systems with periodic backwash. 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Further Volumes of this Series Nonporous Inorganic Membranes Materials Science of Membranes for Gas and Vapor Separation Membranen Membranes in Clean Technologies Membrane Technology and Applications, 4th ed. Peter-Varbanets, M., Hammes, F., Vital, M., Pronk, W., 2010. Stabilization of flux during dead-end ultra-low pressure ultrafiltration. Water research 44, 3607–16. doi:10.1016/j.watres.2010.04.020 Peter-Varbanets, M., Margot, J., Traber, J., Pronk, W., 2011. Mechanisms of membrane fouling during ultra-low pressure ultrafiltration. Journal of Membrane Science 377, 42–53. doi:10.1016/j.memsci.2011.03.029 Pont, J.J.H.H.M. de., Bonting, S.L., 1981. Membrane Transport, 2nd ed. Elsevier/North-Holland Biomedical Press, Amsterdam, New York. Psoch, C., Schiewer, S., 2005. Critical flux aspect of air sparging and backflushing on membrane bioreactors. Desalination 175, 61–71. doi:10.1016/j Qu, R.-J., Wang, X.-H., Feng, M.-B., Li, Y., Liu, H.-X., Wang, L.-S., Wang, Z.-Y., 2013. The toxicity of cadmium to three aquatic organisms (Photobacterium phosphoreum, Daphnia magna and Carassius auratus) under different pH levels. Ecotoxicology and environmental safety 95, 83–90. doi:10.1016/j.ecoenv.2013.05.020 Raffin, M., Germain, E., Judd, S.J., 2012. Influence of backwashing, flux and temperature on microfiltration for wastewater reuse. Separation and Purification Technology 96, 147–153. doi:10.1016/j.seppur.2012.05.030 Rodríguez, S.G.S., Kennedy, M.D., Amy, G.L., Schippers, J.C., 2012. Flux dependency of particulate/colloidal fouling in seawater reverse osmosis systems. Desalination and Water Treatment 42, 155–162. doi:10.1080/19443994.2012.683104 Serra, C., Durand-bourlier, L., Clifton, M.J., Moulin, P., Rouch, J., Aptel, P., 1999. Use of air sparging to improve backwash ef ® ciency in hollow- ® ber modules 161. 71  Speth, T., Guses, A.M., Summers, R.S., 2000. Evaluation of nanofiltration pretreatments for flux loss control, in: AWWA, Mem. Tech. Conf. Long Beach, CA, p. 43. States, U., 1994. Drinking Water Treatment for Small Communities A Focus on EPA ’ s 1–32. Tang, C.Y., Chong, T.H., Fane, A.G., 2011. Colloidal interactions and fouling of NF and RO membranes: a review. Advances in colloid and interface science 164, 126–43. doi:10.1016/j.cis.2010.10.007 Thurman, E.M., 1985. Organic Geochemistry of Natural Waters. Dordrecht. USEPA, 2005. Note on the Membrane Filtration Guidance Manual. Uyak, V., Ozdemir, K., Toroz, I., 2008. Seasonal variations of disinfection by-product precursors profile and their removal through surface water treatment plants. The Science of the total environment 390, 417–24. doi:10.1016/j.scitotenv.2007.09.046 Wang, Z., Wu, Z., Yin, X., Tian, L., 2008a. Membrane fouling in a submerged membrane bioreactor (MBR) under sub-critical flux operation: Membrane foulant and gel layer characterization. Journal of Membrane Science 325, 238–244. doi:10.1016/j.memsci.2008.07.035 Wang, Z., Wu, Z., Yin, X., Tian, L., 2008b. Membrane fouling in a submerged membrane bioreactor (MBR) under sub-critical flux operation: Membrane foulant and gel layer characterization. Journal of Membrane Science 325, 238–244. doi:10.1016/j.memsci.2008.07.035 Wu, D., Howell, J.A., Field, R.W., 1999. Critical ¯ ux measurement for model colloids 152. Y. Choi, 2003. Critical flux, resistance and removal of contaminants in ultrafiltration (UF) of natural organic materials. Pennsylvania State University. Ye, Y., Chen, V., Le-Clech, P., 2011. Evolution of fouling deposition and removal on hollow fibre membrane during filtration with periodical backwash. Desalination 283, 198–205. doi:10.1016/j.desal.2011.03.087 Yeo, A.P.S., Law, A.W.K., Fane, A.G., 2006. Factors affecting the performance of a submerged hollow fiber bundle. Journal of Membrane Science 280, 969–982. doi:10.1016/j.memsci.2006.03.029 Zularisam, a. W., Ismail, a. F., Salim, R., 2006. Behaviours of natural organic matter in membrane filtration for surface water treatment — a review. Desalination 194, 211–231. doi:10.1016/j.desal.2005.10.030    72  Appendix A : Clean Water Fluxes and Initial Membrane Resistances  I. Stage 1 Reactor A : Without Backwash  J0 (LMH) 10.00 20.00 30.00 J0 (m3/m2.s) 2.77778E-06 5.56E-06 8.33E-06 Avg. ∆P (N/m2) 5,488  20,885  26,254  µ (Ns/m2) 0.001002 0.001002 0.001002 Rm (m2/m3) 1.97E+12 3.75E+12 3.14E+12    Reactor B : With Backwash  J0 (LMH) 10.00 20.00 30.00 J0 (m3/m2.s) 2.78E-06 5.56E-06 8.33E-06 Avg. ∆P (N/m2) 13,275  25,233  36,005  µ (Ns/m2) 0.001002 0.001002 0.001002 Rm (m2/m3) 4.77E+12 4.53E+12 4.31E+12  73    II. Stage 2 Reactor C : Passive Membrane Permeation J0 (LMH) 9.20 9.20 9.20 J0 (m3/m2.s) 2.56E-06 2.56E-06 2.56E-06 Avg. ∆P (N/m2) 8,549 7,171 5,861 µ (Ns/m2) 0.001002 0.001002 0.001002 R (m2/m3) 1.13E+12 3.48E+11 7.20E+09   74  III. Stage 3 Reactor D1 : 25 Minutes Off – 5 Minutes On J0 (LMH) 12.13 12.13 12.13 J0 (m3/m2.s) 3.37E-06 3.37E-06 3.37E-06 Avg. ∆P N/m2 11,947  4,756  4,078  µ (Ns/m2) 0.001002 0.001002 0.001002 R (m2/m3) 3.54E+12 1.41E+12 1.21E+12   Reactor E : 4 Hours Off – 30 Minutes On J0 (LMH) 10.50 10.50 10.50 J0 (m3/m2.s) 2.92E-06 2.92E-06 2.92E-06 Avg. ∆P N/m2 3,390  6,772  7,891  µ (Ns/m2) 0.001002 0.001002 0.001002 R (m2/m3) 1.16E+12 2.32E+12 2.70E+12  75    Reactor F : 4 Hours Off – 5 Minutes On  J0 (LMH) 10.60 10.60 10.60 J0 (m3/m2.s) 2.94E-06 2.94E-06 2.94E-06 Avg. ∆P (N/m2) 3,083  5,737  2,961  µ (Ns/m2) 0.001002 0.001002 0.001002 Rm (m2/m3) 1.04E+12 1.94E+12 1.00E+12     76  Reactor G : No Aeration J0 (LMH) 10.80 10.80 10.80 J0 (m3/m2.s) 3.00E-06 3.00E-06 3.00E-06 Avg. ∆P (N/m2) 3,104  2,975  8,215  µ (Ns/m2) 0.001002 0.001002 0.001002 R (m2/m3) 1.03E+12 9.90E+11 2.73E+12   77  Appendix B:  Excel Visual Basic for Applications (VBA) Commands  1. HOBOware datalog transfer:  was used to compile transferred csv file from HOBOware data logger into the master spreadsheet for data analysis. Calculations and analyses in the spreadsheet were automatically updated by the macros every time the transfer was done.  Sub UpdateData() Dim LastRow As Long  'Open Workbooks      Workbooks.Open Filename:="R1_Exp2F.csv"     Windows("R1_Exp2F.csv").Activate      'Delete Blank Cells     Columns("C").SpecialCells(xlCellTypeBlanks).EntireRow.Delete      ' UpdateData Macro      Range("A3:C3", Range("A3:C3").End(xlDown)).Select     Selection.Copy          Windows("EXP2_DataLog.xlsm").Activate     ActiveWorkbook.Sheets("R1_EXP2").Activate     Range("A32203").Select     ActiveSheet.Paste      'Close csv File     Windows("R1_Exp2F.csv").Activate     Workbooks("R1_Exp2F.csv").Close SaveChanges:=False   'Update External Calculations       LastRow = Range("A3").End(xlDown).Row     Range("F18375:L18375").AutoFill Destination:=Range(Range("F18375"), Range("L" & LastRow))  End Sub  78  2. Backwash Data sorting : was used to sort through the logged pressure data and separate the before and after backwash transmembrane pressures. This was required for backwash benefits analysis.  Sub Backwash () Dim i As Integer Last = Cells(Rows.Count, “E”).End(xlUp).Row For i = Last To 1 Step -1  If (Cells(i, “E”).Value = “” Then   Cells (i, “E”).Delet Shift :=xlUp  End If Last2 = Cells(Rows.Count, “f”).End(xlUp).Row For ii = Last2 To 1 Step -1  If (Cells(ii, “f”).Value = “” Then   Cells(ii, “f”). Delete Shift :=xlUp  End If       Next ii       MsgBox “You’re Done!!”  End Sub    79  3. HPLC’s UV Data Transfer : was used to compile and organize all of the arw files, which contained the distinct UV absorbance data of each sample, into the HPLC master spreadsheet.  Sub DataTransfer()  Dim File As String Dim emptyColumn As Long Dim Data As Workbook Dim destination As Worksheet Dim Name As String  '1. Open arw file: change the address of the file File = Dir("C:\Users\Patricia Oka\Documents\School\Classes\MASc THESIS\Data\Exp3\hplc\Feb 11 Calibration\" & "*.arw")  Do While Len(File) > 0 '2. Input the name you gave to this file "xxxx.xlsm" If File = "HPLC_CalibrationFeb11.xlsm" Then Exit Sub End If  Set Data = Workbooks.Open(File) Name = Mid(ActiveWorkbook.Name, 2, 5)  'copy data ActiveSheet.Range("B3", ActiveSheet.Range("b3").End(xlDown)).Select Selection.Copy  'paste: Change the name of the file the same as above "xxx.xlsm" Windows("HPLC_CalibrationFeb11.xlsm").Activate Range("a4").End(xlToRight).Offset(0, 1).Select ActiveSheet.Paste  Application.SendKeys ("N")  Range("a4").End(xlToRight).Offset(-1, 0).Value = Name  Data.Close SaveChanges:=False  File = Dir Loop  End Sub  80  4. HPLC’s TOC Data Transfer : was used to sort through the compiled TOC data for the purposes of extracting the values for the data of interest given the start and end analysis times.  Sub tocTransfer()      Dim Mini As Double, Maxi As Double     Dim RowMini As Long, RowMaxi As Long     Dim MyRg As Range     Dim LastRow As Long     Dim Counter As Long          Sheets("toc").Activate     Counter = 1      'This loop runs until there is nothing in the Next column is Empty Do     Mini = Range("C4").Offset(0, Counter - 1)     Maxi = Range("D4").Offset(0, Counter - 1)          Sheets("TOCRaw").Activate     LastRow = Range("B" & Rows.Count).End(xlUp).Row     Set MyRg = Range("B:B")     RowMini = Application.WorksheetFunction.Match(Mini, MyRg)     RowMaxi = Application.WorksheetFunction.Match(Maxi, MyRg)     Range("C" & RowMini & ":" & "C" & RowMaxi).Copy     Sheets("TOC").Activate     Range("A5").End(xlToRight).Offset(0, 1).Select     ActiveSheet.Paste     Counter = Counter + 1      Loop Until IsEmpty(ActiveCell.End(xlUp).Offset(0, 1))      End Sub 81  Appendix C : Instrument Calibration Curves  Organic Carbon Analysis  A typical Calibration Curve of the Standards with Concentrations Ranging from 1 to 50 ppm    82  High Performance Liquid Chromatography (HPLC) Typical Retention Times in Minutes for the Six Different Molecular Weight Standards  Standard Solution MW (Da) log10(MW) Retention Time (mins) PEG 600 2.78 50.40 PEG 1500 3.18 43.93 PEG 3300 3.52 39.13 PEG 6000 3.78 34.80 PSS 15000 4.18 28.60 PSS 41000 4.61 24.33    A typical Logarithm curve of Standards’ Molecular Weights versus Retention Time   83   Appendix D: Complete Resistance Data for Stage 2   Resistance Plot for the Different Operating Stages in Stage 2’s Constant-Pressure Passive Membrane Filtration84  Appendix E: Flux Reduction in Stage 4   Permeate Flux Reduction over Volume Filtered under Different Aeration Frequencies (a). 25 Minutes off – 5 Minutes on; b). 4 Hours off – 30 Minutes on; c). 4 Hours off – 5 Minutes on; and d). No Aeration)b). c). d). a). 85  Appendix F: Statistical Reports of the Fouling Models for Continuous Aeration  Model’s Fit Error and Estimated Parameter Values for Passive Membrane Permeation with Continuous Aeration   1. Cake Complete  Nonlinear Regression      Sunday, July 13, 2014, 11:19:55 AM Equation: User-Defined, Cake-Complete f = 10/a*(1-exp(-a/(b*100)*(sqrt(1+2*b*100*x)-1)))   R  Rsqr  Adj Rsqr  Standard Error of Estimate 0.9989 0.9977 0.9977  1.5402                Coefficient     Std. Error t P  a -0.7455 0.0331 -22.5528 <0.0001  b 3.0349 0.1512 20.0741 <0.0001  Model SSR Fitted Parameter Values s Cake-Complete 9.01x101 Kb = -0.746, Kc = 3.03 0.0331 0.1512 Cake 5.73x103 Kc = 0.362 0.0226 Cake- Intermediate 5.78x103 Ki = 1.20x10-10, Kc = 0.350 0.0017 0.0408 Cake- Standard 5.81x103 Ks = 1.27x107, Kc = 0.383 1.0629x1012 0.0243 Intermediate 2.14x104 Ki = 0.108 0.0080 Intermediate - Standard 2.14x104 Ki = 0.108, Ks = 1.77x10-19 0.0234 0.0003 Standard 3.41x104 Ks = 0.0345 0.0029 Complete - Standard 3.41x104 Kb= 2.67x10-5, Ks = 0.0345 5266.2123 526.6482 Complete 3.68x104 Kb = 0.179 0.0158   86  Analysis of Variance:     DF SS MS  Regression2 157535.6947 78767.8474  Residual 38 90.1455 2.3723  Total 40 157625.8403 3940.6460   Corrected for the mean of the observations:   DF SS MS F P  Regression1 39831.6776 39831.6776 16790.6676 <0.0001  Residual 38 90.1455 2.3723  Total 39 39921.8232 1023.6365   Statistical Tests:  Normality Test (Shapiro-Wilk)   Failed (P = 0.0014)  W Statistic= 0.8952 Significance Level = 0.0500  Constant Variance Test  Passed (P = 0.3875)  Fit Equation Description: [Variables] x = col(1) y = col(2) reciprocal_y = 1/abs(y) reciprocal_ysquare = 1/y^2 reciprocal_pred = 1/abs(f) reciprocal_predsqr = 1/f^2 'Automatic Initial Parameter Estimate Functions first(q) = if(size(q)<10,size(q)-1,int(0.9*size(q))) ylast(q) = mean(q[data(first(q),size(q))]) [Parameters] 87  a = ylast(y) ''Auto {{previous: -0.745484}} {{MinRange: 6}} {{MaxRange: 18}} b = if(x50(x,y,.5)-min(x)>0, -ln(.5)/(x50(x,y,.5)-min(x)), 1) ''Auto {{previous: 3.03486}} [Equation] f = 10/a*(1-exp(-a/(b*100)*(sqrt(1+2*b*100*x)-1))) fit f to y ''fit f to y with weight reciprocal_y ''fit f to y with weight reciprocal_ysquare ''fit f to y with weight reciprocal_pred ''fit f to y with weight reciprocal_predsqr [Constraints] b>0 [Options] tolerance=0.0000000001 stepsize=1 iterations=200  Number of Iterations Performed = 40  2. Cake  Nonlinear Regression       Wednesday, July 23, 2014, 4:02:46 PM  Equation: User-Defined, 3Cake f = 1/(10*a)*((1+2*a*100*x)^(1/2)-1)  R  Rsqr  Adj Rsqr  Standard Error of Estimate 0.9254 0.8563 0.8563  12.1264     Coefficient Std. Error t P  a 0.3620 0.0226 16.0065 <0.0001     88  Analysis of Variance:     DF SS MS  Regression1 151890.9316 151890.9316  Residual 39 5734.9087 147.0489  Total 40 157625.8403 3940.6460   Corrected for the mean of the observations:   DF SS MS F P  Regression0 34186.9145 (+inf) (+inf) (NAN)  Residual 39 5734.9087 147.0489  Total 39 39921.8232 1023.6365   Statistical Tests:  Normality Test (Shapiro-Wilk)   Failed (P = 0.0036)  W Statistic= 0.9095 Significance Level = 0.0500  Constant Variance Test  Passed (P = 0.3214)  Fit Equation Description: [Variables] x = col(1) y = col(2) reciprocal_y = 1/abs(y) reciprocal_ysquare = 1/y^2 reciprocal_pred = 1/abs(f) reciprocal_predsqr = 1/f^2 'Automatic Initial Parameter Estimate Functions F(q) = ape(x,y,1,0,1) [Parameters] a = F(0)[2] ''Auto {{previous: 0.362012}} {{MinRange: -4.5}} {{MaxRange: 1.5}} 89  [Equation] f = 1/(10*a)*((1+2*a*100*x)^(1/2)-1) fit f to y ''fit f to y with weight reciprocal_y ''fit f to y with weight reciprocal_ysquare ''fit f to y with weight reciprocal_pred ''fit f to y with weight reciprocal_predsqr [Constraints] a>0 [Options] tolerance=0.0000000001 stepsize=1 iterations=200  Number of Iterations Performed = 7  3. Cake-Intermediate  Nonlinear Regression      Sunday, July 13, 2014, 11:22:20 AM  Equation: User-Defined, Cake-Intermediate f = 1/a*Ln(abs(1+a/(b*10)*((1+2*b*100*x)^(0.5)-1)))  R  Rsqr  Adj Rsqr  Standard Error of Estimate 0.9248 0.8553 0.8514  12.3317     Coefficient Std. Error t P  a 1.2005E-0100.0017 7.0872E-008 1.0000  b 0.3500 0.0408 8.5730 <0.0001     90  Analysis of Variance:     DF SS MS  Regression2 151847.1829 75923.5914  Residual 38 5778.6574 152.0699  Total 40 157625.8403 3940.6460   Corrected for the mean of the observations:   DF SS MS F P  Regression1 34143.1658 34143.1658 224.5228 <0.0001  Residual 38 5778.6574 152.0699  Total 39 39921.8232 1023.6365   Statistical Tests:  Normality Test (Shapiro-Wilk)   Failed (P = 0.0035)  W Statistic= 0.9091 Significance Level = 0.0500  Constant Variance Test  Passed (P = 0.0807)  Fit Equation Description: [Variables] x = col(1) y = col(2) reciprocal_y = 1/abs(y) reciprocal_ysquare = 1/y^2 reciprocal_pred = 1/abs(f) reciprocal_predsqr = 1/f^2 'Automatic Initial Parameter Estimate Functions F(q) = ape(x,exp(y),1,0,1) [Parameters] a = 0.1 ' {{previous: 1.20048e-010}} 91  b = 1 ' {{previous: 0.349981}} [Equation] f = 1/a*Ln(abs(1+a/(b*10)*((1+2*b*100*x)^(0.5)-1))) fit f to y ''fit f to y with weight reciprocal_y ''fit f to y with weight reciprocal_ysquare ''fit f to y with weight reciprocal_pred ''fit f to y with weight reciprocal_predsqr [Constraints] a>0 b>0 [Options] tolerance=0.0000000001 stepsize=0.5 iterations=200  Number of Iterations Performed = 49  4. Cake-Standard  Nonlinear Regression      Thursday, July 24, 2014, 12:12:17 AM  Equation: User-Defined, Cake-standard a=sqrt(4/9+4*d/(30*e)+2*d^2*x/(3*e)) b=2/(9*(4/9+4*d/(30*e)+2*d^2*x/(3*e))^1.5)*(4/3+d/(10*e)-d^2*x/e) f = 2/d*(a*cos(2.09-0.33*arccos(b))+1/3)  R  Rsqr  Adj Rsqr  Standard Error of Estimate 0.9244 0.8546 0.8507  12.3614     Coefficient Std. Error t P  d 12653940.4201 1.0629E+012 1.1905E-005 1.0000  e 0.3825 0.0243 15.7600 <0.0001  92  Analysis of Variance:     DF SS MS  Regression2 151819.3031 75909.6516  Residual 38 5806.5372 152.8036  Total 40 157625.8403 3940.6460   Corrected for the mean of the observations:   DF SS MS F P  Regression1 34115.2860 34115.2860 223.2623 <0.0001  Residual 38 5806.5372 152.8036  Total 39 39921.8232 1023.6365   Statistical Tests:  Normality Test (Shapiro-Wilk)   Failed (P = 0.0037)  W Statistic= 0.9097 Significance Level = 0.0500  Constant Variance Test  Passed (P = 0.3260)  Fit Equation Description: [Variables] x = col(1) y = col(2) reciprocal_y = 1/abs(y) reciprocal_ysquare = 1/y^2 reciprocal_pred = 1/abs(f) reciprocal_predsqr = 1/f^2 'Automatic Initial Parameter Estimate Functions first(q) = if(size(q)<10,size(q)-1,int(0.9*size(q))) ylast(q) = mean(q[data(first(q),size(q))]) [Parameters] 93  d = 0.05 ' {{previous: 1.26539e+007}} e = 0.71 ' {{previous: 0.38254}} [Equation] a=sqrt(4/9+4*d/(30*e)+2*d^2*x/(3*e)) b=2/(9*(4/9+4*d/(30*e)+2*d^2*x/(3*e))^1.5)*(4/3+d/(10*e)-d^2*x/e) f = 2/d*(a*cos(2.09-0.33*arccos(b))+1/3) fit f to y ''fit f to y with weight reciprocal_y ''fit f to y with weight reciprocal_ysquare ''fit f to y with weight reciprocal_pred ''fit f to y with weight reciprocal_predsqr [Constraints] [Options] tolerance=0.0000000001 stepsize=1 iterations=200  Number of Iterations Performed = 9  5. Intermediate – Standard  Nonlinear Regression      Tuesday, July 22, 2014, 2:45:21 PM  Equation: User-Defined, 2Intermediate f = if(x>0, 1/a*ln(abs(1+a*10*x)), 0) R  Rsqr  Adj Rsqr  Standard Error of Estimate 0.6807 0.4633 0.4633  23.4389     Coefficient Std. Error t P  a 0.1078 0.0080 13.4463 <0.0001     94  Analysis of Variance:     DF SS MS  Regression1 136199.8984 136199.8984  Residual 39 21425.9419 549.3831  Total 40 157625.8403 3940.6460   Corrected for the mean of the observations:   DF SS MS F P  Regression0 18495.8813 (+inf) (+inf) (NAN)  Residual 39 21425.9419 549.3831  Total 39 39921.8232 1023.6365   Statistical Tests:  Normality Test (Shapiro-Wilk)   Failed (P = 0.0275)  W Statistic= 0.9370 Significance Level = 0.0500  Constant Variance Test  Passed (P = 0.4980)  Fit Equation Description: [Variables] x = col(1) y = col(2) reciprocal_y = 1/abs(y) reciprocal_ysquare = 1/y^2 reciprocal_pred = 1/abs(f) reciprocal_predsqr = 1/f^2 'Automatic Initial Parameter Estimate Functions F(q) = ape(ln(abs(x)),y,1,0,1) [Parameters] a = F(0)[2] ''Auto {{previous: 0.107808}} 95  [Equation] f = if(x>0, 1/a*ln(abs(1+a*10*x)), 0) fit f to y ''fit f to y with weight reciprocal_y ''fit f to y with weight reciprocal_ysquare ''fit f to y with weight reciprocal_pred ''fit f to y with weight reciprocal_predsqr [Constraints] [Options] tolerance=0.0000000001 stepsize=1 iterations=200  Number of Iterations Performed = 13    96  Appendix G: Statistical Reports of the 5 Best-Fit Fouling Models for 25 Minutes Off – 5 Minutes On  Model’s Fit Error and Estimated Parameter Values for Passive Membrane Permeation with ON/OFF Air Ratio of 0.20, Before Recovery Cleaning. Model SSR Fitted Parameters values* s Cake-Complete 1.52x102 Kb = -0.291 ,        Kc = 1.98 0.0215  0.1037 Cake 1.34x103 Kc = 0.713 0.0235 Cake- Intermediate 1.36x103 Ki = 1.61x10-10,    Kc = 0.696 0.0008 0.0177 Cake-Standard 1.37x103 Ks = 5.02x103,  Kc = 0.751 4898964.7397 0.0254 Intermediate 1.16x104 Ki = 0.159 0.0094 Intermediate - Standard 1.16x104 Ki = 0.159,             Ks = 1.39x10-19  0.023 0.0002 Standard 2.04x104 Ks = 0.0487 0.0035 Complete - Standard 2.04x104 Kb = 8.72x10-5 ,  Ks = 0.0487 8344.44468.3834.5430 Complete 2.16x104 Kb = 0.251 0.0193  I. Before Cleaning  1. Cake - Complete  Tuesday, July 08, 2014, 12:16:31 AM  Equation: User-Defined, Cake-Complete f = 10/a*(1-exp(-a/(b*100)*(sqrt(1+2*b*100*x)-1)))  R  Rsqr  Adj Rsqr  Standard Error of Estimate 0.9967 0.9934 0.9933  1.7626    Coefficient Std. Error t P  a -0.2808 0.0215 -13.0849 <0.0001  b 1.8945 0.1037 18.2671 <0.0001   97  Analysis of Variance:     DF SS MS  Regression 2 101128.7056 50564.3528  Residual 49 152.2246 3.1066  Total 51 101280.9302 1985.9006   Corrected for the mean of the observations:   DF SS MS F P  Regression 1 22863.5671 22863.5671 7359.6188 <0.0001  Residual 49 152.2246 3.1066  Total 50 23015.7916 460.3158   Statistical Tests:  Normality Test (Shapiro-Wilk)   Failed (P = 0.0004)  W Statistic= 0.8977 Significance Level = 0.0500  Constant Variance Test  Failed (P = <0.0001)  Fit Equation Description: [Variables] x = col(1) y = col(2) reciprocal_y = 1/abs(y) reciprocal_ysquare = 1/y^2 reciprocal_pred = 1/abs(f) reciprocal_predsqr = 1/f^2 'Automatic Initial Parameter Estimate Functions first(q) = if(size(q)<10,size(q)-1,int(0.9*size(q))) ylast(q) = mean(q[data(first(q),size(q))]) [Parameters] a = ylast(y) ''Auto {{previous: -0.28078}} {{MinRange: 6}} {{MaxRange: 18}} b = if(x50(x,y,.5)-min(x)>0, -ln(.5)/(x50(x,y,.5)-min(x)), 1) ''Auto {{previous: 1.89447}} [Equation] 98  f = 10/a*(1-exp(-a/(b*100)*(sqrt(1+2*b*100*x)-1))) fit f to y ''fit f to y with weight reciprocal_y ''fit f to y with weight reciprocal_ysquare ''fit f to y with weight reciprocal_pred ''fit f to y with weight reciprocal_predsqr [Constraints] b>0 [Options] tolerance=0.0000000001 stepsize=1 iterations=200  Number of Iterations Performed = 28  2. Cake Nonlinear Regression         Wednesday, August 06, 2014, 3:23:36 PM  Equation: User-Defined, 3Cake f = 1/(10*a)*((1+2*a*100*x)^(1/2)-1)  R  Rsqr  Adj Rsqr  Standard Error of Estimate 0.9704 0.9416 0.9416  5.1851     Coefficient Std. Error t P  a 0.7130 0.0235 30.3992 <0.0001   Analysis of Variance:     DF      SS                MS  Regression 1 99936.6740 99936.6740  Residual 50 1344.2562 26.8851  Total  51 101280.9302 1985.9006     99  Corrected for the mean of the observations:    DF  SS   MS    F   P  Regression 0 21671.5354 (+inf) (+inf) (NAN)  Residual 50 1344.2562 26.8851  Total  50 23015.7916 460.3158   Statistical Tests:  Normality Test (Shapiro-Wilk)   Failed (P = 0.0023)  W Statistic= 0.9212 Significance Level = 0.0500  Constant Variance Test  Failed (P = <0.0001)  Fit Equation Description: [Variables] x = col(1) y = col(2) reciprocal_y = 1/abs(y) reciprocal_ysquare = 1/y^2 reciprocal_pred = 1/abs(f) reciprocal_predsqr = 1/f^2 'Automatic Initial Parameter Estimate Functions F(q) = ape(x,y,1,0,1) [Parameters] a = F(0)[2] ''Auto {{previous: 0.713015}} {{MinRange: -4.5}} {{MaxRange: 1.5}} [Equation] f = 1/(10*a)*((1+2*a*100*x)^(1/2)-1) fit f to y ''fit f to y with weight reciprocal_y ''fit f to y with weight reciprocal_ysquare ''fit f to y with weight reciprocal_pred ''fit f to y with weight reciprocal_predsqr 100  [Constraints] a>0 [Options] tolerance=0.0000000001 stepsize=1 iterations=200  Number of Iterations Performed = 8  3. Cake-Intermediate Nonlinear Regression      Tuesday, July 08, 2014, 12:22:37 AM  Equation: User-Defined, Cake-Intermediate f = 1/a*Ln(abs(1+a/(b*10)*((1+2*b*100*x)^(0.5)-1)))  R  Rsqr  Adj Rsqr  Standard Error of Estimate  0.9700 0.9410 0.9398  5.2660     Coefficient   Std. Error t P  a 1.6052E-010    0.0008 2.0368E-007 1.0000  b 0.6961       0.0177 39.2468 <0.0001  Analysis of Variance:    DF SS MS  Regression2 99922.1389 49961.0694  Residual 49 1358.7913 27.7304  Total 51 101280.9302 1985.9006  Corrected for the mean of the observations:   DF SS MS F P  Regression1 21657.0003 21657.0003 780.9831 <0.0001  Residual 49 1358.7913 27.7304  Total 50 23015.7916 460.3158   101  Statistical Tests:  Normality Test (Shapiro-Wilk)   Failed (P = 0.0024)  W Statistic= 0.9216 Significance Level = 0.0500  Constant Variance Test  Failed (P = <0.0001)  Fit Equation Description: [Variables] x = col(1) y = col(2) reciprocal_y = 1/abs(y) reciprocal_ysquare = 1/y^2 reciprocal_pred = 1/abs(f) reciprocal_predsqr = 1/f^2 'Automatic Initial Parameter Estimate Functions F(q) = ape(x,exp(y),1,0,1) [Parameters] a = 0.1 ' {{previous: 1.60516e-010}} b = 1 ' {{previous: 0.696074}} [Equation] f = 1/a*Ln(abs(1+a/(b*10)*((1+2*b*100*x)^(0.5)-1))) fit f to y ''fit f to y with weight reciprocal_y ''fit f to y with weight reciprocal_ysquare ''fit f to y with weight reciprocal_pred ''fit f to y with weight reciprocal_predsqr [Constraints] a>0 b>0 [Options] tolerance=0.0000000001 102  stepsize=0.5 iterations=200  Number of Iterations Performed = 31 4. Cake-Standard  Nonlinear Regression     Wednesday, July 23, 2014, 11:31:07 PM Equation: User-Defined, Cake-standard a=sqrt(4/9+4*d/(30*e)+2*d^2*x/(3*e)) b=2/(9*(4/9+4*d/(30*e)+2*d^2*x/(3*e))^1.5)*(4/3+d/(10*e)-d^2*x/e) f =2/d*(a*cos(2.09-0.33*arccos(b))+1/3)  R  Rsqr  Adj Rsqr  Standard Error of Estimate 0.9698 0.9405 0.9393  5.2860     Coefficient Std. Error t P  d 5024.56634898964.7397 0.0010 0.9992  e 0.7512 0.0254 29.6182 <0.0001   Analysis of Variance:     DF SS MS  Regression2 99911.7891 49955.8946  Residual 49 1369.1411 27.9417  Total 51 101280.9302 1985.9006   Corrected for the mean of the observations:   DF SS MS F P  Regression1 21646.6505 21646.6505 774.7090 <0.0001  Residual 49 1369.1411 27.9417  Total 50 23015.7916 460.3158     103  Statistical Tests:  Normality Test (Shapiro-Wilk)   Failed (P = 0.0023)  W Statistic= 0.9209 Significance Level = 0.0500  Constant Variance Test  Failed (P = <0.0001)  Fit Equation Description: [Variables] x = col(1) y = col(2) reciprocal_y = 1/abs(y) reciprocal_ysquare = 1/y^2 reciprocal_pred = 1/abs(f) reciprocal_predsqr = 1/f^2 'Automatic Initial Parameter Estimate Functions first(q) = if(size(q)<10,size(q)-1,int(0.9*size(q))) ylast(q) = mean(q[data(first(q),size(q))]) [Parameters] d = 0.05 ' {{previous: 5024.57}} e = 0.71 ' {{previous: 0.751211}} [Equation] f =2/d*(a*cos(2.09-0.33*arccos(b))+1/3) a=sqrt(4/9+4*d/(30*e)+2*d^2*x/(3*e)) b=2/(9*(4/9+4*d/(30*e)+2*d^2*x/(3*e))^1.5)*(4/3+d/(10*e)-d^2*x/e) fit f to y ''fit f to y with weight reciprocal_y ''fit f to y with weight reciprocal_ysquare ''fit f to y with weight reciprocal_pred ''fit f to y with weight reciprocal_predsqr [Constraints] [Options] 104  tolerance=0.0000000001 stepsize=1 iterations=200  Number of Iterations Performed = 283  5. Intermediate  Nonlinear Regression     Wednesday, August 06, 2014, 3:22:23 PM Equation: User-Defined, 2Intermediate f = if(x>0, 1/a*ln(abs(1+a*10*x)), 0)  R  Rsqr  Adj Rsqr  Standard Error of Estimate 0.7042 0.4959 0.4959  15.2330    Coefficient Std. Error t P  a 0.1586 0.0094 16.9302 <0.0001   Analysis of Variance:     DF SS MS  Regression1 89678.7339 89678.7339  Residual 50 11602.1963 232.0439  Total 51 101280.9302 1985.9006   Corrected for the mean of the observations:   DF SS MS F P  Regression0 11413.5953 (+inf) (+inf) (NAN)  Residual 50 11602.1963 232.0439  Total 50 23015.7916 460.3158     105  Statistical Tests:  Normality Test (Shapiro-Wilk)   Failed (P = 0.0047)  W Statistic= 0.9294 Significance Level = 0.0500  Constant Variance Test  Passed (P = 0.1467)  Fit Equation Description: [Variables] x = col(1) y = col(2) reciprocal_y = 1/abs(y) reciprocal_ysquare = 1/y^2 reciprocal_pred = 1/abs(f) reciprocal_predsqr = 1/f^2 'Automatic Initial Parameter Estimate Functions F(q) = ape(ln(abs(x)),y,1,0,1) [Parameters] a = F(0)[2] ''Auto {{previous: 0.158583}} [Equation] f = if(x>0, 1/a*ln(abs(1+a*10*x)), 0) fit f to y ''fit f to y with weight reciprocal_y ''fit f to y with weight reciprocal_ysquare ''fit f to y with weight reciprocal_pred ''fit f to y with weight reciprocal_predsqr [Constraints] [Options] tolerance=0.0000000001 stepsize=1 iterations=200  106  Number of Iterations Performed = 13  II. After Cleaning  1. Cake-Complete Nonlinear Regression   Tuesday, July 08, 2014, 12:34:13 AM Equation: User-Defined, Cake-Complete f = 10/a*(1-exp(-a/(b*100)*(sqrt(1+2*b*100*x)-1)))  R  Rsqr  Adj Rsqr  Standard Error of Estimate 0.9992 0.9983 0.9983  0.7353     Coefficient Std. Error t P  a -0.2910 0.0115 -25.3098 <0.0001  b 1.9846 0.0538 36.9190 <0.0001   Analysis of Variance:    DF SS MS  Regression2 67350.1010 33675.0505  Residual 40 21.6262 0.5407  Total 42 67371.7272 1604.0887   Corrected for the mean of the observations:   DF SS MS F P  Regression1 12705.5422 12705.5422 23500.2859 <0.0001  Residual 40 21.6262 0.5407  Total 41 12727.1683 310.4187   Statistical Tests:  Normality Test (Shapiro-Wilk)   Failed (P = 0.0009) 107  W Statistic= 0.8927 Significance Level = 0.0500  Constant Variance Test  Failed (P = 0.0075)  Fit Equation Description: [Variables] x = col(1) y = col(2) reciprocal_y = 1/abs(y) reciprocal_ysquare = 1/y^2 reciprocal_pred = 1/abs(f) reciprocal_predsqr = 1/f^2 'Automatic Initial Parameter Estimate Functions first(q) = if(size(q)<10,size(q)-1,int(0.9*size(q))) ylast(q) = mean(q[data(first(q),size(q))]) [Parameters] a = ylast(y) ''Auto {{previous: -0.290979}} {{MinRange: 6}} {{MaxRange: 18}} b = if(x50(x,y,.5)-min(x)>0, -ln(.5)/(x50(x,y,.5)-min(x)), 1) ''Auto {{previous: 1.98458}} [Equation] f = 10/a*(1-exp(-a/(b*100)*(sqrt(1+2*b*100*x)-1))) fit f to y ''fit f to y with weight reciprocal_y ''fit f to y with weight reciprocal_ysquare ''fit f to y with weight reciprocal_pred ''fit f to y with weight reciprocal_predsqr [Constraints] b>0 [Options] tolerance=0.0000000001 stepsize=1 iterations=200  Number of Iterations Performed = 33 108  2. Cake   Nonlinear Regression      Thursday, July 24, 2014, 1:20:32 PM Equation: User-Defined, 3Cake f = 1/(10*a)*((1+2*a*100*x)^(1/2)-1)  R  Rsqr  Adj Rsqr  Standard Error of Estimate 0.9715 0.9439 0.9439  4.1737                Coefficient Std. Error t P  a   0.7938    0.0257 30.8411 <0.0001   Analysis of Variance:    DF SS MS  Regression 1 66657.4999 66657.4999  Residual 41 714.2273 17.4202  Total 42 67371.7272 1604.0887   Corrected for the mean of the observations:   DF SS MS F P  Regression 0 12012.9411    (+inf) (+inf) (NAN)  Residual 41 714.2273 17.4202  Total 41 12727.1683 310.4187  Statistical Tests:  Normality Test (Shapiro-Wilk)   Failed (P = 0.0037)  W Statistic= 0.9135 Significance Level = 0.0500  Constant Variance Test  Passed (P = 0.1190)  Fit Equation Description: [Variables] 109  x = col(1) y = col(2) reciprocal_y = 1/abs(y) reciprocal_ysquare = 1/y^2 reciprocal_pred = 1/abs(f) reciprocal_predsqr = 1/f^2 'Automatic Initial Parameter Estimate Functions F(q) = ape(x,y,1,0,1) [Parameters] a = F(0)[2] ''Auto {{previous: 0.793829}} {{MinRange: -4.5}} {{MaxRange: 1.5}} [Equation] f = 1/(10*a)*((1+2*a*100*x)^(1/2)-1) fit f to y ''fit f to y with weight reciprocal_y ''fit f to y with weight reciprocal_ysquare ''fit f to y with weight reciprocal_pred ''fit f to y with weight reciprocal_predsqr [Constraints] a>0 [Options] tolerance=0.0000000001 stepsize=1 iterations=200  Number of Iterations Performed = 9  3. Cake-Intermediate  Nonlinear Regression      Thursday, July 24, 2014, 1:11:40 PM  Equation: User-Defined, Cake-Intermediate f = 1/a*Ln(abs(1+a/(b*10)*((1+2*b*100*x)^(0.5)-1)))  110  R  Rsqr  Adj Rsqr  Standard Error of Estimate 0.9712 0.9433 0.9418  4.2488     Coefficient  Std. Error  t   P  a 2.1553E-011 0.0007 3.0802E-008 1.0000  b 0.7768 0.0065 119.2967 <0.0001   Analysis of Variance:        DF      SS     MS  Regression 2 66649.6396 33324.8198  Residual 40 722.0876 18.0522  Total 42 67371.7272 1604.0887   Corrected for the mean of the observations:   DF SS MS F P  Regression 1 12005.0807 12005.0807 665.0207 <0.0001  Residual 40 722.0876 18.0522  Total 41 12727.1683 310.4187   Statistical Tests:  Normality Test (Shapiro-Wilk)   Failed (P = 0.0032) W Statistic= 0.9112 Significance Level = 0.0500  Constant Variance Test  Failed (P = 0.0418)  Fit Equation Description: [Variables] x = col(1) y = col(2) reciprocal_y = 1/abs(y) reciprocal_ysquare = 1/y^2 111  reciprocal_pred = 1/abs(f) reciprocal_predsqr = 1/f^2 'Automatic Initial Parameter Estimate Functions F(q) = ape(x,exp(y),1,0,1) [Parameters] a = .1 ' {{previous: 2.15527e-011}} b = 0.349981 ' {{previous: 0.776815}} [Equation] f = 1/a*Ln(abs(1+a/(b*10)*((1+2*b*100*x)^(0.5)-1))) fit f to y ''fit f to y with weight reciprocal_y ''fit f to y with weight reciprocal_ysquare ''fit f to y with weight reciprocal_pred ''fit f to y with weight reciprocal_predsqr [Constraints] a>0 b>0 [Options] tolerance=0.0000000001 stepsize=0.5 iterations=200  Number of Iterations Performed = 44 4. Cake-Standard  Nonlinear Regression      Thursday, July 24, 2014, 1:15:09 PM  Equation: User-Defined, Cake-standard a=sqrt(4/9+4*d/(30*e)+2*d^2*x/(3*e)) b=2/(9*(4/9+4*d/(30*e)+2*d^2*x/(3*e))^1.5)*(4/3+d/(10*e)-d^2*x/e) f = 2/d*(a*cos(2.09-0.33*arccos(b))+1/3) R  Rsqr  Adj Rsqr  Standard Error of Estimate 0.9710 0.9429 0.9415  4.2625  112          Coefficient Std. Error      t   P  d 923.1748 313672.3129 0.0029 0.9977  e 0.8363 0.0288 29.0144 <0.0001   Analysis of Variance:     DF SS MS  Regression 2 66644.9597 33322.4798  Residual 40 726.7675 18.1692  Total 42 67371.7272 1604.0887   Corrected for the mean of the observations:   DF SS MS F P  Regression 1 12000.4009 12000.4009 660.4809 <0.0001  Residual 40 726.7675 18.1692  Total 41 12727.1683 310.4187   Statistical Tests: Normality Test (Shapiro-Wilk)   Failed (P = 0.0039) W Statistic= 0.9141 Significance Level = 0.0500 Constant Variance Test  Passed (P = 0.1114) Fit Equation Description: [Variables] x = col(1) y = col(2) reciprocal_y = 1/abs(y) reciprocal_ysquare = 1/y^2 reciprocal_pred = 1/abs(f) reciprocal_predsqr = 1/f^2 'Automatic Initial Parameter Estimate Functions first(q) = if(size(q)<10,size(q)-1,int(0.9*size(q))) ylast(q) = mean(q[data(first(q),size(q))]) [Parameters] 113  d = 0.05 ' {{previous: 923.175}} e = 0.71 ' {{previous: 0.836326}} [Equation] a=sqrt(4/9+4*d/(30*e)+2*d^2*x/(3*e)) b=2/(9*(4/9+4*d/(30*e)+2*d^2*x/(3*e))^1.5)*(4/3+d/(10*e)-d^2*x/e) f = 2/d*(a*cos(2.09-0.33*arccos(b))+1/3) fit f to y ''fit f to y with weight reciprocal_y ''fit f to y with weight reciprocal_ysquare ''fit f to y with weight reciprocal_pred ''fit f to y with weight reciprocal_predsqr [Constraints] [Options] tolerance=0.0000000001 stepsize=1 iterations=200  Number of Iterations Performed = 190  5. Intermediate  Nonlinear Regression      Thursday, July 24, 2014, 1:19:19 PM  Equation: User-Defined, 2Intermediate f = if(x>0, 1/a*ln(abs(1+a*10*x)), 0)  R  Rsqr  Adj Rsqr  Standard Error of Estimate 0.7115 0.5062 0.5062  12.3804     Coefficient Std. Error t P  a 0.1758 0.0102 17.1758 <0.0001    114  Analysis of Variance:     DF SS MS  Regression1 61087.4418 61087.4418  Residual 41 6284.2854 153.2753  Total 42 67371.7272 1604.0887   Corrected for the mean of the observations:   DF SS MS F P  Regression0 6442.8830 (+inf) (+inf) (NAN)  Residual 41 6284.2854 153.2753  Total 41 12727.1683 310.4187   Statistical Tests:  Normality Test (Shapiro-Wilk)   Passed (P = 0.0764)  W Statistic= 0.9520 Significance Level = 0.0500  Constant Variance Test  Passed (P = 0.5956) Fit Equation Description: [Variables] x = col(1) y = col(2) reciprocal_y = 1/abs(y) reciprocal_ysquare = 1/y^2 reciprocal_pred = 1/abs(f) reciprocal_predsqr = 1/f^2 'Automatic Initial Parameter Estimate Functions F(q) = ape(ln(abs(x)),y,1,0,1) [Parameters] a = F(0)[2] ''Auto {{previous: 0.175757}} [Equation] 115  f = if(x>0, 1/a*ln(abs(1+a*10*x)), 0) fit f to y ''fit f to y with weight reciprocal_y ''fit f to y with weight reciprocal_ysquare ''fit f to y with weight reciprocal_pred ''fit f to y with weight reciprocal_predsqr [Constraints] [Options] tolerance=0.0000000001 stepsize=1 iterations=200  Number of Iterations Performed = 13    116  Appendix H: Statistical Reports of the 5 Best-Fit Fouling Models for 4 Hours Off – 30 Minutes On  Model’s Fit Error and Estimated Parameter Values for Passive Membrane Permeation with ON/OFF Air Ratio of 0.13 Model SSR Fitted Parameters values* s Cake-Complete 6.69x101 Kb = -0.277,      Kc = 2.80 0.0280 0.1702 Cake 3.59x102 Kc = 1.29 0.0319 Cake- Intermediate 3.62x102 Ki = 5.64x10-10,  Kc = 1.27 0.0012 0.0525 Cake-Standard 3.65x102 Ks = 4.52x106,  Kc = 1.36 100698884844.8935 0.0341 Intermediate 4.05x103 Ki = 0.214 0.0106 Intermediate - Standard 4.05x103 Ki = 0.214,          Ks = 8.66x10-20 0.0305 0.0002 Complete - Standard 6.51x103 Kb= 4.57x10-16,  Ks = 0.0607 272999.3933 0.0000 Standard 7.28x103 Ks = 0.0607 0.0036 Complete 7.62x103 Kb = 0.308 0.0188   1. Cake-Complete  Nonlinear Regression      Tuesday, July 08, 2014, 12:42:03 AM  Equation: User-Defined, Cake-Complete f = 10/a*(1-exp(-a/(b*100)*(sqrt(1+2*b*100*x)-1))) R  Rsqr  Adj Rsqr  Standard Error of Estimate 0.9961 0.9923 0.9921  1.2475     Coefficient Std. Error t P  a -0.2765 0.0280 -9.8674 <0.0001  b 2.8015 0.1702 16.4552 <0.0001    117  Analysis of Variance:     DF SS MS  Regression 2 53868.2406 26934.1203  Residual 43 66.9181 1.5562  Total 45 53935.1587 1198.5591   Corrected for the mean of the observations:   DF SS MS F P  Regression 1 8575.4425 8575.4425 5510.3757 <0.0001  Residual 43 66.9181 1.5562  Total 44 8642.3607 196.4173   Statistical Tests:  Normality Test (Shapiro-Wilk)   Failed (P = 0.0025)  W Statistic= 0.9132 Significance Level = 0.0500  Constant Variance Test  Passed (P = 0.0706)  Fit Equation Description: [Variables] x = col(1) y = col(2) reciprocal_y = 1/abs(y) reciprocal_ysquare = 1/y^2 reciprocal_pred = 1/abs(f) reciprocal_predsqr = 1/f^2 'Automatic Initial Parameter Estimate Functions first(q) = if(size(q)<10,size(q)-1,int(0.9*size(q))) ylast(q) = mean(q[data(first(q),size(q))]) [Parameters] 118  a = ylast(y) ''Auto {{previous: -0.276539}} {{MinRange: 6}} {{MaxRange: 18}} b = if(x50(x,y,.5)-min(x)>0, -ln(.5)/(x50(x,y,.5)-min(x)), 1) ''Auto {{previous: 2.80147}} [Equation] f = 10/a*(1-exp(-a/(b*100)*(sqrt(1+2*b*100*x)-1))) fit f to y ''fit f to y with weight reciprocal_y ''fit f to y with weight reciprocal_ysquare ''fit f to y with weight reciprocal_pred ''fit f to y with weight reciprocal_predsqr [Constraints] b>0 [Options] tolerance=0.0000000001 stepsize=1 iterations=200  Number of Iterations Performed = 31  2. Cake  Nonlinear Regression      Thursday, July 24, 2014, 12:24:56 AM  Equation: User-Defined, 3Cake f = 1/(10*a)*((1+2*a*100*x)^(1/2)-1)  R  Rsqr  Adj Rsqr  Standard Error of Estimate 0.9790 0.9584 0.9584  2.8574                 Coefficient      Std. Error t P  a 1.2887 0.0319 40.4184 <0.0001     119  Analysis of Variance:     DF SS MS  Regression 1 53575.8982 53575.8982  Residual 44 359.2604 8.1650  Total 45 53935.1587 1198.5591   Corrected for the mean of the observations:   DF SS MS F P  Regression 0 8283.1002    (+inf) (+inf) (NAN)  Residual 44 359.2604 8.1650  Total 44 8642.3607 196.4173   Statistical Tests:  Normality Test (Shapiro-Wilk)   Failed (P = 0.0006)  W Statistic= 0.8945 Significance Level = 0.0500  Constant Variance Test  Failed (P = 0.0239)  Fit Equation Description: [Variables] x = col(1) y = col(2) reciprocal_y = 1/abs(y) reciprocal_ysquare = 1/y^2 reciprocal_pred = 1/abs(f) reciprocal_predsqr = 1/f^2 'Automatic Initial Parameter Estimate Functions F(q) = ape(x,y,1,0,1) [Parameters] 120  a = F(0)[2] ''Auto {{previous: 1.28865}} {{MinRange: -4.5}} {{MaxRange: 1.5}} [Equation] f = 1/(10*a)*((1+2*a*100*x)^(1/2)-1) fit f to y ''fit f to y with weight reciprocal_y ''fit f to y with weight reciprocal_ysquare ''fit f to y with weight reciprocal_pred ''fit f to y with weight reciprocal_predsqr [Constraints] a>0 [Options] tolerance=0.0000000001 stepsize=1 iterations=200  Number of Iterations Performed = 9  3. Cake-Intermediate  Nonlinear Regression      Tuesday, July 08, 2014, 12:44:47 AM  Equation: User-Defined, Cake-Intermediate f = 1/a*Ln(abs(1+a/(b*10)*((1+2*b*100*x)^(0.5)-1)))  R  Rsqr  Adj Rsqr  Standard Error of Estimate 0.9788 0.9581 0.9572  2.9008                      Coefficient Std. Error t P  a 5.6415E-010 0.0012 4.6789E-007 1.0000  b 1.2709 0.0525 24.1955 <0.0001    121  Analysis of Variance:    DF SS MS  Regression 2 53573.3213 26786.6607  Residual 43 361.8374 8.4148  Total 45 53935.1587 1198.5591   Corrected for the mean of the observations:   DF SS MS F P  Regression 1 8280.5233 8280.5233 984.0401 <0.0001  Residual 43 361.8374 8.4148  Total 44 8642.3607 196.4173   Statistical Tests:  Normality Test (Shapiro-Wilk)   Failed (P = 0.0006)  W Statistic= 0.8927 Significance Level = 0.0500  Constant Variance Test  Failed (P = 0.0051)  Fit Equation Description: [Variables] x = col(1) y = col(2) reciprocal_y = 1/abs(y) reciprocal_ysquare = 1/y^2 reciprocal_pred = 1/abs(f) reciprocal_predsqr = 1/f^2 'Automatic Initial Parameter Estimate Functions F(q) = ape(x,exp(y),1,0,1) [Parameters] a = 0.1 ' {{previous: 5.64153e-010}} b = 1 ' {{previous: 1.27093}} 122  [Equation] f = 1/a*Ln(abs(1+a/(b*10)*((1+2*b*100*x)^(0.5)-1))) fit f to y ''fit f to y with weight reciprocal_y ''fit f to y with weight reciprocal_ysquare ''fit f to y with weight reciprocal_pred ''fit f to y with weight reciprocal_predsqr [Constraints] a>0 b>0 [Options] tolerance=0.0000000001 stepsize=0.5 iterations=200  Number of Iterations Performed = 29  4. Cake-Standard Nonlinear Regression      Thursday, July 24, 2014, 12:19:47 AM  Equation: User-Defined, Cake-standard a=sqrt(4/9+4*d/(30*e)+2*d^2*x/(3*e)) b=2/(9*(4/9+4*d/(30*e)+2*d^2*x/(3*e))^1.5)*(4/3+d/(10*e)-d^2*x/e) f = 2/d*(a*cos(2.09-0.33*arccos(b))+1/3)  R  Rsqr  Adj Rsqr  Standard Error of Estimate 0.9787 0.9578 0.9568  2.9134                     Coefficient Std. Error t P  d 4523119.0642 100698884844.8935 4.4917E-005 1.0000  e 1.3552 0.0341 39.7177 <0.0001    123  Analysis of Variance:     DF SS MS  Regression 2 53570.1707 26785.0853  Residual 43 364.9880 8.4881  Total 45 53935.1587 1198.5591   Corrected for the mean of the observations:   DF SS MS F P  Regression 1 8277.3726 8277.3726 975.1745 <0.0001  Residual 43 364.9880 8.4881  Total 44 8642.3607 196.4173   Statistical Tests:  Normality Test (Shapiro-Wilk)   Failed (P = 0.0006)  W Statistic= 0.8947 Significance Level = 0.0500  Constant Variance Test  Failed (P = 0.0239)  Fit Equation Description: [Variables] x = col(1) y = col(2) reciprocal_y = 1/abs(y) reciprocal_ysquare = 1/y^2 reciprocal_pred = 1/abs(f) reciprocal_predsqr = 1/f^2 'Automatic Initial Parameter Estimate Functions first(q) = if(size(q)<10,size(q)-1,int(0.9*size(q))) ylast(q) = mean(q[data(first(q),size(q))]) [Parameters] 124  d = 0.05 ' {{previous: 4.52312e+006}} e = 0.71 ' {{previous: 1.35517}} [Equation] a=sqrt(4/9+4*d/(30*e)+2*d^2*x/(3*e)) b=2/(9*(4/9+4*d/(30*e)+2*d^2*x/(3*e))^1.5)*(4/3+d/(10*e)-d^2*x/e) f = 2/d*(a*cos(2.09-0.33*arccos(b))+1/3) fit f to y ''fit f to y with weight reciprocal_y ''fit f to y with weight reciprocal_ysquare ''fit f to y with weight reciprocal_pred ''fit f to y with weight reciprocal_predsqr [Constraints] [Options] tolerance=0.0000000001 stepsize=1 iterations=200  Number of Iterations Performed = 10  5. Intermediate  Nonlinear Regression      Thursday, July 24, 2014, 12:24:15 AM  Equation: User-Defined, 2Intermediate f = if(x>0, 1/a*ln(abs(1+a*10*x)), 0)  R  Rsqr  Adj Rsqr  Standard Error of Estimate 0.7289 0.5312 0.5312  9.5956     Coefficient Std. Error t P  a 0.2142 0.0106 20.1864 <0.0001     125  Analysis of Variance:     DF SS MS  Regression 1 49883.8509 49883.8509  Residual 44 4051.3078 92.0752  Total 45 53935.1587 1198.5591   Corrected for the mean of the observations:   DF SS MS F P  Regression 0 4591.0529 (+inf) (+inf) (NAN)  Residual 44 4051.3078 92.0752  Total 44 8642.3607 196.4173   Statistical Tests:  Normality Test (Shapiro-Wilk)   Failed (P = 0.0098)  W Statistic= 0.9306 Significance Level = 0.0500  Constant Variance Test  Passed (P = 0.2547)  Fit Equation Description: [Variables] x = col(1) y = col(2) reciprocal_y = 1/abs(y) reciprocal_ysquare = 1/y^2 reciprocal_pred = 1/abs(f) reciprocal_predsqr = 1/f^2 'Automatic Initial Parameter Estimate Functions F(q) = ape(ln(abs(x)),y,1,0,1) [Parameters] 126  a = F(0)[2] ''Auto {{previous: 0.214202}} [Equation] f = if(x>0, 1/a*ln(abs(1+a*10*x)), 0) fit f to y ''fit f to y with weight reciprocal_y ''fit f to y with weight reciprocal_ysquare ''fit f to y with weight reciprocal_pred ''fit f to y with weight reciprocal_predsqr [Constraints] [Options] tolerance=0.0000000001 stepsize=1 iterations=200  Number of Iterations Performed = 13    127  Appendix I: Statistical Reports of the 5 Best-Fit Fouling Models for 4 Hours Off – 5 Minutes On  Model’s Fit Error and Estimated Parameter Values for Passive Membrane Permeation with ON/OFF Air Ratio of 0.02 Model SSR Fitted Parameters values* s Cake-Complete 7.77 Kb =-0.381,     Kc = 3.89 0.0202 0.1283 Cake 1.71x102 Kc = 1.73 0.0531 Cake- Intermediate 1.73x102 Ki = 2.41x10-10,  Kc = 1.70  0.0012 0.0343 Cake-Standard 1.73x102 Ks = 1.04 x103,  Kb = 1.82 293937.7702 0.0606 Intermediate 2.00x103 Ki = 0.289 0.0182 Intermediate - Standard 2.00x103 Ki = 0.289,         Ks = 7.01x10-19 0.0468 0.0003 Complete - Standard 3.54x103 Kb = 1.00x10-4,  Ks = 0.0828 7213.7470 721.4330 Standard 3.54x103 Ks= 0.0828 0.0063 Complete 3.70x103 Kb = 0.421 0.0327  1. Cake-Complete Nonlinear Regression      Tuesday, July 08, 2014, 1:00:09 AM  Equation: User-Defined, Cake-Complete f = 10/a*(1-exp(-a/(b*100)*(sqrt(1+2*b*100*x)-1)))  R  Rsqr  Adj Rsqr  Standard Error of Estimate 0.9991 0.9981 0.9981  0.4928     Coefficient Std. Error t P  a -0.3812 0.0202 -18.8332 <0.0001  b 3.8818 0.1283 30.2629 <0.0001  128  Analysis of Variance:     DF SS MS  Regression 2 22272.8813 11136.4407  Residual 32 7.7704 0.2428  Total 34 22280.6518 655.3133   Corrected for the mean of the observations:   DF SS MS F P  Regression 1 4166.7299 4166.7299 17159.3157 <0.0001  Residual 32 7.7704 0.2428  Total 33 4174.5003 126.5000   Statistical Tests:  Normality Test (Shapiro-Wilk)   Failed (P = 0.0092)  W Statistic= 0.9113 Significance Level = 0.0500  Constant Variance Test  Passed (P = 0.5982)  Fit Equation Description: [Variables] x = col(1) y = col(2) reciprocal_y = 1/abs(y) reciprocal_ysquare = 1/y^2 reciprocal_pred = 1/abs(f) reciprocal_predsqr = 1/f^2 'Automatic Initial Parameter Estimate Functions first(q) = if(size(q)<10,size(q)-1,int(0.9*size(q))) ylast(q) = mean(q[data(first(q),size(q))]) [Parameters] 129  a = ylast(y) ''Auto {{previous: -0.381185}} {{MinRange: 6}} {{MaxRange: 18}} b = if(x50(x,y,.5)-min(x)>0, -ln(.5)/(x50(x,y,.5)-min(x)), 1) ''Auto {{previous: 3.88176}} [Equation] f = 10/a*(1-exp(-a/(b*100)*(sqrt(1+2*b*100*x)-1))) fit f to y ''fit f to y with weight reciprocal_y ''fit f to y with weight reciprocal_ysquare ''fit f to y with weight reciprocal_pred ''fit f to y with weight reciprocal_predsqr [Constraints] b>0 [Options] tolerance=0.0000000001 stepsize=1 iterations=200  Number of Iterations Performed = 31  2. Cake  Nonlinear Regression      Thursday, July 24, 2014, 12:43:33 AM  Equation: User-Defined, 3Cake f = 1/(10*a)*((1+2*a*100*x)^(1/2)-1)  R  Rsqr  Adj Rsqr  Standard Error of Estimate 0.9793 0.9591 0.9591  2.2753     Coefficient Std. Error t P  a 1.7322 0.0531 32.6094 <0.0001     130  Analysis of Variance:     DF SS MS  Regression 1 22109.8155 22109.8155  Residual 33 170.8362 5.1769  Total 34 22280.6518 655.3133   Corrected for the mean of the observations:   DF SS MS F P  Regression0 4003.6641 (+inf) (+inf) (NAN)  Residual 33 170.8362 5.1769  Total 33 4174.5003 126.5000   Statistical Tests:  Normality Test (Shapiro-Wilk)   Failed (P = 0.0004)  W Statistic= 0.8578 Significance Level = 0.0500  Constant Variance Test  Passed (P = 0.1576)  Fit Equation Description: [Variables] x = col(1) y = col(2) reciprocal_y = 1/abs(y) reciprocal_ysquare = 1/y^2 reciprocal_pred = 1/abs(f) reciprocal_predsqr = 1/f^2 'Automatic Initial Parameter Estimate Functions F(q) = ape(x,y,1,0,1) [Parameters] a = F(0)[2] ''Auto {{previous: 1.73219}} {{MinRange: -4.5}} {{MaxRange: 1.5}} 131  [Equation] f = 1/(10*a)*((1+2*a*100*x)^(1/2)-1) fit f to y ''fit f to y with weight reciprocal_y ''fit f to y with weight reciprocal_ysquare ''fit f to y with weight reciprocal_pred ''fit f to y with weight reciprocal_predsqr [Constraints] a>0 [Options] tolerance=0.0000000001 stepsize=1 iterations=200  Number of Iterations Performed = 10  3. Cake-Intermediate  Nonlinear Regression      Tuesday, July 08, 2014, 1:01:59 AM  Equation: User-Defined, Cake-Intermediate f = 1/a*Ln(abs(1+a/(b*10)*((1+2*b*100*x)^(0.5)-1)))  R  Rsqr  Adj Rsqr  Standard Error of Estimate 0.9791 0.9587 0.9574  2.3224     Coefficient Std. Error            t                         P  a 2.4066E-010 0.0012 1.9681E-007 1.0000  b 1.7016 0.0343 49.6777 <0.0001     132  Analysis of Variance:    DF SS MS  Regression 2 22108.0554 11054.0277  Residual 32 172.5964 5.3936  Total 34 22280.6518 655.3133   Corrected for the mean of the observations:   DF SS MS F P  Regression 1 4001.9039 4001.9039 741.9676 <0.0001  Residual 32 172.5964 5.3936  Total 33 4174.5003 126.5000   Statistical Tests:  Normality Test (Shapiro-Wilk)   Failed (P = 0.0003)  W Statistic= 0.8515 Significance Level = 0.0500  Constant Variance Test  Failed (P = 0.0017)  Fit Equation Description: [Variables] x = col(1) y = col(2) reciprocal_y = 1/abs(y) reciprocal_ysquare = 1/y^2 reciprocal_pred = 1/abs(f) reciprocal_predsqr = 1/f^2 'Automatic Initial Parameter Estimate Functions F(q) = ape(x,exp(y),1,0,1) [Parameters] a = 0.1 ' {{previous: 2.40664e-010}} b = 1 ' {{previous: 1.70163}} 133  [Equation] f = 1/a*Ln(abs(1+a/(b*10)*((1+2*b*100*x)^(0.5)-1))) fit f to y ''fit f to y with weight reciprocal_y ''fit f to y with weight reciprocal_ysquare ''fit f to y with weight reciprocal_pred ''fit f to y with weight reciprocal_predsqr [Constraints] a>0 b>0 [Options] tolerance=0.0000000001 stepsize=0.5 iterations=200  Number of Iterations Performed = 28  4. Cake-Standard  Nonlinear Regression      Thursday, July 24, 2014, 12:48:27 AM  Equation: User-Defined, Cake-standard a=sqrt(4/9+4*d/(30*e)+2*d^2*x/(3*e)) b=2/(9*(4/9+4*d/(30*e)+2*d^2*x/(3*e))^1.5)*(4/3+d/(10*e)-d^2*x/e) f = 2/d*(a*cos(2.09-0.33*arccos(b))+1/3)  R  Rsqr  Adj Rsqr  Standard Error of Estimate 0.9790 0.9585 0.9572  2.3279     Coefficient Std. Error t P  d 1041.7596 293937.7702 0.0035 0.9972  e 1.8216 0.0606 30.0545 <0.0001     134  Analysis of Variance:     DF SS MS  Regression 2 22107.2358 11053.6179  Residual 32 173.4159 5.4192  Total 34 22280.6518 655.3133   Corrected for the mean of the observations:   DF SS MS F P  Regression 1 4001.0844 4001.0844 738.3099 <0.0001  Residual 32 173.4159 5.4192  Total 33 4174.5003 126.5000   Statistical Tests:  Normality Test (Shapiro-Wilk)   Failed (P = 0.0005)  W Statistic= 0.8592 Significance Level = 0.0500  Constant Variance Test  Passed (P = 0.1597)  Fit Equation Description: [Variables] x = col(1) y = col(2) reciprocal_y = 1/abs(y) reciprocal_ysquare = 1/y^2 reciprocal_pred = 1/abs(f) reciprocal_predsqr = 1/f^2 'Automatic Initial Parameter Estimate Functions first(q) = if(size(q)<10,size(q)-1,int(0.9*size(q))) ylast(q) = mean(q[data(first(q),size(q))]) [Parameters] d = 0.05 ' {{previous: 1041.76}} e = 0.71 ' {{previous: 1.82162}} [Equation] a=sqrt(4/9+4*d/(30*e)+2*d^2*x/(3*e)) b=2/(9*(4/9+4*d/(30*e)+2*d^2*x/(3*e))^1.5)*(4/3+d/(10*e)-d^2*x/e) 135  f = 2/d*(a*cos(2.09-0.33*arccos(b))+1/3) fit f to y ''fit f to y with weight reciprocal_y ''fit f to y with weight reciprocal_ysquare ''fit f to y with weight reciprocal_pred ''fit f to y with weight reciprocal_predsqr [Constraints] [Options] tolerance=0.0000000001 stepsize=1 iterations=200  Number of Iterations Performed = 150  5. Intermediate  Nonlinear Regression      Thursday, July 24, 2014, 12:43:00 AM  Equation: User-Defined, 2Intermediate f = if(x>0, 1/a*ln(abs(1+a*10*x)), 0)  R  Rsqr  Adj Rsqr  Standard Error of Estimate 0.7214 0.5205 0.5205  7.7884     Coefficient Std. Error t P  a 0.2889 0.0182 15.8591 <0.0001   Analysis of Variance:     DF SS MS  Regression 1 20278.9119 20278.9119  Residual 33 2001.7399 60.6588  Total 34 22280.6518 655.3133     136  Corrected for the mean of the observations:   DF SS MS F P  Regression 0 2172.7605 (+inf) (+inf) (NAN)  Residual 33 2001.7399 60.6588  Total 33 4174.5003 126.5000   Statistical Tests:  Normality Test (Shapiro-Wilk)   Passed (P = 0.0725)  W Statistic= 0.9424 Significance Level = 0.0500  Constant Variance Test  Passed (P = 0.6030)  Fit Equation Description: [Variables] x = col(1) y = col(2) reciprocal_y = 1/abs(y) reciprocal_ysquare = 1/y^2 reciprocal_pred = 1/abs(f) reciprocal_predsqr = 1/f^2 'Automatic Initial Parameter Estimate Functions F(q) = ape(ln(abs(x)),y,1,0,1) [Parameters] a = F(0)[2] ''Auto {{previous: 0.288906}} [Equation] f = if(x>0, 1/a*ln(abs(1+a*10*x)), 0) fit f to y ''fit f to y with weight reciprocal_y ''fit f to y with weight reciprocal_ysquare ''fit f to y with weight reciprocal_pred ''fit f to y with weight reciprocal_predsqr 137  [Constraints] [Options] tolerance=0.0000000001 stepsize=1 iterations=200 Number of Iterations Performed = 11  138  Appendix J: Statistical Reports of the 5 Best-Fit Fouling Models for No Aeration  Model’s Fit Error and Estimated Parameter Values for Passive Membrane Permeation with ON/OFF Air Ratio of 0  Model SSR Fitted Parameters values* s Cake-Complete 1.40 Kb = -1.34 ,  Kc = 23.5 0.0773 1.0042 Cake 3.45x101 Kc = 8.50 0.3959 Cake-Standard 3.49x101 Ks = 5.02x106,  Kc = 8.93 111766502193.6843 0.4242 Cake- Intermediate 3.50x101 Ki = 2.90x10-9,  Kc = 8.25 0.0097 0.7458 Intermediate 4.40x102 Ki = 0.945 0.0994 Intermediate - Standard 4.40x102 Ki = 0.945,  Ks = 1.39x10-18 0.1923 0.0006 Standard 8.12x102 Ks = 0.290 0.0415 Complete - Standard 8.12x102 Kb =  4.00x10-4,  Ks = 0.290 12230.6824 1223.1698 Complete 8.87x102 Kb = 1.57 0.2414  1. Cake-complete  Nonlinear Regression      Monday, July 07, 2014, 10:47:36 PM  Equation: User-Defined, Cake-Complete f = 10/a*(1-exp(-a/(b*100)*(sqrt(1+2*b*100*x)-1)))  R  Rsqr  Adj Rsqr  Standard Error of Estimate 0.9993 0.9985 0.9985  0.2157     Coefficient Std. Error t P  a -1.3439 0.0773 -17.3815 <0.0001  b 23.4890 1.0042 23.3917 <0.0001  139  Analysis of Variance:    DF SS MS  Regression 2 2092.5148 1046.2574  Residual 30 1.3955 0.0465  Total 32 2093.9103 65.4347   Corrected for the mean of the observations:   DF SS MS F P  Regression 1 938.2979 938.2979 20171.2234 <0.0001  Residual 30 1.3955 0.0465  Total 31 939.6934 30.3127   Statistical Tests:  Normality Test (Shapiro-Wilk)   Failed (P = 0.0030)  W Statistic= 0.8875 Significance Level = 0.0500  Constant Variance Test  Failed (P = 0.0121)  Fit Equation Description: [Variables] x = col(3) y = col(4) reciprocal_y = 1/abs(y) reciprocal_ysquare = 1/y^2 reciprocal_pred = 1/abs(f) reciprocal_predsqr = 1/f^2 'Automatic Initial Parameter Estimate Functions first(q) = if(size(q)<10,size(q)-1,int(0.9*size(q))) ylast(q) = mean(q[data(first(q),size(q))]) [Parameters] 140  a = ylast(y) ''Auto {{previous: -1.34391}} {{MinRange: 6}} {{MaxRange: 18}} b = if(x50(x,y,.5)-min(x)>0, -ln(.5)/(x50(x,y,.5)-min(x)), 1) ''Auto {{previous: 23.489}} [Equation] f = 10/a*(1-exp(-a/(b*100)*(sqrt(1+2*b*100*x)-1))) fit f to y ''fit f to y with weight reciprocal_y ''fit f to y with weight reciprocal_ysquare ''fit f to y with weight reciprocal_pred ''fit f to y with weight reciprocal_predsqr [Constraints] b>0 [Options] tolerance=0.0000000001 stepsize=1 iterations=200  Number of Iterations Performed = 38  2. Cake  Nonlinear Regression      Thursday, July 24, 2014, 12:57:08 AM  Equation: User-Defined, 3Cake f = 1/(10*a)*((1+2*a*100*x)^(1/2)-1)   R  Rsqr  Adj Rsqr  Standard Error of Estimate 0.9815 0.9632 0.9632  1.0555     Coefficient Std. Error t P  a 8.5026 0.3959 21.4743 <0.0001     141  Analysis of Variance:     DF SS MS  Regression 1 2059.3763 2059.3763  Residual 31 34.5341 1.1140  Total 32 2093.9103 65.4347   Corrected for the mean of the observations:   DF SS MS F P  Regression 0 905.1593 (+inf) (+inf) (NAN)  Residual 31 34.5341 1.1140  Total 31 939.6934 30.3127   Statistical Tests:  Normality Test (Shapiro-Wilk)   Failed (P = 0.0006)  W Statistic= 0.8564 Significance Level = 0.0500  Constant Variance Test  Passed (P = 0.1692)  Fit Equation Description: [Variables] x = col(1) y = col(2) reciprocal_y = 1/abs(y) reciprocal_ysquare = 1/y^2 reciprocal_pred = 1/abs(f) reciprocal_predsqr = 1/f^2 'Automatic Initial Parameter Estimate Functions F(q) = ape(x,y,1,0,1) [Parameters] a = F(0)[2] ''Auto {{previous: 8.50261}} {{MinRange: -4.5}} {{MaxRange: 1.5}} 142  [Equation] f = 1/(10*a)*((1+2*a*100*x)^(1/2)-1) fit f to y ''fit f to y with weight reciprocal_y ''fit f to y with weight reciprocal_ysquare ''fit f to y with weight reciprocal_pred ''fit f to y with weight reciprocal_predsqr [Constraints] a>0 [Options] tolerance=0.0000000001 stepsize=1 iterations=200  Number of Iterations Performed = 11  3. Cake-Standard  Nonlinear Regression      Thursday, July 24, 2014, 1:00:50 AM  Equation: User-Defined, Cake-standard a=sqrt(4/9+4*d/(30*e)+2*d^2*x/(3*e)) b=2/(9*(4/9+4*d/(30*e)+2*d^2*x/(3*e))^1.5)*(4/3+d/(10*e)-d^2*x/e) f = 2/d*(a*cos(2.09-0.33*arccos(b))+1/3)  R  Rsqr  Adj Rsqr  Standard Error of Estimate 0.9813 0.9629 0.9616  1.0783       Coefficient        Std. Error        t      P  d 5023582.1705 111766502193.6843 4.4947E-005 1.0000  e 8.9259 0.4242 21.0401 <0.0001     143  Analysis of Variance:     DF SS MS  Regression 2 2059.0289 1029.5144  Residual 30 34.8815 1.1627  Total 32 2093.9103 65.4347   Corrected for the mean of the observations:   DF SS MS F P  Regression 1 904.8119 904.8119 778.1887 <0.0001  Residual 30 34.8815 1.1627  Total 31 939.6934 30.3127   Statistical Tests:  Normality Test (Shapiro-Wilk)   Failed (P = 0.0005)  W Statistic= 0.8554 Significance Level = 0.0500  Constant Variance Test  Passed (P = 0.1692)  Fit Equation Description: [Variables] x = col(3) y = col(4) reciprocal_y = 1/abs(y) reciprocal_ysquare = 1/y^2 reciprocal_pred = 1/abs(f) reciprocal_predsqr = 1/f^2 'Automatic Initial Parameter Estimate Functions first(q) = if(size(q)<10,size(q)-1,int(0.9*size(q))) ylast(q) = mean(q[data(first(q),size(q))]) [Parameters] 144  d = 0.05 ' {{previous: 5.02358e+006}} e = 0.71 ' {{previous: 8.92586}} [Equation] a=sqrt(4/9+4*d/(30*e)+2*d^2*x/(3*e)) b=2/(9*(4/9+4*d/(30*e)+2*d^2*x/(3*e))^1.5)*(4/3+d/(10*e)-d^2*x/e) f = 2/d*(a*cos(2.09-0.33*arccos(b))+1/3) fit f to y ''fit f to y with weight reciprocal_y ''fit f to y with weight reciprocal_ysquare ''fit f to y with weight reciprocal_pred ''fit f to y with weight reciprocal_predsqr [Constraints] [Options] tolerance=0.0000000001 stepsize=1 iterations=200  Number of Iterations Performed = 13  4. Cake-Intermediate  Nonlinear Regression      Monday, July 07, 2014, 11:43:24 PM  Equation: User-Defined, Cake-Intermediate f = 1/a*Ln(abs(1+a/(b*10)*((1+2*b*100*x)^(0.5)-1)))  R  Rsqr  Adj Rsqr  Standard Error of Estimate 0.9812 0.9627 0.9615  1.0804     Coefficient Std. Error    t P  a 2.8956E-009 0.0097 2.9922E-007 1.0000  b 8.2481 0.7458 11.0591 <0.0001  145  Analysis of Variance:     DF SS MS  Regression 2 2058.8947 1029.4473  Residual 30 35.0157 1.1672  Total 32 2093.9103 65.4347   Corrected for the mean of the observations:   DF SS MS F P  Regression 1 904.6777 904.6777 775.0914 <0.0001  Residual 30 35.0157 1.1672  Total 31 939.6934 30.3127   Statistical Tests:  Normality Test (Shapiro-Wilk)   Failed (P = 0.0011)  W Statistic= 0.8693 Significance Level = 0.0500  Constant Variance Test  Passed (P = 0.4018)  Fit Equation Description: [Variables] x = col(3) y = col(4) reciprocal_y = 1/abs(y) reciprocal_ysquare = 1/y^2 reciprocal_pred = 1/abs(f) reciprocal_predsqr = 1/f^2 'Automatic Initial Parameter Estimate Functions F(q) = ape(x,exp(y),1,0,1) [Parameters] a = 0.1 ' {{previous: 2.89565e-009}} 146  b = 1 ' {{previous: 8.24812}} [Equation] f = 1/a*Ln(abs(1+a/(b*10)*((1+2*b*100*x)^(0.5)-1))) fit f to y ''fit f to y with weight reciprocal_y ''fit f to y with weight reciprocal_ysquare ''fit f to y with weight reciprocal_pred ''fit f to y with weight reciprocal_predsqr [Constraints] a>0 b>0 [Options] tolerance=0.0000000001 stepsize=0.5 iterations=200  Number of Iterations Performed = 31  5. Intermediate  Nonlinear Regression      Thursday, July 24, 2014, 12:56:41 AM   Equation: User-Defined, 2Intermediate f = if(x>0, 1/a*ln(abs(1+a*10*x)), 0)  R  Rsqr  Adj Rsqr  Standard Error of Estimate 0.7293 0.5319 0.5319  3.7668     Coefficient Std. Error t P  a 0.9446 0.0994 9.5045 <0.0001     147  Analysis of Variance:     DF SS MS  Regression 1 1654.0642 1654.0642  Residual 31 439.8462 14.1886  Total 32 2093.9103 65.4347   Corrected for the mean of the observations:   DF SS MS F P  Regression 0 499.8472 (+inf) (+inf) (NAN)  Residual 31 439.8462 14.1886  Total 31 939.6934 30.3127  Statistical Tests:  Normality Test (Shapiro-Wilk)   Failed (P = 0.0008)  W Statistic= 0.8627 Significance Level = 0.0500  Constant Variance Test  Passed (P = 0.4661)  Fit Equation Description: [Variables] x = col(1) y = col(2) reciprocal_y = 1/abs(y) reciprocal_ysquare = 1/y^2 reciprocal_pred = 1/abs(f) reciprocal_predsqr = 1/f^2 'Automatic Initial Parameter Estimate Functions F(q) = ape(ln(abs(x)),y,1,0,1) [Parameters] a = F(0)[2] ''Auto {{previous: 0.944578}} [Equation] 148  f = if(x>0, 1/a*ln(abs(1+a*10*x)), 0) fit f to y ''fit f to y with weight reciprocal_y ''fit f to y with weight reciprocal_ysquare ''fit f to y with weight reciprocal_pred ''fit f to y with weight reciprocal_predsqr [Constraints] [Options] tolerance=0.0000000001 stepsize=1 iterations=200  Number of Iterations Performed = 8   Appendix K: Mass Balance of NOM in a Wasting Passive Membrane System under Continuous Aeration     150   Comparison between Measured and Theoretical NOM Constituents in System Reactor for HMW, HS and LMN over Time for Passive Membrane Filtration under Continuous Aeration and with Daily Wasting  151  Appendix L : Mass Balance of NOM in a Wasting Passive Membrane System under Intermittent Aeration of 25 Minutes off – 5 Minutes On    152   Comparison between Measured and Theoretical NOM Constituents in System Reactor for HMW, HS and LMN over Time for Passive Membrane Filtration under        25 Minutes off-5 Minutes On Aeration Cycles and with Daily Wasting  153  Appendix M : Mass Balance of NOM in a Wasting Passive Membrane System under Intermittent Aeration of 4 Hours off – 30 Minutes On      154   Comparison between Measured and Theoretical NOM Constituents in System Reactor for HMW, HS and LMN over Time for Passive Membrane Filtration under         4 hours off-30 Minutes On Aeration Cycles and with Daily Wasting 155  Appendix N: Mass Balance of NOM in a Wasting Passive Membrane System under Intermittent Aeration of 4 Hours off – 5 Minutes On     156   Comparison between Measured and Theoretical NOM Constituents in System Reactor for HMW, HS and LMN over Time for Passive Membrane Filtration under          4 hours off-5 Minutes On Aeration Cycles and Daily Wasting   157  Appendix O: Mass Balance of NOM in a Wasting Passive Membrane System under No Aeration     158   Comparison between Measured and Theoretical NOM Constituents in System Reactor for HMW, HS and LMN over Time for Passive Membrane Filtration without Aeration and with Daily Wasting   159  Appendix P: Mass Balance of NOM in a Non-Wasting Passive Membrane System without Backwash     160     Comparison between Measured and Theoretical NOM Constituents in System Reactor for HMW, HS and LMN over Time for Constant Low-Flux without Backwash and without Wasting161  Appendix Q: Mass Balance of NOM in a Non-Wasting Passive Membrane System with Backwash     162   Comparison between Measured and Theoretical NOM Constituents in System Reactor for HMW, HS and LMN over Time for Constant Low-Flux with Backwash and without Wasting 

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