Data Envelopment Analysis for Assessing Optimal Operation of Ultra-Filtration Systems for Effluent Polishing Bick Amos, Ben-Gurion University of The Negev, The Department of Industrial Engineering and Management, Beer-Sheva, 84105, Israel. E-mail:
[email protected]. Tel: +972-3-623-0631; Fax: +972-3-623-0672 Oron Gideon, Ben-Gurion University of The Negev, The Institute for Desert Research, Kiryat Sde-Boker, 84990, The Department of Industrial Engineering and Management, Beer-Sheva, 84105, and The Grand Water Research Institute, Technion Haifa, 32000 Israel. E-mail:
[email protected], Tel: +972-8-659-6900; Fax: +972-8-659-6909 Gillerman Leonid, Ben-Gurion University of The Negev, The Institute for Desert Research, Kiryat Sde-Boker, 84990, Israel. E-mail:
[email protected], Tel: +972-8-659-6907; Fax: +972-8-659-6909 Manor Yossi, Central Virology Laboratory, Sheba Medical Center, Tel-HaShomer, 52621, Israel. E-mail:
[email protected], Tel: +972-3-5303063 ABSTRACT The scarcity of fresh water in most of the countries in the Mediterranean Basin makes treated wastewater a valuable alternative water source. The improved technology for the removal of particles, turbidity, bacteria and cysts from effluent, without the use of disinfectants is based on the use of membranes, mainly on Micro-Filtration (MF) and UltraFiltration (UF). Membrane treatment of secondary effluent sounds attractive since it is a stable water source. Pathogens, soluble organic maters, turbidity, color, parasites and viruses can be removed by UF membrane technology. Experiments are in progress in the commercial fields of Gadash Har Hebron Enterprise (GHHE), located near the City of Arad, Israel. Field data collected from a two-stage UF pilot plant (240m3/day) enables to provide performance estimates efficiencies based on the Data Envelopment Analysis (DEA) method. The research focused on individual UF experiments allowing determining the UF performance efficiency in terms of information quality for adequate decision-making. Field results are presented in order to support the theory and related pricing decisions. Keywords: Data Envelopment Analysis (DEA); Effluent Polishing; Membranes; Optimization; Ultra-Filtration INTRODUCTION Spiraling demand for high quality water, coupled with natural shortage, mainly due to intensive exploitation of groundwater from aquifers and continuous reduction in supply, primarily in arid zones, has stimulated the search for alternative sources and improved water treatment methods (Oron et al., 1995; Oron, 1996b). The gap between supply and demand can be primarily closed by implementing two major strategic directions: (i) to import water from external sources, and; (ii) to further develop extra water sources - and under specific conditions to treat the water to acceptable levels (Oron et al., 1996). Potential advanced water treatment includes the use of membrane technology (Bick et al.,
1996; Bick and Oron, 2001), primarily for saline and seawater. However, membranes can also be used for wastewater treatment. Membrane treatment of effluent sounds attractive since it is a stable water source. Brine disposal is of serious concern due to potential environmental nuisances (Mickley, 2001). Effluent treatment has attracted a great deal of attention last decade (Oron et al., 1998). The improved technology for the removal of particles, turbidity, bacteria and cysts, without disinfection is based on the use of membranes, mainly Micro-Filtration (MF) and UltraFiltration (UF) (Oron et al., 1997). The advantages of MF or UF for organic matter removal with selected salt removal by Reverse Osmosis (RO) membranes turn integrated systems into promising processes (Bick and Oron, 2000). Pilot plant studies are in progress in the commercial fields of Gadash Har Hebron Enterprise (GHHE), located near the City of Arad, Israel. Besides providing reliable and quality consistent reclaimed effluent suitable for unrestricted agricultural irrigation the objectives of this study are three folds: (i) to gain more insight into membrane performance and related issues by using practical methodological tools, (ii) to evaluate the technical efficiencies of the sole process of the integrated system using standard operational research analysis, and; (iii), to generate operating data which will be implemented to analyze the performance of the UF component. THE CROSS-FLOW UF MODEL Membrane filtration can be maintained with two main flow regimes: Dead-End and CrossFlow. Conventional Dead-End filtration methods operate with the feed flow in the same direction as the permeate flow (i.e. into the filtration media). The Cross-Flow principal uses shear forces generated by flow across the membrane. While Cross-Flow filtration does not completely eliminate the particle boundary layer, it does lead to higher flow rates. Other advantages of Cross-Flow filtration include (i) continuous operation, and; (ii) less frequent membrane cleaning. Most Cross-Flow models vary in their degree of complexity. The simplest and most common one is based on the driving force. The driving force of the membrane process is described by the Trans-Membrane Pressure (TMP, bar). The TMP variable is defined as the pressure difference between the retentive and the permeate side (Jacangelo et al., 1994): TMP = [(Pin + Pout)/2] - Pp
(1)
where Pin is the inlet or feed pressure, Pout is the outlet or the brine pressure, and Pp is the permeate pressures, all given in bars. The relationship between the flux and the membrane resistance is given by the following equation (Jacangelo et al., 1994): J = K ּ TMP
(2)
where J is the permeate flux, L/(hour-m2) and K is the permeability coefficient, L/(hour-m2bar). Permeate flux is intensified along with increase in TMP. However, this linearity dependence holds only when the feed is pure water: For low quality waters such as effluent and surface-water, the flux depends also on the fouling tendency of the incoming water (ASTM D5090, 2001). For further flux calibration temperature corrections to 20C
are made according to equation (3). This modification is based on the dependence of water viscosity on the temperature (Jacangelo et al., 1994):
J n (Qpu f e- 0.0239 (T - 20) )/Auf
(3)
where Jn is the normalized permeate flux (at 20C), L/(hour-m2); Qpuf is the UF permeate flow rate, L/hour; T is actual operating temperature, C, and, Auf is the UF membrane surface area, m2. Subject to the above expressions it can be concluded that the Cross-Flow UF model has several drawbacks: (i) The quantitative expressions do not account for the water quality, membrane characteristics and fouling processes, and; (ii) there are incomplete explanations for the heavy metal removal and polymer injection into the UF system (Bohdziewicz, 2000). MANAGEMENT MODELING AND DATA ENVELOPMENT ANALYSIS General Management modeling provides effective means of rapidly testing and evaluating different scenarios for a given system operated under various conditions. Well-defined models allow examination diverse hypothetical situations, which yield perceptive insight of the analyzed phenomena. The various aspects of UF systems can be viewed at the following levels: (i) the local level of the isolated process- economic, chemical, microbial and membrane performance criteria (Bick et al., 2001a; Bick et al., 2001b), and; (ii) at the regional level of water sources utilization, including membrane technology issues (Oron, 1996a). At this level, UF membrane performance is only one link in a multi-component system. Other phases to be considered in management modeling include environmental considerations, disposal of concentrates, regulatory and risk issues (Van Ginneken and Oron, 2000; Mickley, 2001). Data Envelopment Analysis Data Envelopment Analysis (DEA) was first introduced as a general method for classifying a population of observations and was designed as a decision support tool for business management (Charnes et al., 1978). It is an empirically based methodology and the research approach has been found to be effective in the depiction and analysis of complex systems, where a large number of mutual interacting variables are involved. According to DEA, efficiency is defined as the ratio between outputs of the system and inputs where it is imperative to consider multiple inputs and outputs (Partangel, 1999). The DEA method differs from other decision supporting methods that it does not focus on the complete data set, but rather on individual Decision-Making Units (DMU). These DMU use a variety of identical inputs to produce a variety of identical output. It can be assumed that there is data available for n DMUs' (UF plants: j=1,2…,n). In order to find the efficiency of a specific k UF plant, the following optimization problem has to be solved (Fraser and Cordina, 1999): R
m
r 1
i 1
Max ( α r y rk / βi x ik )
k 1,2..., K
(4)
subject to a series of constraints given by: R
m
r 1
i 1
( α r y rj / βi x ij ) 1
α r 0 βi 0
j 1,2..., n
(5)
r 1,2..., R i 1,2..., m
(6)
where yrj is output of the r water quality parameter of the j monitored entity (pilot unit or sampling time of one system), xij is the input of the i quality parameter (it is common that i≠j), R is the number of output types (water quality parameters), m is the number of input types (water quality parameters), r is a decision variable related to a weight factor of quality parameter r for the k unit, and similarly i is a decision variable related to the weight factor of the water quality parameter i for the k tested unit. The purpose of the objective function is to maximize the ratio of the weighted outputs vs. the weighted inputs for the DMU under consideration. The optimum is found subject to the condition that the ratio for all DMUs’ will be less than or equal to one [Equation (9)]. It is complicate to solve the above model and in order to avoid infinite number of solutions m
β x
the constraint
i
i 1
ik
1 [Equation (9)] can be imposed by a Linear Programming (LP)
formulation for the k unit and the objective function F(Fraser and Cordina, 1999): R
Max F α r y rk
k 1,2..., K
(7)
r 1
subject to R
m
r 1
i 1
α r yrj - βi x ij 0 m
β i 1
i
x ik 1
α r 0 βi 0
j 1,2..., n k 1,2..., K r 1,2..., R i 1,2..., m
(8) (9) (10)
Alternatively, the DEA model can be described by using the dual LP formulation (Fraser and Cordina, 1999): Min Z k subject to n
y j 1
rj
λ j y rk 0 n
z k x ik x ij λ j 0
k 1,2..., K
(11)
k 1,2..., K r 1,2...R
(12)
k 1,2..., K i 1,2..., m
(13)
j 1
λj 0
j 1,2..., n
(14)
where Zk is expressing the Technical Efficiency (TE) of the k DMU unit having a value between zero and one (scalar). When Zk is equal to one, the DMU is on the frontier and is technically efficient. If Zk
