Property based management and optimization of water usage and discharge in industrial facilities Arwa Rabie and Mahmoud El-Halwagi

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1 Property based management and optimization of water usage and discharge in industrial facilities Arwa Rabie and Mahmoud El-Halwagi Department of Chemical Engineering, Texas A&M University

2 Outline Motivation Problem Scope Literature Survey Problem Statement &Representation ovel Approach Case Study Conclusions 2

3 Motivating Example Fresh chips Digester white liquor white liquor clarifier causticizer pulp weak cond. black liquor mud washer Brown Stock Washing wash water grits Multiple Effect Evaporators mud filter wash water lime mud lime kiln slaker screening Flue gas BleachingWater agents Bleaching Wastewater Fresh Fibers concentrator salt cake cond. SBL weak white liquor wash water Process Paper Fibers Machine I dregs washer & filter Water Paper Machine II Recovery Boiler dust recycle dregs Hydro- Pulper smelt Paper Product I Hydro- Sieve Paper Product II ESP Flue Gas Broke Wastewater Wastewater dissolving tank green liquor clarifier 3

4 Motivation Industrial facilities significantly use fresh water and discharge wastewater Growing public concern as well as environmental regulations Conservation of resources Enhanced market competitiveness 4

5 Problem Scope Given: a batch process with a number of water sources whose composition and flow rate vary over time sinks whose water demand and maximum admissible composition vary over time Objectives: Develop a systematic procedure to Synthesize an optimal batch water network Schedule an operating network of a minimum total annualized cost while meeting all process constraints 5

6 Examples of Previous Literature Wang and Smith(995), Majozi (2005) Graphical method limited to mass transfer based utilities Limited to single contaminant systems Used storage tanks Water sources were not recycled to lower concentration utilities or in previous times of the cycle. Foo, Manan& Tan(2005)-Water Cascade Analysis Graphical method for non-mass transfer based utilities Limited to single contaminant systems Water sources were not recycled to utilities that required water in previous times of the cycle. Mixing of water sources at different impurities in the same tank was not allowed 6

7 Examples of Previous Literature Kim and Smith(2004), Majozi(2005a),Majozi(2005b) Mathematical formulation limited to mass transfer based water units Limited to single contaminant systems Used storage tanks Water sources were not recycled to utilities that required water in previous times of the cycle. Chang & Li(2006) Mathematical formulation not limited to mass transfer based water units Used storage tanks Water sources were not recycled to utilities that required water in previous times of the cycle. 7

8 Limitations of Previous Work One of more of the following limitations: Recycle within the same cycle: water recycle is limited to units that require water later in the same cycle Lumped usage of water over a cycle: this assumption accounts for a total quantity and quality of water supply The objective of minimizing fresh water usage: it is important to consider an objective dealing with fixed cost in addition of operating cost. Lack of global solution procedure 8

9 Lumped usage of water Composition y II Z y I Source I Quantity W I Source II Quantity W II Sink Demand Quantity = W I +W II t t 2 t 3 t 4 t 5 t 6 time Gj = W I + W II Z max Wy I I + Wy II = W+ W I II II 9

10 Problem Statement During a batch cycle (τ) of a given batch process there is a number of: -Sources; process streams impurity concentration of y v, u (t) flow of w v (t) 0 t τ -Sinks; process units that are in need of water maximum inlet impurity composition z s,u (t) flow rate requirement g s (t) 0 t τ Available for service are: -Tanks; used for water storage and dispatch -Fresh water streams Impurity composition x r cost of C r 0

11 Optimization Formulation Dynamic variation of sources and sinks Synthesis: umerous source and sink constraints Tanks selection and assignment Scheduling: When to store sources and when to dispatch them to sinks

12 Mathematical programming approach Characteristics and Features: Mathematical programs can tackle complex systems eed to handle multiple sources eed to handle multiple sink requirements eed to incorporate storage and dispatch tanks 2

13 ovel Approach Reformulate sources and sinks into discrete events Determine target for minimum usage of fresh water and minimum waste water discharge Synthesize a direct-recycle water network using storage and dispatch tanks to achieve the water target Schedule an optimum operating scheme to achieve the target Use insight to further simplify network design Tradeoff water usage, discharge, fixed and operating costs to obtain minimum TAC 3

14 Source Reformulation During a batch cycle τ, the profile for both w v (t) and y v,u (t) are known (0 t τ). Wi = w ( t dt t t q q v ) wv(t) Source water flow profile time (hr) Source compositon profile Y i, u = t t q q w v t y ( ) v, u W i ( t ) dt yv,u(t) time (hr) 4

15 Sink Reformulation During a batch cycle τ, the profile for both g s (t) and z s, u (t) are known (0 t τ). t p Gj = gs( t) dt t p gs(t) Inlet water requirment Time (hr) Maximum Inlet Compostion max t p z j, u = t p g s ( t) z G max s, u j ( t) dt zs,u (t) Time(hr) 5

16 Water Recycle etwork Representation Sources Storage & Dispatch Tanks Sinks Waste Fresh Availability and demand are not concurrent. Assumption: two sets of tanks will be used one for storage and one for dispatch 6

17 Targeting Mathematical Formulation Minimize Fresh r= j = sin ks C r f r, j Subject to: Splitting of Sources W i Sinks = w j= i, j + w i, waste i=, 2,,Sources Waste flow Waste = Sources w i, waste i= Sink Balances G j = i= + Sources Fresh w i, j r= f r, j j=, 2,,Sinks G Z Z j Sources Fresh j, u = wi, jyi, u + i= r= Z max j, u j, u f r, j x r, u j=,2,,sinks and u=,2,,components j=,2,,sinks and u=,2,,components 7

18 Minimize Subject to: I T k Synthesis & Scheduling Mathematical Formulation k k = Tanks k = 2 k I {0,} U k I k k Splitting of Sources W i Tanks = k = w i, k + w i, waste i=,2,,sources Storage Tank Balances T = Sources T k w i k y i = Tank k, u = i= Sources w sin i, k ks j =, k Y T k = t i, u k, j k=,2,,tanks k=,2,,tanks and u=,2,,components k=,2,,tanks 8

19 Synthesis & Scheduling Formulation Continued Waste Flow Waste = sources w i, waste i= Sink Balances G j = k= + Tanks Fresh t k, j r= f r, j j=,2,,sinks G j Z Tanks Tank j, u = tk, j yk, u + k = r= Fresh f r, j x r, u j=,2,,sinks and u=,2,,components Z Z max j, u j, u j=,2,,sinks and u=,2,,components Operating Cost Constraint Fresh r = sin ks j = C r f r, j = Cost 9

20 Approach 20

21 Batch water network Case Study 2 process sources 2 sinks contaminant present in water from sources fresh water stream -x r =0 -cost: $0.2/kg Available tanks -cost: $000/m^3 -instillation cost: $,000 per tank -yearly maintenance: $500 per tank Batch cycle = 8 hours 2

22 Case Study Source Hour Yi Wi (kg) Sink Hour Zjmax Gj (kg)

23 Y=.05 W=20 kg Hour:5-6 Sources Solution to Case Study 20 kg Tanks T=20 kg y= T2=20 kg y2= Sinks Fresh= 50 kg Z=0 G=50kgH our:2 2 Y2=. W2 =30 kg Hour: kg 50 kg 2 Z2= G2=50kg Hour: kg 3 Y3=.85 W3 = 30 kg Hour: kg 40 kg Fresh = 80 kg Waste = 0 kg Minimum TAC = $9,844/year kg Fresh= kg Fresh= kg 3 Z3=.4 G3=50kg Hour: 4 Y4=.9 W4= 40 kg Hour:5-6 Using procedures developed in the past Fresh=00 kg Waste = 20 kg TAC = $24,443 4 Z4= G4=50kg Hour:8 23

24 Conclusion Developed a systematic procedure to synthesize and schedule a batch water network Properly discretized batch cycle into meaningful events Targeting of water usage and discharge ahead of synthesis and scheduling Devised an iterative scheme to achieve total minimum annualized cost 24