Water catching systems optimization from depth wells.

Alexandrescu, Aurora ; Milos, Teodor

1. INTRODUCTION

Profitability of water distribution activity depends largely on the relationships between operational capability and service costs, related to supplier's performance, volume of distributed water and effective operating costs, (Alexandrescu et. al., 2008a). The main variables that influence the total selling price are required investment value, specific consumption of electrical energy for pumping power, unit price of the electrical energy and total volume of monthly consumed water billed. The selection of rehabilitation and modernization measures must rely on market studies results that appropriately establish the quantities of water that may be distributed and billed. Present and future water requirements will be determined based on the analysis of actual operation data and on estimation of future trends in water consumption on national and international levels.

Operational efficiency for a pumping supply system at deep well is determined by the type of pump used. Best performances are obtained when, so that user's needs to be met, submersible pumps are set to operate at ratings located in the neighbourhood of their maximal efficiency which at its turn must have optimal values for the best machines located in the respective class. A case met frequent practice is the collecting front of the phreatic aquiferous from major riverbed of water--course, materialized in the shape of a battery of wells with the specific features identical. The optimization calculation will use two target functions: total maximum efficiency and total electric power consumption required for transport of each cubic meter of supplied water, and cubic meter of sewage water, respectively, (Alexandrescu et al., 2008c). The optimization process will take into account that the profitability of water distribution activity depends on the relationship between supply capability and operating costs. Therefore, the process depends on the volume of required investment, on the specific consumption electrical power for pumping, on the price of electricity, as well as on the volume of water billed on a monthly basis.

It is obtaining the equivalent hydraulic resistance modulus adequate to the different configurations of exploitation of the wells battery [K.sub.gk], k = 1,2, ..., n and of the front--tank--pumping station ensemble (in the case of front collecting with two branches coupled on same coupling) rolling the personal programme of calculus in MATHCAD. It is building the specific features of load equivalent of the battery of wells in different configurations of exploitation with k active drilling ([K.sub.go] and [alpha] are coefficients):

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1)

Using the programme MATHCAD are established the following parameters:

--Pumping debit of active wells ensemble:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (2)

--The load in the knot n, j - 1, respective at the coupling of pump:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (3)

--The load in the section of confluence of the collecting piping front's branch, (Klarbring et al., 2005):

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (4)

--The average debit pumped from each active well:

q(n, [Z.sub.i]) = Q(n, [Z.sub.i])/[n.sub.0]. (5)

--Load damage on portion of pipe j-1, j):

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (6)

--Load damage on the communication ([P.sub.k]-k), (Shun & Lee, 2002):

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (7)

It is used the following notations: hydraulic resistance modulus of the repression communication, [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]; hydraulic resistance modulus of the portion of pipes between well's branching, [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]; hydraulic resistance modulus of the confluences: on the side branch, [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]; on the principal branch (collector), [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]; hydraulic resistance modulus of the bundle portion of pipe (nO), [M.sub.rleg] ; aquiferous's hydrodynamic level, [Z.sub.i]; energetic level in the going out section of collector, [Z.sub.p].

The optimization problem consists in the finding of the values for the functional parameters of the pumping station, what establish a minimum yearly average total specific consumption. It must found those values of the parameters D, L, n what lead at the objective function's minimum, namely at the economic function's minimum CE(D, n). The objective function of the optimization problem CE represents the annual average specific consumption total of energy generated by the water's transport with the pipes under pressure, (MW/year), (Alexandrescu et al., 2008b), and has the following mathematical relation:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (8)

It is used the following notations in relation (8): [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]--investment in pumping station; k--equivalent absolute rugosity of pipe; n--revolution of pump; [W.sub.o]--water volume drawn of source; [p.sub.o]--unitary cost; [alpha]--ccoefficient that takes into account the load state; [gamma]--constant of hydraulic slope; [a.sub.p]"--yearly average expenses quota in pumping station, [a.sub.R]"--yearly average expenses quota in pipe, [T.sub.r]--is the duration normalized of existence r component, (Burns, 2006):

2. EXPERIMENTAL RESULTS

It is propose an analyse method based on the hydraulic system's mathematical shaping; the method is used in drainages catching Timisesti for drinkable water. This hydraulic system feeds with water Iasi city, from Romania. Using the personal programs in MATHCAD are calculated the loads in the knot k, [H.sub.k] and the loads at the coupling of repression [H.sub.pk] ; also are estimated for each active pump the effective debit pumped [Q.sub.pk], the pump's output [[eta].sub.pk] and the power demanded at the pump's shaft [N.sub.pk], (Klarbring et.al., 2005). Figure 1 shows the variation of the economic efficiency of investment depending on time for rehabilitation hydraulic systems Timisesti, after optimization. The symbols utilized are following: I--necessary investment for installation rehabilitation; r--monthly average rate for updating; [u.sub.e] (-) actualisation coefficient; t (month) recovery time of investment; [p.sub.e] ([euro]/kWh)--electric energy unit cost.

[FIGURE 1 OMITTED]

3. CONCLUSIONS

The loads under that work the pumps differ from a well at another; the debit, the output and the specific consumption of energy vary depending on the position of well in system, because of the load damage registered between the collector's knots and of local hydraulic resistance's variation at confluences (Douglass, 2004).

The results obtained through the method's application proposed in the front's case of collecting piping 1 Timisesti, harmonizes very good with the dates obtained through the measurements effected in arrangement.

The deviation from the optimum parameter's values leads at the growth adequate of the operational consumption of energy for pumping. These growths depend by the relative deviation given the optimum parameters considered and the influence what it presents about total consumptions. Such deviations are justified if the growth of the total specific consumptions of energy generated by the supply of water is compensated of a reduction of the total specific consumptions of energy associated to the substructure in that is framing the supplies with water studied.

4. ACKNOWLEDGMENT

The authors wish to thank the National Centre of Management Programmers for their support, financial contract 21-041/2007.

5. REFERENCES

Alexandrescu, A., Alexandrescu, S., A. & Alexandrescu, C., A., (2008a). Contribution as for the Optimization of the Pumping Stations, Proceedings Of International Conference On Computational & Experimental Engineering & Sciences, Icces0820071216415, Tech Science Press, Vol. 415, No. 1, pp. 1-11, ISBN 10:0- 9717880-5-7; 17-22 March 2008, Honolulu, Hawaii, USA

Alexandrescu, A., Alexandrescu, S. A. & Alexandrescu, C. A. (2008b). Contributions Regards the Optimization of the Hydraulic Systems for the Reduction of Energy Consumption, Journal International Scientific Publications Materials, Methods and Technology, Vol. 1, Part. 1, Published by INFO INVEST, ISSN 1313-2539, pp. 24-33, ISSN 1313-2539, 3-6 June, Sunny Beach Resort, Bulgaria

Alexandrescu, A., Alexandrescu, S. A. & Alexandrescu, C. A. (2008c). Contributions Concerning the Power Optimization of the Pumping Stations, The American Society of Mechanical Engineers Proceedings of 11th International Symposium on Advances in Numerical Modeling of Aerodynamics and Hydrodynamics in Turbomachinery, FEDSM2008-55007, 10-14 August 2008, Jacksonville, Florida, USA

Burns, M., Cottage Water Systems: An out--of--the City. Guide to Pumps, Plumbing Water, Purification and Privies, Hardcover, SUA, 2006

Douglass, H. M., Conduit Fluid Flow, Bloomington, IN, Ed. Mc Graw--Hill Science / Engineering / Math, USA, 2004

Klarbring, A., Petersson, J. & Torstenfelt, B., Karlsson, Topology optimization of networks, Computer Methods in Applied Mechanics and Engineering, Vol 192, Issue 35-36, S.U.A., pp. 3909-3932, 2005

Shun D. L., Lee C. C., 2002, Water and Wastewater Calculations Manual, Ed. Mc Graw--Hill Professional, New York, USA