İçme suyu filtrasyonunda geri yıkama hızına ve yatak genleşmesine etkiyen faktörlerin araştırılması

Abstract

ÖZET Bu çalışmada, içme suyu tekniğinde kullanılan filtrele rin geri yıkanması ile ilgili hız ifadeleri araştırılmış ve boyut itibariyle dereceli veya uniform filtre malzemesine uy gulanabilen yatak genleşmesini veren matematik bir model ge liştirilmiştir. Birinci bölümde Çevre Mühendisliğinde filtrasyon olayına genel bir giriş yapılmış ve filtrelerin geri yıkanmasında mey dana gelen yatak genleşmesine ait daha önce verilen amprik, ya rı teorik ve teorik modeller ele alınmıştır. İkinci bölümde filtre malzemesine ait tane karekteristik- ler i incelenmiş, taneye ait eşdeğer çap ve benzeri büyüklükle rin tespiti için lüzumlu bağıntılar verilmiştir. Ayrıca tane biçiminin fonksiyonu olan şekil faktörünün ölçülmesi ile ilgi li dolaylı ve dolaysız metodlar ele alınmıştır. Üçüncü bölümde flüdize olmuş bir yatağın karekteristikle- rini belirten ifadeler ve geri yıkama hızını poroziteye bağla yan bağıntının en genel denklemleri verilmiştir. Dördüncü bölümde filtrelerin geri yıkanması ile ilgili hız ifadeleri geliştirilmiş ve olaya etkiyen çeşitli paramet reler belirlenmiştir. Bu hız denklemlerinden faydalanarak V/K = F(e) şeklinde bir porozite fonksiyonu elde edilmiş, ne ticede çeşitli yatak genleşme katsayıları ortaya konmuştur. Beşinci bölümde boyut itibariyle dereceli veya uniform olan filtrelerde yatak genleşmesinin hesabı için geliştirilen bir matematik model verilmiştir. Altıncı bölümde yapılan deneyler anlatılmış, yedinci bö-. lümde ise geliştirilen modelin deney sonuçları ile karşılaştı rılması ve değerlendirilmesi yapılmıştır. Sekizinci bölümde bu çalışmada elde edilen neticeler özet halinde verilmiştir.

II SUMMARY In this study a new mathematical model has been investi gated for the calculation of expanded bed height of the water filters at various back wash velocities. Although this model is basically for the graded filter media, it can also be used for the uniform sized filter media. Besides this research, different backwash velocity equations have been sought and by the help of these equations different n values, which represent the filter bed expansion coefficient, have been obtained. In the first chapter a brief introduction about the fil ters used in potable water technology and the different expan sion models developed by different researchers have been given This brief introduction covers the function, the type and particle characteristics of the filters. Once the effluent turbidity becomes unacceptable or the total available head loss is used up, filters should be cleaned. In rapid filters this cleaning mechanism is done by applying water alone, air flow followed by water or air and water together. In this research backwashing by water alone was considered. Some of the expansion models given in this chapter are for graded media and some of them are for uniform sized filter media. Table 1.1 represents some of these models in three categories as empirical, theoretical and semi theoretical with their Reynolds number applicability range. In the second chapter the characteristics of filter media particle have been mentioned. The calculation of (dn) equivalent volume particle dia meter, (dft) hydraulically equivalent diameter and (Vs) discrete settling velocity of particle, (Vn) discrete settling velocity of equivalent volume sphere have been given. The calculation of above mentioned parameters are based on the relationship between drag coefficient and particle Reynolds number givenIll for spherical particles. This chapter also covers different formulas given by different investigators about the description of the particle shape. Some researchers called it sphericity and some of them named it as shape factor. The shape factor parameter concept was considered in this study since it is important in backwashing phenomenon. Generally speaking, the techniques for measuring shape can be divided into two groups, namely, direct methods and in direct methods. Direct methods require the individual mea surements of particle dimensions. Indirect methods do not require this type measurement, rather they rely on some non- dimensional property of particle which is based on some sta tistical analysis of a set of particles. In the investigation of expension model which was deve loped in this study, above mentioned d, d^, Vs, Vn parameters and one of the shape factor parameters (DSF) was used. In the third chapter backwashing hydraulic was given. Head loss equation during fluidization phase was considered In this chapter since it was used later in obtaining filter bed expansion coefficients in the fourth chapter. In the fourth chapter different backwash velocity equ ations have been developed as one of the objectives of this research. For this purpose, each of the different head loss equations of the filter bed, and constant head loss equation for the fluidized phase were solved simultaneously. Simul taneous solution of these two type equations resulted backwash velocity equations. The physical and hydraulic parameters which affect^back- washing event were analyzed in the scope of these equations. Using these equations V/K = F(e) type porosity equations were developed for linear and nonlinearIV flow. Once these V/K functions were plotted on a logarithmic scaled graph paper, expansion coefficient n values were obtain ed as the slope of the linear portion of the curve. Some of these n values are the function of Res, particle Reynolds number which is the function of the discrete settling velocity of particle in an infinite medium. These n values were compared with the n values of Richardson and Zaki's, given in Table 1.1 since they are also the function of above men tioned Reynolds number. In the fifth chapter a mathematical model was investi gated for the expansion of graded filter media. For this pur pose two different filter bed expansion coefficients were deve loped. One of these coefficients is the function of Vs/Vn and Res parameters. The other equation is the function of d^/dj^ and Res. These parameters were defined previously. To develope expansion coefficient, n, multiple linear regression method was used. Once these expansion coefficients were available the calculation of expanded bed height of filter at a given back wash velocity was expressed step by step in an order. These steps cover the division of graded filter media Into uniform sized layers, determination of some physical characteristics and Vs, Vn, d^, dn, DSF, Reg, V^ (backwash velocity at poro sity one) parameters and usage of the equations of expansion coefficients and the equations (1.7), (1.30), (5.17), In the sixth chapter results of the experiments performed - about backwashing of two filters have been given. One of these two filters consists of Iowa îîuscatine sand, the other consists of Carbonite filter coal media. Both filter materials were graded and nonspherical. Two groups of experiments were done. First group of experiments comprise the determination of physical characte ristics of filter media such as sieve analysis, particle size determination in different ways, specific mass of particle, fixed bed porosity, particle settling velocity The ASTM standart Test Method was used for sieve analysis. The specific mass of particle measurement was made by water displacement technique. Fixed bed porosity was measured by column technique.The second group of experiments consist of backwashing of fil ters at different backwash velocities at a constant water tempera ture. During the bed expansions, filter heights and the behaviour of media was measured and observed. The purpose of this second group experiments was to check the validity of the expansion model developed in this study. The last part of this chapter covers the evaluation of the experimental results for both sand and coal material. In the seventh chapter the calculations of filter bed heights at different backwash velocities, by using the model developed in this study, were performed and the results were tabulated. Since these calculations consume too much time a computer programme was written in fortran language to ease them. Calculations indicated that Richardson and Zaki's /J/V±=en equation should be limited within the range of e < 0,9 while applying it. This was supported by different investigators studies. The results of the calculations were compared with the experimental results. The comparision was made in high and in practical expansion range. By the help of these comparisions the mathematical model developed in this study was evaluated. In the eighth chapter, a summary of the conclusions of this thesis have been presented. Some basic results are as follows : - Filter bed expansion coefficient, n, developed based on Ergun's equation is the function of particle size. - Two new filter bed expansion coefficients, n n = `spherical ^h^n** a' n = n,. n (Vo/V_) spherical s nVI were developed with the a = f {Res, (dh/dn)} a'= F {Res, (VS/VD)} exponents. - Iowa Muscatine sand and Carbonite filter coal material were used as filter media in the laboratory during the experiments. Each of these media were backwashed at differant back wash, velocities at a constant temperature. - During the expansion of coal media, which is less dense than sand media, a diffused layer over the concentrate coal media x^as observed. It was realized that if higher backwash velocities were used, than the velocities applied in this study, for the coal bed filter there might be media loss. To prevent this case it is suggested to use coal material with a low uniformity coefficient. - The suggested expansion model gave good results when compared with experimental results, especially within the practical application range. Appendixes contains computer programmes, graphs and tables.