Modelling of Domestic Hot Water Tank Size for Apartment Buildings

Transcription

1 Modelling of Domestic Hot Water Tank Size for Apartment Buildings L. Bárta Brno University of Technology, Faculty of Civil Engineering, Institute of Building Services, Czech Republic Abstract The properly designed hot water tank should provide water supply at prescribed parameters during operation time within the apartment building at the lowest investment and operation costs. Its size is based on the graph sketch of two timely dependent functions. The first one describes the energy supply into the tank; the second describes the energy (hot water) output from the tank. Especially the second function depends on factors with random character. The paper deals with the analysis of both functions and evaluates their influence on the tank size. Starting basis for solving these problems are real data series picked up from measurements of hot water consumption within apartment buildings. The paper is focused on central domestic hot water supply systems with small outputs of heat resources which supply the number of flats between 32 to 60. There is created the probability model of hot water demand and following application of this model leads towards the determination of the possible usable tank size. Therefore it can be stated that: (a) in the case of continuous heat supply during the whole period (24 hours) the decisive factor for the tank design is the Sunday curve of hot water demand, heat losses do not influence the tank sizing but they have to be compensated by higher output of heat source, (b) in the case of continual heat supply except night hours (17 hours) during which the heat supply is interrupted there is decisive the characteristic curve for working days, currently there is a distinct increase of tank size which rises with heat losses too and which is most remarkable during working days. Keywords Apartment buildings; hot water consumption; analysis; probability model; usable tank capacity.

2 1 Introduction One of the partial tasks of this currently proceeding research within existing central domestic hot water supply systems which prevail in the apartment buildings in the Czech Republic is the optimalization of the capacity of hot water storage tanks. The object of interest is the system which supplies one apartment building, respectively one residential section with the number of flats between 32 to 60. The energy is usually supplied from the district boiler room which is common for more buildings and which is located in a separated building. During night hours the supply is usually interrupted. The boiler room output stipulated only for water heating is divided into particular tanks, so it is limited for a concrete building. The prepared reconstruction of these systems will have to be focused not only to guarantee a reliable and safety-working function but also to achieve the lowest investment and operation costs. It can be said that the research aim is the system keeping the comfort of hot water supply on the present level or aptly on higher level but currently with lower consumption of water and energy. For the hot water tank design there is the decisive factor the time course of energy supply into the tank and the time course of energy consumption (hot water) during the day. The water supply depends on a number of difficultly characterised factors and it has a probability character. In this contribution there is presented the simulation method for the determination of optimal water tank sizing. The probability behaviour of hot water consumption within apartment buildings results from experimental monitoring. 2 The principle of hot water tank sizing For the determination of the hot water tank capacity there can be used a high number of methods starting with empirical procedures which are suitable especially for preliminary projects to exact calculation methods. But the reliability of results depends always on the accuracy of the input data which is valid especially for exact methods. The method which is currently used in the Czech Republic belongs among exact methods. It concerns mostly the numerically-graphical method whose result is the minimal storage of heat (hot water) which is necessary to take into the water tank. This storage of heat is given by the curve of heat supply into the tank and by the curve of heat consumption (hot water) from the tank (Figure 1). The curve of heat supply is the dependency of the heat supply into the tank which depends on the time τ during the period. It is given by the output of heat source and heat supply duration. The curve of heat consumption is the dependency on heat consumption (hot water) from the tank on the time τ during the period. This curve can be determinated by measurements of water consumption, time analyses of water consumption or it is possible to use the standard curve stated in technical standards. This presented method supposing the knowledge of course of heat consumption from the tank and the course of heat supply into the tank this is the basic element for the calculating algorithm.

3 Figure 1 Principle of hot water tank design 3 Heat supply into the tank For the daily heat demand needed for the production of hot water H 1 and daily heat demand taken away from the tank H 2 there must be applied H 1 = H 2 (1) The amount of taken away heat demand we can determinate according the equation H 2 H 2t + H 2l = (2) where H 2t is the heat amount contained in the consumed hot water and E 2l are the heat losses of storage tanks and the distribution system. For the heat H 2t contained in the hot water there is applied the following equation ( t ) H 2 t m c 2 t1 = (3) where m is the demand of hot water during one period (day), c is the specific thermal capacity of water; t 2 is the temperature of hot water and t 1 is the temperature of cold water. In the following solution there is considered with the thermal difference 45 C o. The heat loss H 2l is given by the geometry of the system, thermally-technical properties of distribution and reculciraculation pipes and thermal insulations, thermal parameters of hot water and the environment and the operation time of this system [2]. The heat loss H 2l does not depend on the consumption of hot water. We usually assume that particular quantities which influence the heat losses do not change with the time, therefore the heat loss can be considered as the quantity periodically not dependent. Within present systems which have not suitable insulation completation, these losses can achieve up to 100 % from the value H 2t, after the reparation of the insulation the losses can be up to 30 %.

4 The output of the heat source can be determinated according the equation H1 Q 1 = (4) τ where τ is the total duration of the heat supply within the whole period. Within the 1st research phase there where included these two simplified cases: continual heat supply into the tank during the whole period, continual heat supply into the tank with interruption due to limited operation time for heat source. The cycled tank heating which occurs within these two observed cases will be the focus of the following research phase and therefore it is not presented in this contribution. 4 Analysis of hot water demand 4.1. Results of experimental monitoring The water consumption in apartment buildings depends on many factors among which ranks e.g. the building category, number of users, their professional orientation and age structures of inhabitants, the way of spending their leisure time, seasonal period or technical realization of the system. Due to influence of these factors the consumption of hot water supply can fluctuate within particular buildings, during the course of a week or day. When we compare the consumption of hot water within several apartment buildings we can identify during its periodical distribution the following trends (Figures 2 through 4): during working days there appear the peak consumptions during evening hours, particular peaks can be observed during morning or midday hours, for Saturdays there is typical a peak consumption before the noon and a particular peak in the evening, Sundays are approximately the opposite of Saturdays. These findings result from experimental observations of hot water consumption within several apartment buildings [1]. By these measurements there was moreover found out further: specific consumptions of hot water supply are lower then it is stated in technical standards, coefficients of water consumption variations among particular buildings do not substantially differ, the highest consumption of hot water supply is during the evening period (17:00 23:00) with the exception of non-working days.

5 Figure 2 - Hourly consumptions within working days examples of measurement Figure 3 - Hourly consumptions within Saturdays examples of measurement Figure 4 - Hourly consumptions within Sundays examples of measurement

6 The analysis of hot water supply within apartment buildings requires higher amount of measured data on different types of apartment buildings. The current data basis is the result of continual measurements during one-week and three-week intervals within three different apartment buildings. 4.2 Probability model On the basis of experimentally observed trends in hot water consumption and on the basis of application of probability theory there is created the probability model of hot water demand. By using the computing simulation we can obtain unlimited number of various daily distributions of water demands. The probability behaviour course of curve of the hot water demand in apartment buildings can be defined as follows: hot water demand is divided into n intervals within one period, demand in the interval i is continuous random variable X i at i=1 up to n, each random variable X i has uniform Probability Density Function f i with parameters a i, b i, where P(X i = x i ) = 1/(b i - a i ) for x i ai, bi, note there can be also used another precondition about shape of PDF e.g. Laplace - Gauss, parameters of particular PDF are determinated on the basis m of experimental measurements (records of water consumption in m periods), if the random variable attains X i value from intervals x i, min, xi, max and by sufficient number of experimental measurement realizations, i.e. m>20 then it is possible to get relatively reliable parameter estimations considering PDF f i, then a i = x i, min a b i = x i, max, above described probability behaviour of the demand curve is then consequently used for its computing simulation i.e. for the realization k trials (Figures 5 through 7), following applications of the above described mathematical model lead towards the determination of the continuous random variable Y and its PDF g, i.e. the possible tank size, further we can define the continuous random variable Z i.e. water demand in the period where Z = X X n. 5 Hot water tank modelling 5.1 Variants of solutions The formed mathematical and probability model of hot water demand can be used for modelling the usable tank capacity by using the computing simulation. On the basis of fundamental factors analysis in Sec. 3, 4 which influence the tank volume there is

7 Figure 5 Time distribution of standardized hot water demand working days Figure 6 Time distribution of standardized hot water demand Saturdays Figure 7 Time distribution of standardized hot water demand Sundays

8 defined 6 variations of solutions. The aim is to found out the influence of particular factors on the tank size. Within all variations there is chosen the same period length corresponding to 24 hours and they are divided into hourly intervals. Within particular intervals there is differentiated the length of continuous heat supply, characteristic curve of daily demands for various days and heat losses within the system (Table 1) Table 1 - Solved variations Variation Day Heat supply Resulting solution A1 Continuous (24 hours) Figure 8 Working day A2 Continuous (17 hours) Figure 8 B1 Saturday Continuous (24 hours) Figure 9 B2 Continuous (17 hours) Figure 9 C1 Saturday Continuous (24 hours) Figure 10, 11 C2 Continuous (17 hours) Figure 10 For each variation there were computed 2999 simulations. 5.2 Results and discussion Results of usable tank volume modelling are presented within the graphical outputs (Figures 8 through 11). Histograms in Figures 8 through 10 show the number appearance of random variables Y i.e. possible standardized the tank size within particular calculated variations. Therefore it can be stated that: in the case of continuous heat supply during the whole period (24 hours) the decisive factor for the tank design is the Sunday curve of hot water demand, heat losses do not influence the tank sizing but they have to be compensated by higher output of heat source, in the case of continual heat supply except night hours (17 hours) during which the heat supply is interrupted there is decisive the characteristic curve for working days, currently there is a distinct increase of tank size which rises with heat losses too and which is most remarkable during working days. Figure 11 is example of outputs for the C1 which show the realization number of twodimensional random variable (Y, Z) where the random variable Y is the possibly standardized tank size and the random variable Z is the possibly standardized water demand during the period. It is obvious that to one value of the daily demand is possible to rank to various tank sizes and visa versa. The stated dependency results from the probability behaviour of the input curve of the water demand. The probability behaviour of the random variable Y or the random vector (Y, Z) can be used for the definition of hot water supply comfort as follows: it is possible to require that this system will never fail or

9 Figure 8 Possible tank capacities for working days Figure 9 Possible tank capacities for Saturdays Figure 10 Possible tank capacities for Sundays

10 Figure 11 Possible tank capacities for Sundays variant C1 it can be taken into account a certain percentage of cases at which there will not be achieved the requested parameters of hot water supply (short-time decrease of water temperature). From the probability point of view the above stated comfort of hot water supply can be defined as 100.γ procentual quantile y(γ) (5) of the random variable Y, where 1-γ is the already mentioned probability of the system failure. ( Y y( γ )) = γ P (5) 6 Conclusions At this present research stage the presented probability model is applied for solution of 6 chosen variations which include the cases which are based on probability distribution of hot water demand and the minimal possible output of the heat source. The results prove that the usable tank size depends on the daily hot water demand, daily distribution of hot water demand, duration of heat supply into the tank, output of the heat source and on heat losses of the complete system. Details are described in Sec The next research task will focus on the enlargement of the data basis enabling the higher accuracy of the model and especially on the system modelling for cases of higher output of the heat resources. Acknowledgements Acknowledgements are made to the Ministry of Education of the Czech Republic for the assignment of research project MSM Development of methods of modelling and management water and transport systems whose support allowed for the mentioned research to be realized.

11 7 References 1 Bárta (Ladislav), Experimental Monitoring of Hot Water Supply Systems, 29 th International Symposium Water Supply and Drainage for Buildings CIB W62, (pp ), Ankara (Turkey), September Bárta (Ladislav), Energy Conservation of Domestic Hot Water Distribution Systems, 27 th International Symposium Water Supply and Drainage for Buildings CIB W62, (pp B6/1-B6/10), Portoroz (Slovenia), September Presentation of Author Ladislav Bárta is the assistant professor at the Brno University of Technology, Faculty of Civil Engineering, Institute of Building Services. His specializations are Plumbing Systems and Pumps Systems. Recently he has been concentrated on the field of internal water supply systems especially with the point of view of possible savings within investments and operation costs.