Oct 14, 1996 - problems affecting a diffusion still, as well as possible extensions and improvements which .... unproven method known as multi-effect diffusion. It is the ... An example of the practical application of distillation can be seen below (Figure. 3.1). ... Figure 3.2: Principal of four-effect evaporator (downflow of brine).
ME4516 - Thesis
ANALYSIS OF A MULTI-EFFECT DIFFUSION STILL
Thesis submitted by: Damien Paul Verrall 14 October 1996
In partial fulfilment of the requirements for the Degree of Bachelor of Mechanical Engineering, in the Department of Mechanical Engineering of James Cook University of North Queensland.
DECLARATION Statement on Access to Thesis: I, the undersigned, the author of this thesis, understand that James Cook University of North Queensland will make it available for use within the James Cook University Library and, by microfilm or other photographic means, allow access to users in other approved libraries. All users consulting this thesis will have to sign the following statement: “In consulting this thesis I agree not to copy or closely paraphrase it in whole or in part without the written consent of the author; and to make proper written acknowledgment for any assistance which I have obtained from it.” Beyond this, I do not wish to place any restriction on access to this thesis.
D. P. Verrall 14 October 1996 Statement of Sources: I declare that this thesis is my own work and has not been submitted in any form for another degree or diploma at any University or other institution of tertiary education. Information derived from the published or unpublished work of others has been acknowledged in the text and a list of references is provided.
D. P. Verrall 14 October 1996
Acknowledgments The author wishes to acknowledge the following people for their assistance during the course of this thesis:
Dr Harry Suehrcke, thesis supervisor, for general assistance and guidance throughout the thesis. Mr Warren O’Donnell and Mr Gordon McNealy, workshop technicians, for the construction of the experimental apparatus and continuing assistance with modifications throughout the thesis.
SUMMARY This thesis develops a numerical model of a diffusion still (a type of desalination apparatus). The numerical model is verified with a single stage experimental diffusion still which has been constructed for this purpose. The numerically predicted fresh water output is in good agreement with measured results from the experimental apparatus.
The major parameters affecting still operation are
analysed, and any assumptions have been justified. Also discussed are many of the problems affecting a diffusion still, as well as possible extensions and improvements which can be made.
TABLE OF CONTENTS
1.0
Introduction
... 1
2.0
The Diffusion Still
... 2
2.1
Principal Idea
... 2
2.2
The Still
... 3
3.0
Literature Review
... 5
3.1
Introduction
... 5
3.2
Other Methods of Desalination
... 5
3.2.1 Distillation
... 5
3.2.2 Flash Evaporation
... 8
3.2.3 Vapour Compression
...10
3.2.4 Reverse Osmosis
...11
3.2.5 Direct Freezing
...13
Multiple-Effect Diffusion Stills
...17
3.3
3.3.1 Solar Water Distillation: The Roof Type Still and a Multiple-Effect Diffusion Still
...17
3.3.2 Numerical Prediction of the Performance of Multiple-Effect Diffusion Stills
...19
3.3.3 Experimental Prediction of the Performance of Multiple-Effect Diffusion Stills
...20
3.3.4 Effects of Parametric Conditions on the Performance of an Ideal Diffusion Still
4.0
...21
Modelling
...23
4.1
The Approach of this Thesis
...23
4.2
Mathematical Model
...23
4.2.1 Developing a model
...23
4.2.2 Other equations
...27
4.2.3 Assumptions
...29
Extensions
...30
4.3.1 Multi-Effect Systems
...30
4.3.2 Heating Fluid
...31
4.4
Application
...32
4.5
Sensitivity Analysis
...32
4.5.1 Salt Water Flow Rate
...33
4.5.2 Diffusion Gap Thickness
...33
4.5.3 Pressure Variation
...34
4.5.4 Diluent Gas
...35
4.5.5 Power Variation
...36
4.3
5.0
6.0
7.0
Experiment
...38
5.1
Objective
...38
5.2
Apparatus
...38
5.3
Procedure
...40
5.4
Results
...41
5.5
Error bounds for Numerical Model
...43
5.6
Discussion and Observations
...47
Analysis of Results
...48
6.1
Comparison of Numerical Model with Experimental Results
...48
6.2
Comparison of Numerical Model with Experimental Results from [3]
...49
6.3
Temperature Distribution Along Evaporating Plates
...51
6.4
Minimum Work
...53
Discussion
...55
7.1
Overview
...55
7.2
Practical Considerations
...55
7.3
Future Work
...56
7.4
Minimum Work and the cost of energy
...59
8.0
Conclusions
...61
9.0
References
...62
Appendices
...64
Appendix 1
Scale & Corrosion
...65
Appendix 2
Adjacent Films
...66
Appendix 3
Programs
...69
Appendix 4
Constant Head Tank
...81
Appendix 5
Experimental Program
...85
Appendix 6
Three-Effect Diffusion Still [3]
...89
Appendix 7
Approximate Temperature Distribution of Evaporating Plates
...94
Appendix 8
Minimum Energy
...97
Appendix 9
Photographs and Drawings
...99
Nomenclature (S.I. Units, unless otherwise stated) The following table comprises a list of the principal notations employed in this thesis. Notations not listed are either so well understood as to render mention unnecessary, or are only rarely employed and are explained as introduced. Where occasionally a symbol is employed with more than one meaning, the local context will take precedence:
Area Width Boiling Point Elevation Specific Heat Diffusion gap thickness Emittance of water film Enthalpy Heat of vapourization Conductivity of Air Mass flow rate Mass flow rate of water vapour (kg/(m2.s)) Molecular weight of diluent gas: 28.97 for air, 4.003 for helium Molecular weight of water vapour Vapour pressure of water (MN/m2) Total pressure in the still (MN/m2) Heat transfer by conduction Heat transfer by evaporation Heat transfer by radiation
Heat transfer rate Heat flux Universal gas constant (8314.34 J/(kmol.K)) Stefan-Boltzmann constant (56.7 x 10-9 W/m2.K4) Temperature (absolute temperature unless otherwise stated) Average temperature (e.g., ( T1+T2)/2) Temperature of condensing plate Temperature of fresh water corresponding to the vapour pressure of saltwater Overall heat transfer coefficient Diffusional volume of the diluent gas: 20.1 for air, 2.88 for helium Diffusional volume of the water vapour: 12.70 Distance along evaporating plate Diffusivity of the water vapour in the diffusion gap (m2/s)
Introduction
1.0 Introduction One of the most important ingredients to sustain human life is fresh water. Unfortunately, only about 3% of available water on the planet falls into this category, and with the ever increasing population and industrial explosion, more and more strain is being placed on these resources. That is why the need for methods of desalination (i.e. the process whereby salt water is converted to fresh water) is becoming increasingly important. Currently there are many methods available to achieve water purification, some of which will be described later. However this thesis will investigate an as yet unproven method known as multi-effect diffusion. It is the intention of this work that a valid numerical model of the diffusion still be derived. At present, all available models make too many assumptions which cast doubt upon their applicability, and since none of the models found have been verified by experimental results, this will become the main objective of the following work.
1
The Diffusion Still
2.0 The Diffusion Still 2.1 Principal Idea The diffusion still is an old idea (first analysed by Dunkle in 1961 [1]) which has received little attention by researchers. The main principal behind its operation is the diffusion of vapour between closely spaced films of water. As Figure 2.1 indicates, water running down the inside of a vertical plate is heated from behind. This raises the water temperature, and correspondingly the vapour pressure. Similarly, the opposite plate is cooled thus lowering the film temperature, and hence the vapour pressure.
Figure 2.1: Basic diffusion process
2
The Diffusion Still
The difference in vapour pressures (or more correctly, the vapour pressure gradient) between these films is the driving potential of the process. The rate of this diffusion is calculable from Stefan's law [4]:
where:
Note: The above equation takes into account the mass transport due to diffusion, and generated convective velocity. 2.2 The Still Implementing the above process in a desalination still is extremely simple. Again, by positioning two vertical plates opposite one another, we introduce salt water at the top of the evaporating plate. As it runs down the plate, it is heated from behind causing pure water vapour to diffuse across the gap, and condense on the cooler plate. This simple process can then be extended to have a number of closely spaced vertical plates next to each other, all of which have salt water introduced on one side. In this extended application, the first plate is heated, and the last plate is cooled. Water vapour diffuses from the first plate, and as it condenses on the plate opposite, it releases its heat of condensation. This heat is then used to raise the temperature of the saltwater on the other side of this condensing plate, with the process then repeated until the final plate is reached. Figure 2.2 shows a two-effect system with the intermediate plate reaching a temperature somewhere between that 3
The Diffusion Still
of the evaporating plate and the condensing plate.
Figure 2.2: Two-effect diffusion still
4
Literature Review
3.0 Literature Review 3.1 Introduction There is currently a wealth of material available on methods of desalination, addressing mainly the well established techniques such as multi-stage flash, vapour compression, etc. Multi-effect diffusion stills receive no mention in texts, and very little elsewhere, (i.e. journals, conference reports). During the literature search conducted for this thesis, four articles were located which dealt with multi-effect diffusion stills. Each of these will be examined after a summary of the most common methods of desalination is presented.
3.2 Other Methods of Desalination 3.2.1 Distillation Distillation is the best known and most widely used method for salt water purification. The process requires that sea water is firstly boiled, thus producing water vapour. This vapour is then collected and condensed, therefore releasing pure water. An example of the practical application of distillation can be seen below (Figure 3.1). Sea water enters the evaporator where it is heated through steam coils submerged in the liquid. The heat transferred from the condensing steam causes pure water to vaporise (this is due to the fact that below 300oC, the salts in saline water are far less volatile than the water itself). The water vapour is then transferred 5
Literature Review
to the condenser where it is cooled until it returns to the liquid state. From here it goes to a storage vessel ready for use.
Figure 3.1: Principal of Single-stage distillation [6]
Although the above process is extremely simplistic, there are problems associated with it. For example, as water evaporates, the concentration of the saline solution (brine) increases, thus decreasing the rate of evaporation (i.e. the boiling point of a solution increases with increasing solute). For this reason the brine must be periodically rejected and replaced. Further, there is the problem of regulating the pressure in both the evaporator and the condenser in order to obtain optimum performance. Although these may seem minor, they do produce operational 6
Literature Review
difficulties which must be overcome. It is perhaps obvious that the above process is not very efficient, since all the heat released during condensation is simply lost. For this reason, multiple-effect distillation was developed. In this process, vapours from the first evaporator flow through the steam coils in the second. As the vapours condense, the heat released boils the salt water in the second evaporator. As can be seen below, this process is then repeated until it is no longer beneficial to do so.
Figure 3.2: Principal of four-effect evaporator (downflow of brine). Pressure and boiling temperature decrease from left to right [6].
Multiple-effect distillation is a widely used method of distillation, however in recent years it has been rejected in favour of processes such as flash evaporation and vapour compression.
7
Literature Review
3.2.2 Flash Evaporation Flash evaporation differs from conventional distillation processes in that the heating and evaporation occur in different chambers. As a result, scale formation is minimised, and the process' inherent simplicity enables it to compete financially with other processes. The process works by heating sea water in tubes, which is then transferred to an evaporation chamber. This chamber is maintained at a lower pressure than that prevailing in the tubes. As a result, when the water enters the chamber, vapour simply flashes off the liquid surface. This vapour condenses on the tubes carrying the incoming sea water, thus providing some preheat to the liquid. Heating of the sea water to the final temperature can be achieved through any means, the most common being steam. Figure 3.3(a) represents this basic process.
8
Literature Review
Figure 3.3: Principal of multi-stage flash evaporation [6].
A major problem with the process is its inefficiency. This is shown by the fact that if 7.1% of water initially at 100oC evaporates, the temperature drops to 60oC [6]. This may seem unviable at first, even with the process' simplicity, however the heating requirements can be reduced significantly if the flashing is carried out in multiple stages. Figures 3.3(b) & 3.3(c) illustrates how this is achieved. A typical plant of this kind can contain as many as 30 different stages. In order to increase operational efficiency, plants incorporate various features in an attempt to improve heat economy. For instance, feedwater is often treated with a product known as Hagevap LP (i.e. a composite of polyphosphates and lignin sulphonate). This promotes the formation of a soft sludge of calcium carbonate, 9
Literature Review
rather than scale. The feed is also passed through a deaerator before entering the heater. This releases a large portion of the air and carbon dioxide contained in the water, thus reducing corrosion. Obviously, keeping these elements low maintains the rate of heat transfer approximately constant. The simplicity of multi-stage flash evaporators have seen them become one of the most widely used forms of distillation in the world. Although other processes have comparable or even better production rates, when all things are considered (i.e. simplicity, outlay, maintenance), the multi-stage flash evaporators usually prevail. 3.2.3 Vapour Compression Vapour compression is unique in that the steam it uses as a heat source is actually generated by the process itself. It is a highly efficient process in terms of power consumption, however this must be supplied in the form of high grade available energy (i.e. mechanical work). Obviously this is more difficult to obtain than a simple heat source. The process can be seen in Figure 3.4 where sea water enters the still, preheated by the outgoing brine. The still consists of two separate sections; the first being a vessel to hold the brine, while the second is an area for the steam to condense and transfer its heat to the sea water. Vapour evaporating off the sea water is pressurised by a compressor and recirculated back to the still to transfer its heat while condensing, after which the condensate is collected. The increased pressure of the vapour causes a corresponding rise in boiling point. When condensation occurs, it therefore happens at a temperature higher than the boiling point of the sea water, 10
Literature Review
thus providing a temperature gradient.
Figure 3.4: Principal of the compression still [6].
3.2.4 Reverse Osmosis Reverse osmosis, also known as hyperfiltration, is a process whereby salts are separated from water. It is essentially a filtering process whereby pressure is applied to a salt solution which is trapped by a semipermeable membrane (i.e. a membrane permeable to water but not salt). The pressure forces the water through the membrane while trapping the salt. 11
Literature Review
The term reverse osmosis is derived from a natural process known as osmosis. This is the tendency for liquids of differing concentrations to attempt to equalize with each other. For example, if sea water were separated from fresh water at the same pressure by a semipermeable membrane, diffusion of fresh water into the sea water would occur until external forces (e.g. gravity) balanced this osmotic force. Reverse osmosis is essentially the opposite of this. It requires the diffusion of fresh water from the salt water side into the fresh water reservoir, hence the name.
Figure 3.5: Hyperfiltration through a membrane [6].
12
Literature Review
In order to effect the process in the desired direction, pressure must be exerted on the salt water (Figure 3.5). It must also be taken into account that as fresh water diffuses from the salt water, the concentration of salts increase. This has the effect of increasing the tendency for osmosis, hence a higher pressure must be applied in order to counteract the effect. A major obstacle in the development of reverse osmosis has been the construction of a suitable membrane. The problem has been approached from several directions, two of these being the development of plastic films such as cellulose acetate, and the exploitation of the phenomenon known as the Donnan effect. This Donnan Effect states that when an ion exchange material is in contact with a salt solution, it takes up water in preference to salt. Both types of membranes have extremely high salt rejection rates, however each also have associated problems. The above discussion outlines the way in which reverse osmosis works. It is a relatively simple method, yet its associated problems are not easily overcome. At present the main problem with membranes is their tendency to clog, and hence high downtime due to cleaning or replacement. If this problem can be overcome, reverse osmosis may gain favour over the more widely preferred methods discussed previously. 3.2.5 Direct Freezing Fresh water can be separated from salt solutions in more ways than just evaporation. Freezing salt solutions produces ice crystals which are essentially salt free. Although ice is harder to handle than liquids or vapours, advantages exist in the fact 13
Literature Review
that the low operating temperatures greatly reduce scale and corrosion, and the latent heat of freezing is less than that of vapourization. One method for salt water purification which utilises the above principle is direct freezing (or the Zarchin process). Precooled sea water (cooled by the exiting products) enters a freezing tower (crystallizer) where the pressure is kept at about 0.005 atmospheric. Liquid evaporates off the surface and is continually drawn away by a compressor, never allowing an equilibrium to be reached. This vapour carries heat from the remaining liquid, therefore causing the salt solution to cool and eventually freeze. For each kilogram of vapour drawn from the chamber, the heat it carries can produce 7.5 kilogram of ice.
14
Literature Review
Figure 3.6: Ice-slurry counterflow washer [6].
The pure ice exists in a slush, with brine filling the space between the crystals. This is removed through countercurrent washing techniques, an example of which can be seen in Figure 3.6. The slurry enters through an inlet in the bottom of a chamber (known as a washer-melter). It then rises until it reaches brine discharge screens in the sides of the vessel. These let the liquid brine exit, while trapping the ice which continues to rise. Fresh water is then fed from the top, washing the ice of remaining salt, before also leaving through the screens. The ice is then harvested by exposing it to the hot water vapour collected from the crystallizer. The vapour melts the ice 15
Literature Review
to water, while itself changing phase and becoming liquid once more. The entire process can be seen in Figure 3.7.
Figure 3.7: Block diagram of direct freezing process with vapour compression [6].
A slight problem exists with the above process in that the compressor which draws vapour from the crystallizer and forces it into the washer-melter actually heats the vapour. This means that too much heat is provided to the ice harvester. If this happens, problems can be encountered in that the ice melts to well above 0oC. The associated vapour pressure at this temperature creates a large pressure differential between the melter and the crystallizer, thus creating problems. For this reason, an auxiliary refrigerator is required in the crystallizer to offset this heat gain. The above has described the way in which direct freezing to desalinate water is achieved. Although not the only method which uses refrigeration for desalination, it is perhaps best representative of how freezing can be used. 16
Literature Review
3.3 Multiple-Effect Diffusion Stills 3.3.1 Solar Water Distillation: The Roof Type Still and a Multiple Effect Diffusion Still This thesis came about, essentially because of an article presented in 1961 by R.V. Dunkle of the CSIRO, who had been working on a desalination still which took advantage of the natural diffusion process described earlier (Section 2.1). The still consists of vertical plates spaced closely within an enclosed gas filled chamber (Figure 3.8). Impure water is introduced at the top of one side of each plate. As it runs down the surface, it is heated from the other side causing a rise in temperature, which causes a corresponding rise in vapour pressure. Assuming for the moment the surface of the plate opposite is at a lower vapour pressure, water will evaporate and diffuse across the gap, condensing on the cooler plate. The heat of condensation of this now purified water provides the heat necessary for the next set of plates.
17
Literature Review
Figure 3.8: Sketch of multi-effect diffusion still [1].
According to Dunkle, the advantages of this still are as follows: 1. The still operates at relatively low temperatures, i.e. 55oC to 70oC, thus reducing scale formation (Appendix 1). 2. Use of an inert diluent gas of low molecular weight (e.g. Hydrogen or Helium), serves to increase the mass transfer rate, and reduce corrosion. 3. The system can be arranged so all flow is by gravity. 4. By using a multiple effect system, the amount of heat per kilogram of distillate is reduced. 18
Literature Review
Dunkle presented the major equations and relationships necessary for analysing the still, however didn't go into detail as to the solution scheme, nor any simplifying assumptions which may have been made. As such it is difficult to predict how applicable the theoretical results are. Although a comparison of theoretical results to experimental results was presented, the true variance between the two could not be determined due to problems with the experimental apparatus. 3.3.2 Numerical Prediction Of The Performance Of Multi-Effect Diffusion Stills Since Dunkle's work in 1961 there appears to have been little attention given to the Multiple-Effect Diffusion Still. The next article found during the literary search which addresses this process was published in 1983 by researchers at King Abdulaziz University in Saudi Arabia [2], and was titled "Numerical Prediction Of the Performance Of Multi-Effect Diffusion Stills". The article presents a numerical analysis of the multiple-effect diffusion still, predicting such variables as distillate output, temperature distribution along the evaporating plate, and performance ratio. It gives an analysis at high and low feed rates, and predicts how these affect still output. The paper outlines and derives the main equations, and also states the assumptions made along the way, however there is still some ambiguity concerning the final solution. This comes from the fact that the effect of radiation seems to have been neglected, along with the vapour pressure depression caused by salt in solution. It is not stated if these have been neglected because they are insignificant, or for some other reason. The authors present the article as a reference for designers of multiple-effect 19
Literature Review
diffusion stills, and in this capacity (i.e. giving an idea of quantities, and important variables to be dealt with), the paper appears satisfactory. 3.3.3 Experimental Prediction Of The Performance Of Multiple-Effect Diffusion Stills The third article [3] was carried out by the same group of investigators from Section 3.3.2, and is titled "Experimental Prediction of the Performance of Multiple-Effect Diffusion Stills". The paper examines a three-effect diffusion Still with given initial conditions. The experimenters observed the output conditions of the still at two different feed rates after steady state, and drew the following conclusions. 1.
Intermediate plates have a linear temperature gradient where the
temperature increases with the distance along the plates, measured from the top. 2.
Increasing the feed rate to the still, decreases intermediate plate
temperatures and thus still output. The best output attained from this experimental apparatus was 1.08 kg/m2.hr for a feed of 9 kg/m2.hr. This corresponds to a ratio of 0.12 for distillate to feedrate which seems low when other methods of distillation operate at ratios of 0.5.
20
Literature Review
3.3.4 Effects of Parametric Conditions on the Performance of an Ideal Diffusion Still Article Four [4], is titled "Effects of Parametric Conditions on the Performance of an Ideal Diffusion Still", and was carried out by Moustafa M. Elsayed of King Abdulaziz University. The equations governing the behaviour of the still are derived and the effect of certain parametric conditions are examined, these being: 1. The ambient temperature 2. Solar irradiation 3. Thickness of the diffusion gap 4. The kind of diluent gas, and 5. The average emittance of the water absorber in the still. As is evident from parametric conditions 1& 2, the still in question is solar operated, and as such, only variables 3, 4 & 5 are of interest to this thesis. Parametric condition 3 is found (not surprisingly) to have a significant effect on still output. Increasing the diffusion gap results in a decrease in both still efficiency and distillate rate. On the other hand, changing condition 4, i.e. kind of diluent gas from air (molecular weight 28.97) to helium (molecular weight 4.003) seems to have caused a negligible change in still output. According to this article, using helium 21
Literature Review
instead of air will not improve still performance and only serves to increase operating costs. This is in contrast to Dunkle (Section 3.3.1), who believes using an inert diluent gas will increase mass transfer, and hence distillate output. Changing parametric condition 5 is an attempt at reducing losses to radiative heat transfer. The value of emittance which was previously about 0.97 was changed to 0.1 by applying a special coating to the water absorber on the evaporating plate, and as with condition 4 was found to have a negligible effect on output*.
*
The author is unclear how the reduction of emittance can be achieved, since 0.97 is the value for the water film, not the absorber. The emittance of the water film cannot be changed, and this would tend to be confirmed by the results obtained.
22
Modelling
4.0 Modelling 4.1 The approach of this thesis The way this thesis will approach the multi-effect diffusion still is through conventional engineering techniques.
This will entail the development of a
mathematical model of the operation of the still, which will then be implemented in a computer program known as Engineering Equation Solver (EES)*.
An
experimental apparatus will then be designed and constructed (i.e. a single-effect diffusion still), and a number of tests performed.
The results from these
experiments will then be compared with results for a similar still from the mathematical model. If the comparison is favourable, the mathematical model can be assumed to be suitable for all input variables (i.e. no. of effects, area of plates, heating values, etc), and can therefore be used for designing diffusion stills in the future.
4.2 Mathematical Model 4.2.1 Developing a model From previous literature on multi-effect diffusion stills, it became obvious that the conditions within the still can vary significantly over the length of the plates. For
*
Engineering Equation Solver (EES) [14] uses Newton's method to solve sets of simultaneous equations. The advantage of this program over other available software is its builtin thermodynamic properties which can be called up at any time. These include such properties as enthalpies, specific heats, pressure-temperature relationships, etc of different common substances (e.g. Air, Water, H2, etc).
23
Modelling
this reason it was decided that the best way to attack the problem is by using a differential element approach. If an energy balance is performed on this differential element, it is expected the results will be quite accurate since conditions will not change significantly over the length of the element. The differential element could then be integrated numerically over the length of the still, therefore providing an accurate picture of conditions anywhere within the still. The most important variable from our point of view is the temperature of the differential element. If this is known, all other parameters can be determined from known relationships. These will be described in more detail in Section 4.2.2. If the differential element is small enough, it can be assumed that the temperature is constant over the length of the element. The following analysis is that of a two plate system with the condensing plate kept isothermal.
Figure 4.1: Differential Element.
For steady state: Energy into element = Energy out of element
24
Modelling
If we take the above differential element as the first at the top of the evaporating plate, then the inlet conditions will be known, (i.e. inlet temperature, inlet flow rate). The expression is therefore required in terms of these inlet conditions.
25
Modelling
Equation (1) represents the important result and can be interpreted as follows. is the change in temperature of the element. Although the element is at constant average temperature T, the outlet temperature changes by
This means
the next differential element will have a constant temperature of
and its inlet
flow rate will be the outlet flow rate of the previous element. As long as the temperature of the element is known, all other properties can be determined from the known relationships discussed in the next section. 26
Modelling
4.2.2 Other equations In order to calculate
for each differential element, obviously the variables in
equation (1) are required. Since Also,
and
is known,
are specified, and
and
are readily available.
is an inlet condition.
If we start with the overall heat transfer coefficient, U, then from Newton's Law of Cooling [9]:
where A, T, & TC are known, and q is simply the total heat given up by the element through all modes of heat transfer (i.e. conduction, radiation, and latent*). Since the conductivity of air is readily available, then the heat transfer between the plates can be expressed as [9]:
If the plates are assumed to be large (infinite) & parallel, then the radiative heat transfer is [9]:
*
The latent heat transfer is a function of temperature only, since the air within the diffusion gap will be saturated.
27
Modelling
Also, the latent heat transfer associated with the evaporation is given by:
where hfg is available from steam tables, and
is found further on.
Therefore:
The rate of evaporation (
), is now required, and this is given by [4]:
where:
It is important to note that although pW2 is simply the vapour pressure of the condensing (pure) water at TC , pW1 is the vapour pressure of the evaporating (salt) water at temperature T. This causes a problem in that although vapour pressures of pure water at a given temperature can be found, the salt in the evaporating film causes a vapour pressure depression. This was overcome by finding the equivalent temperature of a pure water evaporating film which gave the same vapour pressure. The following pair of equations, when solved produced this new temperature TN [5]:
28
Modelling
The above equations introduce another variable which changes along the plate. This is
or rather the salt concentration. Although this will be known initially, as
water evaporates, the concentration will increase accordingly. To compensate for this, the following equation is easily derived:
For the first element, where solve
are known, it is a simple matter to
from the above relationships. The inlet conditions of the next element
are then:
and the process is repeated until the final differential element is reached. 4.2.3 Assumptions The assumptions made while modelling the Multi-Effect Diffusion Still are as follows: 1. Thermal resistance of the plates, and adjacent water film(s) is negligible. This is justified in Appendix 2. 2. The temperature of the differential element is constant. This is reasonable if the differential element is taken to be small enough. In the limit (i.e. for an infinitely small element), this actually becomes exact. 29
Modelling
3. The thickness of the diffusion gap is small, therefore suppressing heat transfer by convection between the plates. 4. The water vapour in the air between the plates has no effect on the conductivity kA.
4.3 Extensions At the moment the model is that of a single-effect diffusion still, with a constant heat flux. However, there are two extensions to the model which will allow it to be used under almost all conditions. The extensions are: 1. Increase the model to multi-effect systems. 2. Allow heating to occur under different conditions, e.g., also with a heating fluid. 4.3.1 Multi-Effect Systems Due to the nature of the model (i.e. differential element), it is relatively simple to increase the number of effects, say from one to two. As the program solves for the first effect, it calculates
(i.e., heat transferred across the diffusion gap) as a matter
of course. This is then used as the heat input of the second effect's differential element, and the remainder of the second effect is solved as if for the first. The only difference is that now the constant temperature assumption must apply for the condensing film of the first effect, and the evaporating film of the second effect 30
Modelling
(Figure 4.2). As mentioned previously, this assumption is justified in Appendix 2.
Figure 4.2: Modified differential element.
This also means that the differential element for the second effect comprises the condensing film of the first effect and the evaporating film of the second. As a result, the flow rate into the differential element is also comprised of the condensing and evaporating film flow rates. 4.3.2 Heating fluid There is only one difference for a program using a heating fluid, and that is the calculation of
For the new case, it is required that the heat transfer coefficient
through the evaporating plate be found, however this quantity varies depending on the situation. Incropera & DeWitt [9] derive equations for almost all circumstances, therefore this thesis will not touch on the subject. Also required is the log mean temperature difference between the evaporating film and the heating fluid. Again, 31
Modelling
calculation of this value is dependent on the situation, and therefore best left to a dedicated text (e.g. Incropera & DeWitt [9]). Suffice to say, the log mean temperature difference will be that of the differential element (now including the heating fluid). Therefore:
4.4 Application The application of the preceding analysis (Sections 4.1 to 4.3.1) can be seen in Appendix 3. These are the computer codes written in EES for a single-effect still, up to a four-effect still.
4.5 Sensitivity Analysis In designing a diffusion still, it is pertinent to know the variables which influence still output. For this reason, a sensitivity analysis was performed on a number of design parameters, these being: 1. Salt water flow rate 2. The diffusion gap thickness 3. Pressure within the still 4. Diluent gas used 32
Modelling
5. Power input in the form of heat The analysis is performed on the single-effect model with unit area. The reference values that all other changes were compared with were: diffusion gap = 0.006 m, pressure = 100 kPa, diluent gas = air, power input = 1000 W. 4.5.1 Salt Water Flow Rate In the following sections (i.e. Sections 4.5.2 to 4.5.5), the other variables are compared with an increasing salt water flow rate. By taking any constant set of conditions in any of the following sections, it is clear that for an increasing flow rate, the fresh water output is decreased. This is due to the fact that higher flow rates mean lower plate temperatures (i.e. more water needs to be heated for the same power input), and therefore lower rates of evaporation. 4.5.2 Diffusion Gap Thickness As can be seen from Figure 4.3, the diffusion gap greatly influences still output. The smaller the gap, the larger the output, therefore from a design perspective this gap should be as small as practicable. Also evident from the diagram is that for the same size change in diffusion gap, a bigger increase in output will occur when the gap is small (e.g., 0.003 m), than when it is large (e.g., 0.009 m).
33
Modelling
4.5.3 Pressure Variation By decreasing the total pressure within the still, intuitively one would think the output would increase, due to the fact that this will increase the diffusivity constant between the plates. This is confirmed by Figure 4.4 which shows the fresh water output at different pressures. As with the diffusion gap, it can be seen for the same size step at lower pressures, the increase in output is larger than at higher pressures.
34
Modelling
4.5.4 Diluent Gas Figure 4.5 shows the comparison of two theoretical stills operating under identical conditions, except for the diluent gas. As suggested by Dunkle, the still output is significantly increased (e.g., 30% at 0.0015 kg/s flow rate) when a low molecular weight diluent gas is used. This contradicts Moustafa [4] whose numerical model indicated no significant improvement in still performance.
35
Modelling
4.5.5 Power Variation Figure 4.6 is a comparison of different power inputs into our Single-Effect Still. Obviously the more energy put into the system, the more evaporation that will occur, and therefore the larger the still output.
36
Modelling
37
Experiment
5.0 Experiment 5.1 Objective The objective of the experiment is to confirm the results obtained from the numerical model. It also serves to provide experience in the practicalities of developing a device to the working stage. 5.2 Apparatus The experimental apparatus is a Single-Effect Diffusion Still designed by the author, and constructed by the James Cook University Mechanical Engineering Workshop. As can be seen in Figure 5.1, it consists of two plates supported by a frame, with the
Figure 5.1: Diagram of Experimental Apparatus
38
Experiment
evaporating plate fixed, but the condensing plate able to be moved in order to vary the diffusion gap. The evaporating plate is heated from behind by two flexible heating elements covering the majority of the plate surface. The condensing plate is essentially one side of a container which is filled with ice and water, and therefore will keep the condensing surface isothermal at 0oC. The evaporating plate is isolated from the frame with plastic spacers, and has water fed to it by a small reservoir at its top. The water film running down the surface is kept uniform by a cotton wick fixed in the reservoir which hangs over the plate surface. The small reservoir has a weir and is kept overflowing due to a constant input from a larger reservoir. This means that the flow into the small reservoir is equal to the flow out, and therefore, the flow rate can be controlled via a tap connected to the large reservoir. This large reservoir was sized so that over the time period of the experiment, the variation in height of salt water was negligible, and therefore the still could be assumed to be fed from a constant head tank (this is proved in Appendix 4). As the brine runs from the bottom of the evaporating plate, and distillate from the condensing plate, they are each collected in separate containers. Because the diffusion gap is so small, a divider is required so the two flows can each be collected without contaminating one another. The heating elements have electricity delivered to them via two DC power supplies connected in series. This allows the power (i.e. P=V.I) delivered to be controlled accurately, and has the property of providing a constant heat flux over the entire plate. 39
Experiment
Other ancillaries which comprise the apparatus include the following:
&
Thermistor
&
Scales
&
Stopwatch
Note: Drawings and photographs of the apparatus can be seen in Appendix 9. 5.3 Procedure The procedure for the experiment is relatively straight forward with the steps required shown below: 1. Fill the large reservoir with a known quantity of water. To this add a quantity of salt equal to 3.45% by weight of the water (i.e. approximately the composition of natural sea water [5]), and mix thoroughly. 2. Open the tap to the desired flow rate and let the small reservoir fill and overflow, soaking the wick. 3. Adjust the diffusion gap to that required, and fill the container behind the condensing plate with ice. Fill the gaps between the ice with water. 4. Turn on the power supplies and adjust the voltage and current so that they produce the required power input (i.e. P=V.I).
40
Experiment
5. Allow the apparatus to reach steady state (i.e. this occurs after about 15 minutes). Steady state is reached when the condensing plate is covered by a uniform film of water. 6. Push the divider beneath the apparatus to separate the distillate and brine. At this point start the stopwatch. 7.
Let the Still run, meanwhile taking measurements of all relevant
parameters (i.e. water inlet temperature, water outlet temperature, voltage, and current). It is also important to take measurements of the ice water at regular intervals. When the temperature begins to increase (this will occur before all the ice has melted), end the experiment. 8. Stop the stopwatch and remove the container which collected the distillate. Measure the weight of the distillate. While the apparatus is still running, measure the flow rate by collecting the salt water input in a container over a known time period, and again measure this quantity on the scales. 9. The experiment is now complete and all inputs can be stopped, and vessels emptied. 5.4 Results Five Experiments were performed with the apparatus. The raw data obtained from these can be seen below:
41
Experiment
Table 5.1: Experimental Results Exp. 1
Exp. 2
Exp. 3
Exp. 4
Exp. 5
Inlet Temp.
28.0oC
25.5oC
25.4oC
26.5oC
28.0oC
Current in
4.0 A
4.15 A
4.4 A
4.8 A
4.3 A
Voltage in
41.5 V
42.5 V
47.0 V
50.0 V
45.0 V
Distillate out
41.1 g
91.9 g
84.9 g
81.8 g
53.8 g
Time period
27 min
43 min
27 min
22 min
20 min
Flow rate in
58.8 g/min
23.2 g/min
11.0 g/min
6.9 g/min
16.2 g/min
Initially, the outlet temperature of the evaporating film was also taken, but it was soon realised that this was a pointless exercise. This was because it was extremely difficult to measure this temperature due to the nature of the available measuring device (i.e. thermistor). Because the apparatus was scaled small, the size of the thermistor in comparison to the thickness of the water film caused problems. Also contributing was the error associated with the still construction. The accuracy of the diffusion gap is limited (i.e. variation of up to 2 mm), and this variation has a significant effect on outlet temperature, therefore the results would be highly dependent on the contour of the diffusion gap above the measuring point. Although the outlet temperature of the salt water film couldn't be measured, for experimental run 5 it was decided to attempt to measure the temperature distribution along the evaporating plate. This was done by using a thermocouple which was insulated on one side, and pressed against the back of the evaporating plate at various intervals. The results can be seen below.
42
Experiment
Table 5.2: Variation of measured temperature along evaporating plate Distance along plate (cm)
Temperature (oC)
0
28
2.5
36.5
5.5
38.5
8.5
39.5
11.5
40.6
14.5
41.9
17.5
41.7
20.5
42.7
23.5
41.6
26.5
41.1
29.5
42.7
32.5
41.5
44
41.2
It should be noted that the above results are not considered accurate, mainly because it was difficult to establish a good contact against the plate, and the measurements had to be taken with the polystyrene removed (i.e. there was an increased heat loss through the back of the plate). 5.5 Error bounds for Numerical Model This section will assign uncertainties to the still parameters. These will then be substituted into the numerical model in Section 6 to see if the experimental results fall within the maximum and minimum error bounds. 43
Experiment
One of the most significant errors is that due to the variation in diffusion gap thickness along the length of the still. Because of this, plans to incorporate various diffusion gap thicknesses into the experimental runs had to be abandoned since it was impossible to measure this gap with sufficient precision. Therefore, a set of measurements were taken for the diffusion gap which were then repeated for each experiment. These were:
In addition to these values, it was evident that at the centre of the plates,
was
even smaller than the above minimum of 5.0 mm. Because of this variation, it is difficult to find even an average value, however a reasonable estimate would be:
It is expected that the uncertainty associated with the heating power will be small. This is because all the electricity supplied to the heating elements will be completely converted to heat. This power input can be measured accurately from the output display on the power packs. Although there will of course be losses to the atmosphere, these have been minimised as much as possible. The evaporating plate was insulated from the metal frame, and the heating elements were covered with polystyrene (40 mm thickness) so that the majority of heat was directed into the salt water film. However, this heat loss through the polystyrene is a calculable quantity, and can be compensated for within the numerical model. As such it will not be considered a loss. Other minor losses (e.g., heat loss through the electric wires) will be neglected. 44
Experiment
The error associated with the condensing plate (which is assumed isothermal at 0oC) is also expected to be small. This is because the ice-water mixture sets the temperature surprisingly accurately. Besides which, even if the temperature was inaccurate by as much as 5oC, this causes a negligible error in the results. As can be seen in Figure 5.2, the vapour pressure is almost constant at low temperatures. We will therefore neglect any errors associated with the condensing plate.
Another variable which could affect still output is the salt water flow rate. From Appendix 4, it can be seen a typical change in flow rate due to change in height of the saltwater reservoir is less than 3.4%. Since small changes in flow rate cause an even smaller change in condensate output (refer Section 4.5), the error due to mass flow rate of salt water can also be neglected. Probably the most significant error occurs due to the gap between the plates not 45
Experiment
being closed around the edges. Unfortunately, this meant the system was open to the atmosphere, and as such, diffusing water vapour was able to escape to the surroundings rather than condense on the opposing plate. During the experimental runs with high power inputs, and low flow rates, this effect was clearly visible, and appeared to be quite significant. Unfortunately, these losses are difficult to predict with any certainty. One possible way (and the method that will be used), is to find the area of the gap around the two plates. If it is then assumed that water vapour has the same chance of escaping through this gap as it does of condensing on the opposing plate, then:
For a diffusion gap of 5.5 mm, the loss of condensate to the surroundings is 6%. Although the above method is crude, it is the best available for the error analysis to come (Section 6). The above analysis has tried to assign reasonable values to errors which are difficult to analyse. As stated, the errors associated with the power input, flow rate of salt water, and the temperature of the condensing plate have been neglected because they are believed to be small in comparison to the errors from the diffusion gap thickness, and the losses to the atmosphere. Also neglected were errors due to measurement of quantities for the same reason.
46
Experiment
5.6 Discussion and Observations As can be seen in the following section, the still performed remarkably well. There was however a shortcoming in the design which became apparent during the experimental runs. Because the ice-water container was at 0oC, water condensed out of the atmosphere onto the surface, and had the potential to contaminate the still output. Fortunately, the experiments were performed on days of low humidity, and what little water condensed on the container actually froze. This could simply be wiped away without risk of tainting the results, and as such it was deemed unnecessary, and time consuming to have the apparatus modified (i.e. insulating the ice-water container from the atmosphere). A possible improvement to the still could be the addition of permanent thermocouples to various parts of the apparatus in order to get temperature measurements to compare with the model. Also, perhaps the gap around the plates could be closed in some manner so that loss of water vapour to the atmosphere are minimised. An interesting phenomenon was observed during the experimental runs which could warrant further attention. This was the formation of a haze over the condensing plate which appeared to be flowing (in fact the flow of this haze appeared to cause the main loss of water vapour to the atmosphere). Also observed was the formation of water droplets suspended in the gap between the plates. Unfortunately, time considerations precluded the further investigation of these occurrences.
47
Analysis of Results
6.0 Analysis of Results 6.1 Comparison of numerical model with experimental results This section will present a comparison of the experimental results with theoretical results predicted by the numerical model. There is also a comparison of the theoretical model with experimental results obtained by Shams et al [3] for a threeeffect system. The following Figure 6.1 is a plot of the experimental results compared with the theoretical results from the model (the program can be seen in Appendix 5). If it is assumed the numerical model is accurate, then by applying the maximum and minimum error bounds from Section 5.5, the precision of the numerical model can be found. If the experimental results fall within these limits, then this will validate the above assumption. The above limits are represented by bars on the plot of numerical results. Although these error bars don't represent the absolute maximum error from all sources, they do represent the major sources of error, and since these are uncertain, there seems little point in including minor errors.
48
Analysis of Results
Figure 6.1: Comparison of results.
Figure 6.1 clearly shows that all experimental results except run 4 are within the limits set by the error bars. This would tend to indicate that the accuracy of the numerical model developed is good. Although experiment 4 is outside the error bounds, this could be explained by many circumstances, the most likely being that the experiment was started before the still had reached steady state. If this was the case then the condensing film wouldn't have reached its final thickness when the measurement of still output began. This means that during the period of the experiment, time was spent developing this film rather than producing an output. As such it is believed that this errant result does not detract from the validity of the model. 6.2 Comparison of numerical model with experimental results from [3] To further test the accuracy of the model, it was compared to experimental results obtained by reference [3]. The article gives an overview of the experiment performed, providing enough information to allow a model to be created. The 49
Analysis of Results
experiment was that of a three-effect still, with plate area 0.45 m x 0.75 m, diffusion gaps of 10 mm, flow rates of 1.01 kg/hr/plate, inlet and condensing temperatures of 30oC, and heating water of 80oC.
Figure 6.2: Comparison of results from [3].
Figure 6.2 shows comparisons of the experimental result with two numerical models. The first comparison is that of the conditions stated in the article (an analysis of these conditions, and the computer program can be seen in Appendix 6). As can be seen, the numerical model predicts a value of 1.16 kg/hr, whereas the experiment yielded 1.08 kg/hr.
This is a variation of about 7%, which in
engineering terms is more than acceptable. Unfortunately, the article only gives an uncertainty pertaining to the heating water (i.e.
). The precision of other
variables are not given, therefore making a comprehensive error analysis impossible. As a matter of interest however, a second comparison of experimental result to numerical model was made (Figure 6.2 - comparison 2). This new model took a heating water temperature at maximum error (i.e. 79oC), and assigned what seems 50
Analysis of Results
a reasonable uncertainty to the diffusion gap thickness of
(i.e. maximum
diffusion gap=0.0105 m)*. When these were substituted into the computer program, the result was a value of 1.06 kg/hr. Uncertainties associated with other variables (e.g. variation in flow rate, heat transfer coefficient, losses to the surroundings) have not been included, but would undoubtedly push the numerical value below 1.06 kg/hr. This means the experimental value falls within the limits of uncertainty, and therefore the numerical model receives further confirmation. 6.3 Temperature distribution along evaporating plates From Sections 6.2 and 6.3, it is obvious the numerical model is quite accurate in terms of predicting still output. However, if a comparison is made between the measured temperature distribution and the predicted temperature distribution, the results are not as conclusive. Figure 6.3 shows this comparison, and although both follow a similar trend (i.e. exponential), the final measured values are about 8oC below the final predicted values. However, it is the author's belief that these predicted values are more representative of the true situation than the measured values, simply because the still output is quite dependent upon the asymptotic temperature of the still. Also, the measured values suffer from significant errors (discussed in Section 5.4), therefore the only verification which can be obtained from this comparison is that the temperature distribution does appear to be exponential.
*
This can be justified if one thinks of the difficulties in keeping a plate of any significant area perfectly flat. For instance, the plate used during this thesis (Section 5) was of significantly less area and had a box steel frame supporting its edges. Nevertheless, it varied by as much as 2 mm in places.
51
Analysis of Results
Figure 6.4 shows the predicted temperature distribution of the three-effect still described in Section 6.2 and Appendix 6. As can be seen, the distributions again appear to be exponential, and this is verified in Appendix 7.
52
Analysis of Results
6.4 Minimum Work According to the Second Law of Thermodynamics, there will be a minimum amount of energy required to desalinate a certain quantity of water. If we can calculate this, then it can be used to investigate just how efficient our process is, and possibly to compare it with other methods of desalination. Appendix 8 shows how to calculate the minimum work required to desalinate 1 kg of water under ideal conditions, i.e. Wideal. To find the efficiency of our still in regards to the theoretical minimum work, we can use:
where Wavailable is the work that could theoretically be produced in our still rather than 1 kg of water*. Therefore in a single-effect diffusion still, Wavailable is simply the heat transferred between the diffusion gap, multiplied by the Carnot efficiency obtainable from the temperature difference between the opposing evaporating and condensing films, i.e.
The above equation is for a single-effect still, however let's consider the three-effect still of Appendix 6 (i.e. our numerical model), i.e.
*
This is assuming a reversible process in the conversion of actual heat in, to potential work out (i.e. the actual energy into the still in the form of heat is converted reversibly into work).
53
Analysis of Results
It is a relatively simple matter to apply the above equation to every differential element within the model, therefore taking into account the exponential nature of the temperature distributions. Applying the result to equation (3):
To now compare this figure with other desalination methods, a value of 6.5% is considered quite good (this efficiency is so low because the process must take place in a finite time, rather than over an infinite period). Although our efficiency is about 1/4 that obtainable by other methods, it is worth noting that the still was run nowhere near optimal conditions, and if a diffusion still were to be implemented practically, it would likely contain 10 or more effects (when more effects are added, the efficiency will increase due to the desalination performed with the previously lost heat of condensation). Also, the issue of heat regeneration was not addressed (N.B. this will be discussed in Section 7.2), and again this would undoubtedly increase the efficiency of our still. As such, no conclusion as to the potential of diffusion stills can be drawn from the above results.
54
Discussion
7.0 Discussion 7.1 Overview This thesis has investigated the problem of accurately predicting the output and internal conditions of a diffusion still. Although this has been done in the past, it was felt that all previous models made too many assumptions, which then cast doubts upon their applicability to real systems. As a consequence, the objective of this thesis was to develop as comprehensive a model as possible. As seen from the thesis so far, a model was developed, with the only significant assumption being a constant temperature of adjacent condensing and evaporating films. Although this assumption could be avoided, it is felt that the increased complexity associated with this task outweighs the negligible gain in accuracy this would produce in the numerical model. This is confirmed by the comparison of model results to experimental results in Section 6. 7.2 Practical Considerations We now have a valid numerical model which could be used to find the optimum conditions at which to construct and operate a diffusion still. From a practical viewpoint however, there are still a number of issues which must be resolved. For instance, if the still is to be as efficient as possible, then heat regeneration becomes an important consideration. As described at the beginning of the thesis, the diffusion still uses heat as its source of energy. Once the distillation process is complete, most of this energy is retained in the increased temperature of the outgoing brine and condensate. By using a heat exchanger between these outputs 55
Discussion
and the inlet feedwater, significant power savings could be made. Another issue to consider is the use of a diluent gas. If the still is to be filled with say Helium, then clearly the system must be free from leaks, or this is simply a wasted exercise. Provided this problem can be overcome, then another problem presents itself, this being the release of air and other non-condensable gases during distillation. If these are allowed into the still, then as they are released, a pressure rise will occur, which as seen in the sensitivity analysis would decrease the rate of diffusion. Clearly these gases must be removed before the feed is allowed entry. It could possibly be that the cost of overcoming these problems (plus the periodic replacement of the diluent gas since some contamination will always occur) is higher than the cost of simply increasing the power input with an air atmosphere. Probably the most important practical issue to be considered is that of keeping the flow uniform over the plates. For our experiment, a cotton wick was used to good effect, however this would not be practical in an industrial application (i.e. deterioration of the material would occur). Perhaps a synthetic material with similar properties to cotton exists, or another approach such as small vertical grooves along the plates could be used. 7.3 Future Work While working on this thesis, some possible extensions in the application of diffusion stills became apparent. One is the possible use of a multi-effect still for fractional distillation (i.e. the separation of a mixture of liquids with differing boiling points and vapour pressures). In a multi-effect still, each plate assumes a 56
Discussion
different temperature, therefore on any particular plate, this may be close to the boiling point of one of the substances. Say for instance we had a mixture of three substances, A, B &C, each with respective boiling points at 40oC, 60oC & 80oC. In a two-effect system, let's assume the evaporating plates are at approximately 60oC, and 40oC. If the mixture is introduced onto the second evaporating plate, then substance C will be most volatile, and therefore the majority of diffusing vapour will be this component. The exiting mixture will now be composed of A & B, which is then introduced onto the first evaporating plate. This time substance B will be most volatile, and therefore will diffuse across the gap and condense. In this manner, all three substances could be collected by using the same heat source.
Figure 7.1: Possible Diffusion still for Fractional distillation.
To improve the fresh water yield, it was seen during the sensitivity analysis that we 57
Discussion
can decrease the diffusion gap. This has the effect of increasing the vapour pressure gradient (i.e.
) between the water films, however we are restricted to
diffusion gaps no smaller than a couple of millimetres due to practical considerations.
One possible way of avoiding this limitation is the use of
hydrophobic membranes [13] which allow vapour to pass through unimpeded, but stop the passage of liquid. There are materials available which have this property and whose thickness are in the order of magnitude of 0.1 mm. These are the sort of materials currently used in reverse osmosis with the application of mechanical work (pressure).
However if these membranes are used in a diffusion still, then
desalination will occur due to heat, which according to the Second Law of Thermodynamics is less valuable than work. A possible application is seen in Figure 7.2.
Figure 7.2: Possible Diffusion still using membrane technology.
58
Discussion
The plates each have a porous, rigid material (possibly sintered) covering them, and sandwiched between these is the membrane. The saltwater is introduced into the porous material on the evaporating plate, and diffuses through the membrane condensing in the porous material on the opposing plate. A possible advantage of the above process over current membrane desalination techniques could be reduced clogging (refer Section 3.2.4), since the salt water flows over the membrane rather than being forced into it. The above applications are simply ideas for further development of the Diffusion Still. It is not known how practical they are, nor if they have already been investigated. 7.4 Minimum Work and the cost of energy It is important to note that even if a desalination method is more efficient than another, it may still be rejected on an economic basis. If for instance one method has an efficiency of 6.0% compared to another at 6.5%, but the capital costs and operating costs are half that of its alternative, then clearly the lower efficiency method should be chosen. As such, anyone comparing desalination methods on an energy basis alone could run into problems. The cost of energy is an important consideration when designing a desalination still. As is evident from the Second Law of Thermodynamics, low quality energy (heat) is much less valuable than high quality energy (work), and as such it is desirable to utilise this low quality energy wherever possible. It is also a fact that this thermal energy is cheaper the closer it is to ambient temperature [12]. As a consequence of 59
Discussion
the above statements, the multi-effect diffusion still appears to have a significant advantage over most other methods of desalination which use either work or high temperature thermal energy (typically the condensing temperature of steam under pressure, i.e. about 130oC).
60
Conclusions
8.0 Conclusions This thesis has attempted to present a comprehensive analysis of the diffusion still. A mathematical model was derived, and implemented in a computer package (EES), with the predicted results verified by experiment. A number of parameters were then analysed to give some idea of the important variables that should be considered when designing a diffusion still. These were the salt water flow rate, diffusion gap, pressure within the still, diluent gas and power input, and all were found to have a significant effect on fresh water output. The thesis also discussed topics such as the future work which could be performed on the diffusion still, and the practical considerations which would have to be taken into account when building a large scale plant. In all, as many topics were covered as possible which are relevant to diffusion stills, however these were only included for completeness. The main focus of the thesis was the development of a good mathematical model, and the author believes this was achieved.
61
References
9.0 References 1.
Dunkle, R.V., Solar Water Distillation: The Roof Type Still and a Multiple Effect Diffusion Still, International Heat Transfer Conference, University of Colorado, U.S.A. Part 5, pp.895-902, (1961).
2.
Fathalah, K.A., Taha, I.S.,Elsayed, M.M. & Sabbagh, J., Numerical Prediction of the Performance of Multi-Effect Diffusion Stills, Alternative Energy Sources V. Part B: Solar Applications, Amsterdam, (1983).
3.
Shams, J.I., Elsayed, M.M. & Sabbagh, J., Experimental Prediction of the performance of Multiple-Effect Diffusion Stills, Alternative Energy Sources V. Part B: Solar Applications, Amsterdam, (1983).
4.
Elsayed, M.M., Effects of Parametric Conditions on the Performance of an Ideal Diffusion Still, Applied Energy Vol. 22, pp. 187-203, (1986).
5.
Bromley, L.A., Singh, D., Ray, P., Sridhar, S., & Read, S.M., Thermodynamic Properties of Sea Salt Solutions, AIChE Journal Vol.20, No.2, pp.326-335, (1974).
6.
Spiegler, K.S., Salt-Water Purification, 2nd Ed., Plenum Press, (1977).
7.
Porteous, A., Saline Water Distillation Processes, Longman, (1975).
8.
Homig, H.E., Seawater and Seawater Distillation, (1978). 62
References
9.
Incropera, F.P., DeWitt, D.P., Fundamentals of Heat and Mass Transfer, 3rd Ed., Wiley & Sons, Inc., (1990).
10.
Brown, T.L., LeMay, H.E., Chemistry-The Central Science, 5th Ed., PrenticeHall, (1991).
11.
Potter, M.C., Wiggert, D.C., Mechanics of Fluids, Prentice-Hall, (1991).
12.
Rautenbach, R., Desalination-present techniques and future trends, SeminarySeawater Desalination and its Energy Supply, Tehran/Iran, (1977).
13.
H. Suehrcke, personal communication (1996).
14.
Klein, S.A., Alvarado, F.L., Engineering Equation Solver Ver. 3.86D, F-chart Software, (1996).
63
Appendices
Appendices
64
Appendices
Appendix 1: Scale & Corrosion The Multi-Effect Diffusion Still has a significant advantage over other methods of desalination when it comes to problems with scale deposition. In a typical distillation process, temperatures can reach well in excess of 100oC. Temperatures of this magnitude result in many different forms of scale and corrosion. Since the Multi-Effect Diffusion Still is designed for temperatures around 70oC, many of the problems associated with other distillation processes are avoided. There are two main types of scale which occur, Alkaline and Calcium Sulphate. Of these, at temperatures below 70oC, Calcium Sulphate scaling will generally not occur. Alkaline scaling occurs in two distinct forms, Calcium Carbonate, CaCO3 and Magnesium Hydroxide, Mg(OH)2. Again Mg(OH)2 usually won't occur below 82oC unless the pH of the water is high, i.e. around 8.5. Designers of Multi-Effect Diffusion Stills will therefore only have to deal with CaCO3, and this can be controlled by lowering the pH of the feedwater. If the pH is reduced, this increases the temperature at which CaCO3 will form, i.e. pH around 6.8. As a result, aciddosing is probably the best way of controlling this problem. Quite distinct from scaling is the problem of corrosion.
The main factors
contributing to this are the quantities of air and CO2 dissolved in the water, as well as the pH of the feed. Due to the reaction of the acid with the Alkaline scaling, additional CO2 is produced thus increasing the problem. It is therefore important to rid the feedwater of these gases. Once this is achieved, the pH of the water can be increased to a more acceptable level.
65
Appendices
Appendix 2: Adjacent Films
Figure A.1: Modified Differential Element.
The assumption that there is negligible thermal resistance between adjacent condensing and evaporating films is justified by the following example calculation. In an analysis of condensing films carried out in Incropera & DeWitt [9] (which can be extended to include low velocity laminar evaporating films), it is claimed momentum and energy transfer by advection can be assumed negligible. This means that heat transfer across the film will be due to conduction only, therefore giving a linear temperature distribution, which allows the heat transfer coefficient to be expressed as:
66
Appendices
The following equation is derived [9] which can be used to find
Obviously, the larger the heat transfer coefficient, the less thermal resistance, therefore from (1) it is clear that if
should be as small as possible. Conversely,
is taken at its largest value, it can be shown whether the negligible thermal
resistance assumption is reasonable. From (2) it can be seen that when
is largest. A value for
of 0.001 kg/s (where
is largest is the flow
rate on the condensing surface) is larger than any which would occur for a width (b) of 0.29 m, and a length of 0.44 m. Taking water properties at a temperature of say 50oC (it makes very little difference what temperature is used), then:
Therefore, rearranging (2) and solving for
67
Appendices
Substituting into (1):
Similarly for the evaporating plate:
Using a brass plate of thickness 1.6 mm, then again using (1) where:
Therefore:
The Overall Heat Transfer Coefficient is then:
A typical heat flux (
) is 1000 W/m2, then from Newton's law of cooling:
A temperature difference of 0.177oC can obviously be neglected when a typical value between plates is 20oC.
68
Appendices
Appendix 3: Programs The following programs are EES codes for a single-effect still (p.70), two-effect still (p.73), three-effect still (p.75) and a four-effect still (p.78), all with a constant initial heat flux. The first program is documented, with the others being obvious extensions of this one.
69
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EES program to calculate the output of a single-effect still The program below is that for a two plate system. It works by dividing the plate into a number of smaller elements, all of which are the width of the plate by a fraction of its length. This is due to the property that the temperature is constant along the width, while it varies along the length. The program works out the temperature in the element by using a heat balance analysis. It starts from the top where the conditions are known, and calculates the heat required by all methods, i.e. evaporation, radiation, conduction, and heating of the salt water film. This analysis predicts the properties of the element, e.g. outlet temperature, flow rate, and uses these as the inlet conditions of the next element. Note: The program variables are represented differently because EES doesn't have the capability to generate Greek letters or subscripts, etc. {Fixed Variables} R=8.314..............................Universal Gas Constant Mw=18.016.........................Molecular weight of water Vw=12.70............................Diffusional volume of water vapour T0=273...............................0oC in degrees Kelvin {Input Variables} Ma=28.97............................Molecular weight of air Va=20.1...............................Diffusional volume of air d=0.006...............................Diffusion Gap b=1.....................................Width of plate L=1.....................................Length of plate T2a=25...............................Temperature of condensing plate in degrees Celsius PowerIn=1000....................Heat into still Pt=100................................Pressure within still {Dependent Variables} dL=L/50.............................Length of individual elements
70
Appendices qflux=PowerIn/(b*L)................Heat flux provided to the heated plate {The block below is used in conjunction with the parametric table, and is essentially a FOR loop. It takes initial conditions, which are provided, and runs through the rest of the program calculating new values. It then takes these new values and goes through the program again, continually repeating the process until it reaches the final element.} T1a=TABLEVALUE(i-1,#T1a)+TABLEVALUE(i-1,#dT).................Temperature of the water m=TABLEVALUE(i-1,#m)-TABLEVALUE(i-1,#W12)...................Mass flow rate x=TABLEVALUE(i-1,#x)+((W12/m)*TABLEVALUE(i-1,#x)).......Concentration of salt qtotal=TABLEVALUE(i-1,#qtotal)+q12............................................Total heat transferred to all elements so far {Main Program - remainder of text.} BPE=(x*((T1b+T0)^2)/13832)*(1+(0.001373*(T1b+T0))-(0.00272*(x^0.5)*(T1b+T0)) +(17.86*x)-(0.0152*x*(T1b+T0)*(((T1b+T0)-225.9)/((T1b+T0)-236))) -(2583*x*(1-x)/(T1b+T0)))...........................Boiling Point Elevation of salt water element T1b=T1a-BPE..............................................Equivalent temperature of fresh water to give the reduced vapour pressure due to salt water T1=T1a+T0..............................................Temperature of salt water element in degrees Kelvin Pw1e=(10^(-(40670/(2.303*R*(T1b+T0)))+10.695))/1000...........Vapour Pressure of salt water element T2=T2a+T0...........................................................Temperature at the condensing plate Pw2c=(10^(-(40670/(2.303*R*T2))+10.695))/1000.........Vapour Pressure at the condensing plate dPw12=Pw1-Pw2.........................................Vapour Pressure difference between the plates Pt=100...........................................................Pressure of the surroundings {Diffusivity at plate} D12=((1e-5*(((T1a+T2a)/2)+273)^1.75)/(Pt*((Va^(1/3))+(Vw^(1/3)))^2)) *(((1/Ma)+(1/Mw))^(1/2)).......................................Diffusivity Constant
71
Appendices W12=((1e6*D12*Mw/((R*1000)*(T1a+273)))*((Pt/1000)/d)*ln((Pt-Pw2c)/(Pt-Pw1e)))*b *dL..................................Mass flow rate across the diffusion gap for the element {Heat transfer by radiation} sb=5.67e-8...........................................................................Stefan-Boltzmann Constant E=0.95.................................................................................Emissivity of water film qr12=(sb*((T1^4)-(T2^4))/((1/E)+(1/E)-1))*b*dL..........Heat transfer by radiation {Heat transfer by conduction} k12=CONDUCTIVITY(Air,T=((T1+T2)/2)-T0).................Conductivity of Air qc12=(k12*(T1-T2)/d)*b*dL.................................................Heat transfer by conductivity {Heat transfer by evaporation} h1g=ENTHALPY(Steam,T=(T1-273),x=1)...................Enthalpy required by diffusing vapour h2f=ENTHALPY(Water,T=(T2-273),x=0)...................Enthalpy of condensing liquid h1f=ENTHALPY(Water,T=(T1-273),x=0)...................Enthalpy of incoming water hfg12=h1g-h1f..................................................................Enthalpy difference qe12=W12*hfg12*1000...................................................Heat transfer by evaporation {Total heat transfer} q12=qr12+qc12+qe12 {Other properties} U=q12/(b*dL*(T1-T2))..........................................Apparent OHTC in the diffusion gap Cp=SPECHEAT(Water,T=T1a,P=Pt)*1000.......Specific heat of water dT=((((U*(T1-T2))-qflux)*b*dL)-(W12*h1f*1000))/(-(m-W12)*Cp).................Temperature difference between salt water into and out of element
72
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Appendix 4: Constant Head Tank Using Bernoulli's equation [11], let's find the velocity of the saltwater outflow:
81
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The head loss will be comprised of friction within the pipe, plus a loss through the valve and can be expressed as:
where k is a constant. Therefore:
At initial conditions:
Similarly at the end of the experiment:
82
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From the beginning of the experiment to the end, there will be a change in velocity, therefore:
Assuming k is not strongly dependent on velocity (i.e. the loss through the tap is significantly more than that due to friction*), then:
Therefore:
The percentage change is then:
*
This is reasonable since the low flow rates in the experiment were achieved with the tap opening restricted to a fraction of its full value.
83
Appendices
The head tank was typically filled to a level of 30 cm above the outlet, and by the end of the experiment this had only dropped by about 2 cm, therefore:
84
Appendices
Appendix 5: Experimental Program The following is the model of experimental run 5 used in Section 6 (p.86). Also shown are the results for this program (p.88). As we move down the page, each row represents consecutive elements, with the last row representing the output conditions.
85
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Appendix 6: Three-Effect Diffusion Still [3] The article describes an experimental apparatus which appears to be quite sophisticated in its design. As can be seen in Figure A.2, saltwater is pumped from a reservoir to an overhead tank. This tank then circulates cooling water behind the condensing plate through the action of gravity. As this cooling water leaves the condensing plate, some of it is diverted and provides the feedwater over the evaporating plates, the rest being returned to the reservoir. The heating power
Figure A.2: Experimental Apparatus [3].
89
Appendices
comes from water whose temperature is raised to 80oC by a heat transfer bench, and is then circulated counter-currently behind the initial evaporating plate. All flows are measured by rotameters, and the temperature profile on each plate is found from thermocouples evenly spaced. The area of each plate is 0.45 m x 0.75 m, and the diffusion gap in all three effects is 10 mm. The feed into each effect is 1.0125 kg/hr at a temperature of 30oC, while the condensing plate remains almost isothermal at 30oC. The heating water temperature varies linearly from inlet to outlet, with the final temperature about 1.5oC below its initial value. It should be noted that the article neglects to provide the heat transfer coefficient between the heating water and the first evaporating film, therefore this had to be estimated. Incropera & DeWitt [9] quote typical values for this type of heat exchange at between 850 & 1700 W/(m2.K), with a figure of 1500 W/(m2.K) being arbitrarily chosen. The computer model was modified according to Section 4.3 (i.e. to make use of the log mean temperature difference), and can be seen in this appendix (p.91).
90
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Appendix 7: Approximate temperature distribution of evaporating plates.
Energy In = Energy Out
Appendices
95
Appendices
The above equation indicates that the temperature distribution along our plates should be exponential. Taking the relevant parameters from the numerical model of experiment 5 (i.e. at exit conditions), k1 & k2 were found. These were then substituted into equation (1) to find this approximate temperature distribution. This was then compared with the results obtained from the mathematical model, and can be seen below (Figure A.3). As is evident, this approximation is quite good, and could perhaps be used to find estimates of still output.
96
Appendices
Appendix 8: Minimum Energy An ideal Diffusion Still would raise the temperature of the evaporating plate so that the vapour pressure of the saltwater is just above that of the condensing fresh water film. This would cause diffusion with the least energy input, albeit over an infinitely long time period. The heat of condensation given up by the now purified water would then be recycled back to the evaporating plate to be used again. Since the heat of condensation will be approximately equal to the heat of vapourization*, the only energy input will that required to pump this latent heat from a low temperature to a higher temperature.
Figure A.4: Conceptual diagram of Ideal Diffusion Still.
*
The evaporating temperature is only just higher than the condensing temperature, and this may in fact be offset by the lowered vapour pressure (due to the salt in solution) of the evaporating plate.
97
Appendices
If we set the condensing temperature TL to 25oC, and the weight fraction of salt to that of normal seawater (3.45%), then from equation (2) in Section 4.2.2, TH = 25.312oC. Using the Second Law (Carnot Efficiency):
Therefore:
From Speigler [6], this quantity is verified (i.e. W=2.54 kJ/kg), and represents the energy required to desalinate 1 kg of water with a negligible change in volume (i.e. final volume of saltwater is almost that of the original) If we want the minimum energy to desalinate 1 kg of water at 50% recovery (i.e. final volume of saltwater is half the original), a similar analysis to that above could be carried out, however it is simpler to use the equation:
which was derived using an analysis for Reverse Osmosis [6].
98
Appendices
Appendix 9: Photographs and Drawings This section contains photographs of the Experimental Apparatus, followed by Orthographic Diagrams. Photo 1: Apparatus (Front View)
... p.100
Photo 2: Apparatus (Back View - with polystyrene)
... p.101
Photo 3: Apparatus (Back View - without polystyrene)
... p.102
Photo 4: Apparatus (Side View)
... p.103
Photo 5: Apparatus (Aerial View)
... p.104
Photo 6: Apparatus (Condensing plate removed)
... p.105
Photo 7: Apparatus (Demonstration of wick)
... p.106
Orthographic Views: Sheet 1
... p.107
Orthographic Views: Sheet 2
... p.108
99
Appendices
Photo 1: Apparatus (Front View)
100
Appendices
Photo 2: Apparatus (Back View - with polystyrene)
101
Appendices
Photo 3: Apparatus (Back View - without polystyrene)
102
Appendices
Photo 4: Apparatus (Side View)
103
Appendices
Photo 5: Apparatus (Aerial View)
104
Appendices
Photo 6: Apparatus (Condensing plate removed)
105
Appendices
Photo 7: Apparatus (Demonstration of wick)
106
