Ind. Eng. Chem. Res. 1994,33, 1501-1509
1501
A New Procedure for Water Decarbonation Process Control Manuel Adroer, Francisco Valero, Manuel Poch,’ and Carles So14 Unitat d’Enginyeria Qutmica, Universitat Autanoma de Barcelona, 08193 Bellaterra, Spain
Water decarbonation has become a standard procedure for the treatment of the water used in industries requiring a bicarbonate, organic matter, and colloid-free, low-hardness supply, for example soft drink beverage industries. One of the keys to efficient decarbonation is using the right concentration of calcium hydroxide. While any amount below the stoichiometric dose would fail t o ensure good removal, any excess hydroxide would increase the alkalinity and hardness of the water. Although different controlling methods have been proposed, this operation has so far, in general, not been automatically controlled. In this paper the authors present a new procedure to control the process based on the execution of a indefinite number of cycles. Rather than maintaining a continuous set point, the aim of the proposed system is to provide a mean base dose equal to the continuous dose, that should be added to the incoming water in order t o neutralize its acidity, in a cycle period. The results obtained in the experimental validation of the procedure show that it may be a good alternative to solve the problem of decarbonation process control.
Introduction alcium hydroxide is widely used for water decarbonation. The process is a neutralization of the carbonic species acidity to carbonate, followed by precipitation of the carbonate as CaC03. (In the Appendix there is an explanation of the term acidity used in this work). If there is enough Ca2+ion, the process lowers the carbonic species concentration in water to residual levels, higher than equilibrium levels in practice, and eliminates water hardness. Water quality can be substantially improved, in many cases, when this removal is a high proportion of its total saline content. Also, the precipitation involved helps to clear the water and remove any colloids it may contain. Decarbonation by precipitation, which was the earliest procedure used to eliminate water hardness, is still occasionally employed, particularly for treating large volumes of water, e.g. in water purifying plants treating town supplies, in processing boiler feed water in power plants, and by textiles finishing industries (David and Beach, 1976; Cosens, 1976; Fox, 1979; Wiersma, 1979). Water decarbonation has become a standard procedure for the treatment of the water used by soft drink beverage industries, which require a bicarbonate, organic matter, and colloid-free, low-hardness supply of completely clear water. Soft drink beverages have a low pH that is adjusted by addition of phosphoric, tartaric, and citric acid, all of which are expensive reagents and would be required in larger amounts if the water concerned contained a substantial bicarbonate concentration; in addition, the amount of acid to be added would vary from supply to supply depending on the concentration of carbonic species present in the water. Carbonic species are thus best removed in the water conditioning process. This is practically never accomplished by ion exchange, but by carbonate precipitation, which also ensures perfect water clarification. One of the keys to efficient decarbonation is using the right concentration of calcium hydroxide; in fact, while any amount below the stoichiometric dose would fail to ensure good removal, any excess hydroxide would increase the alkalinity and hardness of the water. This operation has so far, in general, not been automatically controlled. Different automatic controlling methods have been proposed via a feedback, feedforward, or mixed loop and monitoring one, or several, treated water parameters. In 0888-5885/94/2633-1501$04.50/0
some cases (Slack, 1970; Zagoskin, 1970) this was the conductivity which should be minimal, though with an unpredictable value due to the presence of other salts and to calcium carbonate oversaturation, at the optimal point. An alternative procedure involved monitoring the basicity of the water, measuring it by automatic off-line titration (Smith, 1967). The normal candidate parameter on which to base an automatic control of the decarbonation process should be the pH. However a feedback control loop (Merril et al. 1977;Wedlich, 1967)of this type may pose problems arising from the nonlinear relationship of Ca(0H)zdosing to pH, to the point where one needs to have a long reactor residence time (according to Shinskey (19731, when using calcium hydroxide, it should be of 15 min, at least), which would require that in standard installations the flocculator be included within the control loop, thus increasing the system gain, and to the point that the set point (Gustafsson, 1992) (uiz. the pH at which neutralization of bicarbonate to carbonate is complete, that is, the carbonate equivalence point) depends on the carbonate concentration in the solution and hence on the degree of saturation of calcium carbonate, which in turn is a function of a number of variables including the temperature, suspended matter concentration, etc. In this work we developed a new base dispensing control system based on the execution of an indefinite number of cycles which are assumed to be repeatable and identical. The aim of the proposed system was to provide a mean base dose equal to the continuous dose that should be added to the incoming water in order to neutralize its acidity. Rather than maintaining a continuous set point, a concentration of calcium hydroxide exceeding the theoretical requirement for neutralization of the incoming water flow was supplied over a given interval of each cycle, while no further hydroxide was added during the rest of the cycle.
Description of a Water Decarbonation Plant Notwithstanding specific design differences, most water decarbonation plants operate in a continuous fashion and consist of the following basic elements (Figure 1). (1)A reagent mixing zone, where calcium hydroxide, normally fed as a slurry, and the water to be treated are mixed thoroughly in a turbulent regime over a fairly short 0 1994 American Chemical Society
1502 Ind. Eng. Chem. Res., Vol. 33, No. 6, 1994
(c) The calcium hydroxide concentration in the lime slurry. Industrial lime is far from pure, and its Ca(OH)2 concentration varies from batch to batch. Also, it is rather difficult to accomplish a really constant slurry concentration in all the dispersions prepared. The rather long response time of the system requires any dosing changes to be made gradually in order to avoid under- and overdosing oscillations.
Description of the Proposed Process Control System The proposed system consists of a thoroughly stirred reactor through which a continuous flow of the water to be treated is passed for addition of the reagents. The emerging flow is collected in a larger tank where the water is allowed to flocculate and homogenize. Finally, the precipitate formed is removed and clear water is filtered off. From the hardware point of view this is not very different from the conventional plants. The process involves an indefinite number of cycles that are assumed to be repeatable and identical. Over a given interval of each cycle, calcium hydroxide is added to the incoming flow above the stoichiometric amount required to neutralize the water, whereas no further hydroxide is added during the remainder of the cycle. Obviously, the water emerging from the reaction tank will contain a variable concentration of Ca(OH)2, so it must be kept in a homogenizing tank for a reasonably long residence time in order that the final water supply is as uniform in quality as possible. Each cycle consists of three steps, which shall be denoted by 0-2. During step 0, a constant dose of Ca(OH)2 is added to the water. Its duration, denoted by to (e.g. measured in minutes), is indefinite: as long as required for a minimum pH of 11.2to be reached. The amount of hydroxide added exceeds that theoretically required to neutralize the circulated water. No calcium hydroxide is added during step 1. As water flows in, the hydroxide concentration in the tank decreases gradually. This step begins at t o and lasts until the water emerging from the tank reaches the carbonate equivalence point, at time t = tl. Hence the duration of this step is given by the difference tl - to. During step 2, the still remaining excess of calcium hydroxide added in step 0 is offset by allowing more water in with no further addition of hydroxide. At the end of this step and of the cycle, marked by time t2, the overall amount of caustic base added will be the same as the total acidity of the water treated throughout the cycle. The problem is thus to determine the time required for the acidity of the water flow to be exactly neutralized by the added Ca(OH)2,i.e. t2, after which a new cycle is started. The proposed system allows the use of a small reactor, such as the mixing tank itself, of certain types of conventional plants. After it, in the homogenizing tank (flocculation zone), the reaction would develop gradually to completion with no need for additional control. Therefore, the proposed system requires no changes in the traditional arrangement of many standard facilities, as they all include a flocculator that will aid in smoothing quality oscillations in the treated water. For the proposed control system to be useful, one should be able to calculate t2 from to, which is set arbitrarily, the measured incoming flow rates, and the reactor water pH. No analysis of the water or dosing Ca(OH)2 slurry concentration should be needed. Ideally, all calculations should be performed in real time so the t2 value would be
n BAFFLES
Figure 1. Classic water decarbonation plant.
time, a few minutes at most. This is the zone where the reaction starts and where the solution and reagents become uniformly mixed. The particles contained in the solution emerging from this zone are extremely fine and difficult to separate. Also, the solution is highly oversaturated in CaC03. Inasmuch as precipitation is aided by the presence of abundant suspended particles, most water plants use recirculated slurries from the settling tank going into the reactor, to provide plenty of crystallization nuclei and diminish oversaturation. (2) A flocculation zone, where the water is kept for a somewhat longer time (25-40 min). Some stirring is provided, but any significant turbulences are avoided as far as possible. The previously formed CaC03 crystals grow in size and agglomerate into flocculus. The solution approaches equilibrium and oversaturation diminishes. On leaving this zone, the water containing the suspended flocculus is ready for separation. (3) A settling zone, in which the water is kept under minimal turbulence conditions so as to allow suspended particles to settle. The cleared water emerges from the top while the deposited slurry is purged periodically. (4) A filtration zone, where any suspended particles remaining in the water are finally filtered off. Provided an appropriate calcium hydroxide dose is used, the only carbonic speciespresent in any significant amount, in the water leaving the plant, should be carbonate ion. Also, the water should contain no caustic base. The water is normally titrated acidometrically by using phenolphthalein and Methyl Orange as indicators. The analytical results are normally reported as p and m, which denote the milliequivalents of alkalinity to each indicator per liter of solution. The relation between p and m determines the goodness of the dosing process. Thus, correct dosing corresponds to m = 2p, whereas m values smaller or greater than 2 times p denote excess or deficient dosing, respectively. In practice, small deviations from the above relation are accepted provided m I0.8. Calcium hydroxide dosing control is usually performed manually, which is an arduous task. The amount of reagent to be added to the water is determined by three factors. (a) The water flow rate, which is kept as constant as possible rather than being adjusted to the water demand. Thus, processed water is fed to a reservoir. When this is full, passage of water through the plant is interrupted; otherwise, a constant flow of water is circulated. (b) The composition of the water. This may vary with time, though very slowly in any case. Adjustment of the calcium hydroxide dose for this reason is rarely required more than once or twice a week.
Ind. Eng. Chem. Res., Vol. 33, No. 6, 1994 1503 known before being reached. For this purpose, the functioning of the facility should be computer-controlled in order that a given cycle could be finished when the elapsed time would be equal to the calculated tz value. A new cycle would then be started by adding further Ca(0H)z for a time to, new pH readings would be made, and a new tz would be calculated in order to start a fresh cycle at the right time, and so forth. Correct dosing will result in the overall number of moles of hydroxide added in step 0, of every cycle, equaling that of acidity moles, with respect to the carbonate equivalence point, in the water and other incoming flows (e.g. recirculated slurry) during the whole cycle.
acidozQzto= acidozQzO’To
(1)
where
0’ =
61 +
V Qz + Q3
(b) the flow rates Q1 and Q3 throughout the cycle (acidolQl + acido3Q3)tz= (acidolQl + acido3Q3)(To(O’ - 0”)
+ 0”TJ
(2)
where
Mathematical Model of the Controlling Process Some Previous Definitions. We suppose three flows going into the reactor, namely Q1 = raw water flow; constant along the cycle
Q2 = caustic base flow; different from zero only during step 0 when it has a constant value Q3 = flow coming from the settling tank purge to introduce a high amount of particles (crystallization nuclei); constant along the cycle. All along this exposition we will use the variables acid; these (as it is described in the Appendix) are the acidities with reference to the carbonate equivalence point. The hydroxide alkalinity can be considered as a negative acid: hydroxide alkalinity = -acid
So we will always deal only with acid variables, having either positive or negative values. The acid variables of the incoming flows will be called acidol, acidoz, and acid03, corresponding respectively to the QI, Qz, and Q3 flows. In the mathematical model that will be developed, the equations have a much simpler form if the relative times T are used instead of the regular times t (e.g. measured in seconds or minutes).
where Q is the total flow running through the reactor and V is the reactor volume. T i s a dimensionless parameter which can be easily calculated at any time if the flows and regular time are known. Controlling Criterion. The criterion to be applied in order to control the treatment (and the mathematical model will be developed along these lines) is as follows: the mean water acidity (acid) after a complete cycle should be zero. Even though the zero acidity condition could be tested at the entry or exit, we shall only consider the possibility of the acidity of the overall flow entering the reactor being zero. Therefore, the sum of all the moles of acidity (with positive and negative values) in all incoming flows throughout a cycle should be zero with respect to the carbonate equivalence point. It is supposed that regular time, pH, and flows will be known at any time. Moles of Acidity in the Incoming Flows Entering theReactor duringa Cycle. The overall moles of acidity going into the reactor during the cycle will result from (a) the flow rate Q 2 during step 0
Inasmuch as the sum of (1)and (2) must be zero,
( ; ; );
-acidozQz= (acidolQ, + acido3Q3) 1- - + - -
(3)
This equation can be expressed as a function of the flow rates: acidozQz= (acidolQol+ acido3Q3)(
Q2
-
Let us define a new variable a,given by ff=
acid02QZ (acidolQl + acido3Q3)
or expressed as a function of the flow rates and the relative times TOand Tz, as can be deduced from eq 4:
It is interesting to manitor the changes with time in the acidity concentration within the reactor (considered to be a CSTR) which will not be affected by CaC03 precipitation. In the precipitation process the co32-ions in solution decrease, but [COS”] does not appear in the acid expression (A-2). So the acidity will thus vary according to
-dacid - (acid, - acid)-Q dt
V
(7)
acid, = acid concentration in the input flow Q the solution ofthis differential equation in terms of relative time is acid = acidie-‘T-Ti)+ acid,( 1- e-(T-Ti))
(8)
acidi = acid concentration in the reactor at the initial relative time Ti
Calculation of Tz.The procedure to be used to calculate T2 varies depending on whether two or three time parameters are known. (1)If two time values ( t o and ti) are known, then using them in eq 8 provides the following expressions: acidTo= acidice-TO + acideo(l- e-To)
(9)
1504 Ind. Eng. Chem. Res., Vol. 33, No. 6, 1994
+
acidTl = acidToe-(T1-To'acidel(l- e-(T1-To)) (10)
acidic,acidT,, aCidT1,and acidTzare the acid concentrations in the reactor at relative times 0, TO,TI, and Tz. acideo= acid concentration in the mixed input flow at relative time 0 5 T 5 To acidel = acid,, = acid concentration in the mixed input flow at relative time To I T I T,
Substituting for acidToby (18) and acidl; by (15) into (17) and further rearrangements give rise to the following expression in which the only acidities showing are those of the mixed incoming flows: acidel(1- eT1-To) = acid, (1- e-(TrT1))e-To +
+
acid,(l - e-To)= acido,(e-TO- e-TzeT1-Ta) acid, (1- e-TO) (19) Rearranging gives
Qlacido, + Qzacidoz+ Q3acido3
Q
acidel =
Q = 81 + Qz + Q3
Qlacido, + Q3acido3
Q
acideo eT1-To( 1- e-") -- 1-
(21)
(1- e-TO)
acidel
(12)
Finally, from eqs 12 and 13 it follows that Q=Q1+Q3
(13)
By definition, acidTl = 0 since T1 is the time at which the reactor reaches the carbonate equivalence point. Therefore, eqs 10 and 11 become
Q1 + Q3 acidolQ, + acidozQ2+ acido3Q3acidol Q1 Qz Q3 acidolQl + acido3Q3
-- -
-
+ +
acid02Q2 acidoiQi+ acido3Q3 Q1 + Q 3
8 1+
acid03has a theoretical value of zero since, if the treatment is performed correctly, the water from the recirculated slurry should be at the carbonate equivalence point. In any case, this acidity concentration would be negligible compared to that of the treated flow and, in practice, can be considered to have a value of zero. Taking into account that TOis set at will and TIis known, one has a system of six equations, uiz. (41, (91, and (12)(151,in eight unknowns (acidic,acidTo,acidTz,acids, acidel, so two further equations, or acidol, acid02, and Tz), conditions, are required. One such condition can be that of using the variable a (eq 5) (which is a function of the incoming acid variables) instead of the acidities of all the incoming flow rates. This involves ignoring the absolute values of these acid terms. The other equation can be obtained by assuming that the plant is in a steady state, i.e. that all the cycles are identical and repeatable. Thus, acidTz= acidic
(16)
Even though the above assumption may seem arbitrary, it can be experimentally checked that the plant attains a steady state in one or two cycles. From this point, the calculation proceeds as follows: by writing eq 11 with (16) taken into account and writing again eqs 14 and 15, one has for the whole cycle acidTa= acidTZe-" + acideo(1- e-To)
(17)
acid,, = acidel(l- e-(TrT1))
(15)
Solving eq 16 for aCidT, yields
(18)
(acidel- acid,e)(l - e-To)= acidel eT1-To(l- e-Tz) (20)
these incoming flow acidities will be acideo=
acidTo= acidel(1- eT1-To)
Qz + QB
(1+ a ) (22)
and, by substituting the a value given by eq 6 into eq 22, one has
o= acid, Q1+Q3 ,('+-acid,
Qi
Q2
+ Q2 + Q
+&):I+
Qi
(l
= Q1
+63 Q2
+ Q3+
Qz
Q1 + Q,
+ Q3
-
With eqs 21 and 23 finally the following equation is obtained (24) This equation has no analytical solution but can be solved by using a computerized iteration procedure. In fact, eq 24 only involves relative times, is independent of the flow rates, and is applicable over wide ranges. However, it requires the overall incoming flow rates at the reactor to be known at every time as they are needed to calculate the relative times according to the very definition of relative time. (2) Three time values (to, tl, and t') are known. As in the previous case it is supposed that acid03has a negligible value and that the absolute values of the different input flow acid terms cannot be calculated; instead the variable a is used. If not only T I (i.e. the time at which acid = 0 in the falling pH branch of the cycle), but also T' (the equivalent time for the rising p H branch) is known, then one has a system of zero degrees of freedom which allows Tz to be calculated without the need to assume that the system is in a steady state.
Ind. Eng. Chem. Res., Vol. 33, No. 6, 1994 1505 Thus, by taking T’ as the starting point for calculation of acidTofrom eq 8, one has acidTo= acid$
- e-(TrT))
(25)
Substitution of eq 25 into (14) and rearrangement yields 0 = acide (1- e-(TrT))e-(T1-T~) + acid (1- e-(T~-T~) el
0
) (26)
further rearrangement of which leads to
Figure 2. Experimental plant design.
Finally, substituting the acidity ratio by its value according to eq 23 and solving for TZyields
This equation does not directly depend on the flow rates either.
Implementation of the Proposed Model The experimental procedure to be developed was to allow the times at which the reactor reached the carbonate equivalent point (tl and t’) to be determined. The reactor water reached the carbonate equivalence point twice in each cycle: one within the rising pH branch (dpHldt > 0) and the other within the falling branch (dpH/ dt C 0). However because the carbonate equivalence point (pH value) depends on the overall concentration of carbonic species, it is not the most suitable parameter for determining it. We thus chose instead dpH/dt for this purpose. It was supposed, as a hypothesis, that this derivative should have a maximum (positive) at the carbonate equivalence point in the rising branch (t’ C to) and a minimum (negative) at the equivalence point in the falling branch (tl > to). These two points correspond to the inflections in the pH us time plots. The derivatives of pH with respect to time and the acidity concentration in the reactor are related by dpH - dpH dacid dt dacid dt For a solution of low pH containing carbonic species that are neutralized by adding a strong base (in the absence of Ca2+),the variation (rise) of the pH with the amount of base added will include an inflection corrresponding to the carbonate equivalence point, where the derivative of pH with respect to the amount of base added will be maximal. For a solution of pH higher than that of the equivalence point for some added acid, the derivative of pH at the new inflection of the carbonate equivalence point (falling branch) will have a minimal value. The overall concentration of soluble carbonic species, ci, would remain constant with time in the two examples above. If the rate of base, or acid, addition is kept constant, then the maximum and minimum of dpH/dt will coincide with those of dpH/dacid. However, the decarbonation process is complicated by the fact that dacidldt (in the reactor) is not constant and also by the fact that the solution contains Ca2+,which precipitates as CaC03 and hence diminishes the overall concentration of soluble carbonic species, ci. Therefore, it is not certain whether
the maximum and minimum of dpHldt will coincide with the carbonate equivalence points. Anyway the procedure to be used involves determining t:! on a control system based on the assumption that the integral total acidity of the flows entering the reactor should be equal to zero at the end of the cycle, and on the knowledge of time to (set arbitrarily) and tl (supposed to be the time of minimal dpHldt in the decreasing pH branch of the cycle, determined in an approximate way as the ratio of differences of pH values and time). Finally, it was decided not to use an algorithm based on time t’. It would have been rather imprecise because the rising pH branch is very steep, so the time involved is very short and the potential errors made in estimating dpH/dt could have been very large.
Materials and Methods Description of the Experimental Plant. The experimental plant design is depicted in Figure 2 and consists of the following elements: (1)A 1000-Lcement fiber tank (TI)for storing the water to be treated. (2) A polyethylene tank (Tz)for storing the dosing base. (3) A rapid-mixing, thoroughly stirred polyethylene reactor of variable volume (R1) where the base is added. Its capacity varies between 2.6 and 4.3 L, depending on the height at which the overflow is placed. I t includes four baffles at right angles to the wall intended to improve the mixing efficiency. The water flow enters the reactor from the lower half through a vertical pipe that virtually reaches the bottom of the tank. The caustic base is dispensed through a glass tube that runs concentrically along the water flow pipe and has a narrow-bore, almost capillary end intended to prevent any further base from entering the reactor after the base dispensing pump has been stopped. The outgoing water flow leaves the reactor at the top, where the pH measuring electrodes are placed. (4) A 50-L polyethylene tank (T4) for dampening variations in the concentration arising from the control system itself. It includes four baffles positioned at right angles to the tank wall in order to increase the mixing efficiency. A t the tank outlet is placed the second set of measuring pH electrodes. (5) An AGITASERfast stirrer (AI) intended tomaintain calcium hydroxide suspended in tank Tz by means of a reversed, double-crown turbine actuated by a monophasic motor of 220 V and 0.25 hp. The turbine design ensures thorough agitation. (6) An identical fast stirrer (Ad for reactor R1.
1506 Ind. Eng. Chem. Res., Vol. 33, No. 6, 1994
I I
___ &-
PI2
puMpl PUMP2
i
Figure 3. Electric-electronicassembly of experimentalplant design.
(7) An ASEA-CES slow stirrer furnished with three 45' tilted blades powered by a triphasic motor of 380 V and 0.5 hp, and intended to homogenize the contents of tank T4.
(8) A HEIDOLPH RuMo 100 peristaltic pump (PI)of variable speed between 20 and 100 rpm providing a maximum flow rate of 1.35 L/min (to provide the raw water flow Qi). (9) A similar pump (P2)providing maximum flow rates of 0.17 L/min (to provide the base dosing flow Q2). The electric-electronic assembly (Figure 3) of the system is composed of the following elements: (1) A Hewlett-Packard H P 9915 personal computer equipped with a Matrix ROM for matrix calculus and a memory expansion board providing an overall 32 kB. The programming language used is H P enhanced BASIC. (2) Two CRISON pH-meters of digital output and display. (3) Two pulse generators placed between pumps PI and Pz and consisting of a photodiode-illuminated phototransmitter. Irradiation of the transistor is suspended after each turn of the pump axle by means of a transparent disk soldered to the axle which includes an opaque spot that stops the light flux at a given point of the rotary motion, thereby producing a pulse. (4) Two BCD interfaces linking the computer to its peripherals. One of them (interface 1) allows the output from the two pulse counters of the pumps and the reading from a manually actuated switch to be acquired. This interface is also used to output signals that active some thyristors and to start pumps PI and Pz. The other interface (2) is used to input the pH-meter readings to the computer. (5) A box connected to interface 1 and composed of the following elements: the electronic circuits of the pulse counters, a manually actuated switch used to set the AT1 value (this value and its function will be described later on when discussing the results), and a series of thyristors used to supply the required voltages to pumps PI and Pp according to the commands sent by the computer via interface 1. Control Software. The program used to control the plant functioning is made up of the following parts: (1) Initialization of variables and a series of starting routines that check the flow rates from the pumps and allow input of the parameter values to be subsequently used by the calculation algorithm. (2) A timed routine for measurement of pH in the reactor and homogenizing tank. (3) A timed routine for measurement of the pump flow rates and reading AT1, which is set manually. Flow rates Q1 and Q2 are measured in a continuous fashion by means of the pulse counters on the pumps. (4) The main routine, which directly controls the process, counts time, stores data on magnetic tape for subsequent processing, performs algorithmic calculations, makes logical decisions, and commands the pump motors.
(5) A routine for halting the process every five cycles in order to analytically monitor the control efficiency and change AT1 if necessary. Working Conditions. We chose to work with an alkaline base solution rather than a Ca(0H)z suspension for a number of reasons. First, calcium hydroxide is scarcely soluble (ca. 1.2 g/L), so it has to be dispensed in suspended form; otherwise the volumes to be used would be inordinately large and the procedure would be quite impractical. The action of a Ca(0H)z suspension entails dissolving the Ca(OH)2first and then having it react with the acidity of the raw water. While this latter step is instantaneous, the former one takes some time. The above-described control procedures rely on the assumption that the base supplied to the reactor is immediately available, which in principle, would not hold if a Ca(0H)z suspension were used. On the other hand, it is quite possible that the step of Ca(OH)2dissolution may have, in practice, little effect on the overall control process, because such a handicap might be offset by: (a) the fact that the base concentration in the reactor will always be well below the solubility limit of calcium hydroxide, (b) the use of micronized Ca(OH)z, and (c) the fact that the calcium hydroxide is only dispensed during the first part of each cycle, the reactor receives only water for about two-thirds of the overall time. Therefore, soon after the inflow of Ca(0H)z has been stopped, all the base particles will have been dissolved and, at least for most of the time following to, the plant should behave as if a soluble base had been dispensed. Notwithstanding the above reasoning, we chose to use a soluble base (KOH) and supply the required Ca2+ concentrations by dissolving the appropriate amounts of CaClz in the water to be treated. The oversaturation always present in the precipitation of CaC03 raised the solution pH and resulted in less sharp inflection points in the pH us time curves. It would have been desirable to have had precipitated slurry recirculated in the reactor in order to have a large number of CaC03 crystallization nuclei and hence reduce oversaturation. Anyway, all the experiments were carried out with no slurry recirculation, i.e. with Q3 = 0.
Results Figures 4-7 show the variation of pH and its derivative with respect to time throughout a typical cycle for four types of water encompassing the whole possible range of representative water compositions. The compositions in question and the system features are presented in Table 1. As can be seen, two of the waters had a high carbonic species content whereas the others had a relatively low concentration. In each pair of samples, one contained a small excess of calcium over the stoichiometric amount required to precipitate all carbonic species, whereas the other contained a relative large excess of the alkaline earth cation. Preliminary assays showed that if the minimum of the derivative of pH with respect to time was taken as the carbonate equivalence point, the treated water was underdosed with base (i.e. acid > 0 at T4) in every case, so the calculated Tz was too long because the minimum value of dpH/dt was detected after the carbonate equiva> tl). Depending on the prevailing lence point conditions, the deficiency of dispensed base was more or less marked. One empirical solution to the above problems involves subtracting a fixed amount from the relative time corresponding to the minimum derivative value
Ind. Eng. Chem. Res., Vol. 33, No. 6,1994 1507 12 0 11 5
11 0 10 5 10 0
5
95 90 a5
80
7
5
70
1
1
I
1
j
1
1
~
j
TO
T1 R e l a t i v e time
12 10
8 6
;ivv?q 4
I
2
T)
\
I Q U
0
-2
-4
-6
-8
-1:
-10
TO
T1
-12
Figure 4. Variation of pH and its derivative with respect to time in the two reactors for water 1.
R e l a t i v e : me Figure 5. Variation of pH and its derivative with respect to time in the two reactors for water 2.
T,, = Tmin - AT, tlc = tmin- At, The control algorithm subtracted an amount AT1 from the relative time corresponding to (dpH/dt),i, in order to obtain Tic, and this was introduced in eq 24, as the right 2'1 value, to calculate Tz. At the beginning of the process, the water in Tq was adjusted to the carbonate equivalence point. Then, after a given number of cycles, the process was stopped and the water in this tank was analyzed. If 2p - m was very different from zero, the water in the tank was readjusted by adding more acid or base and AT1 was also altered accordingly. The results obtained in these experiments can be summarized as follows: (a) The absolute (dpH/dt),i, values obtained for the waters containing high carbonic concentrations were larger than those of the waters with low carbonic contents. (b)The waters containing high carbonic concentrations provided pH us time curves with much shaper minima. (c) The dpH/dt curves of the waters with low carbonic and calcium concentrations had ill-defined minima of small absolute values. (d) As a rule, the standard deviation of t2 was higher for the waters containing small amounts of carbonic species than for their more concentrated counterparts. This is consistent with the better defined minima of the latter,
which allow for more precise determinations of tmin that are less markedly affected by noise. (e) The waters with a high concentration of carbonic species were less prone to oversaturation. (f)The smaller the oversaturation and hence the sharper the minimum of the derivative of pH with respect to time, the smaller the AT1 value to be used in order to offset the difference between Tmh and TI. (g) When the complete cycles sequence of an experiment is analyzed, it is seen that,even in the absence of a feedback link, the process has some sort of inherent memory which results in an unusually long cycle arising from a substantial error in the experimental determination of tmin being followed by an uncommonly short cycle and uice versa. This compensates largely for most of the oscillations in the homogenizing tank. The origin of this compensating effect is quite clear: after a rather long cycle, the water in the reactor will have a higher than expected acidity concentration. In the next cycle, after t o (a fixed value), the acid concentration (negative) will be lower than normal in absolute terms, so the water will reach the carbonate equivalence point in a shorter time (Le. a smaller tmin)and hence the cycle will be shorter. (h)No significant differences are observed on comparing the shapes of the dpHldt curves for some trials in which Ca(OH)2 was used instead of KOH if only the standard deviation was somewhat higher in the former case.
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1508 Ind. Eng. Chem. Res., Vol. 33, No. 6, 1994 120 11
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Figure 6. Variation of pH and its derivative with respect to time in the two reactors for water 3.
Conclusions The procedure reported in this work allows water to be decarbonated by dispensing a caustic base and using an automatic control system relying on a mathematical algorithm and on pH measurements that allow the carbonate equivalence point in the falling portion of the pH us time curve to be estimated. It is also necessary to take time and flow rate measurements. This does not require application of a mathematical model for ion equilibria; rather, the system can be considered to behave like a black box. The proposed procedure involves calculating the time tminat which the derivative of pH with respect to time is minimal. Such a derivative is approximated through a finite difference ratio. We found that Tmindid not coincide exactly with the moment at which the reactor reached the carbonate equivalence point (TI),but was somewhat longer. The lack of coincidence between Tminand T1 will result in a greater or lesser error in the calculation of Tz, if Tmin is used instead of T1 in eq 26. The net result will be underdosing of the base. The delay, defined by AT1 = Tmin- T I ,was found to depend on the degree of saturation of the reactor water, so everything contributing to diminish oversaturation will redound to a decreased AT1 value.
TI
Selative time
me
Figure 7. Variation of pH and its derivative with respect to time in the two reactors for water 4. Table la water
[HCOs-] (pprn)
[Ca2+](pprn)
1 2
1500
2000 1500 454 264
3 4
1300 300 250
reactor vol (L) ATl* 2.6 2.6
0.06
4.3
0.055 0.1
2.6
0.22
All the concentrations are expressed as ppm of CaCOs. The parameter AT1 is described below. The values given in this column are those that made it possible to get treated water at roughly the carbonate equivalence point.
It would therefore be desirable, through precipitated slurry recirculation, to ensure a high precipitate concentration in the reactor and homogenizing tank in order to obtain a large number of CaC03 crystallization nuclei and hence decrease oversaturation. More efficient control of the process will often require manual input of a AT1 value for the control algorithm and using time T I , = Tmin- AT1 to calculate Tz from eq 26. Nomenclature acidol = acid concentration in the input flow Q1 acid02 = acid concentration in the input flow Qz acid03 = acid concentration in the input flow Q3 acid, = acid concentration in the input flow Q acid, = acid concentration in the mixed input flow at relative time 0 IT 5 To
Ind. Eng. Chem. Res., Vol. 33, No. 6, 1994 1509 acid,, = acid concentration in the mixed input flow at relative time TOI T I T1 acidi = acid concentration in the reactor at the initial relative time Ti acidic = acid concentration in the reactor at relative time 0 acidT,, = acid concentration in the reactor at relative time To acidT, = acid concentration in the reactor at relative time T1 acidT, = acid concentration in the reactor at relative time T2 m = milliequivalents of alkalinity to methyl orange per liter of solution p = milliequivalents of alkalinity to phenolphthalein per liter of solution Q = total flow running through the reactor 81 = raw water flow Q2 = caustic base flow Q3 = flow coming from the settling tank purge t o = duration of step 0 tl = time for water emerging from the tank to reach the carbonate equivalence point (falling pH branch) t z = total time of cycle To = relative time to TI = relative time tl T2 = relative time t 2 T' = relative time for water emerging from the tank to reach the carbonate equivalence point (rising pH branch) V = reactor volume
Appendix We call the equivalencepoint the pH of a pure solution of a free weak acid, or free weak base, or of a pure salt of a weak acid, or of a weak base. A solution containing a weak acid and its counter salt from a strong base, in any proportion between the pure acid and the pure salt, can be regarded in two different ways: (a) as a pure acid solution to which has been added y equivalents of a strong base per liter (thus, y will denote the alkalinity of the solution with respect to the acid equivalence point); (b) as a pure salt solution to which z equivalents of a strong acid per liter of solution are to be added (in this case, z will denote the acidity of the solution with respect to the salt equivalence point). Acidity and alkalinity are capacity factors that represent the respective neutralization capacities of the solution against strong bases and acids. They are always relative to a given equivalence point, whether that of the salt or free acid. Proton Condition Concept. At equilibrium, the total proton excess in some of the species existing in a solution, prepared by adding a pure product (e.g. an acid HB or a salt NaB) to pure water, will be equal to the total proton deficiency of some other ones. This excess or deficiency is measured from a zero level (uiz.that of HzO and HB or NaB, which can be assumed to be initially nonionized). From this standpoint, the acidity or alkalinity of a solution can be defined with respect to any of the equivalence points of the system. According to the above reasoning, the species deriving from carbonic acid (a diprotic acid) will result in three equivalence points corresponding to each of the following pure species: HzC03 (carbonic acid), HCO3- (bicarbonate),and Cos2- (carbonate). The expressions for the acidity and alkalinity for each of these species can be derived from the proton balance by assuming that the system contains no weak bases and carbonic acid is
the sole weak acid present. As a result of the addition of a strong acid (HC1) or base (NaOH) (considered to ionize completely), it wouldgive rise, on ionization of the solution, to the ionic species H+, C1-, Na+, and OH- (as well as to all the possible species of the carbonic system). We shall consider here the alkalinity with respect to the equivalence point of carbonic acid alk = 2[C032-l + [HCOLI
+ [OH-] - [H'I
(A-1)
and the acidity with respect to the carbonate equivalence point acid = 2[H2C0,1 + [HCOLI + [H'I - [OH-]
(A-2)
Throughout this paper we refer to alk = alkalinity with respect to the carbonic acid equivalence point acid = acidity with respect to the carbonates equivalence point By titrating the alkalinity of a solution with an acid and Methyl Orange, one will obtain alk (Le. m). On the other hand, acid cannot be obtained directly because the color change of the indicator is imperceptible, so it must be calculated. This arises from the ill-defined inflection point corresponding to the carbonate equivalence point for a solution containing carbonic species. For a given equivalence point, the alkalinityof a solution is the inverse (equal to the absolute value with changed sign) of its acidity.
Literature Cited Cosens,K. W. Modern designupdatessofteningplant. Water Wastes Eng. 1976, 13 (ll),75,76, 79-80. David, A.; Beach, P. E. Gainesvillegets sophisticated. Water Wastes Eng. 1976, 13 (ll),83,85,92. Fox, G.T.J. The hardness of water and methods of softening it. Water Sew. 1979,83, (1003),727. Gustafsson, Tore K.; Waller, Kurt V. Nonlinear and adaptive control of pH. Znd. Eng. Chem. Res. 1992,31 (12),2681. Merril, D. T.Wide range pH control licks plant problems. Water Wastes Eng. 1977, 14 (8),28. Shinskey, E. G. pH and pIon control in process and waste streams. Environ. Sci. and Technology Series; John Wiley and Sons: New York, 1973. Slack, J. G.The use of differential conductivity measurements for controlof lime and lime/sodasoftening. Water Treat. Exam 1970, 19, 204. Smith, D. W. Control of lime-soda softening at Sheffield Corporation Waterworks. Znstrum. Eng. 1967,4 (7),134. Wedlich, E. Die Bedeutung einer pH-Regelung fur die Automatisierung einer Schnellentkarbonisierungsanlage(Importance of a pH regulator to automated rapid decarbonation). Text.-Praxis 1967,586.
Wiersma, D. J. Kalk in waterbehandeling (Chalk in Water Treatment). WRC Znf. 1979, 12 (12),274. Zagoskin, E. I. Automatic regulation of the process of liming water in a water treatment installation. USSR Patent 724.456,Class No. C02C1/18;G05D27/00,1978. Received for review February 22, 1994 Accepted March 10,19948 Abstract published in Advance ACS Abstracts, April 15, 1994.
