Continuous Measurement of Dissolved Oxygen in Water H.
S. LEVINE, W. V. WARREN, E. C. TSIVOGLOU,
and
W. W. WALKER
U. S. Public Health Service, Robert A. Taft Sanitary Engineering Center, Cincinnati 26, O h i o A method for the continuous measurement of dissolved 0x5 gen in water has been developed, based on establishing a IIenry's law equilibrium between a flowing water sample and the oxygen content of a gas at constant presstire and volume. The results are not influenced b y temperature, salt content, pollution, aeration constant, barometric pressure, or the dissolved nitrogen content of water. Experimental confirmation of the method for dissolved oxygen in wrater is presented. The design and performance characteristics of the major components of a practical instrument are given.
C
OSTISI-OL-S measurement of dissolved oxygen has long been recognized as a practical solution to many economic and technical problems in water pollution abatement and control programs. Hence, there is an interest not only in establishing permanent diwolved oxygen gaging stations a t critical points on impoi t m t streams, but also in developing means for rapidljobtaining the oxygen profile of polluted surface waters.
Methods for the continuous mcdsurenient of dissolved 01)gcn in water include chemical, polarographic, and gaseous procedurps. Rriggs and others (2) described an intermittent instrument based on the Kinkler method ( I ) , in which a water sample is taken and :t stepwise chemical test made automatically in a cycle of opcmtions. Thayer and Robinson ( I O ) reported a continuous recording instrument based on a gaseous stripping technique. Other instrumental methods have been desci ihed (6-9) which apptar to have limited application. A method has been developed for obtaining a continuous rpcoid of the dissolved oxygen content of mater, in nhich the determination of dissolved oxygen is made bv analysis of a gas whose composition conforms with the dissolved oxygen content of water by Henrj 's law ( 4 ) . Principles are presented for the design and operation of an instrument using this method, as well as experimental confirmation of its feasibility and design information for the construction of a practical instrument. THEORY
Principle of Operation. To conform 1% ith the convention adopted b y American Public Health Association (1 j, the solubility of oxygen in water is defined as that concentration of the gas in water which is in equilibrium ~ i t hoxygen in watersaturated air a t 1 atm. total pressure. The solubilitj of oxygen in water depends on temperature. salt concentration, and the like The actual concentration of dissolved oxygen in water, times 100, divided by its solubility as defined above is referred t o in this work as per cent saturation. Henry's law states t h a t the equilibrium partial pressure of oxygen gas is proportional t o the concentration of dissolved oxygen in water a t any given temperature and salt content. This relationship is completely independent of temperature and salt content if the dissolved oxygen content of water is expressed in terms of per cent saturation as defined above. Hence, H e n n '5 law presents an attractive basis for development of a method for continuous measurement of dissolved oxygen in water. A typical device, referred to as an aspirator unit, for continuously maintaining a Henry's law equillbrium between the oxygen content of a small quantity of gas and the dissolved oxygen content of flowing water is illustrated schematically in Figure 1 .
WATER I N L E T
TO FLOW CONTROL
TO P R E S S U R E REGULATOR AND E X T E R N A L GAS SUPPLY
-
Legend -
[ [
WATER
-1 -
GAS-WATER
I,$M I X T U R E
4
GAS FLOW
T h e system consists of a fixed volume of gas saturated n i t h water vapor within the aspirator unit, through which water flows a t a constant rate. ,4n external gas supply a t A , connected to the system through a pressure regulator, maintains a constant total pressure of gas in the aspirator unit. An aspirator on the water inlet a t B intimately mixes the gas within the system with the flowing water. The gas then separates from the water and remains in the unit, cycling back through the aspirator. Water is continuously withdrawn from the bottom of the unit a t a rate that maintains a constant liquid level and thus a constant gas volume. It is assumed that the volume of gas pumped through the aspirator per unit time, the time of contact betLyeen the gas bubbles and the Iyater, the average size of the gas bubbles, and the temperature of the gas and water are all constant Cnder actual conditions, physical entrainment of some of the gas in the water floaing out of the unit will occur. This can be minimized but not completely eliminated. This behavior IS approximated by assuming t h a t gas is aithdrawn from the a$pirator unit a t a constant rate a t C.
WATER O U T L E T
Figure 1.
Typical system
The debign and performance characteristics of a dissolved oxygen analyzer are related t o projected uses. Performance requirements usually would call for dissolved oxygen measurements n-ith an accuracy of about i 5 % of saturation in the range from 0 to 150% of saturation for water temperatures from 0" t o 35' C. General application of the method t o a variety of n ater samples would also require accommodation of variations in suspended matter, dissolved solids, and composition and amount of pollution in the water. Design objectives for a dissolved oxygen analyzer include mobility and rapid response t o changes in dissolved oxygen content, so t h a t the instrument may be rapidly moved along the stream in a boat to obtain the oxygen profile.
For this system t o function as a dissolved oxygen anallzer, the gas within t h e aspirator unit must be in contact with a nondestructive gas analyzer t h a t will relate the oxygen content of the gas t o the dissolved oxygen content of the water.
343
344
ANALYTICAL CHEMISTRY
111 operation, if the actiial partial pressure of oxygen gas xithin the unit is greater or less than that corresponding t o the dissolved oxygen content of t,he water, t,hen oxygen will transfer across the gas-u-at,er interface until a stable Henry's law condition is reached. Any net change in the quantity of gas within the unit during this transfer process is immediately compensated by an equivaleiit flow of gas in either direction through the pressure regulator at d (Figure 1). It is important t o establish whether any combination of variables will prevent the formation of a Henry's law equilibrium for oxygen. Furthermore, it is necessary to establish practical operating requirements for the instrument experimentally. Some of the variables that require more complete examination arc total gas pressure, barometric pressure variations, temperature, dissolved nitrogen content of water, aeration constant of oxygen and nitrogen, and other gasw dissolved in water.
Nomenclature. = mole fraction of oxygen in the gas that is entering or leaving the svstem (dry baqiq) K 1 = aeration tonstait for oxygen Kf = aeration constant for nitrogen K3 = entrainment rate L = maximum lag in gas composition in terms of per cent saturation .lf = maximum rate of change of dissolved oxygen in water in terms of per rent saturation per unit time s = number of moles of gas P = constant total pressure of the s j stem P = P - IT7 R = molar gas constant T = constant uniform temperature of water and gas 1 = time 17 volume of gas entrained in water v = constant volume of the system W = partial pressure of water vapor = partial pressure of oxygen Y = partial pressure of nitrogen
The total number of moles of oxygen and nitrogen ga- dissolved in or removed from the water passing through the aspirator per (YI- Y O ) ] .The number of unit time is -Kl[(X1 - X,) moles of oyygen leaving the sj-stem by entrainment is - K J , / R T . The total number of moles of oyrgen and nitrogen leaving tlie system a t tlie same opening is -KnpIRT. T o maintain P constant, an equal quantity of gas must enter or leave the systc,m through the pressure regulator a t opening A . The number of moles of water involved in such exchanges need not be considered, for any loss or gain of water vapor is immediately compensated bv evaporation or condensation of an equivalent amount of water in the system to maintain It.' constant. If J is the mole fraction of oxygen (dry basis) entering or leaving the system through the pressure regulator, then the net change per unit time in the oxygen content of the gas in the aspirator unit is:
+
J
x
Let the subscripts 0 = partial pressure of ovygen or nitrogen in equilibrium with water as determined by temperature and Henry's law 1 = actual partial pressure of oxygen or nitrogen a t time t 2 = initial partial pressure of oxygen or nitrogen 3 = partial pressure of oxygen or nitrogen at t = 33 4 = partial pressure of oxygen or nitrogen i n air saturated with water vapor at a temperature T at a total pressure of 1 atm. x = oxygen gas 11 = nitrogen gas w = watervapor General Relationships. It is assumed that the rate at which oxygen or nitrogen transfers across a gas-liquid interface is described by
The solution of Equation 4 depends on the value of J . Assuming for the moment, that the entrainment rate, K 3 ,is negligible, then it can be shown that, if
xo < P
-
yo
(5)
t,here will be a positive flow of gas ivith a constant oxygen content into the aspirator unit from the ext'ernal gas supply. If, on the other hand,
s,, >p
-
Yo
(6)
then there will be a flow of gas ivith a variable oxygen content out of the aspirator unit. Finally, if the entrainment rate is significant, the situation described by Equation 6 seldom exists. Equations 5 and 6 define dissolved oxygen regions for which the partial pressure of oxygen in the aspirator unit exhibits a specific type of functional behavior. Equation 5 represents a dissolved oxygen range less than the difference between the gas pressure and t>hedissolved nitrogen content' of the mater, whereas Equation 6 defines a range greater than this value. Consider first the dissolved oxygen region defined by Equation 5, with a constant value of J . Because
(7) then Equation 4 reduces to
whcre the constants '1, R, and C are
d
RT
= - K , (1
+
RT B = - Ki(1 - J ) where K , and K2 are aeration constants that depend on the size and number of gas bubbles, temperature, and the flow rate of water. They are also influenced by materials dissolved in the water ( 5 ) . To simplify the subsequent development, it is assumed that K1 = K2. It is assumed further that the rate of gas entrainment dV/dt -K3. Since P , U , T , and W a r e constant, the system must conform a t all times to the following conditions of restraint:
PV = A\7RT
where
s,+ .Yv+ 'Y%
,v
=
p
= XI
+ Y1 = X? + YP
If for t = 0, XI = Xz, and for t > 0, and the dissolved oxygen content of water, X O ,is any arbitrary constant value within the region defined by Equation 5, then the solution of Equation 8 is as f 0110 n-s:
(3) = x 3
+ Ys
(13)
345
V O L U M E 2 8 , NO. 3, M A R C H 1 9 5 6
c
20
I
I
40
60
I
Figure 2.
I
I
I
I
I
123
140
160
183
200
I
83
D0
I33
, PERCENT
220
Figure 3.
Ox?-gencontent of system
~
KiKT
That i.4, if initially the gas within the aspirator unit is any arbitraq- oxygen-nitrogen mixture; and if, at that time taken :is zero, the dissolved oxygen content of water suddenly changes to any arbitrary value consistent with Equation 5 , then the partial pressure of oxygen gas will approach a final stead!. value, Xi; cy,onentinlly with time according t o Equation 12. A final Henry’s l a ~ v equilibrium, independent of temperature, salt contcnt, dissolved nitrogen content of the water: and aeration rates, wliirh is the only result of interest here, can b e attained only if the esternal gas supply is nitrogen ( J = 0), and the entrainment rate is relatively small. For if J = 0, t>hen X; = XOonly if Ka 0, the dissolved oxygen eontent of the water passing through the system is any arbitrary constant value in the region X,, > p - Yo:
XI
OxFgen content of s>stem
Kd Valuei on c u r v e s = KiRT
J = O
K,
