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Development of a membrane respirometer
Wat. Res. Vol. 31, No. 1, pp. 23-32, 1997
Pergamon PII: S0043-1354(96)00214-X
Copyright © 1996 ElsevierScience Ltd Printed in Great Britain. All rights reserved 0043-1354/97 $17.00 + 0.00
DEVELOPMENT OF A M E M B R A N E RESPIROMETER R. P. G A R G ~ and R. P. M A T H U R 2 ~Department of Civil Engineering, Thapar Institute of Engineering & Technology, Patiala 147 001, India and 2Civil Engineering Department, University of Roorkee, Roorkee, India
(First received July 1993; accepted in revised form June 1996) Abstraet--']?he respirometric technique relies upon reoxygenation of a wastewater sample through a quality conLrolled polyethylene membrane. The fluid sample is surrounded by a low density polyethylene membrane permeable to oxygen and the sample is stirred in the respirometer. In studies the DO saturation concentration of the sample in the respirometer was experimentally determined. The respirometer was initially standardized and the rate of oxygen transfer was estimated. The experimental data was fitted to Fick's linear law of diffusion, using a quality controlled polyethylene membrane, the rate of oxygen transfer wa,,;found to be reproducible. In oxygen uptake studies, DO vs time recorder plots were obtained. The course of oxygen uptake is depicted and a complete fingerprint of the course of oxidation of the organic co~tents in the wastewater may be obtained. Copyright © 1996 Elsevier Science Ltd
Key words--oxygen uptake, respirometer, membrane respirometer, DO profile, membrane
geneous medium for diffusion of oxygen in the respirometer. The main objective of this paper is to report the investigations carried out to evaluate the feasibility of this polyethylene film chamber serving as respirometer.
INTRODUCTION Oxygen uptake by an organic substance is an important parameter in the field of water pollution control. The five-day dilution technique is the standard method for the measurement of B O D of a wastewater sample (APHA, 1985). Dilution technique is simple and highly skilled laboratory staff are not required. Manometric and respirometric methods have been reviewed by Jenkins (1960) and later by M o n t g o m e r y (1967). Warburg's respirometric units have a relatively large ratio o f glass:liquid interface to sample volume which is a limitation as suspended solids accumulate an the flask walls, especially when measurements are made over extended time periods. Although the respi:rometric methods permit the use of less dilute sample:s for oxygen uptake studies, the apparatus involved is complex, lssacs and Gaudy (1968a) have described a 6681 simulated stream for conducting the oxygen uptake studies, but the apparatus was found to be unsuitable for routine use due to the large volume o f sample required for testing (Issacs and Gaudy, 1967). The present pal~.~r discusses a respirometer* which is innovative in that gas and liquid phases are separated by a membrane permeable to oxygen. The liquid is placed i~L a chamber, the walls of which consist of an oxygen permeable polyethylene membrane. Crystallites in polyethylene are highly anisometric and the membrane is heterogeneous on microscale. Investigations were carried out to evaluate whether the membrane acts as a homo-
MATERIALS AND METHODS
Respirometer The apparatus (Fig. 1) used in the present study consists of a closed and completely filled cylindrical chamber whose sides are a low density polyethylene (LDP) membrane which is supported on a framed structure to maintain the geometric mode (shape and size) of the respirometer. The framed structure consists of a base plate (1) and a cover plate (2) held apart by equidistant supports (3) and is fabricated from Plexiglas. The cover plate has a central hole (4) for introduction of a dissolved oxygen probe. The cover plate and base plate are provided with a groove for accommodating O-rings (5). The annular LDP membrane (6) is held to the base and cover plates by means of complementary collars (7). The collars hold the membrane tight and make the chamber leak proof. A collar is fixed on the cover plate for storing additional liquid under test, thus forming a water seal (8). A rotor (9) is supported on a vertical axis terminating in a circular groove (10). The respirometer was placed on a magnetic stirrer working electrically. The chamber of the respirometer has a volumetric capacity of 180 + 10 ml (with DO probe inserted) when the base and cover plates of 65 mm dia. are held apart at a clear distance of 55 mm (Fig. 1). The area-to-volume ratio of the respirometer was 0.6 cm -L. The annular membrane used for this experimental work was 67 mm dia.
Operation Annular membrane was slipped over the base and cover plates to form the cylindrical wall surface (Fig. 1) and the membrane was secured to the base plate with the complementary collar. The liquid sample was introduced
*US Patent No. 5,125,262. 23
24
R.P. G a r g a n d R. P. Mathur
4 15
•
6
~rSmm -
--
I ii
|
.._~
1051~
LE6E. ND !. BASE PLATE COVER PLATE SUPPORTS 4. HOLE FOR DO PROBE 5. O-RIN6S 6. MEMBRANE 7. COLLARS 8. WATER SEAL ROTOR 10. g. GROOVE
(COLLARSREMOVED} Fig. 1. Respirometer.
through the hole in the cover plate so as to completely fill the chamber and entrapped air was removed. The upper portion of the membrane was held tightly and secured to the cover plate with the complementary collar. The calibrated DO probe was introduced into the chamber of the respirometer. The respirometer was placed on a magnetic stirrer in an incubator. The magnetic stirrer worked electrically and was set to rotate the rotor at 100 + 10 rev/ min. The probe was connected to a potentiometric chart recorder or interfaced to a computer. Polyethylene membrane Quality controlled polyethylene film was used in the work reported here. Polyethylene film was prepared from polymer granules having uniform density so as to fix the volume fraction of the amorphous phase and the blowing of the film was carried out under approx, uniform environmental temperature conditions to control the size and shape distribution of the crystallites (Michaels and Parker, 1959). The lower the density of polyethylene, the higher is the fraction of amorphous phase. Hence, a low density polyethylene membrane was used for obtaining an increased rate of diffusion of oxygen through the membrane. The annnular polyethylene membranes were prepared from polymer granules having uniform density. The density of the granules was not determined in the laboratory and was taken as 0.916 g/cm 3 as given by the manufacturer. An annular membrane of 67 mm dia. was prepared by the blowing process. In the machine, quality control of the diameter of the annular membrane was possible, but control of its thickness at various locations over the membrane was limited. From a quantity of ~ 5 kg of the membrane, 20 random samples of 200 mm length were taken for estimating the average unit weight. From the average unit weight and density of the membrane, the average thickness (T) and relative error in T were estimated. Membrane type I This type of membrane was prepared from branched low density polyethylene granules (variety DFDI 0114) manufactured by Union Carbide (India). The membranes were prepared at ambient temperature (30°C) by the blowing process. Membranes having a thickness of 0.015 and 0.025 mm were used for the experimental work. The average unit weight of 0.025 mm thick membrane was 2.247 mg cm -2.
Membrane type H This type of membrane was blown under similar conditions and the same variety of low density polyethylene granules were used as for type I, but the bag of granules came from a different sample. A membrane thickness of 0.013 mm was used for the experimental work. Membrane type I11 This type of membrane was prepared from low density polyethylene granules (variety OBFX 0114) manufactured by Oswal Petrochemicals (India) previously owned by Union Carbide (India). Membrane type I V This type of membrane was prepared from linear low density polyethylene granules (variety FD 0374) manufactured by Qatar Petrochemials Co., Qatar. Calibration of DO probe The DO in the liquid sample in the respirometer was determined with a DO probe which was calibrated at the start of every experiment and the calibration was checked at the termination of the experiment. Synthetic wastewater The synthetic wastewater consisted of a carbon source supplemented with inorganic salts. The synthetic waste was composed of glucose and glutamic acid (in equal proportions) 100 rag/l, phosphate buffer solution (,pH 7.0) 10 ml/1, MgSO4.7H20 100 rag/l, FeCh.6H:O 0.5 rag/l, MnSO4.H20 10 mg/l, CaCI2 7.5 rag/l, tap water 100 ml/1 and acclimated sewage seed 5 ml/l, made up to 1 1 with distilled water. Seed Settled domestic sewage was used as seeding material. Before using the inoeulum for different experiments, the seed was acclimatized in a separate respirometer. Initially, 25 ml of settled domestic sewage was added in one litre of medium (synthetic wastewater) containing 100mg/l of glucose and glutamic acid. The respirometer (with synthetic waste and seed) was maintained at 20°C with continuous stirring. The medium was replaced three times after every 24 h to get the acclimatized seed.
Development of a membrane respirometer EXPERIMENTAL APPROACH Permeability of oxygen through different varieties of polyethylene has bc~n determined (Michaels and Parker, 1959; Michaels and Bixler, 1961). However, it is difficult to estimate the mass (o~ygen) transfer coefficients for a sample of polyethylene membrane (when used in the respirometer) from the known properties of the polymer (Michaels and Parker, 1959; Michaels and Bixler, 1961) since, in the respirometer, polyethylene membrane as well as laminar layer of the liquid offer resistance to oxygen transfer. Moreover, after using the membrane for oxygen uptake study, it needs to be washed if it is to be used again. In order to avoid the inconvenience of washing, the used membrane is wasted and a new membrane is used every time a test is repeated. Though the quality of membrane was controlled, the following aspects were experimentally investigated to ascertain whether the experimental apparatus can be used as a respirometer or not. (a) The liquid sample in the respirometer is not in direct contact with atmospheric air, rather the polyethylene film is exposed to air. TItLe polyethylene membrane has quite different thermodynamic properties in comparison to those of the water sample in the respirometer. To ascertain the ,
Gas
25
effect of surrounding the water sample with a polyethylene membrane, the DO saturation concentration of water in the respirometer was experimentally investigated. (b) To confirm the working of the respirometer using a two phase heterogeneous film of polyethylene, variations in the rate of oxygen transfer in it were studied for the four types of membranes. Oxygen demands of synthetic wastewater samples were also studied. M A T H E M A T I C A L M O D E L FOR M A S S TRANSFER
Diffusion o f oxygen from atmospheric air to the liquid (water) in the respirometer takes place by diffusion of oxygen from the gas phase to the gas-membrane interface and dissolution of oxygen at the surface of the membrane exposed to atmospheric air (Fig. 2). It has been assumed that equilibrium is established instantaneously at the gas-membrane interface. Further, diffusion of oxygen takes place in the amorphous phase of the membrane along the concentration gradient. At the membrane-liquid
Phase Membrane
Liquid film
Liquid
Phase
cQa
Pg
X
t=oc
•
P = Pg
o o 0
t=t in th o L.
o
P=P
t2. t~
interface
~2 n
Pressure
Gas
Phase
Membrane
Gradients
Liquid
film
Liquid P h a s e
E
t =cc,
Csat t-
°~
C = CSo t
o
.r" O
o
i..
to •
tO
t,.) O O
¢-
t--t
, c --c
O a
-Interface Distance ---------Concentration
Gradients
Fig. 2. Pre~sure and concentration gradients in the membrane and liquid phase of the respirometer.
R. P. Garg and R. P. Mathur
26
interface, oxygen is desorbed and transfer of oxygen from the membrane-liquid interface to the liquid phase takes place by mixing. Steady state permeability of oxygen in polyethylene is determined from Fick's linear law of diffusion by considering polyethylene as a "porous medium" (Michaels and Parker, 1959), the "particles" of which are the crystallites and the "pores" of which are composed of the amorphous phase. Amount of oxygen (J) passing through the unit area of the membrane per unit time may be written as (Fig. 2): J =
o~IS,DI(p~ - pi)/L, = S2D2(Pi - p)/L2,
(I)
where ctt is the area fraction of amorphous phase at the gas-membrane interface, S~ and $2 are the solubility coefficients of oxygen for the membrane and the liquid in the respirometer respectively, D1 and D2 are the diffusion constants of oxygen for the membrane and the liquid respectively, L~ and L2 are the thicknesses of the membrane and the laminar liquid layer (Fig. 2) respectively and p~, pi and p are the partial pressures of oxygen in the bulk gas phase, membrane-liquid interface and in the bulk liquid phase (Fig. 2), respectively. Value of D~ depends on polymer morphology (Michaels and Parker, 1959; Michaels and Bixler, 1961); and (2)
D i = ct'Dp/r'fl*,
where Dp is the diffusivity of oxygen in completely amorphous polyethylene, ct is the volume fraction of amorphous phase in the polymer polyethylene, (I/T) is the tortuosity factor representing fractional reduction in oxygen diffusivity arising from the geometric impedence offered by the crystallites, and (I/E*) represents the fractional reduction in oxygen diffusivity due to restriction of chain movement in the amorphous phase. For system isotropy ~t~ is taken equal to c¢. The value of pi is not known and is difficult to determine accurately. Equation (1) may be written as: J = (p~ - p)/[L,/(ccS,DO + L2/(S2D2)].
(3)
Writing equation (3) in terms of DO concentration of water in the respirometer, [multiplying and dividing equation (3) by $2]: dD/dt
= -- rc(Csat
-
-
C),
(4)
where dD/dt = - J ( A / V ) , A = area of the membrane surrounding water in the respirometer and V = volume of water in the respirometer. r~ = I/[(L~S2)/(ot~StD,) + L~/D2]
(5)
Cs,, = S~Ps = limiting DO concentration in liquid (water) in the respirometer at test temperature and pressure.
c = S~p = DO concentration in liquid (water) in the respirometer at test temperature and pressure at any time t. O = (Csat- c). D is the DO deficit. The limiting DO concentration in the polymer is not known and is difficult to determine accurately. For modeling, the limiting DO concentration in the polymer at the gas-membrane interface (Fig. 2) is taken as the limiting concentration of DO in the liquid phase of the respirometer termed as Cs~, (Fig. 2). rc is termed as the respirometer constant (units t -~) and its value depends on the factors given in Eq. (5). The value of rc specifies the rate of oxygen transfer into the respirometer per unit saturation deficit under specified conditions of temperature, pressure, polyethylene membrane thickness, rate of stirring and area to volume ratio of the respirometer. In the integrated form equation (4) is written as: D = D0 exp( - rot),
(6)
where Do is the initial DO deficit. RESULTS AND DISCUSSION
Respirometric parameters
Following the procedure as explained in the operation of the respirometer, it was filled with water/wastewater. The initial temperature of water/ wastewater was between 19.5 to 20.5°C and the incubator was set to operate at 20 + 0.5°C. One or more magnetic stirrers were placed inside the incubator and the heat generated by the magnetic stirrers was dissipated inside the incubator when the ambient temperature was less than 25°C. But during summer, when the ambient temperature was more than 25°C, the air temperature at the bottom panel of the incubator was usually 19.5 to 20°C and at the top panel it was about 21°C. The base plate of the respirometer was fabricated from Plexiglas that acted as insulator of heat. Since the magnetic stirrer and respirometer were placed at the bottom panel of the incubator, the temperature of the liquid inside the respirometer usually varied from 19.5 to 20.5°C and the maximum temperature of the liquid was never more than 20.7°C. All the experiments were performed at the prevailing atmospheric pressure at Patiala (India). The average atmospheric pressure at Patiala (India) was 99.3 kPa which varied from an upper limit of 100.3 kPa to a lower limit of 98.5 kPa. Variations in rate of oxygen transfer in the respirometer depend upon the variations in the thickness of the membrane. Variations in the thickness at ten locations over a membrane were determined by Optical Path Difference (OPD) with Michelson's Interferometer. The refractive index for each type of membrane was also determined by the reflectance method. The thickness of each type of membrane w a s
Development of a membrane respirometer estimated from the: average value of OPD at ten locations and the determined value of the refractive index. The thickness (as estimated by the OPD method) of the four types of membranes was approximately 10% less in comparison to the value of T by unit weight method. Variation in the thickness of a membrane worked out by unit weight and OPD methods is obvious since in the unit weight method, total length (about 200 ram) is weighed, whereas, OPD is determined at ten locations of a sample of membrane. The relative error in OPD (Table 1) gives an estimate of the variations in the thickness at variou:~ locations over the membrane. The relative error in the diameter of the random samples for the various types of membranes varied from 0 . 4 o to 1.0%. It was observed that when the diameter of the mere brahe was more than the average diameter for that type of membrane, its unit weight was less than that o1' the average unit weight for that membrane sample and vice versa. Thus, the errors due to variations in diameter (resulting in variations in area to volume ratio) and T were partly compensating. The ~.verage thickness (T) and relative error in T for the four types of membranes are given in Table 1. Humidity of air affects the partial pressure of oxygen in atmospheric air. One side of the membrane of the respirometer was exposed to water/wastewater and depending on the permeabilty of the membrane to water, the membrane must always be saturated with water. Thus, the variations in humidity of air will not affect the diffusion properties of the membrane. Experiments were carried out in the incubator and the chamber of the incubator was always saturated with water vapours due to the water seal (Fig. 1) at the top of the respirometer. The effect
27
of humidity of air was not felt on Cs~, and to, although, experiments were conducted during summer as well as rainy season. The effect of vapour pressure on the solubility of oxygen in water may be neglected for temperatures below 25°C (APHA, 1985). INVESTIGATIONS RELATING TO MASS TRANSFER
Values of Cs~t and rc were estimated from unsteady reaction tests on diffusion of oxygen in the respirometer. DO of water in the respirometer was brought in equilibrium with atmospheric air surrounding the respirometer at the test temperature and pressure and the limiting DO value was the Csat value. Following the procedure as outlined in the operation of the respirometer, the respirometer was filled with distilled water. DO of distilled water was reduced by bubbling nitrogen gas in it. DO probe was introduced into the chamber of the respirometer and either a continuous recorder plot (DO vs time) was obtained by connecting the probe to a chart recorder or a DO profile (DO vs time) was obtained by interfacing the probe to a computer. Continuous recorder plots of DO concentration of distilled water, in the respirometer, were obtained on the same chart for 0.015 mm and 0.025 mm thick type I membrane at 20°C (Fig. 3). Recorder plots were also obtained for 0.025 mm thick type I membrane at 15°C, 25°C and 30°C temperatures. Recorder plots were also obtained for 0.013 mm thick type II membrane for distilled water and salt water of salinity 5 g/kg. Recorder plots for water of salinity 5 g/kg were obtained after adjusting the DO meter for salinity correction. DO profiles (Fig. 4) for 0.020 and 0.025 mm thick type III membrane were obtained.
Table 1. DO saturation concentration, membrane characteristics and respirometer constants Relative error in Test temperature (°C)
Cs,, (mg/l)
Cs (mg/l)
(T) (ram)
20 15 20 25 30
7.75 8.75 7.75 7.60 7.20
8.91 9.88 8.91 8.08 7.41
20 --
7.90 7.7t
8.91 8.66
20 --
8.40 7.80-
8.91 --
0.020 --
---
8.40 7.80-
---
0.025 --
20
8.00
8.91
0.063
--
7.80-
--
--
(r) (h-')
Membrane type I 0.015 0.85 0.025 0.44 0.025 0.60 0.025 0.81 0.025 1.04
N for (r)
(T) (%)
(OPD*) (%)
4.1
(r) (%)
7.1
6
3.9
6.8
2.6
6 6
4.5 4.5
7.3 7.3
3.8 4.5
0.89 1.06
10 10
4.9 --
31.3 --
5.6 4.1
0,64 0.75
I0 I0
4.3 --
14.4 --
5,3 5.0
0.14
I0
2.9
8.7
1.4
0.15
10
--
--
1.2
Membrane type ii 0.013 0.013
0.92 0.90
Membrane type III
Membrane
type IV
*Optional path difference determined by Michelson's interferometer. ?For water of salinity (5 g/kg). - - F o r 1:he adjusted value of Cs~. C. in contact with water saturated air and 99.3 kPa atmospheric pressure. WR 31/I--B
R. P. Garg and R. P. Mathur
28
/ 8
,,--- DO vs t
"Cgat = 7 . 7 5 r a g / t 0-06
0:025ram
0.015ram
7
0"08 6
Recorder plot - o - , 4 - Regression tines o O-015mm Membrane 0"2 • 0"025ram Membrane
5
E O
0"1
KEY
3
~
D=D o
exp ( - 0 . 5 8 t )
D = DO
exp ( - 0 - 8 5 t )
o t:) t:3
0"4
2
0-6
~ 0
1
2
3
4
5
6
7
8
9
0" 8 1"0 10
Time-, t , ( h ) Fig. 3. Recorder plots and regression lines for type I membrane.
DO P r o f i l e s KEY
0.04
CSot (mglt)
7.8
8.4
O. 020
•, e
-o-, o
0.025
e,e
~),®
T {mm)
1.08
• , e,-o-,¢ Computed volues
t
~.20 Q
O ¢3
0.60
1.00 2
11
4
5
Time(h)
Fig. 4. DO profiles and regression lines for type IIl membrane.
Development of a membrane respirometer Similarly, DO profiles for 0.063 mm thick type IV membrane were ah;o obtained. DO saturation concentration The asymptotic nature of the DO plots or DO profiles (Figs 3 and 4) is clearly indicated and it may be concluded that the DO concentration of water in the respirometer reaches a limiting value. These experiments were continued for two days (only 5 to 9 hours of data presented in figures) but no increase in DO value was observed. To complement the results, the respirometer was filled with distilled water having a DO value more than the observed limiting DO value for the membrane and it was found that the DO in the respirometer decreased and ultimately stabilized to observed limiting DO value which was taken as the DO saturation concentration (Cs~0 of water in the respirometer. The limiting DO concentration in the respirometer is Cs~t, whereas the limiting partial pressure of oxygen is pg (Fig. 2). For determining variations in Cs~t, replicate experiments were performed for the four types of membranes. Average values of Csat are given in Table 1. Observed Cs~ values of distilled water for the four types of the membranes varied between + 0.1 mg/1. The Csat value of distilled water at 20°C and 99.3 kPa atmospheric pressure are of the same magnitude when 0.015 mm or 0.025 mm thick type I membranes were used. The Csa, values of water are of the same magnitude for 0.015mm and 0.025mm thick type III membranes. The Cs~ values of water are less than the reported DO saturation (Cs) values (APHA, 1985) of water in direct contact with atmospheric air at the same temperature and pressure (Table l).It may be concluded that $2 is less than the solubility constant of oxygen in water directly exposed to atmosphere. Dissolution of oxygen in the membrane or water takes place due to molecular impacts from the gas on to the surface of the membrane or water. At the membrane-liquid interface, the frequency of molecular impacts from the gas (in the transient holes in the polyethylene membrane) on to water is less than the frequency of molecular impacts from the gas on to water surface when it is in direct contact with atmospheric air. Moreover, the transient holes are formed in a fraction of the membrane area equal to ~q. Thus, the Csa~ values of water are less than the corresponding C, (APHA, 1985) values of water at the same temperature and pressure (Table 1). For the same variety of membrane Cs~t values are of the same magnitude (Table 1) for different thicknesses of the membrane, since, frequency of molecular impacts from the gas and ~t~ are of the same magnitude at the membrane-liquid interface. DO saturation concentration for wastewater (Cs~,.O In studies on Cs~, for distilled water and water of salinity 5 g/kg, the ,~'s~tvalue of distilled water and water of salinity :5 g/kg was the same without
29
adjusting DO meter for salinity correction. Had there been any effect on Cs~t due to surrounding the water (of salinity 5 g/kg) with the membrane, Cs~t value of water of salinity 5 g/kg would have been different to that of distilled water. Cs~, value of water of salinity 5 g/kg decreased only when correction for salinity was applied. Thus, the decrease in DO due to salinity of water is the same whether it is put in the respirometer or directly exposed to atmospheric air. Driving force for the diffusion of oxygen in the respirometer is (Cs~,- c) [equation (4)] and for a batch reactor such as the respirometer, c approaches Cs~, for distilled water or tap water and Cs~t.w for wastewater (Ramalho, 1983) as aeration proceeds. Accordingly, the effect of the nature of effluent in the respirometer on the Cs~ value is primarily due to the inorganic matter and to a lesser extent due to non-biodegradable organic matter. The effect of the non-biodegradable organic matter on Cs~t may be neglected since its concentration in the respirometer is usually negligible except in a case where the wastewater contains a considerable portion of nonbiodegradable organic matter. In such a situation Cs~t.w may be experimentally estimated. Thus, the effect of the nature of the effluent on Cs~, will be mainly due to dissolved inorganic salts in it. Decrease in Cs~, due to a salinity of 5 g/kg is 0.2 mg/1 (Table 1) and a decrease in Cs~, of 0.1 mg/l will result in due to a salinity of 2.5g/kg. Membrane to membrane variations of Cs~, are __+0.1 mg/1 resulting in an error of 1.3% in the computed value of oxygen uptake. If the dissolved inorganic salts in a wastewater are 1500 mg/1, its salinity would be less than 1.5 g/kg. In case correction in Cs~, due to dissolved inorganic matter of 1500 mg/1 is neglected, appreciable error in the computed value of oxygen uptake will not be introduced. Oxygen uptake study of wastewaters of up to 150 mg/l of BOD5 may be carried out in the respirometer. Thus, strong wastewaters are to be diluted for estimating their oxygen uptake and the concentrations of dissolved inorganics for the diluted waste in the respirometer is not expected to be more than 1500 mg/l. Where the concentration of dissolved salts in the diluted wastewater is expected to be more than 1500 mg/l, Cc~,w may be estimated from its salinity. Various wastewaters, studied in the respirometer, contained dissolved inorganic solids of less than 1500 mg/1. rc value Regression lines for rc are shown in Figs 3 and 4. The ln(D/Do) vs t plots (Fig. 3) for 0.015 and 0.025 mm thick type I membrane are linear when the value of Cs~t was taken as 7.75 mg/l. It may be concluded that the rate of oxygen transfer in the respirometer follows Fick's linear law of diffusion [equation (6)] up to DO concentration of 7.75 mg/l (Issacs and Gaudy, 1968b). Similar results were obtained for 0.013 mm thick type II membrane with distilled water and water of salinity 5 g/kg when the
30
R.P. Garg and R. P. Mathur
values of C~, were taken as 7.9 mg/1 and 7.7 mg/l, respectively. However, ln(D/Do) vs t plot (Fig. 4, curve 1) for 0.025 mm thick type III membrane is not linear when the value of Cs~, was taken as 8.4 mg/1.The ln(D/Do) vs t plot (Fig. 4, curve 2) for 0.020 mm thick type III membrane was linearized (Issacs and Gaudy, 1968b) when the adjusted value of Ca, (7.8mg/1) was taken for curve fitting. The ln(D/Do) vs t plot for 0.020mm thick type III membrane showed a linear trend (Fig. 4, curves 3 and 4) when the value of Csat was taken as 7.8 mg/1. Similarly, ln(D/Do) for 0.063 mm thick type IV membrane was linearized when Csat was taken as 7.8rag/1. Computed values of c for 0.020 and 0.025 mm thick type III membrane are shown in Fig. 4 and it is evident that residual errors decrease when Cs~t is 7.80 mg/l compared to the errors when Cs~ is 8.40 mg/l. For determining variations in r¢, replicate experiments were performed with the four types of the membranes, m new membrane was used for each test. Average values of re, number of replicate experiments for rc and the relative error in rc are given in Table 1. It is seen (Table 1) that relative errors in T, OPD and rc are less for a thicker membrane compared to that of a thinner membrane. For type III membrane, relative error in OPD is more compared to that in the other three types of membranes. For this reason, relative error in re is more compared to that in T. Quality control on the thickness of type III membrane was limited because of considerably lower viscosity of the polymer melt in comparison to that for other three types of the polymers. The accuracy of DO measurement and variations in temperature during the course of experiments result in variations in the value of r0. A 5% variation in the value of r~ is obtained if an error of 0.1 mg/1 is made in the determination of DO. The purpose of the present investigations was to evaluate the feasibility of using a polyethylene membrane as a medium for diffusion of oxygen in the respirometer and no attempt has been made to relate the mass transfer data with polymer morphology of the four types of the membranes. An account of polymer morphology affecting fl, and r has been explained elsewhere (Michaels and Parker, 1959; Michaels and Bixler, 1961). For type I and type II membranes Fick's linear law of diffusion is obeyed up to the observed value of Csa,, whereas, for type III and type IV membranes Fick's linear law of diffusion is not obeyed up to the observed value of Cs~t. Diffusion of gas molecules occurs as a result of redistribution of the free volume within the amorphous phase of the polymer. If an individual hole is not large enough to accommodate a diffusing molecule, the co-operative motion of several neighbouring molecules may allow two or more holes to merge into one hole large enough for a diffusional jump to occur. Thus, distribution of free volume in series would be expected to exist for a given diffusion channel
through a polymer film. As the concentration of the gas in the diffusion channel approaches more closely to the saturation limit, the diffusing molecule encounters "tight" regions, since the formation of free volume by merging two or more holes into one hole for a successful diffusional jump is limited, due for instance to the fact that one of the holes might be already occupied with the gas molecule (Michaels and Parker, 1959; Kumins and Kwei, 1968). From the experimental results, it is clear that Fick's linear law of diffusion is obeyed within a narrow range of Csa, value of 7.75 to 7.9 mg/l for the four types of the membrane. A Cs,t value of 7.80 mg/l may be taken for regression for mass transfer in the respirometer. From the Arrhenius plot of r0, the apparent energy of activation for permeability of oxygen for 0.025 mm thick type I LDP membrane was estimated to be 10.3 kcal/gmol. The reported apparent energy of activation (Michaels and Parker, 1959) for permeability of oxygen through a branched polyethylene membrane of density 0.9135 is 10.2 kcal/gmol. The experimental conditions of the present investigations were slightly different than those of the reported studies. The apparent energies of activation for oxygen permeability are in close agreement. Keeping in view the limitations in the accuracy of DO measurements with a DO probe, the observed relative errors in rc are within experimental error. A coefficient of correlation of 0.99 or better for the regression lines for mass transfer suggests that the rate of oxygen transfer in the respirometer, using a heterogeneous polyethylene membrane, is determinable by Fick's linear law of diffusion and the value of rc is reproducible. Any one type of the membrane may be used in the fabrication of the respirometer.
Oxygen uptake Oxygen demand studies were carried out in the respirometer with synthetic wastewater containing 100 mg/l of a 1:1 mixture of glucose glutamic acid. For the oxygen uptake studies, type I membrane was used and DO concentration of the sample in the respirometer was monitored and continuous recorder plots of DO concentration were obtained. The oxygen demand was estimated by numerical integration of the basic differential equation of the sag curve (Issacs and Gaudy, 1967). The change in DO deficit, due to the combined effects of reoxygenation and deoxygenation, is depicted by the recorder plot. The oxygen demand was estimated without assuming any rate law for the biological deoxygenation in the respirometer. The recorder plot was divided into small portions each having approximately uniform slope and for each portion oxygen demand (A IO was estimated bythe equation:
A Y = fl[rc{(D2 + Dt)/2}'(t2 - t,) +_ (D2 - D0], (8) where t2, D2, tl and DI are time and DO deficits at the end and beginning of the portion of the recorder plot,
Development of a membrane respirometer
31
Substrate : Glucose Glutamic Acid 100mg/l. Curve 2,2': + Nitrification Inhibited with0.1M NI-I4(N]
125
100 ~
75
~
'
Y
~
"
O0 Profites _ I
0 x
o
50
25
,,=, 25
x o
50
75 Time
100
125
(h)
Fig. 5. DO profiles and oxygen uptake curves for the synthetic wastewater.
rc is the respirometer constant. Where fl = CSa,.w/Csat and values of DO deficits have not been corrected for salinity. Value of A Y was integrated for "n" portions of the recorder plot for obtaining the value of cumulative oxygen uptake. DO profiles and oxygen uptake curves for 100 mg/l of glucose glutamic acid are shown in Fig. 5. While calculating values of oxygen uptake, fl factor was taken as unity. The ~,eneral trends of the DO profiles (Fig. 5) are a rapidly decreasing downward leg until a minimum value of DO was reached, followed by a rapidly increasing upward leg and, thereafter, a slight change in the slope of the DO profile occurs. The rapidly decreasing downward leg represents the log growth phase, the rapidly increasing upward trend represents the declining growth phase, and the terminal leg (where s]ight changes in the slopes of DO curve occur) represents the endogenous phase of the oxygen uptake curve. Similar trends in DO profiles were observed by Is:sacs and Gaudy (1967) in their simulated stream experiments.
Cumulative oxygen uptake At the end of fifth day, DO deficit was 0.30 mg/l and oxygen uptake was 114.2mg/l (Fig. 5, curve 1), whereas the theoretical oxygen demand (ThOD) of 100 mg/l of 1: 1 glucose glutamic acid is 102.3 mg/1. In order to investigate the discrepancy between the estimated oxygen uptake and oxygen demand, the experiment was performed with 100 mg/l 1 : 1 mixture of glucose glutaric acid, in which, nitrification was inhibited by 0.1 M ammonia nitrogen (Fig. 5, curve 2). The same acclimated domestic sewage seed was used as in the earlier experiment. In this experiment,
the value of Csa, as well as the DO concentrations were corrected for chlorinity. At the end of fifth day, the DO concentration was 7.30 mg/l (DO deficit of 0.3 mg/i with Cs~, = 7.6 mg/I) and the oxygen uptake was 101 mg/l. At the end of 6th day, the saturation deficit was 0.05 mg/1 and the oxygen uptake was 104.6 mg/l, which is in agreement with the ThOD of 102;3 mg/l with an error of 2.3%. The discrepancy in the estimated oxygen uptake value (Fig. 5) and the ThOD of glucose glutamic acid mixture without inhibition of nitrification was apparently due to nitrification, since, a 100mg/1 1:1 mixture of glucose glutamic acid has a ThOD of 102.3 mg/1 and a nitrogenous oxygen demand of 24.5mg/1. Oxygen uptake at the termination of the decreasing growth phase is 43.5 and 44.5mg/1 without and with inhibition of nitrification, respectively. These oxygen uptake values are synonymous with the plateau B a D and are in agreement with the reported results (Busch, 1958). This indirectly validates the proposed mathematical model and the determined value of the respirometer constant for type I membrane. The respirometer may be adopted for application where oxygen depletion is a problem in oxygen uptake studies. CONCLUSIONS Based on the results of this study the following conclusions can be made: I. A respirometer can be fabricated in which reoxygenation of a wastewater sample can be affected
32
R.P. Garg and R. P. Mathur
through an oxygen permeable polyethylene membrane. The respirometer is completely filled and closed to atmospheric air, thus, the necessity of absorbing carbon dioxide from the gas phase is eliminated. 2. The D O concentration of water in the respirometer, at a particular temperature and pressure, reaches a saturation value which is less than that of water exposed directly to atmosphere. 3. When the liquid sample is stirred in the respirometer, the rate of oxygen transfer can be modeled based on Fick's linear law of diffusion up to 7.8 mg/l D O saturation concentration of water in the respirometer for the different types of membranes used in this study. 4. The rate of oxygen transfer in the respirometer is reproducible within experimental error. 5. The respirometer may be used for oxygen uptake study of a wastewater sample and the course of oxidation of the organics in the wastewater may be obtained. Acknowledgements--This work was supported from the sponsored research grant of the Civil Engineering Department of Thapar Institute of Engineering and Technology (Deemed University) Patiala (India). Guidance and support from Prof V. V. Sastry, Deputy Director, Thapar Institute of Engineering and Technology, Patiala, is gratefully acknowledged.
REFERENCES
APHA (1985) Standard Methods for the Examination of Water and Wastewater, 16th ed. American Public Health Association, Washington, DC. Busch A. W. (1958) BOD progression in soluble substrates. Sewage Ind. Wastes 30, 1336. Issacs W. P. and Gaudy A. F. Jr (1967) Comparison of BOD exertion in a simulated stream and in standard BOD bottles. Proc. 22nd Ind. Waste Conf., Purdue Univ. Engng Ext. Ser. 52, 165. Issacs W. P. and Gaudy A. F. Jr (1968a) Atmospheric oxygenation in a simulated stream. J. Sanit. Eng. Div. Amer. Soe. Civil Engng 94, NOSA 2, 319. Issacs W. P. and Gaudy A. F. Jr (1968b) Constants of first order reactions. Biotechnol. Bioengng 10, No. 1. Jenkins D. (1960) The use of manometric methods in the study of sewage and trade wastes. Waste Treatment (Edited by P. C. G. Issacs). Pergamon Press, Oxford. Kumins C. A. and Kwei T. K. (1968) Free volume and other theories. Diffusion in Polymers (Edited by J. Crank and G. S. Park). Academic Press, London. Michaels A. S. and Parker R. B. Jr (1959) Sorption and flow of gases in polyethylene. J. Polymer Sci. 1, 53. Michaels A. S. and Bixler H. J. (1961) Flow of gases through polyethylene. J. Polymer Sci. 50, 413. Montgomery H. A. C. (1967) The determination of biochemical oxygen demand by respirometric methods. Wat. Res. 1, 631. Ramalho R. S. (1983) Introduction to Wastewater Treatment Processes, 2nd edn, p. 172. Academic Press, New York. Stack V. T. (1972) Biochemical oxygen demand measurement. WaterWater Pollution Handbook (Edited by L. L. Ciaccio). Marcel Dekker Inc., New York.
Pergamon PII: S0043-1354(96)00214-X
Copyright © 1996 ElsevierScience Ltd Printed in Great Britain. All rights reserved 0043-1354/97 $17.00 + 0.00
DEVELOPMENT OF A M E M B R A N E RESPIROMETER R. P. G A R G ~ and R. P. M A T H U R 2 ~Department of Civil Engineering, Thapar Institute of Engineering & Technology, Patiala 147 001, India and 2Civil Engineering Department, University of Roorkee, Roorkee, India
(First received July 1993; accepted in revised form June 1996) Abstraet--']?he respirometric technique relies upon reoxygenation of a wastewater sample through a quality conLrolled polyethylene membrane. The fluid sample is surrounded by a low density polyethylene membrane permeable to oxygen and the sample is stirred in the respirometer. In studies the DO saturation concentration of the sample in the respirometer was experimentally determined. The respirometer was initially standardized and the rate of oxygen transfer was estimated. The experimental data was fitted to Fick's linear law of diffusion, using a quality controlled polyethylene membrane, the rate of oxygen transfer wa,,;found to be reproducible. In oxygen uptake studies, DO vs time recorder plots were obtained. The course of oxygen uptake is depicted and a complete fingerprint of the course of oxidation of the organic co~tents in the wastewater may be obtained. Copyright © 1996 Elsevier Science Ltd
Key words--oxygen uptake, respirometer, membrane respirometer, DO profile, membrane
geneous medium for diffusion of oxygen in the respirometer. The main objective of this paper is to report the investigations carried out to evaluate the feasibility of this polyethylene film chamber serving as respirometer.
INTRODUCTION Oxygen uptake by an organic substance is an important parameter in the field of water pollution control. The five-day dilution technique is the standard method for the measurement of B O D of a wastewater sample (APHA, 1985). Dilution technique is simple and highly skilled laboratory staff are not required. Manometric and respirometric methods have been reviewed by Jenkins (1960) and later by M o n t g o m e r y (1967). Warburg's respirometric units have a relatively large ratio o f glass:liquid interface to sample volume which is a limitation as suspended solids accumulate an the flask walls, especially when measurements are made over extended time periods. Although the respi:rometric methods permit the use of less dilute sample:s for oxygen uptake studies, the apparatus involved is complex, lssacs and Gaudy (1968a) have described a 6681 simulated stream for conducting the oxygen uptake studies, but the apparatus was found to be unsuitable for routine use due to the large volume o f sample required for testing (Issacs and Gaudy, 1967). The present pal~.~r discusses a respirometer* which is innovative in that gas and liquid phases are separated by a membrane permeable to oxygen. The liquid is placed i~L a chamber, the walls of which consist of an oxygen permeable polyethylene membrane. Crystallites in polyethylene are highly anisometric and the membrane is heterogeneous on microscale. Investigations were carried out to evaluate whether the membrane acts as a homo-
MATERIALS AND METHODS
Respirometer The apparatus (Fig. 1) used in the present study consists of a closed and completely filled cylindrical chamber whose sides are a low density polyethylene (LDP) membrane which is supported on a framed structure to maintain the geometric mode (shape and size) of the respirometer. The framed structure consists of a base plate (1) and a cover plate (2) held apart by equidistant supports (3) and is fabricated from Plexiglas. The cover plate has a central hole (4) for introduction of a dissolved oxygen probe. The cover plate and base plate are provided with a groove for accommodating O-rings (5). The annular LDP membrane (6) is held to the base and cover plates by means of complementary collars (7). The collars hold the membrane tight and make the chamber leak proof. A collar is fixed on the cover plate for storing additional liquid under test, thus forming a water seal (8). A rotor (9) is supported on a vertical axis terminating in a circular groove (10). The respirometer was placed on a magnetic stirrer working electrically. The chamber of the respirometer has a volumetric capacity of 180 + 10 ml (with DO probe inserted) when the base and cover plates of 65 mm dia. are held apart at a clear distance of 55 mm (Fig. 1). The area-to-volume ratio of the respirometer was 0.6 cm -L. The annular membrane used for this experimental work was 67 mm dia.
Operation Annular membrane was slipped over the base and cover plates to form the cylindrical wall surface (Fig. 1) and the membrane was secured to the base plate with the complementary collar. The liquid sample was introduced
*US Patent No. 5,125,262. 23
24
R.P. G a r g a n d R. P. Mathur
4 15
•
6
~rSmm -
--
I ii
|
.._~
1051~
LE6E. ND !. BASE PLATE COVER PLATE SUPPORTS 4. HOLE FOR DO PROBE 5. O-RIN6S 6. MEMBRANE 7. COLLARS 8. WATER SEAL ROTOR 10. g. GROOVE
(COLLARSREMOVED} Fig. 1. Respirometer.
through the hole in the cover plate so as to completely fill the chamber and entrapped air was removed. The upper portion of the membrane was held tightly and secured to the cover plate with the complementary collar. The calibrated DO probe was introduced into the chamber of the respirometer. The respirometer was placed on a magnetic stirrer in an incubator. The magnetic stirrer worked electrically and was set to rotate the rotor at 100 + 10 rev/ min. The probe was connected to a potentiometric chart recorder or interfaced to a computer. Polyethylene membrane Quality controlled polyethylene film was used in the work reported here. Polyethylene film was prepared from polymer granules having uniform density so as to fix the volume fraction of the amorphous phase and the blowing of the film was carried out under approx, uniform environmental temperature conditions to control the size and shape distribution of the crystallites (Michaels and Parker, 1959). The lower the density of polyethylene, the higher is the fraction of amorphous phase. Hence, a low density polyethylene membrane was used for obtaining an increased rate of diffusion of oxygen through the membrane. The annnular polyethylene membranes were prepared from polymer granules having uniform density. The density of the granules was not determined in the laboratory and was taken as 0.916 g/cm 3 as given by the manufacturer. An annular membrane of 67 mm dia. was prepared by the blowing process. In the machine, quality control of the diameter of the annular membrane was possible, but control of its thickness at various locations over the membrane was limited. From a quantity of ~ 5 kg of the membrane, 20 random samples of 200 mm length were taken for estimating the average unit weight. From the average unit weight and density of the membrane, the average thickness (T) and relative error in T were estimated. Membrane type I This type of membrane was prepared from branched low density polyethylene granules (variety DFDI 0114) manufactured by Union Carbide (India). The membranes were prepared at ambient temperature (30°C) by the blowing process. Membranes having a thickness of 0.015 and 0.025 mm were used for the experimental work. The average unit weight of 0.025 mm thick membrane was 2.247 mg cm -2.
Membrane type H This type of membrane was blown under similar conditions and the same variety of low density polyethylene granules were used as for type I, but the bag of granules came from a different sample. A membrane thickness of 0.013 mm was used for the experimental work. Membrane type I11 This type of membrane was prepared from low density polyethylene granules (variety OBFX 0114) manufactured by Oswal Petrochemicals (India) previously owned by Union Carbide (India). Membrane type I V This type of membrane was prepared from linear low density polyethylene granules (variety FD 0374) manufactured by Qatar Petrochemials Co., Qatar. Calibration of DO probe The DO in the liquid sample in the respirometer was determined with a DO probe which was calibrated at the start of every experiment and the calibration was checked at the termination of the experiment. Synthetic wastewater The synthetic wastewater consisted of a carbon source supplemented with inorganic salts. The synthetic waste was composed of glucose and glutamic acid (in equal proportions) 100 rag/l, phosphate buffer solution (,pH 7.0) 10 ml/1, MgSO4.7H20 100 rag/l, FeCh.6H:O 0.5 rag/l, MnSO4.H20 10 mg/l, CaCI2 7.5 rag/l, tap water 100 ml/1 and acclimated sewage seed 5 ml/l, made up to 1 1 with distilled water. Seed Settled domestic sewage was used as seeding material. Before using the inoeulum for different experiments, the seed was acclimatized in a separate respirometer. Initially, 25 ml of settled domestic sewage was added in one litre of medium (synthetic wastewater) containing 100mg/l of glucose and glutamic acid. The respirometer (with synthetic waste and seed) was maintained at 20°C with continuous stirring. The medium was replaced three times after every 24 h to get the acclimatized seed.
Development of a membrane respirometer EXPERIMENTAL APPROACH Permeability of oxygen through different varieties of polyethylene has bc~n determined (Michaels and Parker, 1959; Michaels and Bixler, 1961). However, it is difficult to estimate the mass (o~ygen) transfer coefficients for a sample of polyethylene membrane (when used in the respirometer) from the known properties of the polymer (Michaels and Parker, 1959; Michaels and Bixler, 1961) since, in the respirometer, polyethylene membrane as well as laminar layer of the liquid offer resistance to oxygen transfer. Moreover, after using the membrane for oxygen uptake study, it needs to be washed if it is to be used again. In order to avoid the inconvenience of washing, the used membrane is wasted and a new membrane is used every time a test is repeated. Though the quality of membrane was controlled, the following aspects were experimentally investigated to ascertain whether the experimental apparatus can be used as a respirometer or not. (a) The liquid sample in the respirometer is not in direct contact with atmospheric air, rather the polyethylene film is exposed to air. TItLe polyethylene membrane has quite different thermodynamic properties in comparison to those of the water sample in the respirometer. To ascertain the ,
Gas
25
effect of surrounding the water sample with a polyethylene membrane, the DO saturation concentration of water in the respirometer was experimentally investigated. (b) To confirm the working of the respirometer using a two phase heterogeneous film of polyethylene, variations in the rate of oxygen transfer in it were studied for the four types of membranes. Oxygen demands of synthetic wastewater samples were also studied. M A T H E M A T I C A L M O D E L FOR M A S S TRANSFER
Diffusion o f oxygen from atmospheric air to the liquid (water) in the respirometer takes place by diffusion of oxygen from the gas phase to the gas-membrane interface and dissolution of oxygen at the surface of the membrane exposed to atmospheric air (Fig. 2). It has been assumed that equilibrium is established instantaneously at the gas-membrane interface. Further, diffusion of oxygen takes place in the amorphous phase of the membrane along the concentration gradient. At the membrane-liquid
Phase Membrane
Liquid film
Liquid
Phase
cQa
Pg
X
t=oc
•
P = Pg
o o 0
t=t in th o L.
o
P=P
t2. t~
interface
~2 n
Pressure
Gas
Phase
Membrane
Gradients
Liquid
film
Liquid P h a s e
E
t =cc,
Csat t-
°~
C = CSo t
o
.r" O
o
i..
to •
tO
t,.) O O
¢-
t--t
, c --c
O a
-Interface Distance ---------Concentration
Gradients
Fig. 2. Pre~sure and concentration gradients in the membrane and liquid phase of the respirometer.
R. P. Garg and R. P. Mathur
26
interface, oxygen is desorbed and transfer of oxygen from the membrane-liquid interface to the liquid phase takes place by mixing. Steady state permeability of oxygen in polyethylene is determined from Fick's linear law of diffusion by considering polyethylene as a "porous medium" (Michaels and Parker, 1959), the "particles" of which are the crystallites and the "pores" of which are composed of the amorphous phase. Amount of oxygen (J) passing through the unit area of the membrane per unit time may be written as (Fig. 2): J =
o~IS,DI(p~ - pi)/L, = S2D2(Pi - p)/L2,
(I)
where ctt is the area fraction of amorphous phase at the gas-membrane interface, S~ and $2 are the solubility coefficients of oxygen for the membrane and the liquid in the respirometer respectively, D1 and D2 are the diffusion constants of oxygen for the membrane and the liquid respectively, L~ and L2 are the thicknesses of the membrane and the laminar liquid layer (Fig. 2) respectively and p~, pi and p are the partial pressures of oxygen in the bulk gas phase, membrane-liquid interface and in the bulk liquid phase (Fig. 2), respectively. Value of D~ depends on polymer morphology (Michaels and Parker, 1959; Michaels and Bixler, 1961); and (2)
D i = ct'Dp/r'fl*,
where Dp is the diffusivity of oxygen in completely amorphous polyethylene, ct is the volume fraction of amorphous phase in the polymer polyethylene, (I/T) is the tortuosity factor representing fractional reduction in oxygen diffusivity arising from the geometric impedence offered by the crystallites, and (I/E*) represents the fractional reduction in oxygen diffusivity due to restriction of chain movement in the amorphous phase. For system isotropy ~t~ is taken equal to c¢. The value of pi is not known and is difficult to determine accurately. Equation (1) may be written as: J = (p~ - p)/[L,/(ccS,DO + L2/(S2D2)].
(3)
Writing equation (3) in terms of DO concentration of water in the respirometer, [multiplying and dividing equation (3) by $2]: dD/dt
= -- rc(Csat
-
-
C),
(4)
where dD/dt = - J ( A / V ) , A = area of the membrane surrounding water in the respirometer and V = volume of water in the respirometer. r~ = I/[(L~S2)/(ot~StD,) + L~/D2]
(5)
Cs,, = S~Ps = limiting DO concentration in liquid (water) in the respirometer at test temperature and pressure.
c = S~p = DO concentration in liquid (water) in the respirometer at test temperature and pressure at any time t. O = (Csat- c). D is the DO deficit. The limiting DO concentration in the polymer is not known and is difficult to determine accurately. For modeling, the limiting DO concentration in the polymer at the gas-membrane interface (Fig. 2) is taken as the limiting concentration of DO in the liquid phase of the respirometer termed as Cs~, (Fig. 2). rc is termed as the respirometer constant (units t -~) and its value depends on the factors given in Eq. (5). The value of rc specifies the rate of oxygen transfer into the respirometer per unit saturation deficit under specified conditions of temperature, pressure, polyethylene membrane thickness, rate of stirring and area to volume ratio of the respirometer. In the integrated form equation (4) is written as: D = D0 exp( - rot),
(6)
where Do is the initial DO deficit. RESULTS AND DISCUSSION
Respirometric parameters
Following the procedure as explained in the operation of the respirometer, it was filled with water/wastewater. The initial temperature of water/ wastewater was between 19.5 to 20.5°C and the incubator was set to operate at 20 + 0.5°C. One or more magnetic stirrers were placed inside the incubator and the heat generated by the magnetic stirrers was dissipated inside the incubator when the ambient temperature was less than 25°C. But during summer, when the ambient temperature was more than 25°C, the air temperature at the bottom panel of the incubator was usually 19.5 to 20°C and at the top panel it was about 21°C. The base plate of the respirometer was fabricated from Plexiglas that acted as insulator of heat. Since the magnetic stirrer and respirometer were placed at the bottom panel of the incubator, the temperature of the liquid inside the respirometer usually varied from 19.5 to 20.5°C and the maximum temperature of the liquid was never more than 20.7°C. All the experiments were performed at the prevailing atmospheric pressure at Patiala (India). The average atmospheric pressure at Patiala (India) was 99.3 kPa which varied from an upper limit of 100.3 kPa to a lower limit of 98.5 kPa. Variations in rate of oxygen transfer in the respirometer depend upon the variations in the thickness of the membrane. Variations in the thickness at ten locations over a membrane were determined by Optical Path Difference (OPD) with Michelson's Interferometer. The refractive index for each type of membrane was also determined by the reflectance method. The thickness of each type of membrane w a s
Development of a membrane respirometer estimated from the: average value of OPD at ten locations and the determined value of the refractive index. The thickness (as estimated by the OPD method) of the four types of membranes was approximately 10% less in comparison to the value of T by unit weight method. Variation in the thickness of a membrane worked out by unit weight and OPD methods is obvious since in the unit weight method, total length (about 200 ram) is weighed, whereas, OPD is determined at ten locations of a sample of membrane. The relative error in OPD (Table 1) gives an estimate of the variations in the thickness at variou:~ locations over the membrane. The relative error in the diameter of the random samples for the various types of membranes varied from 0 . 4 o to 1.0%. It was observed that when the diameter of the mere brahe was more than the average diameter for that type of membrane, its unit weight was less than that o1' the average unit weight for that membrane sample and vice versa. Thus, the errors due to variations in diameter (resulting in variations in area to volume ratio) and T were partly compensating. The ~.verage thickness (T) and relative error in T for the four types of membranes are given in Table 1. Humidity of air affects the partial pressure of oxygen in atmospheric air. One side of the membrane of the respirometer was exposed to water/wastewater and depending on the permeabilty of the membrane to water, the membrane must always be saturated with water. Thus, the variations in humidity of air will not affect the diffusion properties of the membrane. Experiments were carried out in the incubator and the chamber of the incubator was always saturated with water vapours due to the water seal (Fig. 1) at the top of the respirometer. The effect
27
of humidity of air was not felt on Cs~, and to, although, experiments were conducted during summer as well as rainy season. The effect of vapour pressure on the solubility of oxygen in water may be neglected for temperatures below 25°C (APHA, 1985). INVESTIGATIONS RELATING TO MASS TRANSFER
Values of Cs~t and rc were estimated from unsteady reaction tests on diffusion of oxygen in the respirometer. DO of water in the respirometer was brought in equilibrium with atmospheric air surrounding the respirometer at the test temperature and pressure and the limiting DO value was the Csat value. Following the procedure as outlined in the operation of the respirometer, the respirometer was filled with distilled water. DO of distilled water was reduced by bubbling nitrogen gas in it. DO probe was introduced into the chamber of the respirometer and either a continuous recorder plot (DO vs time) was obtained by connecting the probe to a chart recorder or a DO profile (DO vs time) was obtained by interfacing the probe to a computer. Continuous recorder plots of DO concentration of distilled water, in the respirometer, were obtained on the same chart for 0.015 mm and 0.025 mm thick type I membrane at 20°C (Fig. 3). Recorder plots were also obtained for 0.025 mm thick type I membrane at 15°C, 25°C and 30°C temperatures. Recorder plots were also obtained for 0.013 mm thick type II membrane for distilled water and salt water of salinity 5 g/kg. Recorder plots for water of salinity 5 g/kg were obtained after adjusting the DO meter for salinity correction. DO profiles (Fig. 4) for 0.020 and 0.025 mm thick type III membrane were obtained.
Table 1. DO saturation concentration, membrane characteristics and respirometer constants Relative error in Test temperature (°C)
Cs,, (mg/l)
Cs (mg/l)
(T) (ram)
20 15 20 25 30
7.75 8.75 7.75 7.60 7.20
8.91 9.88 8.91 8.08 7.41
20 --
7.90 7.7t
8.91 8.66
20 --
8.40 7.80-
8.91 --
0.020 --
---
8.40 7.80-
---
0.025 --
20
8.00
8.91
0.063
--
7.80-
--
--
(r) (h-')
Membrane type I 0.015 0.85 0.025 0.44 0.025 0.60 0.025 0.81 0.025 1.04
N for (r)
(T) (%)
(OPD*) (%)
4.1
(r) (%)
7.1
6
3.9
6.8
2.6
6 6
4.5 4.5
7.3 7.3
3.8 4.5
0.89 1.06
10 10
4.9 --
31.3 --
5.6 4.1
0,64 0.75
I0 I0
4.3 --
14.4 --
5,3 5.0
0.14
I0
2.9
8.7
1.4
0.15
10
--
--
1.2
Membrane type ii 0.013 0.013
0.92 0.90
Membrane type III
Membrane
type IV
*Optional path difference determined by Michelson's interferometer. ?For water of salinity (5 g/kg). - - F o r 1:he adjusted value of Cs~. C. in contact with water saturated air and 99.3 kPa atmospheric pressure. WR 31/I--B
R. P. Garg and R. P. Mathur
28
/ 8
,,--- DO vs t
"Cgat = 7 . 7 5 r a g / t 0-06
0:025ram
0.015ram
7
0"08 6
Recorder plot - o - , 4 - Regression tines o O-015mm Membrane 0"2 • 0"025ram Membrane
5
E O
0"1
KEY
3
~
D=D o
exp ( - 0 . 5 8 t )
D = DO
exp ( - 0 - 8 5 t )
o t:) t:3
0"4
2
0-6
~ 0
1
2
3
4
5
6
7
8
9
0" 8 1"0 10
Time-, t , ( h ) Fig. 3. Recorder plots and regression lines for type I membrane.
DO P r o f i l e s KEY
0.04
CSot (mglt)
7.8
8.4
O. 020
•, e
-o-, o
0.025
e,e
~),®
T {mm)
1.08
• , e,-o-,¢ Computed volues
t
~.20 Q
O ¢3
0.60
1.00 2
11
4
5
Time(h)
Fig. 4. DO profiles and regression lines for type IIl membrane.
Development of a membrane respirometer Similarly, DO profiles for 0.063 mm thick type IV membrane were ah;o obtained. DO saturation concentration The asymptotic nature of the DO plots or DO profiles (Figs 3 and 4) is clearly indicated and it may be concluded that the DO concentration of water in the respirometer reaches a limiting value. These experiments were continued for two days (only 5 to 9 hours of data presented in figures) but no increase in DO value was observed. To complement the results, the respirometer was filled with distilled water having a DO value more than the observed limiting DO value for the membrane and it was found that the DO in the respirometer decreased and ultimately stabilized to observed limiting DO value which was taken as the DO saturation concentration (Cs~0 of water in the respirometer. The limiting DO concentration in the respirometer is Cs~t, whereas the limiting partial pressure of oxygen is pg (Fig. 2). For determining variations in Cs~t, replicate experiments were performed for the four types of membranes. Average values of Csat are given in Table 1. Observed Cs~ values of distilled water for the four types of the membranes varied between + 0.1 mg/1. The Csat value of distilled water at 20°C and 99.3 kPa atmospheric pressure are of the same magnitude when 0.015 mm or 0.025 mm thick type I membranes were used. The Csa, values of water are of the same magnitude for 0.015mm and 0.025mm thick type III membranes. The Cs~ values of water are less than the reported DO saturation (Cs) values (APHA, 1985) of water in direct contact with atmospheric air at the same temperature and pressure (Table l).It may be concluded that $2 is less than the solubility constant of oxygen in water directly exposed to atmosphere. Dissolution of oxygen in the membrane or water takes place due to molecular impacts from the gas on to the surface of the membrane or water. At the membrane-liquid interface, the frequency of molecular impacts from the gas (in the transient holes in the polyethylene membrane) on to water is less than the frequency of molecular impacts from the gas on to water surface when it is in direct contact with atmospheric air. Moreover, the transient holes are formed in a fraction of the membrane area equal to ~q. Thus, the Csa~ values of water are less than the corresponding C, (APHA, 1985) values of water at the same temperature and pressure (Table 1). For the same variety of membrane Cs~t values are of the same magnitude (Table 1) for different thicknesses of the membrane, since, frequency of molecular impacts from the gas and ~t~ are of the same magnitude at the membrane-liquid interface. DO saturation concentration for wastewater (Cs~,.O In studies on Cs~, for distilled water and water of salinity 5 g/kg, the ,~'s~tvalue of distilled water and water of salinity :5 g/kg was the same without
29
adjusting DO meter for salinity correction. Had there been any effect on Cs~t due to surrounding the water (of salinity 5 g/kg) with the membrane, Cs~t value of water of salinity 5 g/kg would have been different to that of distilled water. Cs~, value of water of salinity 5 g/kg decreased only when correction for salinity was applied. Thus, the decrease in DO due to salinity of water is the same whether it is put in the respirometer or directly exposed to atmospheric air. Driving force for the diffusion of oxygen in the respirometer is (Cs~,- c) [equation (4)] and for a batch reactor such as the respirometer, c approaches Cs~, for distilled water or tap water and Cs~t.w for wastewater (Ramalho, 1983) as aeration proceeds. Accordingly, the effect of the nature of effluent in the respirometer on the Cs~ value is primarily due to the inorganic matter and to a lesser extent due to non-biodegradable organic matter. The effect of the non-biodegradable organic matter on Cs~t may be neglected since its concentration in the respirometer is usually negligible except in a case where the wastewater contains a considerable portion of nonbiodegradable organic matter. In such a situation Cs~t.w may be experimentally estimated. Thus, the effect of the nature of the effluent on Cs~, will be mainly due to dissolved inorganic salts in it. Decrease in Cs~, due to a salinity of 5 g/kg is 0.2 mg/1 (Table 1) and a decrease in Cs~, of 0.1 mg/l will result in due to a salinity of 2.5g/kg. Membrane to membrane variations of Cs~, are __+0.1 mg/1 resulting in an error of 1.3% in the computed value of oxygen uptake. If the dissolved inorganic salts in a wastewater are 1500 mg/1, its salinity would be less than 1.5 g/kg. In case correction in Cs~, due to dissolved inorganic matter of 1500 mg/1 is neglected, appreciable error in the computed value of oxygen uptake will not be introduced. Oxygen uptake study of wastewaters of up to 150 mg/l of BOD5 may be carried out in the respirometer. Thus, strong wastewaters are to be diluted for estimating their oxygen uptake and the concentrations of dissolved inorganics for the diluted waste in the respirometer is not expected to be more than 1500 mg/l. Where the concentration of dissolved salts in the diluted wastewater is expected to be more than 1500 mg/l, Cc~,w may be estimated from its salinity. Various wastewaters, studied in the respirometer, contained dissolved inorganic solids of less than 1500 mg/1. rc value Regression lines for rc are shown in Figs 3 and 4. The ln(D/Do) vs t plots (Fig. 3) for 0.015 and 0.025 mm thick type I membrane are linear when the value of Cs~t was taken as 7.75 mg/l. It may be concluded that the rate of oxygen transfer in the respirometer follows Fick's linear law of diffusion [equation (6)] up to DO concentration of 7.75 mg/l (Issacs and Gaudy, 1968b). Similar results were obtained for 0.013 mm thick type II membrane with distilled water and water of salinity 5 g/kg when the
30
R.P. Garg and R. P. Mathur
values of C~, were taken as 7.9 mg/1 and 7.7 mg/l, respectively. However, ln(D/Do) vs t plot (Fig. 4, curve 1) for 0.025 mm thick type III membrane is not linear when the value of Cs~, was taken as 8.4 mg/1.The ln(D/Do) vs t plot (Fig. 4, curve 2) for 0.020 mm thick type III membrane was linearized (Issacs and Gaudy, 1968b) when the adjusted value of Ca, (7.8mg/1) was taken for curve fitting. The ln(D/Do) vs t plot for 0.020mm thick type III membrane showed a linear trend (Fig. 4, curves 3 and 4) when the value of Csat was taken as 7.8 mg/1. Similarly, ln(D/Do) for 0.063 mm thick type IV membrane was linearized when Csat was taken as 7.8rag/1. Computed values of c for 0.020 and 0.025 mm thick type III membrane are shown in Fig. 4 and it is evident that residual errors decrease when Cs~t is 7.80 mg/l compared to the errors when Cs~ is 8.40 mg/l. For determining variations in r¢, replicate experiments were performed with the four types of the membranes, m new membrane was used for each test. Average values of re, number of replicate experiments for rc and the relative error in rc are given in Table 1. It is seen (Table 1) that relative errors in T, OPD and rc are less for a thicker membrane compared to that of a thinner membrane. For type III membrane, relative error in OPD is more compared to that in the other three types of membranes. For this reason, relative error in re is more compared to that in T. Quality control on the thickness of type III membrane was limited because of considerably lower viscosity of the polymer melt in comparison to that for other three types of the polymers. The accuracy of DO measurement and variations in temperature during the course of experiments result in variations in the value of r0. A 5% variation in the value of r~ is obtained if an error of 0.1 mg/1 is made in the determination of DO. The purpose of the present investigations was to evaluate the feasibility of using a polyethylene membrane as a medium for diffusion of oxygen in the respirometer and no attempt has been made to relate the mass transfer data with polymer morphology of the four types of the membranes. An account of polymer morphology affecting fl, and r has been explained elsewhere (Michaels and Parker, 1959; Michaels and Bixler, 1961). For type I and type II membranes Fick's linear law of diffusion is obeyed up to the observed value of Csa,, whereas, for type III and type IV membranes Fick's linear law of diffusion is not obeyed up to the observed value of Cs~t. Diffusion of gas molecules occurs as a result of redistribution of the free volume within the amorphous phase of the polymer. If an individual hole is not large enough to accommodate a diffusing molecule, the co-operative motion of several neighbouring molecules may allow two or more holes to merge into one hole large enough for a diffusional jump to occur. Thus, distribution of free volume in series would be expected to exist for a given diffusion channel
through a polymer film. As the concentration of the gas in the diffusion channel approaches more closely to the saturation limit, the diffusing molecule encounters "tight" regions, since the formation of free volume by merging two or more holes into one hole for a successful diffusional jump is limited, due for instance to the fact that one of the holes might be already occupied with the gas molecule (Michaels and Parker, 1959; Kumins and Kwei, 1968). From the experimental results, it is clear that Fick's linear law of diffusion is obeyed within a narrow range of Csa, value of 7.75 to 7.9 mg/l for the four types of the membrane. A Cs,t value of 7.80 mg/l may be taken for regression for mass transfer in the respirometer. From the Arrhenius plot of r0, the apparent energy of activation for permeability of oxygen for 0.025 mm thick type I LDP membrane was estimated to be 10.3 kcal/gmol. The reported apparent energy of activation (Michaels and Parker, 1959) for permeability of oxygen through a branched polyethylene membrane of density 0.9135 is 10.2 kcal/gmol. The experimental conditions of the present investigations were slightly different than those of the reported studies. The apparent energies of activation for oxygen permeability are in close agreement. Keeping in view the limitations in the accuracy of DO measurements with a DO probe, the observed relative errors in rc are within experimental error. A coefficient of correlation of 0.99 or better for the regression lines for mass transfer suggests that the rate of oxygen transfer in the respirometer, using a heterogeneous polyethylene membrane, is determinable by Fick's linear law of diffusion and the value of rc is reproducible. Any one type of the membrane may be used in the fabrication of the respirometer.
Oxygen uptake Oxygen demand studies were carried out in the respirometer with synthetic wastewater containing 100 mg/l of a 1:1 mixture of glucose glutamic acid. For the oxygen uptake studies, type I membrane was used and DO concentration of the sample in the respirometer was monitored and continuous recorder plots of DO concentration were obtained. The oxygen demand was estimated by numerical integration of the basic differential equation of the sag curve (Issacs and Gaudy, 1967). The change in DO deficit, due to the combined effects of reoxygenation and deoxygenation, is depicted by the recorder plot. The oxygen demand was estimated without assuming any rate law for the biological deoxygenation in the respirometer. The recorder plot was divided into small portions each having approximately uniform slope and for each portion oxygen demand (A IO was estimated bythe equation:
A Y = fl[rc{(D2 + Dt)/2}'(t2 - t,) +_ (D2 - D0], (8) where t2, D2, tl and DI are time and DO deficits at the end and beginning of the portion of the recorder plot,
Development of a membrane respirometer
31
Substrate : Glucose Glutamic Acid 100mg/l. Curve 2,2': + Nitrification Inhibited with0.1M NI-I4(N]
125
100 ~
75
~
'
Y
~
"
O0 Profites _ I
0 x
o
50
25
,,=, 25
x o
50
75 Time
100
125
(h)
Fig. 5. DO profiles and oxygen uptake curves for the synthetic wastewater.
rc is the respirometer constant. Where fl = CSa,.w/Csat and values of DO deficits have not been corrected for salinity. Value of A Y was integrated for "n" portions of the recorder plot for obtaining the value of cumulative oxygen uptake. DO profiles and oxygen uptake curves for 100 mg/l of glucose glutamic acid are shown in Fig. 5. While calculating values of oxygen uptake, fl factor was taken as unity. The ~,eneral trends of the DO profiles (Fig. 5) are a rapidly decreasing downward leg until a minimum value of DO was reached, followed by a rapidly increasing upward leg and, thereafter, a slight change in the slope of the DO profile occurs. The rapidly decreasing downward leg represents the log growth phase, the rapidly increasing upward trend represents the declining growth phase, and the terminal leg (where s]ight changes in the slopes of DO curve occur) represents the endogenous phase of the oxygen uptake curve. Similar trends in DO profiles were observed by Is:sacs and Gaudy (1967) in their simulated stream experiments.
Cumulative oxygen uptake At the end of fifth day, DO deficit was 0.30 mg/l and oxygen uptake was 114.2mg/l (Fig. 5, curve 1), whereas the theoretical oxygen demand (ThOD) of 100 mg/l of 1: 1 glucose glutamic acid is 102.3 mg/1. In order to investigate the discrepancy between the estimated oxygen uptake and oxygen demand, the experiment was performed with 100 mg/l 1 : 1 mixture of glucose glutaric acid, in which, nitrification was inhibited by 0.1 M ammonia nitrogen (Fig. 5, curve 2). The same acclimated domestic sewage seed was used as in the earlier experiment. In this experiment,
the value of Csa, as well as the DO concentrations were corrected for chlorinity. At the end of fifth day, the DO concentration was 7.30 mg/l (DO deficit of 0.3 mg/i with Cs~, = 7.6 mg/I) and the oxygen uptake was 101 mg/l. At the end of 6th day, the saturation deficit was 0.05 mg/1 and the oxygen uptake was 104.6 mg/l, which is in agreement with the ThOD of 102;3 mg/l with an error of 2.3%. The discrepancy in the estimated oxygen uptake value (Fig. 5) and the ThOD of glucose glutamic acid mixture without inhibition of nitrification was apparently due to nitrification, since, a 100mg/1 1:1 mixture of glucose glutamic acid has a ThOD of 102.3 mg/1 and a nitrogenous oxygen demand of 24.5mg/1. Oxygen uptake at the termination of the decreasing growth phase is 43.5 and 44.5mg/1 without and with inhibition of nitrification, respectively. These oxygen uptake values are synonymous with the plateau B a D and are in agreement with the reported results (Busch, 1958). This indirectly validates the proposed mathematical model and the determined value of the respirometer constant for type I membrane. The respirometer may be adopted for application where oxygen depletion is a problem in oxygen uptake studies. CONCLUSIONS Based on the results of this study the following conclusions can be made: I. A respirometer can be fabricated in which reoxygenation of a wastewater sample can be affected
32
R.P. Garg and R. P. Mathur
through an oxygen permeable polyethylene membrane. The respirometer is completely filled and closed to atmospheric air, thus, the necessity of absorbing carbon dioxide from the gas phase is eliminated. 2. The D O concentration of water in the respirometer, at a particular temperature and pressure, reaches a saturation value which is less than that of water exposed directly to atmosphere. 3. When the liquid sample is stirred in the respirometer, the rate of oxygen transfer can be modeled based on Fick's linear law of diffusion up to 7.8 mg/l D O saturation concentration of water in the respirometer for the different types of membranes used in this study. 4. The rate of oxygen transfer in the respirometer is reproducible within experimental error. 5. The respirometer may be used for oxygen uptake study of a wastewater sample and the course of oxidation of the organics in the wastewater may be obtained. Acknowledgements--This work was supported from the sponsored research grant of the Civil Engineering Department of Thapar Institute of Engineering and Technology (Deemed University) Patiala (India). Guidance and support from Prof V. V. Sastry, Deputy Director, Thapar Institute of Engineering and Technology, Patiala, is gratefully acknowledged.
REFERENCES
APHA (1985) Standard Methods for the Examination of Water and Wastewater, 16th ed. American Public Health Association, Washington, DC. Busch A. W. (1958) BOD progression in soluble substrates. Sewage Ind. Wastes 30, 1336. Issacs W. P. and Gaudy A. F. Jr (1967) Comparison of BOD exertion in a simulated stream and in standard BOD bottles. Proc. 22nd Ind. Waste Conf., Purdue Univ. Engng Ext. Ser. 52, 165. Issacs W. P. and Gaudy A. F. Jr (1968a) Atmospheric oxygenation in a simulated stream. J. Sanit. Eng. Div. Amer. Soe. Civil Engng 94, NOSA 2, 319. Issacs W. P. and Gaudy A. F. Jr (1968b) Constants of first order reactions. Biotechnol. Bioengng 10, No. 1. Jenkins D. (1960) The use of manometric methods in the study of sewage and trade wastes. Waste Treatment (Edited by P. C. G. Issacs). Pergamon Press, Oxford. Kumins C. A. and Kwei T. K. (1968) Free volume and other theories. Diffusion in Polymers (Edited by J. Crank and G. S. Park). Academic Press, London. Michaels A. S. and Parker R. B. Jr (1959) Sorption and flow of gases in polyethylene. J. Polymer Sci. 1, 53. Michaels A. S. and Bixler H. J. (1961) Flow of gases through polyethylene. J. Polymer Sci. 50, 413. Montgomery H. A. C. (1967) The determination of biochemical oxygen demand by respirometric methods. Wat. Res. 1, 631. Ramalho R. S. (1983) Introduction to Wastewater Treatment Processes, 2nd edn, p. 172. Academic Press, New York. Stack V. T. (1972) Biochemical oxygen demand measurement. WaterWater Pollution Handbook (Edited by L. L. Ciaccio). Marcel Dekker Inc., New York.