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Thermodynamic study of the aeration kinetic in treatment of refinery waste water in bio-aeration tanks
Desalination 248 (2009) 941–960
Thermodynamic study of the aeration kinetic in treatment of refinery waste water in bio-aeration tanks Mirjana Sˇevaljevica*, Miroslav Stanojevic´b, Stojan Simic´c, Milan Pavlovic´d a
High Technical School in Zrenjanin, University of Novi Sad, Serbia Faculty of mechanical engineering, University of Belgrade, Serbia c Oil refinery a.d. Modricˇa, Bosnia and Herzegovina d Technical Faculty ‘‘Mihajlo Pupin’’, University of Novi Sad, Serbia email: [email protected] b
Received 29 July 2008; accepted 10 November 2008
Abstract The intention of this article is the examination of effects of aeration regimes on the agreement between technical parameters measured in prior works, with calculations, in this article based on thermodynamic considerations. In the aeration tank with waste water, the technical characteristics of the air distributors based on volume transport coefficients of oxygen are dependent on variation of air flow and added motor oil contents. In this work, it was shown that the oxygen solubility degree compared to distilled water is controlled with the ratio between the periods of saturation of aerated water and oxygen relaxation over-pressure time. In longer saturation period, it was controlled by thermal gas oxygen distribution but in shorter saturation period, by mass-balanced dissolution in liquid. The rate constants for achieving partial local equilibrium (PLE) of oxygen could be identified based on agreement between experimentally obtained and calculated parameters of aeration kinetics. Keywords: Aeration; Solubility degree; Partial local thermodynamic equilibrium; Relaxation processes; Equilibrium temperatures
1. Introduction The aeration technique for water enrichment with oxygen enables removal of some oxidized components (iron, manganese) combined by flocculation–sedimentation treatment, flotation
*Corresponding author. Presented at the 2nd Conference on Small and Decentralized Water and Wastewater Treatment Plants (SWAT), Skiathos Island, Greece, May 2–4, 2008
of dispersed particles and removal of volatile compound prior biological treatment. The efficiency of aeration is dependent on the nature of dispersed particles (metal, electrolyte, coalescence of oil drops, presence of catalytic substances, etc.) adsorbed in contact surface between gas and liquid, after saturation is achieved. According to literature [1], in refinery waste water, the average content of pollutants are found up to 150–250 g/m3 BOD5, 300–600 g/m3 COD, 100–300 g/m3 fat and oil,
0011-9164/09/$– See front matter © 2009 Published by Elsevier B.V. doi:10.1016/j.desal.2008.11.009
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20–200 g/m3 fenols, 1–100 g/m3 benzen, 1– 100 g/m3 benzpiren, 1–100 g/m3 chrom and up to 0.2–10 g/m3 lead. All production lines and auxiliary installations in refineries create during the production process certain amounts of wastewater-containing oil that is removed in tanks, by using scrapers during pretreatment processes. Flocculation–sedimentation and flocculation–flotation processes are used for complete removal of free hydrocarbons from water. After that the water is biologically purified in tanks with activated sludge or in aerated lakes and lagoons. According to literature [2–8], the efficiency of aeration is dependent on the volume coefficient of oxygen transport, based on theoretical researches with the adequate psychical–chemical models and on the empirical formulas. The experimental data obtained in the prior works with procedure are treated [9] based on the gas-phase material balance [2, 3]. Factors influencing oxygen transfer in fine pore-diffused aeration of water are described in literature [10, 11]. According to literature [12], the equilibrium is achieved if in open system the fluctuations of equilibrium due to thermodynamic parameters, temperature, pressure and chemical potential can be neglected in the small local part and within small time period during aeration. To the other author [13, 14], at contact surface between two phases, entropy-driven processes in Helmholtzes and diffusion layers the entropy-balanced processes activate electrons and ions transport determined with electrode kinetic for keeping equal temperatures in the both phases. The correlation of the aeration efficiency that enables the most efficient purification, with active and passive relaxation processes rate constants, has to be enabled to control the dominant influence. The oxygen-successive diffusion step and parallel adsorption step processes rate constants in oxygen dissolution during aeration can be determined by the corresponding methods, according to literature [12, 14, 15].
When aeration systems are designed, it is necessary to use aeration devices with an actual oxygen introduction capacity higher or equal to the actual need for oxygen in the treatment process of wastewater with biochemical reactions. Actual efficiency of the transport system defined as the ratio between the real capacity of oxygen introduction and the total oxygen introduced by the aeration was influenced by air flow and motor oil concentration [2, 3], according to literature [10, 11]. The oxygen accumulation rate constants were determined on the basis of the mass balance of oxygen during saturation period. An innovative aspect of this article is the study of passive processes rate constants that control the dominant resistances with an aim to achieve a better oxygen solubility degree in comparison with distilled water, in shorter aeration period. The significance of thermodynamic study of aeration kinetic in treatment refinery wastewater in bio-aeration tanks in this work is illustrated with application in determining of oxygen solubility degree in dependence of agreement between:
•
•
experimentally obtained (active transport processes rate constant as volume coefficient of oxygen transport, drift rate constants in saturation time) and calculated kinetic parameters of passive transport processes rate constants (chemical potential-driven saturation rate constant, concentration gradient-driven diffusion and by potential fields-driven adsorption and charging rate constants).
2. Experimental study According to literature [2, 3], the used material and procedure are described with apparatus constituted from a polypropylene column
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with dimensions 700 700 2200 mm with accompanying connections and construction frame for experimental work in batch conditions (Fig. 1).
• • •
2.1. Apparatus
•
A list of measured values and instruments on the described installation is presented in Fig. 1 The measuring equipment can be described with the measured values and with used instruments:
• •
tG, 8C – air temperature, Mercury thermometer tL, 8C – water temperature in the column, Mercury thermometer (pm)p, mm Hg – air over-pressure, U-pipe with mercury
L L L co 6 7 8 9
•
Dpp, mm Alc. – pressure loss through the orificeplate, Micro manometer with alcohol (pm)d, mm Hg – Air over-pressure in front of the air distributor, U-pipe withmercury uL, m2/s – Kinematical viscosity of water in thecolumn, Modified Oswald viscosimeter rL, kg/m3 – Water density in the column, Laboratory pycnometer co, mg/L – Starting mass concentration of dissolved oxygen in water, ‘‘HANNAINSTRUMENTS 9142’’ c(t), mg/L – Mass concentration of dissolved oxygen in water, ‘‘HANNAINSTRUMENTS 9142’’
Air flow is measured on the pipe with dimension Lp = 3000 mm and diameter Dp = 52.3 mm. The name diameters of the used valves NV15, NV20 and NV50 are given (Fig. 1). The volume
tL 5
8
water air measurement equipment connections
NV15
c() 10 9
measuring point NV15
7 Lp3000; Dp52,3
5
4 (pm)d
4
NV50
NV20
6
NV20
tG 1
3 pp
NV15
•
•
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Fl tOK pa 11 12
3 NV20
2
M ~
1
2 (pm)p
Fig. 1. Scheme of experimental installation. 1 – low pressure compressor; 2 – air inflow pipe valve; 3 – relief valve; 4 – air flow regulator; 5 – air flow measuring orifice plate; 6 – column with corresponding connections and framework; 7 – disk-shaped membrane air distributor (HD 340, 0.06m2); 8 – water supply; 9 – sampling connection.
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of the water tanks was VL = 1 m3 and the height was h = 2 m.
5 and 10 mg/L, respectively. In oil maximal contaminated water, at maximal air flow of 10 m3/h, thin oil film appeard on the water surface.
2.2. Procedure Before starting the experiment, kinematic viscosity, density and surface tension of water in the experimental installation had to be determined. Complete experimental system for defining the process parameters of water aeration with certain characteristics, started by measuring the temperature of the surrounding air and water in the column. The over-pressure value before the distributor (pm)d and the orifice plate (pm)p, that is the pressure difference before and after the orifice plate (Dpp), was measured, when the first air bubble entered in the water. The column was initially filled with previously prepared water (pH = 7.21–7.29) from which oxygen was extracted using a chemical method of introducing sodium sulfite in the presence of a cobalt chloride hexa-hydrate catalyst. After that, the determined amount of waste oil was added into the water. Air flow regulation was performed using a flow regulator and relief valve until a set value for the applied analysis system was attained. When the flow is stabilized, water samples were taken from the column in equal time intervals (Dt = 60 s). The dissolved oxygen content was measured with HANNA instrument with sensors (with accuracy 0.05 g/m3) until the same value appeared three times. After one regime was analysed, the compressor was switched off and the relief valve was opened completely. Water from the column was released into drains via a draining valve. The column was then filled with a fresh amount of water. Thus, the installation was ready for a new investigation regime, that is the described procedure was repeated. The investigated regimes are defined with the air flows up to 2, 6 and 10 m3/h for each of the three water samples, respectively: with motor oil un-contaminated and contaminated water of
2.3. Material In the installation for water treatment in the oil refinery in Modricˇa, the average characteristics of wastewater during the period of investigation were pH 7–8, temperature 15–258C, oil content 13–23 mg/L, inorganic salts 0.38–0.40 mg/L, TSS 0.5–0.7 mg/L, HPK 80–180 mg/L BPK, up to 0–7 mg/L, CaO 18.5–21.5 mg/L and electric conductivity 670–770 mS/cm. The characteristics of the examined water are dependent on the content of added motor oil content up to zero as 5 g/m3 and 10 g/m3 of viscous waste motor oil (SAE 15 W-40, with 132.0 mm2/s viscosity index, inflammation temperature 231.08C, 3.18 mg KOH/g TAN, 9.73 mg KOH/g TBN, Zn 0.039%, Ca 0.310%, Fe 13.4 ppm, Cu 4.11 ppm, Cr 0.98 ppm and Al 44.87 ppm) was added. Densities of the three examined samples of water were in the range of 992–996 kg/m3, viscosity in range of 0.81 106 to 0.99 106 m2/s and surface tension coefficients were 76.2, 64.8 and 57.3 mN/m, respectively. 2.4. Treatment of experimental data The experimental data obtained with the described procedure were treated based on the gas-phase material balance [9], with the intention to study the influence of system of aeration (air flow and motor oil concentration) on the efficiency of the transport system (the ratio between the real capacity of oxygen introduction and the total oxygen introduced by the aeration of the refinery wastewater [2, 3], based on the determination of volume coefficients of oxygen transport). According to literature [2, 3], the content of the absorbed oxygen from the dry air in
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treated volume of wastewater was obtained as difference of oxygen content in output air and in the air prior entry, based on the gas-phase material balance [9]: :
V G ðcul ciz Þ ¼ A KL ½c ðciz Þ c ð1Þ where c ¼ c ðciz Þ, kg/m3 – equilibrium mass concentration of oxygen in dependence on the mass concentration of oxygen in air at the output, A ¼ a VL , m2 – total contact surface between air and water, a, m2/m3 – specific surface of contact between air and water, 3 V G or dVG=dt , m /s – air flow, cul, kg/m3 – mass concentration of oxygen in air at the input, ciz, kg/m3 – mass concentration of oxygen in air at the output, VL, m3 – water volume, c, kg/m3 – mass concentration of oxygen in the influent and effluent, The total coefficient of oxygen transport in the water, KLa, is dependent on the transport coefficient in the water phase and in air bubbles. If the resistance to transport in air can be neglected, KL is approximately equal with the volume coefficient of oxygen transport in water, kL. The volume coefficient of oxygen transport is the product of the transport coefficient in liquid and the specific area of gas bubbles in contact with water, a: 1 ð2Þ KL a ¼ k L a s can be determined as kL a ¼
ðcul ciz ÞdVG 1 VL ðc ðciz Þ cÞdt s
ð3Þ
The described device (Fig. 1) for the water phase was used [2, 3] for the measuring of the
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volume coefficient of the oxygen transport, based on the material balance according to literature [8, 10]: dVG cul VL RO2 ðtÞ dt dVG dc ¼ Qc þ ciz þ VL dt dt
Qcin þ
ð4Þ
where: Q, m3/s – water flow (for batch process conditions Q = 0), cin, kg/m3 – mass concentration of oxygen in the influent, RO2 ðtÞ, kg/(m3s) – specific oxygen consumption during biological treatment. Equilibrium mass concentration of oxygen in water is dependent on oxygen concentration of air at the output, based on Henry law c ðciz Þ ciz RT ¼ cL Ha
ð5Þ
is determined by equation with modified Henry’s constant, Hc Hc ¼
Ha R TG CL
ð5aÞ
that gives c ðciz Þ ¼
ciz Hc
ð6Þ
where: Ha, Pakmol (O2 + L)/kmol O2 – Henry’s constant in oxygen distribution coefficient between air and water, R, J/, kmolK – the universal gas constant, TG, K – absolute air temperature, CL, kmol/m3 – molar concentration of water. Equations (5) and (6) give the expression for calculating the output mass concentration of oxygen in air controlled with the constant outer air pressure in dependence of temperature:
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HaðVG cul þ VkL acÞ ciz ¼ VG Ha þ VL kL aRTG cL
ð7Þ
Time dependence of dissolved oxygen concentration is presented by the following equation: Y ¼mX
ð8Þ
tL, 8C – water temperature y = 1.024 – temperature correction factor. Based on the known value for the coefficient of oxygen transport (kLa)s and actual capacity of oxygen introduction OC’, the product of the standard capacity of oxygen introduction and corresponding correction factors that convert standard investigation conditions to real ones are defined [3]:
ðpul MO2 =RTG Þ ðHa=RTR cL Þco Y ¼ ln ðpul MO2 =RTG Þ ðHa=RTR cL ÞcðtÞ ð9Þ where: m, slope coefficient of the equilibrium curve: m¼
ðHa=RTR cL Þk L a RO2 ðtÞ ðHa=RTR cL Þ þ ðVL =VG ÞkL a ð10Þ X ¼t
ð11Þ
The value of Y given for each value of c(t) is determined by experiments for defined time intervals. The previous equations result in the formulae for determining the coefficient of oxygen in waste water as: kL a ¼
Haðm þ RO2 ðtÞÞVG VG Ha ðm þ RO2 ÞVL RTR cL
ð12Þ
Based on the known value for the coefficient of oxygen transport (kLa), actual capacity of oxygen (OC) is determined to [11]: ðkL aÞs ¼
ðkL aÞtL ytL 20
1 s
ð13Þ
where: ðkL aÞtL – experimentally obtained oxygen transport coefficient
OC ¼ ðkL aÞs cs VL
OC 0 ¼ a OC
ð14Þ
b ch co ðtL 20Þ kg ð15Þ y ; h cs
where: OC, kg/h – standard capacity of oxygen introduction into wastewater corresponds to velocity of oxygen dissolution after the total surface between the air and water is achieved. cs , kg/m3 – equilibrium mass concentration of dissolved oxygen in clean water, for normal conditions. According to literature [11], the actual efficiency of the transport system represents the ratio between the real capacity of oxygen introduction, OC’and GO2 , the total oxygen introduced by the aeration: E0 ¼
OC 0 OC 0 ¼ 100 ð%Þ GO2 ðVG Þn rG yO2
ð16Þ
The technical characteristics [2] determined from the aeration system based on the material balance are presented in Table 1. The intention of this article is to enable the examination of the effects of aeration regimes on agreement of experimentally measured volume coefficients of oxygen transport and saturation time and drift time with theoretically obtained passive rate constant (of diffusion and adsorption processes) that controls the degree solubility of oxygen.
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Table 1
3 3 1 V G = dV =dt, m /h – air flow rate coil , g/m added oil content, kL a, min volume coefficient of oxygen transport, OC’, g/h – actual capacity (Eqn (15)), E’, % – technical efficiency (Eqn (16))
Reg. Nb.
coil (g/m3)
3 V G (m /h)
kL a (min1)
OC’ (g/h)
E’ (%)
1 2 3 4 5 6 7 8 9
– – – 5 5 5 10 10 10
2 6 10 2 6 10 2 6 10
0.04 0.04 0.08 0.03 0.03 0.07 0.03 0.03 0.04
11.7 12.4 21.9 9.5 9.5 19.0 8.2 8.8 10.7
1.46 0.62 0.55 1.12 0.46 0.62 1.00 0.43 0.27
3. Thermodynamic study of aeration kinetics during the partial local thermodynamic equilibrium The degree solubility of oxygen during saturation period is defined by the ratio of the measured stationary concentration in water, saturated with oxygen with the equilibrium oxygen concentration (defined for distilled water in dependence of temperature of liquid phase at normal pressure, to Henry law). Chemical and phase transformations enable relaxation of oxygen chemical potential in contact surface of heterogeneous system, to equilibrium value, and/or mass transport, which enable homogeneous dissolution. In contact surfaces between air and water, oxygen Gibbs energy (G = E + pV + w ST) achieves states of local partial equilibrium with the stationary Gibbs energy per one exchanged mol (m = Vdp) after saturation time at equilibrium chemical potential, equilibrium temperature and pressure. Pressure-driven relaxation processes are dependent on oxygen adsorption affinity enabling equilibrium state. Air-diffuse distributor activates the energy ðCV T þ pdV ¼ TdSÞ in contact surfaces between gas and water phases. In fixed contact surface, volume of gas drift transport frequency defines the time for the transport of gas volume equals with the liquid
volume. In mobile contact surface, the volume coefficient of oxygen transport at normal pressure defines the time for the transport of molar oxygen volume. In contaminated water, constant temperature and pressure enable entropy-driven processes activated with coupled exothermic and endothermic chemical processes. If the potential field are present (electric potential, ’, or field of surface tension, s, on surface, A), the balance of exchanged number of oxygen moles at constant chemical potential enables passive relaxation processes in contact surfaces (SdT ¼ V dp þ w, where w ¼ nm þ zF’ or w ¼ nm þ sA). Agreement of experimentally obtained active rate constants with calculated rate constants of passive transport rate constant for achieving local partial thermodynamic equilibrium (LPTE) makes possible the explanation of the mechanism of oxygen dissolution during aeration process, in dependence of the nature of contact surfaces between air and water in investigated regimes. 3.1. Treatment based on the material balance After the equivalent point of titrated components dissoluted in water is achieved, during aeration, oxygen can be adsorbed in contact surfaces between air and water. Great number of particles
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with adsorbed oxygen in saturated water prevents the fluctuations of equilibrium of thermodynamic parameters (temperature, pressure, chemical potential). According to literature [12], within the small time period, oxygen can achieve the state of PLE in local part of system – saturated gas or water film in contact surfaces. According to Eqn (3), active oxygen coefficients of volume transport are determined on the basis of oxygen mass balance in the gas phase: kL a ¼
ðcul ciz Þ tdr ðc ðciz Þ cÞ
ð17Þ
According to Eqn (17b): ks n ns ¼ kL a nul niz
The active rate constant determined as technical parameter, kL a, in resonance with relaxation time of some of the passive processes enables PLE of oxygen during aeration:
• •
where drift or retention time of oxygen tdr ¼
•
VL dVG =dt
determines the drift rate constant or frequency of transitions of air through water volume, k dr ¼ 1=tdr . According to Eqn (1): aVL ðc ðciz Þ cÞ dVG ðcul ciz Þ ¼ tL tG
ð17aÞ
The relaxation time of volume transport of one mole oxygen in liquid tL with air drift, through unit specific contact surface, a = 1 m2, have to be equal with the relaxation time of chemical potential with transport of one mol oxygen from gas phase tG , by air flow and determined with saturation period, ts : nul niz ¼ Kaðn ðniz Þ ns Þ ts
homogeneous density with diffusion rate constant, kd equilibrium chemical potential among two phases in saturation period, of chemical and phase transitions, with saturation rate constant, ks Electrochemical potential by charging rate constants, k # .
The accumulation of oxygen in fixed total contact surfaces after saturation time can be described to literature [16] after solving Eqn (1): cs c ðciz Þ ¼ c0 c ðciz Þ ekL ats
ð19Þ
Theoretical calculation of oxygen solubility cs (for c0 = 0), is based on degree, wm ¼ c ðc iz Þ over-pressure relaxation time and saturation time in mass-balanced conditions: cs c ðc
iz Þ
¼ 1 ekL ats
ð19aÞ
Equilibrium oxygen concentration can be determined if active rate constants and saturation period are measured:
ð17bÞ c ðciz Þ ¼
The ratio between drift rate constant (frequency) with saturation rate constant corresponds to the number of oxygen moles transported through the liquid during saturation time: kdr tG ðVL Þ ¼ ks ks ðV M Þ
ð18aÞ
ð18Þ
cs 1 ekL ats
ð19bÞ
The obtained equation enables the determination of degree of oxygenation according to literature [14], to Fick’s law that describes the slowest successive step that controls the overall kinetic of dissolution processes by diffusion from adsorbed saturated layer in the water, in
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dependence of the depth of the diffusion layer, d, as well as of the diffusion coefficient, D, and specific contact area, a = A/VL: dc DA ðc ðciz Þ cÞ ¼ dt VL d
kL a ¼
D a d
ð21Þ
ð22Þ
In aerated water that contains irreversible oxidabiles impurities, with rate constants of irreversible oxide dissolution processes, kir , according to literature [16], material balance of oxygen : ðcV Þiz ðcV Þul dðcV Þw þ þ kir VL cw ¼ 0 ð23Þ dt dt At good mixing, ciz= cw (to the differential Eqn (25)), after solving defines oxygen concentration in water after the saturation time t ¼ ts : cs ¼ c ðciz Þ 1 eðkir þðdVG =VL dtÞts Þ
ð24Þ
whereas: kL a ¼ kir þ kdr
ð25Þ
Adsorption of greater number of oxygen moles in monolayer on good conductors (some noble metals and metals) and semiconductors metals with oxide layers (of Al, Ni, etc.) or on thick layers of ventils conductors (SnO) activate dissotiative adsorption and the discharging of electrons current through oxygen can cause dissociation of the covalent bonds of
ð26Þ
Electrochemical equilibrium at surface electric potential, Dw, enables equilibrium of the number of exchanged oxygen moles between gas and liquid phases
In diffusion layer, the volume coefficient of oxygen transport can be in resonance with diffusion rate constant: kL a ¼ kd
gas molecules (of 463 kJ/mol) with water productions [17]: kir ¼ k #
ð20Þ
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nul niz RT ¼ Kaðn ðniz Þ ns ÞFDw ð26aÞ ts
When kL a FDw ¼ ks RT
ð26bÞ
the power for achieving equilibrium by thermal energy of adsorbed oxygen gas molecules equals with the power that enables relaxation of surface potentials, Dw. 3.2. Treatment based on the chemical potential equilibrium When electric and concentration gradient through contact surface determine the passive rate constants, rate of electrons transfer can be greater than the rate of dissociative adsorbtion of oxygen and then peroxide is formed as stabile intermediates, but good catalysts enhance the rate of oxygen dissociation and favor peroxide decomposition and water production. On the carbon in contact surface Jaeger was found highly reversible redox processes of oxygen in equilibrium with hydroperoxide. According to the literature [17], in the aerated water with pH >7, by reversible electron transitions in saturated water with oxygen, the ozonide ions will be formed with the coupled reactions with complicated build-up and decay. The volume coefficients of oxygen ransport are dependent on the affinity of oxygen for
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adsorption that influences on time for achieving stationary oxygen concentrations at equilibrium chemical potential in contact surface, to Gibbs–Helmholtz – van ’t Hoff Equation [18]. When equilibrium of the chemical potentials of oxygen in contact surfaces is achieved:
mL ðO2 Þ ¼ mG ðO2 Þ
ð27Þ
3.3. Treatment based on the electrochemical potential equilibrium
and where mi ¼ ðdG=dni Þp;T;nj , or mðO2 Þ ¼ my ðO2 Þ þ RT ln c ðO2 Þ
ð28Þ
The slope of the obtained linear function (Eqn (29)) is determined with the molar adsorption Gibbs energy (Dads Gy, J/mol – molar adsorption affinity): ln cs ðO2 ÞL ¼ ln cs ðO2 ÞG
During aeration through the charged contact surfaces, the active oxygen transport activates relaxation processes in dependence of the oxygen adsorption affinity, which enable achieving the equilibrium of electrochemical potentials (sum of chemical and electric potential gradient in contact surfaces between the two phases).
Dads Gy ðO2 Þ RTL
ð29Þ
where y ¼ yo tg’x 1 ; y ¼ ln cðO2 ÞL ; y0 ¼ ln cðO2 ÞG ; TL Dads Gy ðO2 Þ tg’ ¼ ð30Þ R
According to literature [20], the dependence of overpotentials for achieving the equilibrium velocity of the oxygen adsorption in saturated layers is explained with the non-faradaic electrochemical modification of the catalytic activity (NEMCA) in contact surfaces with the local potentials determined with electrochemical equilibrium. According to the literature [21], the kinetics of the oxygen dissolution during coal oxidation is controlled with the fastest simultaneous hydrogen adsorption rate constant coupled with redox–electrochemical reaction of adsorbed molecules in electrochemical equilibrium ðD’ þ Dm ¼ 0Þ:
x¼
kL a ¼
FD’max RT DtF
ð32Þ
The adsorption affinity in physical or chemical transformations of the adsorbed oxygen from gas bubble can be calculated based on the slope of the linear functions (Eqn (30)):
According to the literature [15, 22], evolution of hydrogen is enabled with oxidized components during achieving equilibrium of surface electric potential in double electric layer between the Helmcholtze s surfaces:
Dads Gy ¼ R tg ’
kd;i 3RT ¼ it ð2Z f0i Þ
ð31Þ
According to the literature [19], the presence of the oil oxidation products and radical initiators OH–, H2O2, Fe2+ in the presence of HCO3–/CO32–, PO43–, humid acids, aryl-R, tert-butyl alcohol can change the standard oxygen chemical potentials in the contact surface.
ð33Þ
where it ¼ kL aF, A – electrons current, defined with thermal equilibrium with the carriers of migration current in electric field ZH2 , V – hydrogen overpotential on metal in contact with the two phases
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D’Wi , V – standard redox potentials of adsorbed oxidized components kd;i – diffusion rate constant of the fastest oxidized component in diluted solution. The power of oxygen energy during aeration defined with volume coefficient of oxygen transport is dependent on the passive relaxation processes rate constant after adsorption:
• •
of oriented hydrated molecules of oxygen in layer influenced with the potential field of oxygen with kinetic energy in concentration gradient in the two diffusion layers in both the phases
to the following equation: dEtot dEkin dEpot ¼ þ dttot dtd dta
ð34Þ
That can be defined for molar relaxation processes: ¼ kd 2Ed þ ka Dads G kL a Etot
ð34aÞ
for the two adsorbed films in contact surface between gas and liquid:
ka Dads G kL a ¼ kd þ Etot
ð35Þ
where kd , 1/s – passive diffusion transport rate constant of molar kinetic energy ka , 1/s – adsorption rate constant at constant dependent on bond energy ¼ 3RT , J/mol – molar total energy Etot Ekin ¼ 3RT =2, J/mol – molar kinetic energy. Linear equations y ¼ yo þ tg’x; y ¼ kL a; x ¼ Dads my ; ð36Þ ka tg’ ¼ Etot
951
enable calculation passive rate constants: ka ¼ 3RT tg’
ð37Þ
kd ¼ yo
ð38Þ
and
After electrochemical equilibrium is achieved, determination is possible of the passive (diffusion and absorption) rate constants. 3.4. Treatment based on diffusion of gas ionized oxygen Passive rate constant are dependent on the nature and the quantity of contact surface between the gas and liquid phases. According to literature [23], on the contact surfaces, the oxygen evolution is enabled by electron currents on conductor metals and metals–oxide layers of Rutenijum, Platina, Iridijum as well as on the monolayers of semiconductor oxides of Aluminijum, Titan, Tantal, Nikal, Zirkonijum. On the thick layers of ventil conductors (Tin–oxide, Titan–oxide), thermal state of electrons can be achieved with the enough great thickness that enables relaxation of electron temperatures with temperature of carrier of the migration current. The presence of traces of unspecific metals in the diffusion layer of water enables the relaxation processes with rate constants dependent on kinetic energy after adsorption of the stable intermediate as the peroxide or the fuel cells. According to literature [24], coupled irreversible diffusion transport can be activated with greater molar adsorption energies when flux of present kind of molecules may induce fluxes of other, that is referred to as irreversible codiffusion process through contact surface that is not expected on the basis of their electrochemical potential. According to the literature [25], the thermal electron transitions are activated by
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neutral/ion collisions through contact surface with gas phase, to the dynamic equation: Ni mi
dvi Df Dpi Ni mi vi ¼ Ni e Dx Dx dt tin
ð39Þ
where the ratio of potential difference and dx is the potential gradient along the depth of the layer (the strenght of the electric field) function of relaxation–adsorption rate constant, ka. Adsorption rate constants are dependent on the nature and the quantity of adsorbed oxygen molecules adsorbed in contact surface between the gas and liquid phases in dependence of ratio between drift and saturation rate constants. Achieved equilibrium concentrations and temperature after saturation time, during shorttime interval [12], in local partial thermodynamic equilibrium state enable the relaxation time constants of the change of electric potential in electrochemical equilibrium of contact surface (and chemical equilibrium to Eqn (29)): D’ d’ ¼ fð Þ dt dx
ð40Þ
as well as concentration balance with diffusion (to Eqn (20)), dp dp ¼ fð Þ dt dx
ð41Þ
Ni v i ¼ Ki
Df dni Di dx dx
ð41aÞ
where kB ¼ R=NA , J/kmol – Boltzmann constant mi, kg – the molecular mass Ni, number of adsorbed molecules in air bubbles of electroneutral gas oxygen in plasma state vi, m/s – the molecular average square velocity tin ¼ lvii , s – the time period between neutral and ions collision
ð43Þ
that gives the Einstein’s equation: Di kB Ti ¼ Ki e
ð43aÞ
After defining diffusion coefficient in the gas phase to the molecular kinetic theory: 1 Di ¼ vi li 3 Ki ¼
ð44Þ
vi li D’
ð44aÞ
where Di, m/s – diffussion coefficients Ki, m2/sV – electrical mobilities ions. Combining with Einstein equation, the energy for the monolayer completion with oxygen ions corresponds to relaxation of over-potentials to zero by diffusion and migration of adsorbed ions (to Eqn (33)): zF D’ ¼ 3RT
In thermal equilibrium: dp DNi ¼ kB Ti dx Dx
li, m – average intermolecular distance. After saturation for achieving the equilibrium chemical potential (to Eqn (39)), dvi =dt ¼ 0, the Nernst-Plank equation is obtained:
ð44bÞ
To the Einstein equation, coefficient of ambipolar diffusion of oppositely charged ions or ion and electron:
Damb
Te ¼ Di 1 þ Ti
ð45Þ
gives twice greater ambipolar than simple diffusion rate constant. The exchange of gas molecules from gas phase during saturation time is coupled with
M. Sˇevaljevic et al. / Desalination 248 (2009) 941–960
charging rate constant and with pressure relaxation rate constant: k # ¼ kL a ¼ kamb ¼ 2kd
953
saturation measured concentrations and active rate constant (volume coefficient of oxygen transport):
ð45aÞ c ðciz Þt ¼ cs ð1 þ ekL a=ks Þ
ks RT ¼ ka zFDwW
ð45bÞ
The Helmholtz potential on contact of hydrophilic surface for maximal air flow rate can be balanced with faster electron transitions that enable reduction of water molecules. The velocity of recombination of oxygen and hydrogen to water enabled by fast electron transitions are determined by charging rate constant of oxygen. After thermal equilibrium of ions and electrons is achieved, according to literature [25], resistance to oxygen transport in air cannot be neglected, compared to resistance in liquid. 3.5. Treatment based on thermal distribution of gas molecules to Boltzmann law According to literature [26, 27], after saturation time is achieved, thermal collisions of gas oxygen enable distribution of molecules in the two thermal-balanced equilibrium states in gas and liquid phases defined with the potential difference to the Boltzmann law, so as to obtain oxygen solubility degree for liquid phase, cs : wm ¼ c ðc iz Þ cs c ðc
iz Þ
¼
1 DE=RTt
1þe
ð46Þ
According to literature [15, 21] and Eqn (32) and (33), if active rate constants activate relaxation processes in gas phase ððkL a=ks Þ ¼ ðDE=RT ÞÞ: cs 1 ¼ c ðciz Þ 1 þ ekL a=ks
Measured oxygen degree solubility after period of saturation is defined by comparison with concentration defined to Henry law: wexp ¼
cs c ðtL Þ
ð49Þ
The agreement of experimental oxygen degree solubility in saturation period, wH , to Eqn (49), with the theoretical after relaxation: – to thermal equilibrium, with oxygen solubility degree, wt ; calculated to Eqn (48), – to material balance with oxygen solubility degree, wm ; calculated to Eqn (19a) define the phase of passive relaxation processes (gas phase for Boltzmann distribution of oxygen molecules, liquid phase for material balanced transport, or the both). 3.6. Treatment based on the Gibbs adsorption of hydrophobic particles The hydrated molecules can diffuse across the contact surface with adsorbed liquids between air and water very poorly but many small and uncharged atoms can be dehydrated and dissolved in liquids by virtue of their kinetic energy of motion and decrease the free molar contact surfaces between air and water, based on the Gibbs adsorption isotherm: dc AM ds ¼ cs dt RT dta
ð47Þ
Equilibrium concentration of gas oxygen molecules can be determined based on the
ð48Þ
where 1 ¼ ks cs ts
ð50Þ
M. Sˇevaljevic et al. / Desalination 248 (2009) 941–960
954
gives the dependence of adsorption rate constants, molar contact surfaces (AM) and of difference among the surface tension of contaminated and distilled water ðdsÞ: ks ¼ ka
AM ds RT
ð51Þ
During saturation period, relaxation of energy is activated to thermal value by hydrophobicadded oil adhered to oxygen molecules during Gibbs adsorption in the free water surface in the aeration tank: ks RT ¼ ka AM Ds
ð52Þ
Experimentally determined temperatures, the change of surface tension in the surface active substances present compared to surface tension of pure water, as well calculated adsorption and saturation rate constants make possible the determination of the molar contact surfaces between liquid and surrounding air: AM ¼
ks RT ka Ds
ks RT Dw ¼ ka F W
Experimentally obtained technical parameters [2, 3] are presented in Table 1, and temperatures and saturation times and oxygen contents in Table 1a. Investigated aeration regimes are defined with Regime numbers for corresponded air flow rate, added oil content, height of tank, h=1 m with volume of tank 0.5 m3, and h= 2 m with for tank volume 1 m3. In regimes with added oil content 5 g/m3, oxygen capacities are twice greater than in regimes with a maximum of examined air flow. Technically efficiencies decreased twice in regimes when air flow is 6 m3/h. Decreased oxygen solubility in water could not be improved significantly with increased air flow. The study of the Gibbs energy adsorption dependence from oil concentrations shows:
•
ð53Þ
When the drift velocity is greater twice than the saturation rate constant, the power of surface electric potential can prevent control surface transport rate constant in resonance with adsorption rate constant in condition: kL a ¼ ka
4. Results
ð54Þ
ð55Þ
The Helmholtz potential can be balanced with irreversible slow production of gas oxygen by anodic slow successive relaxation reactions of processes that determine the velocity of recombination of oxygen and hydrogen to the water.
oxygen adsorption is activated with parallel endothermic and exothermic oxygen processes at air flows up to 2 m3/h and 6 m3/h in the clean water, respectively
Table 1a Experimentally obtained data: Regime numbers, tL ;
C – temperatures of liquid, tG ; C – temperature of gas and tR ; C – temperature of surrounding air, cs ; g/m3 – oxygen concentration in saturated water and ts , min – saturation time
Reg Nb.
tL (8C)
tG (8C)
tR (8C)
ts (min)
cs (mg/mL)
1 2 3 4 5 6 7 8 9
13.0 13.0 14.0 15.0 12.1 14.5 13.5 13.2 14.1
15.5 17.6 18.7 13.5 14.3 13.4 16.2 17.4 16.3
16.0 17.5 14.2 12.5 15.2 15.3 17.2 19.1 19.1
25 24 22 26 24 20 25 23 20
7.5 7.6 7.9 6.4 6.7 7.0 5.9 6.1 6.4
M. Sˇevaljevic et al. / Desalination 248 (2009) 941–960
•
oxygen adsorption is activated with spontaneous exothermic electrons transitions with the most adsorption affinity at the air flow of 10 m3/h in the contaminated water.
4.1. Calculated adsorption affinities and oxygen solubility degree of aerated water in investigated regimes Calculated equations that enable determination of the adsorption affinity, Dads Gy (O2) (Eqn (29, 31)) are presented in the Table 2. The equations are obtained on the basis of linear dependence of logarithm of oxygen concentrations in saturated water of reciprocal value of liquid temperatures in investigated regimes. Molar adsorption affinities of oxygen characteristics for analysed investigated regimes are presented in Table 3.
955
Table 3 presents also molar oxygen concentrations, Cs, and oxygen solubility degree compared to distilled water, wexp , calculated to Eqn (49). To the obtained results presented, molar adsorption oxygen affinities are dependent only on the air flow rates that determine drift rate constants for air flow 2, 6 and 10 m3 /h of 0.03, 0.10 and 0.16 min1 respectively. The maximum obtained values correspond to the enthalpy of dissociative adsorption, three times greater than dissociation energy of covalent bond. The oxygen solubility degree obtained by comparison with solubility of oxygen in distilled water were 72–77% for clean water and oil-contaminated water was decreased for about 7% for each added 5 g/m3 oil content. The improved procedure of aeration increases oxygen solubility degree, by explanation of relaxation processes based on agreement
Table 2 The Eqn (29) for calculation the adsorption affinity, Dads Gy (O2), to Eqn (29,31), for the investigated regimes, defined with: c, mg/L – oil concentration; h, m – height of water column; V G , m3/h – air flow
c-h-V G
y = yo tg fx
R2
Dads GY(O2) kJ/mol
0-2-2 0-2-6 0-2-10 0-2-2 0-2-6 5-2-10 5-1-6 0-2-10 5-2-10 10-2-10 0-2-10 5-2-2 5-1-2 5-1-10 5-2-6 10-2-2 10-2-6 10-1-2 10-1-6 10-1-10 10-2-10
y = 3663 x + 4.45
0.92
30.45
y = 4367 x 23.62
0.97
36.3
y = 165691 x 586
0.75
1377
y = 8959 x 39.57
0.61
74.5
y = 7727 x 35.57
0.99
64.2
y = 8492 x 38.10
0.94
70.6
956
M. Sˇevaljevic et al. / Desalination 248 (2009) 941–960
Table 3 Obtained adsorption oxygen affinities Dads GY(O2) to Eqns (29) and (31), calculated molar oxygen concentrations in saturated water, equilibrium concentration to Boltzmann and to material balance and equilibrium temperatures for distilled water to Henry Reg. Nb.
DadsGY(O2) (kJ/mol)
ct ðmg=LÞ
cm ðmg=LÞ
tt ( C)
tm ( C)
1 2 3 4 5 6 7 8 9
30.4 36.3 30.4 36.3 30.4 1377 74.5 64.2 64.2 1377 64.2 64.2 70.6 1377
10.3 10.4 9.1 9.1 9.7 8.4 9.1 11.1 9.7
11.9 11.2 9.4 11.4 12.2 9.4 11.1 11.0 12.8
14 14 20 20 17 25 20 11 17
8 10 19 10 7 19 11 11 5
on experimentally obtained and calculated relaxation processes rate constants. 4.2. Effects of aeration regimes on agreement between measured and calculated transport rate constants According to theory [12] in this work are calculated diffusion and adsorption rate constants based on Eqn (38) presented in Fig. 2. Agreement between experimentally obtained active and calculated relaxation, passive rate constants is indicator of resonance of measured active rate constants (volume coefficient of oxygen transport and drift) with saturation, diffusion, adsorption or charging rate constants (to Eqn (25) and (26)), that control oxygen solubility degree:
• •
with mass balanced transport to Eqn (19a) with thermal equilibrium of electrons and ions in two possible equilibrium states of gas molecules, to Boltzmann Eqn (47)
The agreement between the experimentally obtained active and calculated passive rate constant have to be correlated with the oxygen solubility degree obtained theoretically based on Boltzmann equilibrium in gas phase and material balance in liquid phase.
Diagrams in Fig. 2. (Eqn (35)) enable the calculation of passive transport rate constants diffusion rate constant (Eqn (38) and adsorption rate constant Eqn (37)) (Table 4). 4.3. Agreement between experimentally obtained and calculated oxygen solubility degree The agreement between measured oxygen solubility degree and calculated to Boltzmann distribution Eqn (47), as well with calculated to mass balance Eqn (19a), enable the determination of process that control the resistance of volume gas transport. The equal number of oxygen molecules exchanged from adsorbed gas oxygen film with liquid film ðDnL ¼ DnG Þ, in relaxation period during aeration is defined to Eqns (1) and (18a). Tables 5 and 6 present the ratio: ks tL ¼ kL a ts determined to Eqns (1) and (18a) corresponds to: tL n ns ¼ tG niz nul exchanged number of oxygen moles between two phase in PLTE, activate relaxation processes for
M. Sˇevaljevic et al. / Desalination 248 (2009) 941–960
y 3E – 05x 0.043 R 2 0.9965 1500 1000
500
0.1 0.08 0.06 0.04 0.02 0
kLa, 1/min
kLa, 1/min f (ads GΘ (O2) kJ/mol) c (waste oil) 0 mg/L, h 2m
4.4. Effects of potential fields (surface electric potential and surface tension) between air and gas phase
kLa, 1/min
0.08 0.06
2000 1000 ⌬ads GΘ (O2) kJ/mol kLa, 1/min f (ads GΘ (O2) kJ/mol) c (waste oil) 10 mg/L, h 2m y 6E – 06x 0.03 R 2 0.9395 2000 1000 ⌬ads GΘ (O2) kJ/mol
0.04 0.02 0 0
According to Eqns (45) and (45b), maximum air flow rate ðkL a ¼ k # ¼ 2kd Þ activates molar surface electric potential (Table 7) in oil uncontaminated water that enables the resonance of charging rate constants with volume coefficient of oxygen transport: W at surfaces # potential in Regime Nb. 3, Dw ¼ ks RT k 2F = 0.005 V/mol in Regime Nb. 6., • at surfaces potential DwW ¼ ks RT k # 2F = 0.006 V/mol.
•
0.05 0.04 0.03 0.02 0.01 0
kLa, 1/min
y 2E – 05x 0.0322 R2 1
thermal relaxation is enabled in twice-longer aeration period. The diffusion transport (in Reg. Nb. 4 and 5) enables achieving equilibrium temperature in liquid or with the both thermal and mass transport processes (Reg. Nb. 7, 8 and 9) that enable also free surface energy equilibrium (chemical potential and surface tension).
0
⌬ads GΘ (O2) kJ/mol kLa, 1/min f (ads GΘ (O2) kJ/mol) c (waste oil) 5 mg/L, h 2m
957
0
Fig. 2. Diagrams with 3 points (where two for the 2 m3/ h and 6 m3/h air flow are approximately equal but different from 10 m3/h that enable the calculation of passive transport rate constants.
achieving corresponding temperatures for distilled water to Boltzmann (of volatile oxides after flocculation if tR;G tt 1 in gas phase), and/or to material balance (with oxidation, floc1 culation-sedimentation processes if tL tm in liquid). The equal chemical relaxation rate constant with over-pressure rate constant enables relaxation to equilibrium temperatures for distilled water in Reg. Nb. 1 and 2. In Reg. Nb. 3 and 6
The molar contact surfaces (Eqn (53)) and molar surface electric potentials in unit of time also are calculated in dependence of the change of the surface tension in oil-contaminated water compared to pure water 72 mN/m, during aeration (Eqn (57)). Then the kinetic energy of ions in active transport equals the kinetic energy of electrons in passive chemical reaction, which is achieved according to Eqns (54) and (55). At surface potential, RT =F ¼ Dwy in oilcontaminated water (Reg. Nb. 7, 8 and 9), the resonance between adsorption rate constant ðkL a ¼ ka 0:75ks Þ makes possible simultaneous mass transport of hydrophobic oxygen with oil particles and thermal relaxation processes of hydrophilic hydrated oxygen molecules. 5. Conclusions The results obtained in this work enable the following conclusions:
M. Sˇevaljevic et al. / Desalination 248 (2009) 941–960
958
Table 4 Measured active rate constants (as volume coefficient of oxygen transport and drift rate constant of 0.03; 0.10 and 0.16 min1 respectively, in dependence of examined air flow (2; 6 and 10 m3 =h) and calculated rate constants: diffusion, adsorption and charging rate constants Reg. Nb.
kL a (min1 )
kd (min1 )
ka (min1 )
1 ts
(min1 )
1 2 3 4 5 6 7 8 9
0.04 0.04 0.08 0.03 0.03 0.07 0.03 0.03 0.04
0.04 0.03 0.03 0.04 0.03 0.03 0.04 0.03 0.03
0.21 0.21 0.21 0.14 0.14 0.14 0.04 0.04 0.04
0.04 0.04 0.04 0.04 0.04 0.04 0.05 0.05 0.05
k # (min1 ) 0.01 0.06 0.08 0.00 0.07 0.09 0.00 0.07 0.12
*measured period of aeration time that enable the achieving of constant oxygen concentration: ts ¼ tG
1. The control of oxygen solubility degree as well as the overall velocity of oxygen dissolution is based on the agreement of experimentally obtained ratio among active transport
rate constant (measured oxygen coefficient of oxygen transport in liquid and drift relaxation time) with relaxation processes that enable equilibrium temperature, equilibrium
Table 5 Experimentally obtained oxygen solubility degree calculated to Eqns (19a) and (47) and ratio between saturation and active transport rate constants
tWL tWS
Reg. Nb.
wexp ð%Þ
wt ð%Þ
wm ð%Þ
1 2
74 72
73 73
63 67
1 1
3
77
88
86
0.5
4
63
72
63
1.3
5
62
68
65
1.3
6
69
84
82
0.6
7
57
54
45
1.6
8
58
64
45
1.6
9
62
69
55
1.3
Compared measured with the calculated aeration rate constants
ks ks ks ks ks ks ks ks ks ks ks ks ks ks ks ks ks
¼ kd ¼ kL a ¼ 0:2ka ¼ kL a ¼ kd ¼ 0:2ka ¼ 1:3kd ¼ 0:5k ¼ 0:5kL a ¼ 0:4ka ¼ kd ¼ kdr ¼ 1:3kL a ¼ 0:3ka ¼ 1:3kd ¼ 1:3kL a ¼ 0:3ka ¼ 1:6kL a ¼ 1:3kd ¼ 0:4k # ¼ 0:3ka ¼ 1:3kdr ¼ 1:3kL a ¼ 0:7k ¼ 1:25kd ¼ 1:7kd ¼ 1:7kL a ¼ 0:7ka ¼ 1:25ka ¼ 1:25kL a ¼ 1:7kd
M. Sˇevaljevic et al. / Desalination 248 (2009) 941–960 Table 6 Effects of aerations regimes after the saturation period on agreement of experimental obtained temperatures of liquid, gas and surrounding phase (Table 1a) with calculated equilibrium temperatures for distilled water that enable distribution of gas molecules to Boltzmann and experimental obtained tt , and mass transport tm oxygen solubility degree with calculated, wexp ¼ wcalc , exchanged number of moles between water and gas phases Reg. Nb.
ðn ns Þw ðniz nul ÞG
1 2 3 4 5 6 7 8 9
1 1 0.5 1.3 1.3 0.6 1.6 1.6 1.3
¼ kkLsa
tR;G tt
tL tm
wexp ¼ wcalc
1.1 1.2 0.9G 0.7 0.9 0.6 0.9 1.6 1
1.6 1.3 0.7 1.5 1.7 0.8 1.2 1.2 2.8
wt wt wt; m wm wm wt; m
•
•
wt þwm 2 wt þwm 2 wt þwm 2
over-pressure, as well as chemical, electrochemical potential and free surface energy. 2. The effect of aeration regimes on agreement between experimentally obtained and calculated thermodynamic and kinetic parameters enables the identification of the relaxation processes of exchanged number of oxygen molecules after achieving PLTE. 3. The results obtained for investigated regimes show:
•
•
Equal active and passive rate constants in oil-uncontaminated water at less air
959
flows, enable oxygen solubility degree in oil-uncontaminated water 72–74%, by the thermal relaxation processes defined for gas-adsorbed molecules to Boltzmann Equal over-pressure relaxation with charging rate constant enhanced oxygen solubility degree for 5%, in oil-uncontaminated or small oil-contaminated water at maximal air flows Velocity of overall oxygen dissolution process and oxygen solubility degree of 63%, control diffusion rate constants in small oil-contaminated water at less air flows Equal adsorption rate constant with volume coefficient of oxygen transport and chemical relaxation rate constants enable thermal, mechanical and chemical equilibrium in maximal oil-contaminated water. Decreased oxygen solubility degree to 57–62%. controls the presence of hydrophobic oil drops and dehydrated oxygen molecules in free contact surface of water.
4. The improved results for oxygen solubility degree could be achieved by pretreatment for removal of colloidal particles by microfiltration after flocullation–sedimetation treatment and for oil-contaminated water by flocculation–flotation treatment, or with combined treatment [29]. 5. The electrochemical investigation could be usefull also in aim to improve oxygen solubility degree by optimization of contents of catalytic substances in control of relaxation processes.
Table 7 The surface tension and temperatures of water in investigated regimes, the changes of the surface tension, molar contact surface between water and surrounded air and the surface electric potentials Reg. Nb. sðmN=mÞ T ðKÞ DsðmN=mÞ AM m2 =m DwW ðV=molÞ 1,2,3 4,5,6 7,8,9
76.2 64.8 57.3
286 287 287
4.2 7.8 14.7
107.8 87 41.6
0.005 0.007 0.025
960
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References [1] Pollution Prevention and Abatement Handbook, World bank group, Effective, July 1998. [2] Stanojevic´, M., Radic´, D., Simic´, S., Determining the Technical Characteristics of The Aeration Systems for Oil Refinery’s Wastewater Treatment, 16th International Congress of Chemical and Process Engineering, CHISA Praha, Czech Republic, 2004, pp. 3863–3887. [3] Simic, N.S, Influence of Sistem of Aeration on The Efficiency of The Biologycal Treatment of The Refinery Waste Water, Ph.D. Thesis, Faculty of Mechanical Engineering, Belgrade, Serbia, 2006. [4] Dudley, J., Mass Transfer in Bubble Column-S Comparison of Correlations, Water Research, Swindon, 1995. [5] Fujie, K., Air Diffuser Performance in Activated Sludge Aeration Tanks, Journal of Water Pollution Control Federation, Washington, 1985. [6] Mc Gregor, R., Diffusion and Sorption in Fibres and Films, Vol. 1, Fiber Chemistry, Marcel Decer, New York, 1973. [7] Montgomery, J., Water Principles and Design, John Wiley & Sons, 1985. [8] Mc Whirter, J., Hutter, J., Improved Oxygen Mass Transfer Modeling for Diffused/Subsurface Aeration Systems, Deparment of Chemical Engineering, The Pennsylvania State University Park, PA 16802, AIChE Journal, 1989. [9] Fujie, K., Tsuchiya, K., Fran, L., Determination of oxygen transfer coefficient by off-gas analysis, J. Ferment. Bioeng., 1994. [10] Ashley, K., Hall, K., Mavinic, D., Factors Influencing Oxygen Transfer in Fine Pore Diffused Aeration, University of British Columbia, Water Research 25, Vancouver, 1998, pp. 1479–1486. [11] Wagner, M., P€opel, J., Oxygen Transfer and Aeration Effciency – Influence of Diffuser Submergence, Diffuser Desity and Blower Type, Water Quality International, IAWQ 19th Bienia International Conference, Vancouver, Canada, 1998. [12] Prigogine, I., Introduction to Thermodynamics of Irreversible Processes, Wiley, New York, 1967.
[13] Delachay, P., Bersins, J., J. Am. Chem. Soc., 21 (1953) 1063. [14] Lingane, J.J., Electroanalytical Chemistry, Interscience Publishers, Inc., New York, 1958. [15] Sˇevaljevic, M.M., Development of the Galvanostatic Method for Gaseous Arsenic Hydride Generation and Successive Lead and Cadmium Pre-Concentration for Increasing AAS Determination Sensitivity, Ph.D. Thesis, Faculty of Technology, Novi Sad., 2000. [16] Gilbert M. Masters, Introduction to Environmental Engineering and Science, CRC Press, 1995. [17] Bard, A., Parsons, R., Jordan, J., Standard Electrochemical Potentials in Aqueous Solutions, JUPAC ed., New York, Base, 1983. [18] Wall, F.T., Chemical Thermodynamic, Frezenius & Co., San Francisco, 1965. [19] Von Gunten, U., Ozone reaction mechanisms, Water Res., 37 (2003) 1469–1487. [20] Vayenas, G., Bebelis, S., Ladas, S., NEMCA effect, Nature (1991) 343, 625, London. [21] Sˇusˇic´, M., Minic´, D., Marinkovic´, S., Kinetic of coal activation by oxidants, J. Serb. Chem. Soc., 57 (1992) 705–713. [22] Sˇevaljevic´, M.M., Mentus, S.V., Marjanovic´, N.J., A new technique of arsenic determination based on electrolytic arsine generation and AAS, J. Serb. Chem. Soc., 66 (2001) 419–426. [23] Mentus, S., Electrochemistry, 2nd ed., University in Belgrade, 2001. [24] Katchalshy, Curran, Nonequilibrium Thermodynamics in Biophysics, Harvard, 1965, Chapter 8. [25] Perovic´, B., Physic of the Ionised Gases, Belgrade, 1971. [26] Stanisavljecic´, M., The Study of Degree of Partial Local Thermodynamic Equilibrium of Stabilized Arc Plasma in Argon, Ph.D. Thesis, Institute of Physics, Belgrade, 1972. [27] Forsterling, H.-D., Kuhn, H., Physicalische Chemie in Experimenten, Verlag Chemie, 1971. [28] Gleston, S., Physical Chemistry, Science Book, 1967. [29] Efrosyni, N.P., Maria, M.F., Mavros, P.P., Matis, K.A., Desalination, 194 (2006) 135–145.
Thermodynamic study of the aeration kinetic in treatment of refinery waste water in bio-aeration tanks Mirjana Sˇevaljevica*, Miroslav Stanojevic´b, Stojan Simic´c, Milan Pavlovic´d a
High Technical School in Zrenjanin, University of Novi Sad, Serbia Faculty of mechanical engineering, University of Belgrade, Serbia c Oil refinery a.d. Modricˇa, Bosnia and Herzegovina d Technical Faculty ‘‘Mihajlo Pupin’’, University of Novi Sad, Serbia email: [email protected] b
Received 29 July 2008; accepted 10 November 2008
Abstract The intention of this article is the examination of effects of aeration regimes on the agreement between technical parameters measured in prior works, with calculations, in this article based on thermodynamic considerations. In the aeration tank with waste water, the technical characteristics of the air distributors based on volume transport coefficients of oxygen are dependent on variation of air flow and added motor oil contents. In this work, it was shown that the oxygen solubility degree compared to distilled water is controlled with the ratio between the periods of saturation of aerated water and oxygen relaxation over-pressure time. In longer saturation period, it was controlled by thermal gas oxygen distribution but in shorter saturation period, by mass-balanced dissolution in liquid. The rate constants for achieving partial local equilibrium (PLE) of oxygen could be identified based on agreement between experimentally obtained and calculated parameters of aeration kinetics. Keywords: Aeration; Solubility degree; Partial local thermodynamic equilibrium; Relaxation processes; Equilibrium temperatures
1. Introduction The aeration technique for water enrichment with oxygen enables removal of some oxidized components (iron, manganese) combined by flocculation–sedimentation treatment, flotation
*Corresponding author. Presented at the 2nd Conference on Small and Decentralized Water and Wastewater Treatment Plants (SWAT), Skiathos Island, Greece, May 2–4, 2008
of dispersed particles and removal of volatile compound prior biological treatment. The efficiency of aeration is dependent on the nature of dispersed particles (metal, electrolyte, coalescence of oil drops, presence of catalytic substances, etc.) adsorbed in contact surface between gas and liquid, after saturation is achieved. According to literature [1], in refinery waste water, the average content of pollutants are found up to 150–250 g/m3 BOD5, 300–600 g/m3 COD, 100–300 g/m3 fat and oil,
0011-9164/09/$– See front matter © 2009 Published by Elsevier B.V. doi:10.1016/j.desal.2008.11.009
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20–200 g/m3 fenols, 1–100 g/m3 benzen, 1– 100 g/m3 benzpiren, 1–100 g/m3 chrom and up to 0.2–10 g/m3 lead. All production lines and auxiliary installations in refineries create during the production process certain amounts of wastewater-containing oil that is removed in tanks, by using scrapers during pretreatment processes. Flocculation–sedimentation and flocculation–flotation processes are used for complete removal of free hydrocarbons from water. After that the water is biologically purified in tanks with activated sludge or in aerated lakes and lagoons. According to literature [2–8], the efficiency of aeration is dependent on the volume coefficient of oxygen transport, based on theoretical researches with the adequate psychical–chemical models and on the empirical formulas. The experimental data obtained in the prior works with procedure are treated [9] based on the gas-phase material balance [2, 3]. Factors influencing oxygen transfer in fine pore-diffused aeration of water are described in literature [10, 11]. According to literature [12], the equilibrium is achieved if in open system the fluctuations of equilibrium due to thermodynamic parameters, temperature, pressure and chemical potential can be neglected in the small local part and within small time period during aeration. To the other author [13, 14], at contact surface between two phases, entropy-driven processes in Helmholtzes and diffusion layers the entropy-balanced processes activate electrons and ions transport determined with electrode kinetic for keeping equal temperatures in the both phases. The correlation of the aeration efficiency that enables the most efficient purification, with active and passive relaxation processes rate constants, has to be enabled to control the dominant influence. The oxygen-successive diffusion step and parallel adsorption step processes rate constants in oxygen dissolution during aeration can be determined by the corresponding methods, according to literature [12, 14, 15].
When aeration systems are designed, it is necessary to use aeration devices with an actual oxygen introduction capacity higher or equal to the actual need for oxygen in the treatment process of wastewater with biochemical reactions. Actual efficiency of the transport system defined as the ratio between the real capacity of oxygen introduction and the total oxygen introduced by the aeration was influenced by air flow and motor oil concentration [2, 3], according to literature [10, 11]. The oxygen accumulation rate constants were determined on the basis of the mass balance of oxygen during saturation period. An innovative aspect of this article is the study of passive processes rate constants that control the dominant resistances with an aim to achieve a better oxygen solubility degree in comparison with distilled water, in shorter aeration period. The significance of thermodynamic study of aeration kinetic in treatment refinery wastewater in bio-aeration tanks in this work is illustrated with application in determining of oxygen solubility degree in dependence of agreement between:
•
•
experimentally obtained (active transport processes rate constant as volume coefficient of oxygen transport, drift rate constants in saturation time) and calculated kinetic parameters of passive transport processes rate constants (chemical potential-driven saturation rate constant, concentration gradient-driven diffusion and by potential fields-driven adsorption and charging rate constants).
2. Experimental study According to literature [2, 3], the used material and procedure are described with apparatus constituted from a polypropylene column
M. Sˇevaljevic et al. / Desalination 248 (2009) 941–960
with dimensions 700 700 2200 mm with accompanying connections and construction frame for experimental work in batch conditions (Fig. 1).
• • •
2.1. Apparatus
•
A list of measured values and instruments on the described installation is presented in Fig. 1 The measuring equipment can be described with the measured values and with used instruments:
• •
tG, 8C – air temperature, Mercury thermometer tL, 8C – water temperature in the column, Mercury thermometer (pm)p, mm Hg – air over-pressure, U-pipe with mercury
L L L co 6 7 8 9
•
Dpp, mm Alc. – pressure loss through the orificeplate, Micro manometer with alcohol (pm)d, mm Hg – Air over-pressure in front of the air distributor, U-pipe withmercury uL, m2/s – Kinematical viscosity of water in thecolumn, Modified Oswald viscosimeter rL, kg/m3 – Water density in the column, Laboratory pycnometer co, mg/L – Starting mass concentration of dissolved oxygen in water, ‘‘HANNAINSTRUMENTS 9142’’ c(t), mg/L – Mass concentration of dissolved oxygen in water, ‘‘HANNAINSTRUMENTS 9142’’
Air flow is measured on the pipe with dimension Lp = 3000 mm and diameter Dp = 52.3 mm. The name diameters of the used valves NV15, NV20 and NV50 are given (Fig. 1). The volume
tL 5
8
water air measurement equipment connections
NV15
c() 10 9
measuring point NV15
7 Lp3000; Dp52,3
5
4 (pm)d
4
NV50
NV20
6
NV20
tG 1
3 pp
NV15
•
•
943
Fl tOK pa 11 12
3 NV20
2
M ~
1
2 (pm)p
Fig. 1. Scheme of experimental installation. 1 – low pressure compressor; 2 – air inflow pipe valve; 3 – relief valve; 4 – air flow regulator; 5 – air flow measuring orifice plate; 6 – column with corresponding connections and framework; 7 – disk-shaped membrane air distributor (HD 340, 0.06m2); 8 – water supply; 9 – sampling connection.
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of the water tanks was VL = 1 m3 and the height was h = 2 m.
5 and 10 mg/L, respectively. In oil maximal contaminated water, at maximal air flow of 10 m3/h, thin oil film appeard on the water surface.
2.2. Procedure Before starting the experiment, kinematic viscosity, density and surface tension of water in the experimental installation had to be determined. Complete experimental system for defining the process parameters of water aeration with certain characteristics, started by measuring the temperature of the surrounding air and water in the column. The over-pressure value before the distributor (pm)d and the orifice plate (pm)p, that is the pressure difference before and after the orifice plate (Dpp), was measured, when the first air bubble entered in the water. The column was initially filled with previously prepared water (pH = 7.21–7.29) from which oxygen was extracted using a chemical method of introducing sodium sulfite in the presence of a cobalt chloride hexa-hydrate catalyst. After that, the determined amount of waste oil was added into the water. Air flow regulation was performed using a flow regulator and relief valve until a set value for the applied analysis system was attained. When the flow is stabilized, water samples were taken from the column in equal time intervals (Dt = 60 s). The dissolved oxygen content was measured with HANNA instrument with sensors (with accuracy 0.05 g/m3) until the same value appeared three times. After one regime was analysed, the compressor was switched off and the relief valve was opened completely. Water from the column was released into drains via a draining valve. The column was then filled with a fresh amount of water. Thus, the installation was ready for a new investigation regime, that is the described procedure was repeated. The investigated regimes are defined with the air flows up to 2, 6 and 10 m3/h for each of the three water samples, respectively: with motor oil un-contaminated and contaminated water of
2.3. Material In the installation for water treatment in the oil refinery in Modricˇa, the average characteristics of wastewater during the period of investigation were pH 7–8, temperature 15–258C, oil content 13–23 mg/L, inorganic salts 0.38–0.40 mg/L, TSS 0.5–0.7 mg/L, HPK 80–180 mg/L BPK, up to 0–7 mg/L, CaO 18.5–21.5 mg/L and electric conductivity 670–770 mS/cm. The characteristics of the examined water are dependent on the content of added motor oil content up to zero as 5 g/m3 and 10 g/m3 of viscous waste motor oil (SAE 15 W-40, with 132.0 mm2/s viscosity index, inflammation temperature 231.08C, 3.18 mg KOH/g TAN, 9.73 mg KOH/g TBN, Zn 0.039%, Ca 0.310%, Fe 13.4 ppm, Cu 4.11 ppm, Cr 0.98 ppm and Al 44.87 ppm) was added. Densities of the three examined samples of water were in the range of 992–996 kg/m3, viscosity in range of 0.81 106 to 0.99 106 m2/s and surface tension coefficients were 76.2, 64.8 and 57.3 mN/m, respectively. 2.4. Treatment of experimental data The experimental data obtained with the described procedure were treated based on the gas-phase material balance [9], with the intention to study the influence of system of aeration (air flow and motor oil concentration) on the efficiency of the transport system (the ratio between the real capacity of oxygen introduction and the total oxygen introduced by the aeration of the refinery wastewater [2, 3], based on the determination of volume coefficients of oxygen transport). According to literature [2, 3], the content of the absorbed oxygen from the dry air in
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treated volume of wastewater was obtained as difference of oxygen content in output air and in the air prior entry, based on the gas-phase material balance [9]: :
V G ðcul ciz Þ ¼ A KL ½c ðciz Þ c ð1Þ where c ¼ c ðciz Þ, kg/m3 – equilibrium mass concentration of oxygen in dependence on the mass concentration of oxygen in air at the output, A ¼ a VL , m2 – total contact surface between air and water, a, m2/m3 – specific surface of contact between air and water, 3 V G or dVG=dt , m /s – air flow, cul, kg/m3 – mass concentration of oxygen in air at the input, ciz, kg/m3 – mass concentration of oxygen in air at the output, VL, m3 – water volume, c, kg/m3 – mass concentration of oxygen in the influent and effluent, The total coefficient of oxygen transport in the water, KLa, is dependent on the transport coefficient in the water phase and in air bubbles. If the resistance to transport in air can be neglected, KL is approximately equal with the volume coefficient of oxygen transport in water, kL. The volume coefficient of oxygen transport is the product of the transport coefficient in liquid and the specific area of gas bubbles in contact with water, a: 1 ð2Þ KL a ¼ k L a s can be determined as kL a ¼
ðcul ciz ÞdVG 1 VL ðc ðciz Þ cÞdt s
ð3Þ
The described device (Fig. 1) for the water phase was used [2, 3] for the measuring of the
945
volume coefficient of the oxygen transport, based on the material balance according to literature [8, 10]: dVG cul VL RO2 ðtÞ dt dVG dc ¼ Qc þ ciz þ VL dt dt
Qcin þ
ð4Þ
where: Q, m3/s – water flow (for batch process conditions Q = 0), cin, kg/m3 – mass concentration of oxygen in the influent, RO2 ðtÞ, kg/(m3s) – specific oxygen consumption during biological treatment. Equilibrium mass concentration of oxygen in water is dependent on oxygen concentration of air at the output, based on Henry law c ðciz Þ ciz RT ¼ cL Ha
ð5Þ
is determined by equation with modified Henry’s constant, Hc Hc ¼
Ha R TG CL
ð5aÞ
that gives c ðciz Þ ¼
ciz Hc
ð6Þ
where: Ha, Pakmol (O2 + L)/kmol O2 – Henry’s constant in oxygen distribution coefficient between air and water, R, J/, kmolK – the universal gas constant, TG, K – absolute air temperature, CL, kmol/m3 – molar concentration of water. Equations (5) and (6) give the expression for calculating the output mass concentration of oxygen in air controlled with the constant outer air pressure in dependence of temperature:
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946
HaðVG cul þ VkL acÞ ciz ¼ VG Ha þ VL kL aRTG cL
ð7Þ
Time dependence of dissolved oxygen concentration is presented by the following equation: Y ¼mX
ð8Þ
tL, 8C – water temperature y = 1.024 – temperature correction factor. Based on the known value for the coefficient of oxygen transport (kLa)s and actual capacity of oxygen introduction OC’, the product of the standard capacity of oxygen introduction and corresponding correction factors that convert standard investigation conditions to real ones are defined [3]:
ðpul MO2 =RTG Þ ðHa=RTR cL Þco Y ¼ ln ðpul MO2 =RTG Þ ðHa=RTR cL ÞcðtÞ ð9Þ where: m, slope coefficient of the equilibrium curve: m¼
ðHa=RTR cL Þk L a RO2 ðtÞ ðHa=RTR cL Þ þ ðVL =VG ÞkL a ð10Þ X ¼t
ð11Þ
The value of Y given for each value of c(t) is determined by experiments for defined time intervals. The previous equations result in the formulae for determining the coefficient of oxygen in waste water as: kL a ¼
Haðm þ RO2 ðtÞÞVG VG Ha ðm þ RO2 ÞVL RTR cL
ð12Þ
Based on the known value for the coefficient of oxygen transport (kLa), actual capacity of oxygen (OC) is determined to [11]: ðkL aÞs ¼
ðkL aÞtL ytL 20
1 s
ð13Þ
where: ðkL aÞtL – experimentally obtained oxygen transport coefficient
OC ¼ ðkL aÞs cs VL
OC 0 ¼ a OC
ð14Þ
b ch co ðtL 20Þ kg ð15Þ y ; h cs
where: OC, kg/h – standard capacity of oxygen introduction into wastewater corresponds to velocity of oxygen dissolution after the total surface between the air and water is achieved. cs , kg/m3 – equilibrium mass concentration of dissolved oxygen in clean water, for normal conditions. According to literature [11], the actual efficiency of the transport system represents the ratio between the real capacity of oxygen introduction, OC’and GO2 , the total oxygen introduced by the aeration: E0 ¼
OC 0 OC 0 ¼ 100 ð%Þ GO2 ðVG Þn rG yO2
ð16Þ
The technical characteristics [2] determined from the aeration system based on the material balance are presented in Table 1. The intention of this article is to enable the examination of the effects of aeration regimes on agreement of experimentally measured volume coefficients of oxygen transport and saturation time and drift time with theoretically obtained passive rate constant (of diffusion and adsorption processes) that controls the degree solubility of oxygen.
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947
Table 1
3 3 1 V G = dV =dt, m /h – air flow rate coil , g/m added oil content, kL a, min volume coefficient of oxygen transport, OC’, g/h – actual capacity (Eqn (15)), E’, % – technical efficiency (Eqn (16))
Reg. Nb.
coil (g/m3)
3 V G (m /h)
kL a (min1)
OC’ (g/h)
E’ (%)
1 2 3 4 5 6 7 8 9
– – – 5 5 5 10 10 10
2 6 10 2 6 10 2 6 10
0.04 0.04 0.08 0.03 0.03 0.07 0.03 0.03 0.04
11.7 12.4 21.9 9.5 9.5 19.0 8.2 8.8 10.7
1.46 0.62 0.55 1.12 0.46 0.62 1.00 0.43 0.27
3. Thermodynamic study of aeration kinetics during the partial local thermodynamic equilibrium The degree solubility of oxygen during saturation period is defined by the ratio of the measured stationary concentration in water, saturated with oxygen with the equilibrium oxygen concentration (defined for distilled water in dependence of temperature of liquid phase at normal pressure, to Henry law). Chemical and phase transformations enable relaxation of oxygen chemical potential in contact surface of heterogeneous system, to equilibrium value, and/or mass transport, which enable homogeneous dissolution. In contact surfaces between air and water, oxygen Gibbs energy (G = E + pV + w ST) achieves states of local partial equilibrium with the stationary Gibbs energy per one exchanged mol (m = Vdp) after saturation time at equilibrium chemical potential, equilibrium temperature and pressure. Pressure-driven relaxation processes are dependent on oxygen adsorption affinity enabling equilibrium state. Air-diffuse distributor activates the energy ðCV T þ pdV ¼ TdSÞ in contact surfaces between gas and water phases. In fixed contact surface, volume of gas drift transport frequency defines the time for the transport of gas volume equals with the liquid
volume. In mobile contact surface, the volume coefficient of oxygen transport at normal pressure defines the time for the transport of molar oxygen volume. In contaminated water, constant temperature and pressure enable entropy-driven processes activated with coupled exothermic and endothermic chemical processes. If the potential field are present (electric potential, ’, or field of surface tension, s, on surface, A), the balance of exchanged number of oxygen moles at constant chemical potential enables passive relaxation processes in contact surfaces (SdT ¼ V dp þ w, where w ¼ nm þ zF’ or w ¼ nm þ sA). Agreement of experimentally obtained active rate constants with calculated rate constants of passive transport rate constant for achieving local partial thermodynamic equilibrium (LPTE) makes possible the explanation of the mechanism of oxygen dissolution during aeration process, in dependence of the nature of contact surfaces between air and water in investigated regimes. 3.1. Treatment based on the material balance After the equivalent point of titrated components dissoluted in water is achieved, during aeration, oxygen can be adsorbed in contact surfaces between air and water. Great number of particles
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948
with adsorbed oxygen in saturated water prevents the fluctuations of equilibrium of thermodynamic parameters (temperature, pressure, chemical potential). According to literature [12], within the small time period, oxygen can achieve the state of PLE in local part of system – saturated gas or water film in contact surfaces. According to Eqn (3), active oxygen coefficients of volume transport are determined on the basis of oxygen mass balance in the gas phase: kL a ¼
ðcul ciz Þ tdr ðc ðciz Þ cÞ
ð17Þ
According to Eqn (17b): ks n ns ¼ kL a nul niz
The active rate constant determined as technical parameter, kL a, in resonance with relaxation time of some of the passive processes enables PLE of oxygen during aeration:
• •
where drift or retention time of oxygen tdr ¼
•
VL dVG =dt
determines the drift rate constant or frequency of transitions of air through water volume, k dr ¼ 1=tdr . According to Eqn (1): aVL ðc ðciz Þ cÞ dVG ðcul ciz Þ ¼ tL tG
ð17aÞ
The relaxation time of volume transport of one mole oxygen in liquid tL with air drift, through unit specific contact surface, a = 1 m2, have to be equal with the relaxation time of chemical potential with transport of one mol oxygen from gas phase tG , by air flow and determined with saturation period, ts : nul niz ¼ Kaðn ðniz Þ ns Þ ts
homogeneous density with diffusion rate constant, kd equilibrium chemical potential among two phases in saturation period, of chemical and phase transitions, with saturation rate constant, ks Electrochemical potential by charging rate constants, k # .
The accumulation of oxygen in fixed total contact surfaces after saturation time can be described to literature [16] after solving Eqn (1): cs c ðciz Þ ¼ c0 c ðciz Þ ekL ats
ð19Þ
Theoretical calculation of oxygen solubility cs (for c0 = 0), is based on degree, wm ¼ c ðc iz Þ over-pressure relaxation time and saturation time in mass-balanced conditions: cs c ðc
iz Þ
¼ 1 ekL ats
ð19aÞ
Equilibrium oxygen concentration can be determined if active rate constants and saturation period are measured:
ð17bÞ c ðciz Þ ¼
The ratio between drift rate constant (frequency) with saturation rate constant corresponds to the number of oxygen moles transported through the liquid during saturation time: kdr tG ðVL Þ ¼ ks ks ðV M Þ
ð18aÞ
ð18Þ
cs 1 ekL ats
ð19bÞ
The obtained equation enables the determination of degree of oxygenation according to literature [14], to Fick’s law that describes the slowest successive step that controls the overall kinetic of dissolution processes by diffusion from adsorbed saturated layer in the water, in
M. Sˇevaljevic et al. / Desalination 248 (2009) 941–960
dependence of the depth of the diffusion layer, d, as well as of the diffusion coefficient, D, and specific contact area, a = A/VL: dc DA ðc ðciz Þ cÞ ¼ dt VL d
kL a ¼
D a d
ð21Þ
ð22Þ
In aerated water that contains irreversible oxidabiles impurities, with rate constants of irreversible oxide dissolution processes, kir , according to literature [16], material balance of oxygen : ðcV Þiz ðcV Þul dðcV Þw þ þ kir VL cw ¼ 0 ð23Þ dt dt At good mixing, ciz= cw (to the differential Eqn (25)), after solving defines oxygen concentration in water after the saturation time t ¼ ts : cs ¼ c ðciz Þ 1 eðkir þðdVG =VL dtÞts Þ
ð24Þ
whereas: kL a ¼ kir þ kdr
ð25Þ
Adsorption of greater number of oxygen moles in monolayer on good conductors (some noble metals and metals) and semiconductors metals with oxide layers (of Al, Ni, etc.) or on thick layers of ventils conductors (SnO) activate dissotiative adsorption and the discharging of electrons current through oxygen can cause dissociation of the covalent bonds of
ð26Þ
Electrochemical equilibrium at surface electric potential, Dw, enables equilibrium of the number of exchanged oxygen moles between gas and liquid phases
In diffusion layer, the volume coefficient of oxygen transport can be in resonance with diffusion rate constant: kL a ¼ kd
gas molecules (of 463 kJ/mol) with water productions [17]: kir ¼ k #
ð20Þ
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nul niz RT ¼ Kaðn ðniz Þ ns ÞFDw ð26aÞ ts
When kL a FDw ¼ ks RT
ð26bÞ
the power for achieving equilibrium by thermal energy of adsorbed oxygen gas molecules equals with the power that enables relaxation of surface potentials, Dw. 3.2. Treatment based on the chemical potential equilibrium When electric and concentration gradient through contact surface determine the passive rate constants, rate of electrons transfer can be greater than the rate of dissociative adsorbtion of oxygen and then peroxide is formed as stabile intermediates, but good catalysts enhance the rate of oxygen dissociation and favor peroxide decomposition and water production. On the carbon in contact surface Jaeger was found highly reversible redox processes of oxygen in equilibrium with hydroperoxide. According to the literature [17], in the aerated water with pH >7, by reversible electron transitions in saturated water with oxygen, the ozonide ions will be formed with the coupled reactions with complicated build-up and decay. The volume coefficients of oxygen ransport are dependent on the affinity of oxygen for
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950
adsorption that influences on time for achieving stationary oxygen concentrations at equilibrium chemical potential in contact surface, to Gibbs–Helmholtz – van ’t Hoff Equation [18]. When equilibrium of the chemical potentials of oxygen in contact surfaces is achieved:
mL ðO2 Þ ¼ mG ðO2 Þ
ð27Þ
3.3. Treatment based on the electrochemical potential equilibrium
and where mi ¼ ðdG=dni Þp;T;nj , or mðO2 Þ ¼ my ðO2 Þ þ RT ln c ðO2 Þ
ð28Þ
The slope of the obtained linear function (Eqn (29)) is determined with the molar adsorption Gibbs energy (Dads Gy, J/mol – molar adsorption affinity): ln cs ðO2 ÞL ¼ ln cs ðO2 ÞG
During aeration through the charged contact surfaces, the active oxygen transport activates relaxation processes in dependence of the oxygen adsorption affinity, which enable achieving the equilibrium of electrochemical potentials (sum of chemical and electric potential gradient in contact surfaces between the two phases).
Dads Gy ðO2 Þ RTL
ð29Þ
where y ¼ yo tg’x 1 ; y ¼ ln cðO2 ÞL ; y0 ¼ ln cðO2 ÞG ; TL Dads Gy ðO2 Þ tg’ ¼ ð30Þ R
According to literature [20], the dependence of overpotentials for achieving the equilibrium velocity of the oxygen adsorption in saturated layers is explained with the non-faradaic electrochemical modification of the catalytic activity (NEMCA) in contact surfaces with the local potentials determined with electrochemical equilibrium. According to the literature [21], the kinetics of the oxygen dissolution during coal oxidation is controlled with the fastest simultaneous hydrogen adsorption rate constant coupled with redox–electrochemical reaction of adsorbed molecules in electrochemical equilibrium ðD’ þ Dm ¼ 0Þ:
x¼
kL a ¼
FD’max RT DtF
ð32Þ
The adsorption affinity in physical or chemical transformations of the adsorbed oxygen from gas bubble can be calculated based on the slope of the linear functions (Eqn (30)):
According to the literature [15, 22], evolution of hydrogen is enabled with oxidized components during achieving equilibrium of surface electric potential in double electric layer between the Helmcholtze s surfaces:
Dads Gy ¼ R tg ’
kd;i 3RT ¼ it ð2Z f0i Þ
ð31Þ
According to the literature [19], the presence of the oil oxidation products and radical initiators OH–, H2O2, Fe2+ in the presence of HCO3–/CO32–, PO43–, humid acids, aryl-R, tert-butyl alcohol can change the standard oxygen chemical potentials in the contact surface.
ð33Þ
where it ¼ kL aF, A – electrons current, defined with thermal equilibrium with the carriers of migration current in electric field ZH2 , V – hydrogen overpotential on metal in contact with the two phases
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D’Wi , V – standard redox potentials of adsorbed oxidized components kd;i – diffusion rate constant of the fastest oxidized component in diluted solution. The power of oxygen energy during aeration defined with volume coefficient of oxygen transport is dependent on the passive relaxation processes rate constant after adsorption:
• •
of oriented hydrated molecules of oxygen in layer influenced with the potential field of oxygen with kinetic energy in concentration gradient in the two diffusion layers in both the phases
to the following equation: dEtot dEkin dEpot ¼ þ dttot dtd dta
ð34Þ
That can be defined for molar relaxation processes: ¼ kd 2Ed þ ka Dads G kL a Etot
ð34aÞ
for the two adsorbed films in contact surface between gas and liquid:
ka Dads G kL a ¼ kd þ Etot
ð35Þ
where kd , 1/s – passive diffusion transport rate constant of molar kinetic energy ka , 1/s – adsorption rate constant at constant dependent on bond energy ¼ 3RT , J/mol – molar total energy Etot Ekin ¼ 3RT =2, J/mol – molar kinetic energy. Linear equations y ¼ yo þ tg’x; y ¼ kL a; x ¼ Dads my ; ð36Þ ka tg’ ¼ Etot
951
enable calculation passive rate constants: ka ¼ 3RT tg’
ð37Þ
kd ¼ yo
ð38Þ
and
After electrochemical equilibrium is achieved, determination is possible of the passive (diffusion and absorption) rate constants. 3.4. Treatment based on diffusion of gas ionized oxygen Passive rate constant are dependent on the nature and the quantity of contact surface between the gas and liquid phases. According to literature [23], on the contact surfaces, the oxygen evolution is enabled by electron currents on conductor metals and metals–oxide layers of Rutenijum, Platina, Iridijum as well as on the monolayers of semiconductor oxides of Aluminijum, Titan, Tantal, Nikal, Zirkonijum. On the thick layers of ventil conductors (Tin–oxide, Titan–oxide), thermal state of electrons can be achieved with the enough great thickness that enables relaxation of electron temperatures with temperature of carrier of the migration current. The presence of traces of unspecific metals in the diffusion layer of water enables the relaxation processes with rate constants dependent on kinetic energy after adsorption of the stable intermediate as the peroxide or the fuel cells. According to literature [24], coupled irreversible diffusion transport can be activated with greater molar adsorption energies when flux of present kind of molecules may induce fluxes of other, that is referred to as irreversible codiffusion process through contact surface that is not expected on the basis of their electrochemical potential. According to the literature [25], the thermal electron transitions are activated by
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952
neutral/ion collisions through contact surface with gas phase, to the dynamic equation: Ni mi
dvi Df Dpi Ni mi vi ¼ Ni e Dx Dx dt tin
ð39Þ
where the ratio of potential difference and dx is the potential gradient along the depth of the layer (the strenght of the electric field) function of relaxation–adsorption rate constant, ka. Adsorption rate constants are dependent on the nature and the quantity of adsorbed oxygen molecules adsorbed in contact surface between the gas and liquid phases in dependence of ratio between drift and saturation rate constants. Achieved equilibrium concentrations and temperature after saturation time, during shorttime interval [12], in local partial thermodynamic equilibrium state enable the relaxation time constants of the change of electric potential in electrochemical equilibrium of contact surface (and chemical equilibrium to Eqn (29)): D’ d’ ¼ fð Þ dt dx
ð40Þ
as well as concentration balance with diffusion (to Eqn (20)), dp dp ¼ fð Þ dt dx
ð41Þ
Ni v i ¼ Ki
Df dni Di dx dx
ð41aÞ
where kB ¼ R=NA , J/kmol – Boltzmann constant mi, kg – the molecular mass Ni, number of adsorbed molecules in air bubbles of electroneutral gas oxygen in plasma state vi, m/s – the molecular average square velocity tin ¼ lvii , s – the time period between neutral and ions collision
ð43Þ
that gives the Einstein’s equation: Di kB Ti ¼ Ki e
ð43aÞ
After defining diffusion coefficient in the gas phase to the molecular kinetic theory: 1 Di ¼ vi li 3 Ki ¼
ð44Þ
vi li D’
ð44aÞ
where Di, m/s – diffussion coefficients Ki, m2/sV – electrical mobilities ions. Combining with Einstein equation, the energy for the monolayer completion with oxygen ions corresponds to relaxation of over-potentials to zero by diffusion and migration of adsorbed ions (to Eqn (33)): zF D’ ¼ 3RT
In thermal equilibrium: dp DNi ¼ kB Ti dx Dx
li, m – average intermolecular distance. After saturation for achieving the equilibrium chemical potential (to Eqn (39)), dvi =dt ¼ 0, the Nernst-Plank equation is obtained:
ð44bÞ
To the Einstein equation, coefficient of ambipolar diffusion of oppositely charged ions or ion and electron:
Damb
Te ¼ Di 1 þ Ti
ð45Þ
gives twice greater ambipolar than simple diffusion rate constant. The exchange of gas molecules from gas phase during saturation time is coupled with
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charging rate constant and with pressure relaxation rate constant: k # ¼ kL a ¼ kamb ¼ 2kd
953
saturation measured concentrations and active rate constant (volume coefficient of oxygen transport):
ð45aÞ c ðciz Þt ¼ cs ð1 þ ekL a=ks Þ
ks RT ¼ ka zFDwW
ð45bÞ
The Helmholtz potential on contact of hydrophilic surface for maximal air flow rate can be balanced with faster electron transitions that enable reduction of water molecules. The velocity of recombination of oxygen and hydrogen to water enabled by fast electron transitions are determined by charging rate constant of oxygen. After thermal equilibrium of ions and electrons is achieved, according to literature [25], resistance to oxygen transport in air cannot be neglected, compared to resistance in liquid. 3.5. Treatment based on thermal distribution of gas molecules to Boltzmann law According to literature [26, 27], after saturation time is achieved, thermal collisions of gas oxygen enable distribution of molecules in the two thermal-balanced equilibrium states in gas and liquid phases defined with the potential difference to the Boltzmann law, so as to obtain oxygen solubility degree for liquid phase, cs : wm ¼ c ðc iz Þ cs c ðc
iz Þ
¼
1 DE=RTt
1þe
ð46Þ
According to literature [15, 21] and Eqn (32) and (33), if active rate constants activate relaxation processes in gas phase ððkL a=ks Þ ¼ ðDE=RT ÞÞ: cs 1 ¼ c ðciz Þ 1 þ ekL a=ks
Measured oxygen degree solubility after period of saturation is defined by comparison with concentration defined to Henry law: wexp ¼
cs c ðtL Þ
ð49Þ
The agreement of experimental oxygen degree solubility in saturation period, wH , to Eqn (49), with the theoretical after relaxation: – to thermal equilibrium, with oxygen solubility degree, wt ; calculated to Eqn (48), – to material balance with oxygen solubility degree, wm ; calculated to Eqn (19a) define the phase of passive relaxation processes (gas phase for Boltzmann distribution of oxygen molecules, liquid phase for material balanced transport, or the both). 3.6. Treatment based on the Gibbs adsorption of hydrophobic particles The hydrated molecules can diffuse across the contact surface with adsorbed liquids between air and water very poorly but many small and uncharged atoms can be dehydrated and dissolved in liquids by virtue of their kinetic energy of motion and decrease the free molar contact surfaces between air and water, based on the Gibbs adsorption isotherm: dc AM ds ¼ cs dt RT dta
ð47Þ
Equilibrium concentration of gas oxygen molecules can be determined based on the
ð48Þ
where 1 ¼ ks cs ts
ð50Þ
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954
gives the dependence of adsorption rate constants, molar contact surfaces (AM) and of difference among the surface tension of contaminated and distilled water ðdsÞ: ks ¼ ka
AM ds RT
ð51Þ
During saturation period, relaxation of energy is activated to thermal value by hydrophobicadded oil adhered to oxygen molecules during Gibbs adsorption in the free water surface in the aeration tank: ks RT ¼ ka AM Ds
ð52Þ
Experimentally determined temperatures, the change of surface tension in the surface active substances present compared to surface tension of pure water, as well calculated adsorption and saturation rate constants make possible the determination of the molar contact surfaces between liquid and surrounding air: AM ¼
ks RT ka Ds
ks RT Dw ¼ ka F W
Experimentally obtained technical parameters [2, 3] are presented in Table 1, and temperatures and saturation times and oxygen contents in Table 1a. Investigated aeration regimes are defined with Regime numbers for corresponded air flow rate, added oil content, height of tank, h=1 m with volume of tank 0.5 m3, and h= 2 m with for tank volume 1 m3. In regimes with added oil content 5 g/m3, oxygen capacities are twice greater than in regimes with a maximum of examined air flow. Technically efficiencies decreased twice in regimes when air flow is 6 m3/h. Decreased oxygen solubility in water could not be improved significantly with increased air flow. The study of the Gibbs energy adsorption dependence from oil concentrations shows:
•
ð53Þ
When the drift velocity is greater twice than the saturation rate constant, the power of surface electric potential can prevent control surface transport rate constant in resonance with adsorption rate constant in condition: kL a ¼ ka
4. Results
ð54Þ
ð55Þ
The Helmholtz potential can be balanced with irreversible slow production of gas oxygen by anodic slow successive relaxation reactions of processes that determine the velocity of recombination of oxygen and hydrogen to the water.
oxygen adsorption is activated with parallel endothermic and exothermic oxygen processes at air flows up to 2 m3/h and 6 m3/h in the clean water, respectively
Table 1a Experimentally obtained data: Regime numbers, tL ;
C – temperatures of liquid, tG ; C – temperature of gas and tR ; C – temperature of surrounding air, cs ; g/m3 – oxygen concentration in saturated water and ts , min – saturation time
Reg Nb.
tL (8C)
tG (8C)
tR (8C)
ts (min)
cs (mg/mL)
1 2 3 4 5 6 7 8 9
13.0 13.0 14.0 15.0 12.1 14.5 13.5 13.2 14.1
15.5 17.6 18.7 13.5 14.3 13.4 16.2 17.4 16.3
16.0 17.5 14.2 12.5 15.2 15.3 17.2 19.1 19.1
25 24 22 26 24 20 25 23 20
7.5 7.6 7.9 6.4 6.7 7.0 5.9 6.1 6.4
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•
oxygen adsorption is activated with spontaneous exothermic electrons transitions with the most adsorption affinity at the air flow of 10 m3/h in the contaminated water.
4.1. Calculated adsorption affinities and oxygen solubility degree of aerated water in investigated regimes Calculated equations that enable determination of the adsorption affinity, Dads Gy (O2) (Eqn (29, 31)) are presented in the Table 2. The equations are obtained on the basis of linear dependence of logarithm of oxygen concentrations in saturated water of reciprocal value of liquid temperatures in investigated regimes. Molar adsorption affinities of oxygen characteristics for analysed investigated regimes are presented in Table 3.
955
Table 3 presents also molar oxygen concentrations, Cs, and oxygen solubility degree compared to distilled water, wexp , calculated to Eqn (49). To the obtained results presented, molar adsorption oxygen affinities are dependent only on the air flow rates that determine drift rate constants for air flow 2, 6 and 10 m3 /h of 0.03, 0.10 and 0.16 min1 respectively. The maximum obtained values correspond to the enthalpy of dissociative adsorption, three times greater than dissociation energy of covalent bond. The oxygen solubility degree obtained by comparison with solubility of oxygen in distilled water were 72–77% for clean water and oil-contaminated water was decreased for about 7% for each added 5 g/m3 oil content. The improved procedure of aeration increases oxygen solubility degree, by explanation of relaxation processes based on agreement
Table 2 The Eqn (29) for calculation the adsorption affinity, Dads Gy (O2), to Eqn (29,31), for the investigated regimes, defined with: c, mg/L – oil concentration; h, m – height of water column; V G , m3/h – air flow
c-h-V G
y = yo tg fx
R2
Dads GY(O2) kJ/mol
0-2-2 0-2-6 0-2-10 0-2-2 0-2-6 5-2-10 5-1-6 0-2-10 5-2-10 10-2-10 0-2-10 5-2-2 5-1-2 5-1-10 5-2-6 10-2-2 10-2-6 10-1-2 10-1-6 10-1-10 10-2-10
y = 3663 x + 4.45
0.92
30.45
y = 4367 x 23.62
0.97
36.3
y = 165691 x 586
0.75
1377
y = 8959 x 39.57
0.61
74.5
y = 7727 x 35.57
0.99
64.2
y = 8492 x 38.10
0.94
70.6
956
M. Sˇevaljevic et al. / Desalination 248 (2009) 941–960
Table 3 Obtained adsorption oxygen affinities Dads GY(O2) to Eqns (29) and (31), calculated molar oxygen concentrations in saturated water, equilibrium concentration to Boltzmann and to material balance and equilibrium temperatures for distilled water to Henry Reg. Nb.
DadsGY(O2) (kJ/mol)
ct ðmg=LÞ
cm ðmg=LÞ
tt ( C)
tm ( C)
1 2 3 4 5 6 7 8 9
30.4 36.3 30.4 36.3 30.4 1377 74.5 64.2 64.2 1377 64.2 64.2 70.6 1377
10.3 10.4 9.1 9.1 9.7 8.4 9.1 11.1 9.7
11.9 11.2 9.4 11.4 12.2 9.4 11.1 11.0 12.8
14 14 20 20 17 25 20 11 17
8 10 19 10 7 19 11 11 5
on experimentally obtained and calculated relaxation processes rate constants. 4.2. Effects of aeration regimes on agreement between measured and calculated transport rate constants According to theory [12] in this work are calculated diffusion and adsorption rate constants based on Eqn (38) presented in Fig. 2. Agreement between experimentally obtained active and calculated relaxation, passive rate constants is indicator of resonance of measured active rate constants (volume coefficient of oxygen transport and drift) with saturation, diffusion, adsorption or charging rate constants (to Eqn (25) and (26)), that control oxygen solubility degree:
• •
with mass balanced transport to Eqn (19a) with thermal equilibrium of electrons and ions in two possible equilibrium states of gas molecules, to Boltzmann Eqn (47)
The agreement between the experimentally obtained active and calculated passive rate constant have to be correlated with the oxygen solubility degree obtained theoretically based on Boltzmann equilibrium in gas phase and material balance in liquid phase.
Diagrams in Fig. 2. (Eqn (35)) enable the calculation of passive transport rate constants diffusion rate constant (Eqn (38) and adsorption rate constant Eqn (37)) (Table 4). 4.3. Agreement between experimentally obtained and calculated oxygen solubility degree The agreement between measured oxygen solubility degree and calculated to Boltzmann distribution Eqn (47), as well with calculated to mass balance Eqn (19a), enable the determination of process that control the resistance of volume gas transport. The equal number of oxygen molecules exchanged from adsorbed gas oxygen film with liquid film ðDnL ¼ DnG Þ, in relaxation period during aeration is defined to Eqns (1) and (18a). Tables 5 and 6 present the ratio: ks tL ¼ kL a ts determined to Eqns (1) and (18a) corresponds to: tL n ns ¼ tG niz nul exchanged number of oxygen moles between two phase in PLTE, activate relaxation processes for
M. Sˇevaljevic et al. / Desalination 248 (2009) 941–960
y 3E – 05x 0.043 R 2 0.9965 1500 1000
500
0.1 0.08 0.06 0.04 0.02 0
kLa, 1/min
kLa, 1/min f (ads GΘ (O2) kJ/mol) c (waste oil) 0 mg/L, h 2m
4.4. Effects of potential fields (surface electric potential and surface tension) between air and gas phase
kLa, 1/min
0.08 0.06
2000 1000 ⌬ads GΘ (O2) kJ/mol kLa, 1/min f (ads GΘ (O2) kJ/mol) c (waste oil) 10 mg/L, h 2m y 6E – 06x 0.03 R 2 0.9395 2000 1000 ⌬ads GΘ (O2) kJ/mol
0.04 0.02 0 0
According to Eqns (45) and (45b), maximum air flow rate ðkL a ¼ k # ¼ 2kd Þ activates molar surface electric potential (Table 7) in oil uncontaminated water that enables the resonance of charging rate constants with volume coefficient of oxygen transport: W at surfaces # potential in Regime Nb. 3, Dw ¼ ks RT k 2F = 0.005 V/mol in Regime Nb. 6., • at surfaces potential DwW ¼ ks RT k # 2F = 0.006 V/mol.
•
0.05 0.04 0.03 0.02 0.01 0
kLa, 1/min
y 2E – 05x 0.0322 R2 1
thermal relaxation is enabled in twice-longer aeration period. The diffusion transport (in Reg. Nb. 4 and 5) enables achieving equilibrium temperature in liquid or with the both thermal and mass transport processes (Reg. Nb. 7, 8 and 9) that enable also free surface energy equilibrium (chemical potential and surface tension).
0
⌬ads GΘ (O2) kJ/mol kLa, 1/min f (ads GΘ (O2) kJ/mol) c (waste oil) 5 mg/L, h 2m
957
0
Fig. 2. Diagrams with 3 points (where two for the 2 m3/ h and 6 m3/h air flow are approximately equal but different from 10 m3/h that enable the calculation of passive transport rate constants.
achieving corresponding temperatures for distilled water to Boltzmann (of volatile oxides after flocculation if tR;G tt 1 in gas phase), and/or to material balance (with oxidation, floc1 culation-sedimentation processes if tL tm in liquid). The equal chemical relaxation rate constant with over-pressure rate constant enables relaxation to equilibrium temperatures for distilled water in Reg. Nb. 1 and 2. In Reg. Nb. 3 and 6
The molar contact surfaces (Eqn (53)) and molar surface electric potentials in unit of time also are calculated in dependence of the change of the surface tension in oil-contaminated water compared to pure water 72 mN/m, during aeration (Eqn (57)). Then the kinetic energy of ions in active transport equals the kinetic energy of electrons in passive chemical reaction, which is achieved according to Eqns (54) and (55). At surface potential, RT =F ¼ Dwy in oilcontaminated water (Reg. Nb. 7, 8 and 9), the resonance between adsorption rate constant ðkL a ¼ ka 0:75ks Þ makes possible simultaneous mass transport of hydrophobic oxygen with oil particles and thermal relaxation processes of hydrophilic hydrated oxygen molecules. 5. Conclusions The results obtained in this work enable the following conclusions:
M. Sˇevaljevic et al. / Desalination 248 (2009) 941–960
958
Table 4 Measured active rate constants (as volume coefficient of oxygen transport and drift rate constant of 0.03; 0.10 and 0.16 min1 respectively, in dependence of examined air flow (2; 6 and 10 m3 =h) and calculated rate constants: diffusion, adsorption and charging rate constants Reg. Nb.
kL a (min1 )
kd (min1 )
ka (min1 )
1 ts
(min1 )
1 2 3 4 5 6 7 8 9
0.04 0.04 0.08 0.03 0.03 0.07 0.03 0.03 0.04
0.04 0.03 0.03 0.04 0.03 0.03 0.04 0.03 0.03
0.21 0.21 0.21 0.14 0.14 0.14 0.04 0.04 0.04
0.04 0.04 0.04 0.04 0.04 0.04 0.05 0.05 0.05
k # (min1 ) 0.01 0.06 0.08 0.00 0.07 0.09 0.00 0.07 0.12
*measured period of aeration time that enable the achieving of constant oxygen concentration: ts ¼ tG
1. The control of oxygen solubility degree as well as the overall velocity of oxygen dissolution is based on the agreement of experimentally obtained ratio among active transport
rate constant (measured oxygen coefficient of oxygen transport in liquid and drift relaxation time) with relaxation processes that enable equilibrium temperature, equilibrium
Table 5 Experimentally obtained oxygen solubility degree calculated to Eqns (19a) and (47) and ratio between saturation and active transport rate constants
tWL tWS
Reg. Nb.
wexp ð%Þ
wt ð%Þ
wm ð%Þ
1 2
74 72
73 73
63 67
1 1
3
77
88
86
0.5
4
63
72
63
1.3
5
62
68
65
1.3
6
69
84
82
0.6
7
57
54
45
1.6
8
58
64
45
1.6
9
62
69
55
1.3
Compared measured with the calculated aeration rate constants
ks ks ks ks ks ks ks ks ks ks ks ks ks ks ks ks ks
¼ kd ¼ kL a ¼ 0:2ka ¼ kL a ¼ kd ¼ 0:2ka ¼ 1:3kd ¼ 0:5k ¼ 0:5kL a ¼ 0:4ka ¼ kd ¼ kdr ¼ 1:3kL a ¼ 0:3ka ¼ 1:3kd ¼ 1:3kL a ¼ 0:3ka ¼ 1:6kL a ¼ 1:3kd ¼ 0:4k # ¼ 0:3ka ¼ 1:3kdr ¼ 1:3kL a ¼ 0:7k ¼ 1:25kd ¼ 1:7kd ¼ 1:7kL a ¼ 0:7ka ¼ 1:25ka ¼ 1:25kL a ¼ 1:7kd
M. Sˇevaljevic et al. / Desalination 248 (2009) 941–960 Table 6 Effects of aerations regimes after the saturation period on agreement of experimental obtained temperatures of liquid, gas and surrounding phase (Table 1a) with calculated equilibrium temperatures for distilled water that enable distribution of gas molecules to Boltzmann and experimental obtained tt , and mass transport tm oxygen solubility degree with calculated, wexp ¼ wcalc , exchanged number of moles between water and gas phases Reg. Nb.
ðn ns Þw ðniz nul ÞG
1 2 3 4 5 6 7 8 9
1 1 0.5 1.3 1.3 0.6 1.6 1.6 1.3
¼ kkLsa
tR;G tt
tL tm
wexp ¼ wcalc
1.1 1.2 0.9G 0.7 0.9 0.6 0.9 1.6 1
1.6 1.3 0.7 1.5 1.7 0.8 1.2 1.2 2.8
wt wt wt; m wm wm wt; m
•
•
wt þwm 2 wt þwm 2 wt þwm 2
over-pressure, as well as chemical, electrochemical potential and free surface energy. 2. The effect of aeration regimes on agreement between experimentally obtained and calculated thermodynamic and kinetic parameters enables the identification of the relaxation processes of exchanged number of oxygen molecules after achieving PLTE. 3. The results obtained for investigated regimes show:
•
•
Equal active and passive rate constants in oil-uncontaminated water at less air
959
flows, enable oxygen solubility degree in oil-uncontaminated water 72–74%, by the thermal relaxation processes defined for gas-adsorbed molecules to Boltzmann Equal over-pressure relaxation with charging rate constant enhanced oxygen solubility degree for 5%, in oil-uncontaminated or small oil-contaminated water at maximal air flows Velocity of overall oxygen dissolution process and oxygen solubility degree of 63%, control diffusion rate constants in small oil-contaminated water at less air flows Equal adsorption rate constant with volume coefficient of oxygen transport and chemical relaxation rate constants enable thermal, mechanical and chemical equilibrium in maximal oil-contaminated water. Decreased oxygen solubility degree to 57–62%. controls the presence of hydrophobic oil drops and dehydrated oxygen molecules in free contact surface of water.
4. The improved results for oxygen solubility degree could be achieved by pretreatment for removal of colloidal particles by microfiltration after flocullation–sedimetation treatment and for oil-contaminated water by flocculation–flotation treatment, or with combined treatment [29]. 5. The electrochemical investigation could be usefull also in aim to improve oxygen solubility degree by optimization of contents of catalytic substances in control of relaxation processes.
Table 7 The surface tension and temperatures of water in investigated regimes, the changes of the surface tension, molar contact surface between water and surrounded air and the surface electric potentials Reg. Nb. sðmN=mÞ T ðKÞ DsðmN=mÞ AM m2 =m DwW ðV=molÞ 1,2,3 4,5,6 7,8,9
76.2 64.8 57.3
286 287 287
4.2 7.8 14.7
107.8 87 41.6
0.005 0.007 0.025
960
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