Effect Dynamic Stability of Atmospheric Boundary Layer on Plume Downward Flux Emitted from Daura Refinery Stacks

Abstract


Introduction
Atmospheric stability is defined as the response of air parcels to vertical motion, which largely depends on the vartical variations of wind speed and temperature, such that these elements are considered indicators used to calculate atmospheric stability conditions (Anad et al., 2019).There is no physical law that specifically determines atmospheric stability, but there is a wide range of schemes, such as Pasquill, Richardson number, Monin-Obukhov, etc. (Albdiri, 2018).The contamination of the atmosphere by pollutants has serious impacts on different sectors, and their deposition is affected by many factors.For instance, dry deposition in urban areas depends on particle properties, concentrations, local conditions of air-to-surface flux, and surface characteristics such that smooth surfaces compared to rough surfaces have lower deposition rates per unit area (Giardina et al., 2019).The transport of some chemical compounds, such sulfur oxides, nitrogen and ammonium, base cations and heavy metals, is responsible for many urban air pollution problems (e.g., visibility reduction, respiratory diseases, etc.).The deposition rate depends on the size of particles; where coarse particles are rapidly settled by sedimentation or impaction processes, while, Brownian diffusion is effective for small particles (Jacob, 1999).Due to urban and industrial activities, the formation of pollutants is quite inevitable, and they are deposited on human beings, surfaces of plants such as trees and crops, buildings and wate rbodies (Dolske, 1995), where the dry deposition of pollutants on water surfaces will cause a degradation in water quality and may spoil the aquatic ecosystems, while wet deposition is active during the rain (Mohan, 2016).There are many studies directed at deposition velocity, one of which comprises a comparison between many models used to study the rate of deposition and the use of a proposed model that covers a wider range of conditions, replacing complicated calculations of atmospheric stability and friction velocity with a simpler algorithms that includes the usage of meteorological data such as wind speed (Abbasi et al., 2018).Dry deposition flux is calculated via several methods, and the relationship between dry deposition flux and particle concentration has been reviewed in a comprehensive study (Mohan, 2016).A similar study was made, but for stacks brick production factories to study the effect of stack emission on the occurrence of high voltage insulators flashover in Diwanyah Governorate in Iraq, and to test the effect of some meteorological data on dispersion and deposition rates of PM10, in which Gaussian dispersion model is adopted to simulate local air pollution with distance.The results show that the atmospheric stability conditions have a major role in determining the deposition rate of PM10; the study found that the thickness of the deposited layer changes when the atmospheric stability changes from a moderately unstable conditions to a strongly unstable conditions (changing stability classes from class B to stable conditions class F) (Albdiri, 2018).Another study is made to design a mathematical model, operating at different stability conditions to calculate the deposition velocity of particulates over Baghdad City by using wind speed and temperature data near the earth's surface at 20 m height, and the results show a direct relationship between deposition velocity and friction velocity, but the relation is opposite for wind speed (Saad, 2012).This study aims to determine the effect of atmospheric stability by using the similarity theory of Monin-Obukhov and Pasquill Turner stability on deposition downward flux for PM10 at different distances resulting from emitted plume stacks from the Daura refinery, according to the domain of wind direction, and finally to calculate the amount of deposited dust in the specified area in this domain direction.

Location of the Study Area
Al-Daura Refinery is one of the main refineries in Iraq, located in Al-Daura region, about a few kilometers from the city center in the southeastern suburb of Baghdad, near the Tigris River, with an area of approximately 205 Hectares (1620m x 860m) as shown in Fig. 1a, bounded on the north and the west by Karada city, one of the largest cities in Baghdad province, while it is bounded on the east by a highway, and on the south by the refinery workers households (Hamiza et al. , 2021).Fig. 1a, b show the location of the Daura refinery relative Baghdad province and Baghdad center.Daura refinery operates twenty-four hours per day, processing large quantities of crude oil and producing about 210,000 barrels per day (Anad et al., 2022;Anad et al., 2019).
Most of the atmospheric data are obtained from the European Center for Medium-Range Weather Forecasts (ECMWF).This center is considered a research institute and operational service, producing global numerical weather predictions and other data for members and other states and communities.ECMWF considers one of the largest supercomputer facilities and meteorological data archives in the world.Grid data is used over Baghdad center with grid clarity of 0.125x0.125degrees, and the nearest grid point to Daura refinery is 33.28ºN lat.and 44.25ºE, data from this point are considered a refinery point station for atmospheric data.Fig. 1 (a and b) shows the distribution of ECMWF grid stations over the Baghdad map, and the station near to refinery region, respectively.Hourly data at 00, 03, 06, 09, 12, 15, 18, and 21 for some atmospheric parameters, including sensible heat flux H, air temperature above the surface T, eastward and northward shear stress x, and y, wind speed compounds, and wind direction at altitude 10 m, from this point and for January (as the winter season) and July (as the summer season), were used to estimate the atmospheric stability condition by Obukhov length and Pasquill Turner stability classes using references standard tables.These atmospheric data and stability parameter index, in addition to amount of fuel burned inside the refinery in 2019 during the January and July, are considered in the Gussain model to estimate PM10 concentration and finally determine the flux deposition amount for PM10.

Monin-Obukhov Length Stability Indices
The hypothesis of Monin-Obukhov similarity state that any mean flow or turbulence quantity in the surface layer, when normalized by an appropriate scaling parameter, must be a unique function of z/L only, where L is Obu-khov length calculated byHassoon and Tawfiq (2019).
Where g is the gravitational acceleration (m.s -2 ), ρair is air density (1.2kg m -3 ), cp is the specific heat at a constant pressure (1004 J K -1 kg -1 ), is the mean potential temperature between two levels (°K), and u * is the friction velocity (m s -1 ), where friction velocity and sensible heat flux must be estimated to determine L according to equation 1, and vice versa.

Friction Velocity
The friction velocity (also known as the shear-stress velocity), is a measure of the wind shearing stress on the surface below.Friction velocity is less accurate, but commonly estimated from more routine meteorological measurements of wind speed and temperature at multiple levels (Czernecki et al., 2017).It is derived from the similarity theory of the atmospheric boundary layer proposed by Monin and Obukhov (Mrokowska et al., 2015) and can be estimated from the following equation (Castellví and Cavero, 2020): Where τi : is shear stress in northward (y-axis), or eastward (x-axis) directions, i: refers to x-axis or y-axis, and the average shear stress can be substituted in the following equation (Hassoon and Tawfiq, 2019):

Turner Pasquill stability Classes
Different techniques are used for stability determination, but there is some complexity in measuring some parameters to calculate stability, such as heat flux from a surface or friction speed, etc., thus, some schemes were developed to facilitate the classification of atmospheric stability conditions, such as the Pasquill scheme.Pasquill (1961) proposed a discrete classification scheme of atmospheric stability which was modified later by Turner (1969) (Mohan and Siddiqui, 1998).The scheme depends on atmospheric observations near the surface at 10 m, such as wind, solar radiation, and cloudiness.There are mainly six atmospheric stability classes labeled as (A) extremely unstable, (B) unstable, (C) slightly unstable, (D) neutral, (E) slightly stable, and (F) extremely stable.Later, class G is involved to represent low wind speed at nighttime conditions (stable conditions) (Chapman, 2017) (Table 1).

Gaussian Model
The Gaussian plume dispersion model is obtained from the analytical solution of the simplified diffusion equation, which is mostly used in regulatory dispersion models.It describes a continuous point source release in origin in a uniform (homogeneous) turbulent flow.The final form of the Gaussian plume equation is for an unrestricted elevated plume as given in the following equation ( 4) (Anad et al., 2022;Albdiri, 2018): Where C: is the point of concentration at the receptor (μg/m 3 ), x, y, z: is the ground level coordinates of the receptor relative to the source with wind direction (m), and Hp: is the effective release height of emissions (m), Q: is the mass flow rate of a given pollutant from a source located at constant location (μg/s), ̅ p is the wind speed (m/s),  and : is the standard deviation of plume concentration distribution in y and z plane (m) where they are calculated according to stability by Pasqual and Turner classes (Albdiri, 2018;Shubbar et al., 2019).The estimation of mass flow rate (emission rate) for any location depends on the methods of the recent research with change from the amount of fuel burned (Hamiza et al., 2021, Anad et al., 2019and Anad et al., 2022).

Particulate Matter
Particulate matter (PM10) recieved growing attention from researchers due to their impacts on human health.The exposure to high concentrations of PM10 increases mortality rates and more cases of respiratory and cardiovascular diseases.The concentration of PM10 changes according to interrelated, environmental and anthropogenic factors.For example, the occurrence of temperature inversion can enhance the accumulation of particulate matter in the surface boundary layer (Czernecki et al., 2017).

Gravitational Settling Velocity
In cases of dust deposition, which is a coarse aerosol, the velocity of gravitational settling is significant, and it can be calculated through the equilibrium between gravitational force and drag force, neglecting the buoyancy force (due to the larger density of particle compared to the density of air).If the Stokes law is established (Re < 0.01), the settling velocity can be calculated from the following equation (Abbasi et al., 2018): Where, ρp: particale density (2 g/cm 3 ), μ:the absolute viscosity of air (~1.81x10 -4 g⁄cm.s),g: the gravitational acceleration (9.8 m/s 2 ).

Particulate Matter Deposition Flux
The dry deposition velocity Vd depends on several factors: the height above the ground surface (altitude), the surface topographic conditions, as well as the behavior of turbulence in the atmosphere.The general approach used in this calculation is the deposition velocity equation that depends on the explicit resistance methods, including parameterizations of Brownian diffusion, inertial impact, and gravitational settling.The deposition velocity is written as the inverse of the sum of resistances ( referred to as Ra and Rd in equation 6) to pollutant transfer, Ra and Rd are defined as aerodynamic resistance and land surface resistance, respectively) through various layers, plus gravitational settling as in the following equation (Fang et al., 2010;Szep et al., 2016). Where: where Sc: is Schmidt number that is defined as the ratio of momentum diffusivity (viscosity) and mass diffusivity (dimensionless) (Bergman et al., 2011), St: is stokes number (dimensionless), νa: is kinematic viscosity of air (~0.15 cm 2 ⁄s), and Db: is the Brownian diffusivity (cm 2 /s) of the pollutant in air.

Atmospheric Stability classes at nighttime
Atmospheric stability is considerably important in calculating of the concentration particulate matter (PM10), and its deposition velocity.In this study, two approaches are applied to determine the stability based on the ECMWF gridded data at a point near the Daura refinery.The first approach includes the calculation of Monin-Obukhov length according to equation 1, and the friction velocity in equation 1 is calculated from equations 2 and 3.The used data comprise the sensible heat flux, instantaneous shear stress and temperature near the Earth surface.Fig. 2, shows the behavior of friction velocity in the area near Daura refinery in the January and July every 3 hours from 00 to 21; the velocity in July is greater than that in January in most observations due to great turbulence and unstable atmosphere as a result of convection.Large values of friction velocity are proportional to unstable conditions, according to the theory of Monin-Obukhov in equation 1.This stability parameter also depends on surface sensible heat flux.Fig. 3a shows the difference between the observed instantaneous sensible heat flux in July and January, where it has negative values in most observations; this refers to the effect of the positive sign.Because there is an open area, that does not effect on large values of positive flux, although there are large values of air temperature in July (Fig. 3b).This method of stability is used to find the gravity velocity of the PM10 according to equation 5.
The second approach is the stability classes, which depend on the first approach and on Table 2 that correlated to the Monin-Obukhov length (L).The Pasquill Turner stability classes are constructed of three classes: A, B, and C, which are considered as unstable; D class as neutral, and E, and F as stable.
classes were used in the Gaussian model to calculate the concentration of PM10 at different distances by using equation 4.

Emission PM10 from stacks Daura Refinery
The Daura refinery operates twenty-four hours per day, with two types of fuel burned inside the refinery units.According to the issued reports from the environment department in the refinery, the latter has twelve units, consuming fuel oil and fuel gas as an operating fuel.Nearly 46606.1 m 3 and 64171115 m 3 of fuel oil and fuel gas, respectively, were burned through January, while nearly 31436.1 m 3 and 9290554 m 3 of fuel oil and fuel gas were burned in January and July, respectively, in 2019.Knowing these amounts of fuel is very important to estimating the emission rate of PM10 from stack outlets (Table 4).Atmospheric data such as wind speed, direction, and other parameters from ECMWF used to estimate atmospheric stability, according to the Pasquill Turner stability scheme, while atmospheric stability classes are used to calculate PM10 concentration above the surface according to the Gussain model, equation 4. Fig. 5 shows the many circle lines around the refinery center point that represent the distance of particulate pollutants, reaching also the direction of wind speed domain in January and July plotted by GIS program.
According to equation 4, PM10 dispersed from refinery stacks can be estimated according to the Gaussain model and depending on data from the ECMWF.The emission rate is necessary to determine PM10 concentration at different distances assuming homogenous turbulence.The emission rate is governed by fuel oil and fuel gas supplied to the refinery during the study period.Gaussian model estimates PM10 concentration over the surface at a different distance from the refinery center (Fig. 5), but it does not represent the amount of deposit particles.

Evaluation Flux Deposition at Stable Conditions
The boundary layer structure is different throughout daytime and nighttime according to stability, such that in the daytime it is constructed from the surface layer and mixed layer, while at nighttime it is constructed from the stability inversion layer and residual layer.This arrangement of the stacked layer is different for the winter season than for the summer season.This study is an attempt to evaluate aerosol deposition amounts in the regions around the Daura refinery according to the distance from the stacks source.The calculation passed through two stages: the first stage was to evaluate flux deposition for aerosol particles with a diameter of 10 um.The equations from 5 to 10 were used to calculate flux deposition depending on atmospheric stability in the surface layer.The important parts of the first stage included gravity deposition, velocity deposition and stability parameter Obukhov length.The second stage is to determine aerosol concentration at 10 μm according to the Gaussian model for dispersion in equation 4.This model needs many parameters, such as wind speed at the stack exit height, atmospheric stability classes, and diffusion coefficients, in addition to emission rate.Knowledge of aerosol deposition velocity and aerosols concentration at 10 μm is necessary to determine downward the flux deposition, where flux is defined as the transport of any aersols amount per unit area per unit time, the amount here refers to the PM 10 calculated by the Gaussian model, and it depends on the amount of burned fuel inside refinery units released by 35 stack located inside the refinery by plume derived by exit velocity of 23.45m/s.Two types of experimented data represent different weather conditions in January and July which perhaps represents extreme weather condition, it is very important to reflect stability conditions in the boundary layer through these study periods.

Spatial Distribution of Flux Deposition According to Wind Direction Domain
This study is not concerned only about the downward flux of PM10 pollutant amount released from Daura stacks from the known surface boundary layer, friction velocity, stability classes and Monin abu khov length, but it also takes into account how to determine the accumulation amount of PM10 resulting from burning products at different locations around the refinery through average periods of the day, month and year, thus the domain of wind direction at there time periods must be known (Fig. 4).
The Gaussian model can be utilized to give downward deposition concentration of pollutant with distance from point sources.Fig. 5 shows three circles for distances of 1000, 5000, and 10000 m from the refinery center, each circle considered the amount of deposition rate.The refinery needs 24 hours to complete the daily operation, which will take time for deposition to determine the thickness of accumulated dust.The figure also shows the flux deposition for different conditions (January and July).According to the wind direction domain, most amounts of accumulated dust can be specified at any location.The importance of this study is in determining whether the center of regions have a large deposition amounts of aerosols that are loaded into the atmosphere, which is considered a prediction that can be introduced for those interested in knowing the lines of deposition flux.

Conclusions
Flux is a vector amount describing the magnitude and direction of the flow of a substance or property, measured in units amount per unit area per unit time.In this study, pollutant aerosol flux at 10 um (PM10) emitted from refinery stacks calculated in this study resulted from burning of oil crude in operation systems.When pm10 is emitted from the Daura refinery stacks it will be deposit after some duration through it movement and deposited (accumulated) in the area surrounding the Daura refinery according to domain wind direction.Atmospheric stability effected on flux transformed and deposition PM10 concentration.In this study, atmospheric stability at different behavior climate months was estimated with two methods, its Monin-Obukhov similarity theory length and Turner stability classes, first method uses z/L as stability index depends on data of wind speed, friction velocity, deposition velocity, shear stress, air temperature, sensible heat flux, obtained or calculated using ECMWF archive data for grid point stations near to refinery location, and second one used to calculeate PM10 concentration by used gussain model.
This study focuses on the deposition flux of PM10 concentration because this particulate matter has large size and is deposited in a large amounts around the refinery and causes side effects on humans.There are also many additional parameters used to determine flux deposition in addition to stability, such as emission flow rate from refinery stacks, effective stack height, and other elements related to the environment, such as wind speed, and air temperature.Results of deposition flux with the domain of wind direction are considered very important indices for air pollutants, since aerosol emissions seem to be the most serious problem in the area, considering suspended particles are at high levels and exceed local and international standards, in addition to the calculation of the dust deposition amount with times and distances for specified time and distance around the refinery.The areas located to the south and southeast of the refinery received large amounts of deposited flux values per squre meters through stable weather conditions.The accumulated PM10 amounts during one month have recorded 1.5 million μg /m 2 .s in January at a distance of 1000 m from refinery center stacks, while this amount reaches 532 million μg/m 2 .sduring July due to the high emission rates resulting from burning fuel oil during July.The percentages of PM10 sedimentation decreased with the distance from the refinery to 1712 and 322839 μg /m 2 .sat a distance of 10 km from the refinery in January and July, respectively.According to this method, the accumulated amount of PM10 per squares meter can be estimated at any time, if atmospheric stability conditions and the domain of wind direction are known.

Fig 1 .
Fig 1. Location study, (a) Baghdad province and Baghdad center map; (b) Baghdad center located Daura refinery and nearest grid data of ECMWF.

Fig 2 .
Fig 2. Friction velocity in January and July months observed for each 3 hours in area around Daura refinery calculated from ECMWF data, 2019

Fig. 3 .
Fig. 3. Show (a) Sensible heat flux differences between January and July hour month; (b) air temperature in January and July month

Fig. 4 .
Fig. 4. Blowing domain from wind speed and direction over Durra refinery by windrose in (a) January; (b) July

Table 3 .
Relationship between number of frequency stability classes of January and July and average stability Monin-Obukhov length

Table 4 .
Fuel oil and fuel gas burned in refinery units also emission rate of PM10 resulted from burning at January and July 2019.

Table 5 .
Average amount of the flux deposition according to blowing domain of wind direction and distance from stack refinery through stable atmospheric conditions and average time