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the calculations of both the (Ra, ux/Ra) parameters and the (C*max c) concentrations for chlorides and sulfates are the main topics of this paper. All of the calculations presented here concern the unpublished measurement series of October 1982. Additionally, the parameters calculated here (Ra, ux/Ra) are also compared to the same parameters in relation to the two earlier measurement series for the same studied sandy ground presented by different scale (length) of concentration plumes and simultaneously different and changeable micro and macroscopic ground heterogeneities (as geometrical similarity) (Johnson et al. 2003), different numerical data of many parameters being part of these transport models (equations) along with different defining methods of these parameters (Szymaski and Janowska 2016), inclusion or exclusion of positive or negative sources and sinks in all mathematical models (equations) (see qs parameter in given below equation 1). Nonetheless, for a general description of all the above-mentioned processes we can use the partial differential governing equation in 3D domain of species ko. This equation (as mass balance one with the terms of all the above-mentioned processes) is as follows: (mC k0 ) C k0 k = (mDij )- (mui C k0 ) + q s C s 0 + t xi x j xi Rn (1) the solute concentration in flowing groundwater in aqueous phase (in the local equilibrium conditions) of species ko [g · m-3], ui the component of the pore groundwater velocity in pore space [m · s-1], m he effective porosity of the porous medium , xi he distance along the Cartesian co-ordinate axis [m], Di j the hydrodynamic dispersion coefficient symmetrical tensor [m2 · s-1], qs the volumetric flow rate per unit volume of aquifer representing fluid sources (positive) and sinks (negative) [s-1], k0 Cs the concentration of the source or sink flux for species ko [g · m-3], t the co-ordinate of time [s], Rn the function describing generally biological and chemical reactions treated as aqueous-solid surface ones [g · s-1 · m-3] (see the Rn function later in the further part of this paper). The simplified assumptions for all the parameters considered in equation (1) were presented in detail by Aniszewski 2013. Although the adsorption process in various grounds is relatively known and described in the literature (but still not conclusively), the main problem is related every time to the proper determination of optimum parameters describing this process. However, the adsorption process is understood in this paper as a reversible physical one corresponding to models of statics (in form of various adsorption isotherms) (Chiang 2005, Seidel-Morgenstern 2004). Adsorption parameters strongly depend on the kind of contaminants relocating with groundwater and agroclimatic zones. It should to be noted that in various agroclimatic zones, physico-chemical and biological processes of relocating contaminated groundwater differ considerably from one another. Based on the literature, we can say that these processes also impact on the adsorption process (Chiang 2005, Fang et al. 2012, Taniguchi and Holman 2010, Zheng and Wang 1996). C k0 where: Aniszewski 2009 (November 1981) and Aniszewski 2013 (May 1982). Dx * = Dx ux L x = ; L Dy ux L y = ; L C = C*; Co ux t = ; L Material and methods Taking into consideration in equation (1) advection, two-dimensional dispersion, adsorption process (R 1) and neglecting simultaneously biological and chemical reactions in the ground ( Rn = 0), the simplified 2D form of equation (1) can be expressed as follows: = D* ; y m = A1 ( N -1) ( N -1) m + N K Co C (4) S C C 2C 2C 1+ + ux = Dx 2 + D y 2 m C t x x y where: S (2) the mass of the solute species adsorbed on the grounds per unit bulk dry mass of the porous medium (in the local equilibrium conditions) , Dx, Dy the components of the longitudinal and transverse dispersion coefficients along the x and y axes that depend on the longitudinal and transverse dispersivities(L ,T) [m2 · s-1], [1+(/m) · (S/C)] the constant in time, so-called retardation factor R (R 1.00) resulting from adsorption process  (Chiang 2005). The explanation of all the remaining parameters being considered in equation (2) is given earlier under equation (1). The adopted assumptions were related to in situ measurements made by the Institute of Environmental Development in Pozna (cited by Aniszewski 2009). The source of groundwater contamination in the chosen site (aquifer) was a real ground lagoon (marked by its user as lagoon 4). The lagoon 4 was filled with liquid manure from a pig breeding farm, "Redlo", near widwin and located in the West Pomeranian Voivodeship of Poland. For the exact examination of contaminants relocating with groundwater, a certain number of piezometers were installed near the existing ground lagoon 4. An illustrative map of only the chosen natural site, along with a detailed numeration of the existing and chosen four piezometers is presented by Aniszewski 2013. These four piezometers were used in numerical calculations based on the dimensionless transport model presented below (3) (see also in Table 1 all of these piezometers with both their numeration and distances from the leakage source lagoon 4). Such late, in a sense of time, measurement series of October 1982 adopted for analysis and calculations was taken in this paper intentionally due to access for a short time to the measurement series of October 1982 presented here with the necessary field data (as the last part of the technical report cited by Aniszewski 2009 see also final acknowledgements). The dimensionless form of equation (2) is the following: 2 2 C C C C + A1 = A1 Dx + A1 D y 2 2 The L parameter presented in equation (4) represents the measured distance from the source of the contaminant outflow (as lagoon 4) to the last cross-section [as piezometer X(5)] in the chosen ground and the Co parameter represents the initial measured contaminant concentrations in the source of the outflow into the chosen natural aquifer. The initial numerical Co concentration values (for the chosen chloride and sulfate indicators) are given in a further part of this paper for the measurement series analysed here of October 1982. For the numerical solution of equation (3), appropriate initial and boundary dimensionless conditions (presented by Aniszewski 2009) were also adopted. The updated computational program "PCCS 2.1" was used by the author for numerical calculations of the dimensionless maximum concentrations (C*max c) (see Table 1). For a description of the adsorption term in equation (3), the Freundlich non-linear isotherm (S = K · CN) was assumed, as the isotherm is often used in practice due to its simple mathematical notation (Chiang 2005, Seidel-Morgenstern 2004). The numerical values of the K and N parameters were calculated based on the author's updated laboratory research for all the chosen indicators just in relation to the measurement series of October 1982 analysed here. The updated numerical values of the K and N parameters are: K = 0.3098 m3 · g-1 and N = 0.4978 for the chloride indicator and K = 1.0645 m3 · g-1 and N = 0.7269 for the sulfate indicator, respectively. All these above numerical values of the K and N parameters differ (as smaller ones) from the K and N parameters related to the two earlier measurement series presented by Aniszewski 2009 and Aniszewski 2013. So, using the parameters K and N, the general equation describing the dimensionless retardation factor (R) in equation (2) takes the form: R = 1+ m C = 1+ N K C ( N -1) (5) (3) in which the following auxiliary dimensionless parameters were taken into account: Numerical values of the calculated retardation factors (R) based on equation (5) (treated as average values Ra) for the two chosen indicators are given in the explanations under Table 1 (in footnotes 1 and 2). According to the measurement series of October 1982 presented here, the initial measured contaminant concentrations in the source of the outflow into the chosen natural aquifer (being lagoon 4 with liquid manure inside) are: Co 309.0 g · m-3 for chlorides and Co 405.0 g · m-3 for sulfates, respectively. These above-mentioned initial numerical Co concentration values for the measurement series analysed here differ also (as greater ones) from the Co ones related to the two earlier measurement series. The dimensionless initial measured contaminant concentrations in relation to the initial measured contaminant difference one that is described, in detail, e.g, by Szymkiewicz 2010). This program allows one to obtain the dimensionless values of the contaminant concentrations in the range < 0, 1 >. In the adopted numerical solution of equation (3), the values of dimensionless steps of the difference scheme grids [h*(x), k*(y) and w*(t)] were taken based on Aniszewski 2013 and under the certain assumptions: ones in lagoon 4, for the two indicators presented here, are also given in Table 1 as footnote a (as values equal to 1.00). All the measured concentration data (Co and C*max m) related to both the measurement series of October 1982 analysed here and the chosen indicators were described in the last part of the technical report. This report, cited by Aniszewski 2009, was recently given to the author (see also final acknowledgements). It should be noted that the measured chloride and sulfate concentration values (C*max m) between the particular piezometers are burdened with certain measurement errors. For this reason the variation between them does not have the character of an exponential curve. Thus, these measured concentrations (for chlorides and sulfates) were not combined between the particular piezometers in Figs. 3 and 4. At the same time, the numerical optimum values of all the remaining required parameters being considered in the presented equation (3) (as updated parameterization of this equation in relation to both the two chosen contaminants and the considered sandy ground medium) are the following: (ux = 1.17 × 10-3 m/s, = 1.69 g/m3, m = 0.38) as the adopted real ground parameters in relation to the measurement series of October 1982 (based on last part of the technical report cited by Aniszewski 2009), [Dx = 7.21 × 10-3 m2/s (L = 7.0 m), Dy = 6.08 × 10-4 m2/s (T = 0.56 m)] as the optimum dispersion parameters calculated by the author of this paper. The above-mentioned parameter values related to the measurement series of October 1982 differ from the ones related to the two earlier measurement series. One can say, for example, that in all cases the dispersion parameter values (Dx, Dy) are smaller than those calculated in the two earlier measurement series (presented by Aniszewski 2009 and Aniszewski 2013). Pe = and u x x (y ) u x x (y ) x (y ) = 2 = Dx ( D y ) L u x ( T u x ) L ( T ) (6) Ca = ux · t/x 1 Such numerical values of both the Peclet (Pe) and the Courant (Ca) numbers minimize simultaneously the "numerical dispersion" and "artificial oscillations" in relation to equation (3), where the contaminant transport in ground is dominated not only by the advection process. For such above-mentioned assumptions, the well-known "upwind" scheme (being an "explicit" finite difference one) is particularly suitable for numerical calculations (Szymkiewicz 2010). In these numerical calculations the important consistency, stability and convergence conditions were also preserved. The Peclet number constraint is often relaxed outside the area of interest, where a lower predictive accuracy is acceptable. More details concerning both the applied numerical solution and method of numerical calculations used by the author are given by Szymkiewicz 2010, Aniszewski 2009 and Aniszewski 2013. General description of applied numerical solution In the numerical calculations the computational program "PCCS 2.1" mentioned earlier was chosen, also using the well-known "upwind" scheme (being an "explicit" finite Results of research All the results of the numerical calculations, presented here, of the dimensionless concentration values (C*max c) according to equation (3) along with the dimensionless measured concentration values (C*max m) in the chosen four piezometers are given in Table 1. Table 1. Calculated (C*max c) and measured (C*max m) values of the contaminant concentrations in the measurement series of October 1982 Measurement series Numbers of chosen piezometers with dimensionless () and dimensional (x) distances from the leakage source in lagoon 4 [total distance L to the last piezometer X (5) L 105.0 m] III (8) x 40.0 m Chlorides (NaCl) [adsorption process] Sulfates (Na2SO4) [adsorption process] 0.41761) 1.00a) (C*max m = 0.3906) 0.32562) 1.00a) (C*max m = 0.3048) IX (4) x 70.0 m 0.23991) 1.00a) (C*max m = 0.2274) 0.15622) 1.00a) (C*max m = 0.1489) VII (6) x 90.0 m 0.16281) 1.00a) (C*max m = 0.1588) 0.09822) 1.00a) (C*max m = 0.0969) X (5) x (L) 105 m 0.11721) 1.00a) (C*max m = 0.1065) 0.07822) 1.00a) (C*max m = 0.0690) Chosen contamination in relation to considered processes Explanations: 1) MDC (maximal dimensionless concentrations C*max c) according to equation (3) with adsorption (Ra = 1.01 for chlorides), 2) MDC according to equation (3) with adsorption (Ra = 2.04 for sulfates), a) Initial dimensionless concentrations in relation to the initial measured ones in the lagoon 4 with liquid manure (for the presented here unpublished measurement series of October 1982). Measurement series of October 1982 C*max c = Cma x c /C0  Fig. 1. Dimensionless values of the calculated chloride concentrations (C*max c) (based on equation 3) both for the measurement series analysed here (Oct 1982) and the two earlier ones C*ma x c = Cma x c /C0  0.7 Fig. 2. Dimensionless values of the calculated sulfate concentrations (C*max c) (based on equation 3) both for the measurement series analysed here (Oct 1982) and the two earlier ones C*max c = Cma x c /C0  Fig. 3. Dimensionless values of the measured chloride concentrations (C*max m) both for the measurement series analysed here (Oct 1982) and the two earlier ones C*ma x c = Cma x c /C0  Fig. 4. Dimensionless values of the measured sulfate concentrations (C*max m) both for the measurement series analysed here (Oct 1982) and the two earlier ones Based on the numerical calculations given in Table 1, it was possible to calculate the (Ra, ux/Ra) parameters for the measurement series of October 1982: the dimensionless value of (Ra) amounts to 1.01 for chlorides see explanations under Table 1 (footnote 1) and 2.04 for sulfates see explanations under Table 1 (footnote 2). However, the greater values of these parameters calculated for sulfates of the two earlier measurement series amount to: Ra = 2.18 (November 1981) and Ra = 2.11 (May 1982), the dimensional value of (ux/Ra) amounts to 1.16·10-3 [m · s-1] for chlorides and 0.57·10-3 [m · s-1] for sulfates in relation to the initial real pore velocity of groundwater ux = 1.17 · 10-3 [m · s-1] (without adsorption process Ra = 1.00). However, the lower values of these parameters calculated also for sulfates of the two earlier measurement series amount to: ux/Ra = 0.53 · 10-3 [m · s-1] (November 1981) and ux/Ra = 55 · 10-3 [m · s-1] (May 1982). Graphic results of the numerical values of the calculated concentrations are given in Figs. 1 and 2 (as black square symbols). However, the measured concentration values are given respectively in Figs. 3 and 4 (also as black square symbols). Simultaneously, both the calculated and the measured concentrations for the two earlier measurement series are also given in Figs. 1, 2, 3 and 4 (as black circle and triangle symbols, respectively). General conclusions 1. Taking into consideration the calculated value of the average dimensionless retardation factor (Ra = 1.01), in relation to chlorides, we can point out the almost total depletion of adsorbing capacity for the last measurement series of October 1982 (Ra = 1.01 1.00 and S = 0). In relation to sulfates, we can indicate a considerably lower depletion of adsorbing capacity because the time for total depletion of the adsorbing capacity in this case will be considerably longer (Ra = 2.04 > 1.00 and S 0). 2. Nonetheless, taking also into consideration the numerical values of (Ra, ux/Ra) parameters for the two earlier series of November 1981 (Aniszewski 2009) and May 1982 (Aniszewski 2013), one can finally mention a gradual depletion in time of the adsorbing capacity for the analysed ground. This above-mentioned remark can only be related to a more or less one year period of time (as the series: November1981 May 1982 October 1982), chosen indicators (i.e., chlorides and sulfates) as well as the fine sandy ground. 3. It should also be emphasized that all the measured concentration values for all the contaminants chosen here are lower compared to the calculated ones (see Table 1). This creates a greater margin of error for the prognosis and simulation of concentration values calculated based on the presented transport model (3). In the opposite case, the practical use of the presented transport model (3) could be questionable for calculations of contaminant concentrations in the chosen ground. 4. The calculations presented in this paper also prove that the chosen contaminants (i.e., chlorides and sulfates) distinguish different adsorbing capacity (as adsorption value) during their relocating with groundwater in the chosen sandy ground. For sulfates, this capacity is considerably higher compared to chlorides, which have a considerably lower one (see Table 1 and Figs. 1 and 2). This regularity also occurs for the two earlier measurement series of November 1981 (Aniszewski 2009) and May 1982 (Aniszewski 2013). 5. Based on Figs. 3 and 4, it should also be noticed that all the measured concentration values from the measurement series of October 1982, presented here, are the greatest ones compared to the measured concentration values in the two earlier measurement series presented by Aniszewski 2009 and Aniszewski 2013. One can say that this regularity is caused mainly by the adsorbing capacity decreasing in time (as adsorption value) for the same sandy natural ground. 6. Nonetheless, it should also be to note that all the above-mentioned general conclusions can only be related to the contaminants analysed here relocating with groundwater in the chosen fine sandy ground. Transmission of all these conclusions (based on the calculations made in this paper) to other contaminants and grounds (other agroclimatic zones) would be highly questionable. Acknowledgements The author wishes to acknowledge the Management of the Agricultural Complex Smardzko-farm (a swine farm) in Redlo near widwin (in the West Pomeranian Voivodeship of Poland) for making accessible the unpublished technical report (in Polish) with measured maximal concentration values and ground parameters (which forms last part of this report). All of these data were related to the measurement series of October 1982 analysed in this paper. This report was used by the author in numerical calculations (for all chosen contaminants and piezometers). This unpublished report is cited by Aniszewski 2009 and may be obtained from the author (this information is also given in the earlier part of this paper).
Archives of Environmental Protection – de Gruyter
Published: Mar 1, 2017
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