Matthew Otwinowski
Scaling Analysis Of Acid Rock Drainage
5.2 Acid Generation Rates
In the absence of bacteria, the Acid Generation Rate is practically proportional to the oxygen consumption rate. We limit our attention to the qualitative features of the temperature dependence of acid generation rates.
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Several existing linear models produce incorrect profiles of acid generation rate as the function of distance from pile surface. For the symmetric boundary conditions used in this study, the iron and sulphate production rates are given by the relations:
and
The molar coefficients MFe=0.29 and MSO42-=0.58 define the rates of iron and sulphate production in absence of bacteria, when quasi-equilibrium concentrations of ferric iron are small [SyT]. In general, the values of p and q have to be determined by laboratory tests discussed in Section 5.3.
Fig.5.8 presents the dependence of pyrite oxidation rate as the function of temperature for the same entry data as in Table 5.1 (Temperature profiles, T(x), are presented in Figs. 5.2 and 5.4; q=2.1 and p=1).
According to our mathematical analysis, the maximum acid generation rates occur at some distance from the pile surface, at the temperature TRm(xRm)=37.5°C. For L=7.6 m in Scenario 1, the maximum pyrite oxidation rates occur close to the center of the pile at the distance xRm=5 m from the pile surface. The maximum value of pyrite oxidation rate, 1.35 mol/(m3s) corresponds to about 510 grams of pyrite per year per cubic meter.
According to our mathematical analysis, the maximum acid generation rates occur at some distance from the pile surface, at the temperature TRm(xRm)=37.5°C. For L=7.6 m in Scenario 1, the maximum pyrite oxidation rates occur close to the center of the pile at the distance xRm=5 m from the pile surface. The maximum value of pyrite oxidation rate, 1.35 mol/(m3s) corresponds to about 510 grams of pyrite per year per cubic meter.
| Fig. 5.8 Temperature dependence of pyrite oxidation rates expressed in units [mol/(m3s)]. The maximum pyrite oxidation rate occurs for an intermediate temperature value TRm= 37.5°C. The value of TRm is determined by the competitive effects of increasing temperature and decreasing oxygen concentration. The oxidation rate goes to zero when the temperature approaches the value Tm*=54.5°C; Tb=10°C. The entry data listed in Table 5.1 are used. |
The total acid generation rate increases 4 times as the result of the thermodynamic catastrophe at δ*=2.75 in Scenario 2. This is a dramatic effect indicating the importance of waste rock pile design. (The total acid generation rates can be obtained after integrating the profile R(x) over the pile volume).
For nonsymmetric boundary conditions, the oxygen concentration and temperature are related by eq. (4.3a). For the stronglynonsymmetric boundary conditions, the pyrite oxidation rates may show spatial oscillations. Such spatially oscillating patterns have been observed in Heath Steele [NoD], (We have obtained approximate solutions expressed in terms of Bessel function for thenonsymmetric boundary problem - the discussion of this problem goes beyond the scope of the scaling analysis presented in this report).
This post first appeared on Maciej Otwinowski - Synergetic Technology, please read the originial post: here
