Oferta de drogas y control de la misma
Y CANTIDADES DE DROGAS DECOMISADAS La evolución del número de decomisos de
The solution of the equations to determine the steady state operating conditions was done using the sequential modular approach. A schematic overview of the solution methodology is shown in Figure 6.2. The balances on the second stage slurry preparation tank were solved firstly to determine the flow rate of the fresh slurry feed to the flash recycle tank (stream 5).
In order to calculate the temperature, flow rate, and composition of stream 7, the mass transfer between the vapour and liquid phases in the flash recycle tank had to be determined, and the temperature and composition of the recycle stream (stream 9) had to be known. Based on the assumptions discussed in Section 6.2, it was assumed that the only mass transfer occurring between the liquid phase and the vapour phase in the flash recycle tank is the evaporation of water from the recycle stream. This implies that the vent stream leaving the first autoclave compartment pass through the recycle tank unaffected. Initial guessed values were assigned to the temperature of the recycle stream 9, the mass fraction solids in stream 9, and the composition of both the liquid and solid phases in stream 9.
The temperature, flow rate, and composition of stream 7, as calculated using the guessed properties of stream 9, were used as inputs to subsequently perform mass and energy balances on the first compartment of the autoclave. Because the compartments were treated as ideal continuously stirred tank reactors, the composition and temperature of stream AC1 (the slurry stream flowing from the first autoclave compartment to the second compartment) and the autoclave compartment content were assumed to be equal to that of stream 9. The mass balances required the extent of reaction to be calculated for the respective reactions.
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Figure 6.2. Schematic overview of the solution strategy followed to determine the steady state operating conditions of the autoclave.
Specify operating conditions: Flow rates (1, 2, 3, 4, 9, 18, 20)
Temperatures (5, 21) % excess O2 O2distribution
Calculate stream 5 properties (balances on 2ndstage slurry
preparation tank)
Assign initially guessed values to stream 9 temperature and composition
Calculate stream 7 properties (balances on flash recycle
tank)
Calculate stream 9 and stream AC1 properties (balances on first autoclave
compartment)
Difference between calculated and initial stream 9 properties less than allowable tolerance? Recalculate initially guessed values based on calculated values
No Assign initially guessed values to stream AC2 flow
rate and composition Yes
Calculate compartment 2 cooling requirements
Calculate stream AC2 properties (balances on
second autoclave compartment) Difference between calculated
and initial stream AC2 properties less than allowable
tolerance? Yes Recalculate initially guessed values based on calculated values No
Assign initially guessed values to stream 14 flow rate
and composition Calculate stream 14 properties (balances on third
autoclave compartment) Difference between calculated
and initial stream 14 properties less than allowable
tolerance? Recalculate initially guessed values based on calculated values Calculate compartment 3 cooling requirements Yes No
Assign initially guessed values to stream 22 flow rate, composition, and temperature as well as stream 13 flow rate
Calculate stream 15 properties (balances on 2nd stage leach discharge tank)
Calculate stream 16 and 17 properties (balances on 2nd
stage leach discharge thickener)
Calculate stream 21 properties (balances on 3rd stage slurry preparation tank)
Calculate stream 22 and 13 properties (balances on fourth
autoclave compartment)
Difference between calculated and initial stream 22 and 13 properties less than allowable
tolerance? Recalculate initially guessed values based on calculated values No Yes Steady state conditions
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A schematic overview of the solution strategy that was followed to calculate the extents of reactions is shown in Figure 6.3. This involved calculating the reaction rates for the assumed flow rates and compositions, which were used to calculate the amount of each of the solid components consumed (or produced, in cases where solid species are reaction products). The physical and stoichiometric limitations on the amount of each species that could be consumed or produced were applied. These amounts were used to estimate the extent of reaction for the respective reactions, where after the amounts of dissolved species produced (leaching product) or consumed (reagent) were calculated. For reactions where dissolved species rather than solid species were found to be the limiting reagent, the extent of reaction was recalculated. As a result, the extent of reaction for the reactions depending on dissolved species limited reactions had to be recalculated and it had to be verified that the recalculated extents of reactions were achievable given the calculated reaction rates.
The temperature of stream 9, the mass fraction solids in stream 9, and the composition of both the liquid and solid phases in stream 9 were subsequently calculated and compared to the initial guessed values. Successive substitution was used to iteratively calculate the properties of stream 9 until the user specified convergence criteria were met. These criteria were typically selected that the initial guessed values and the newly calculated values for any of the properties did not differ by more than 0.01%. To prevent the successive substitution method from incrementing the property value with too large steps, the initial values were recalculated using Equation 6.3:
E.Y ! · 0 [6.3] where x(j) refers to the initially guessed value for any property x, x(j+1) indicates the recalculated value for the particular property, and E.Y represents the recalculated initial guess. The multiplication factor, f, was typically selected to be a value between 0.005 and 0.2, depending on the variable to be solved.
The mass and energy balances for the second and third compartments were subsequently solved in a similar fashion. The temperature of these two compartments was assumed to be the same as the temperature calculated for the first compartment. In the case of the second autoclave compartment, the flow rate and composition of stream AC2 (the slurry stream flowing from the second autoclave compartment to the third compartment) were guessed initially, while the flow rate and composition of stream 14 were guessed initially to solve the material balances for the third compartment. Once the material balances had been solved,
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energy balances were used to determine the rate at which heat must be removed from the respective compartments to maintain a constant temperature; as discussed, heat removal can be varied by varying the flow rate of water through the cooling coils.
Figure 6.3. Schematic overview of the solution strategy followed to determine the extent of reaction for the respective reactions.
The material balances for the second stage leach discharge tank, the second stage leach discharge thickener, and the third stage slurry preparation tank were solved in succession, assuming that perfect solid-liquid separation is achieved in the thickener. The material and energy balances for the fourth autoclave compartment (third stage leach) were finally solved, again using successive substitution. The temperature, flow rate, and composition of the final discharge stream (stream 22) as well as the flow rate of the steam (stream 13) were assigned guessed values initially, and solved using an approach similar to that used for the autoclave compartments in the second stage leach. The flow rate of steam was calculated by performing an energy balance on the third stage leach based on the assumption that the third stage leach temperature is the same as that of the second stage leach. In cases where a negative steam flow rate was calculate (i.e. where energy had to be removed from the third stage leach to achieve the same temperature as in the second stage leach), the steam flow rate was set to zero and the actual operating temperature of the third stage leach subsequently calculated.
120 6.3.3 Dynamic modelling
The same assumptions regarding the mass transfer between the vapour and liquid phase in the recycle tank and the temperatures of the respective autoclave compartments discussed for the steady state calculations were applicable to the dynamic modelling. In addition, the dynamics of flow into and out of the respective unit operations had to be incorporated. No process control loops were implemented in the dynamic simulation. The flow rates of material from the auxiliary process units (slurry preparation tanks, flash recycle tank, discharge tank, and discharge thickener) were set proportional to the square root of the mass of slurry in the respective process units. The proportionality constants for the respective process units were calculated based on the initial steady state conditions and user-specified initial steady state volumes in the respective unit operations. Slurry flow between the different compartments in the first three compartments of the autoclave occurs by overflowing weirs with fixed heights between the compartments. Under typical operating conditions, the level in the autoclave is maintained at a level that allows continuous slurry flow between the different compartments. It was hence assumed that there is no accumulation of material in any of the autoclave compartments. The effect of oxygen flow rate on the pressure in the autoclave was not taken into account explicitly. The developed model requires the user to specify a constant operating pressure for the autoclave which will affect the oxygen solubility in the slurry, and hence the reaction rates. It was furthermore assumed that the volume of the vapour space inside the autoclave would remain approximately constant over time, and that there would hence not be accumulation of gaseous components in the vapour space at a constant pressure.
Unless a step change was introduced in the rate of heat removal from the second compartment, the rate of heat removal from the third compartment, or the rate of steam addition to the fourth autoclave compartment at a specific time instance, these variables were kept constant and equal to the rates calculated for the initial steady state conditions for the dynamic simulation. The temperatures of these autoclave compartments were thus not controlled during the dynamic simulation.
The resulting set of 217 ordinary differential equations, which are described in detail in Appendix F, were solved simultaneously making use of an ordinary differential solver in MATLAB. A compact disc containing an electronic copy of the MATLAB code is included in Appendix H.
121 6.4 Results