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Cole, Mike C. Journal of Chemical Theory and Computation , 10 12 , The Journal of Physical Chemistry B , 33 , Steven K. Burger, Jeremy Schofield, and Paul W. The Journal of Physical Chemistry B , 48 , Johnson, and Paul W. Journal of Chemical Theory and Computation , 9 11 , Lee, Daniel J. Jorgensen, and Mike C.
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Ofelia B. ChemPhysChem , 17 18 , This law states that matter is neither created nor destroyed in the process and the total mass remain s unchanged. The general principle of material balance calculations is to put and solve a number of independent equations involve number of unknowns of co mpositions and mass flow rates of streams enter and leave the system or process.
The system can be defined as any arbitrary portion of a process that you want to consider for analysis such as a reactor. The system boundary must be fixed in each problem by d rawing an imaginary boundary around it as shown in the following figure: Basic Principles First Year Asst.
Ahmed Daham 3 There are two important classes of systems: 1. Closed system : The material neither enters nor leaves the vessel system , as shown below: Figure 1: Closed system 2. Open system flow system : The material cross the system boundary, as shown below: Figure 1: Open system Flow system The chemical processes can be classified as batch, continuous and semi -batch : 1. The products are removed all at once after this time. No masses crossed the system boundary during this time.
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Batch process fall into the category of closed systems. Ahmed Daham 4 This equation can be applied for every substance component balance or for total materials total material balance. Semi -batch process: A semi -batch reactor of stirred type tank as shown in the Figure 4 , often used for its own particular characteristics.
In this type, all quantity of one reactant is initially put in the reactor, and then other reactants are continuously fed. Only flows enter the systems, and no leave, hence the system is an unsteady state. This arrangement is useful when the heat of reaction is large. The heat evolved can be controlled by regulating the rate of addition of one of the reactants.
Ahmed Daham 5 3. Continuous process Flow process : The input and output materials are continuously transferred across the system boundary; i. A convenient period of time such as minute, hour, or day must chosen as a basis ov er which material balance calculations be made. This type of processes can be classified as " steady state " and " unsteady state " processes.
In such process there is no accumulation in the system, and the equation of material balance can be written as: Figure 5: Steady state system b- Unsteady state process: For an unsteady state process, not all of the operating conditions in the process e. Ahmed Daham 6 Remarks: 1. By their nature, batch and semi -batch processes are unsteady state operations since the concentration within the closed system is continuously changed with time.
Continuous processes are usually runs as close as possible to the steady state by using suitable control units. However, unsteady state transient conditi ons exist during the start up of a process. All material balance and design calculations are done for steady state conditions.
Batch processes are commonly used for small scale processes in which relatively small quantities of a product are to be produced, while continuous process is better suited to large production rates. All material balance calculations in this chapter are made on steady state processes in which the accumulation term is zero. However, material balance on a batch process can be made over a residence time and on the basis of one batch integral balance. Figure 6: Initial conditions for an open unsteady state system with accumulation. These two equations should be intuitively clear, as the mathematical statements of the concept that all fractions of any quantity must add up to the whole.
Equation 4. K i is a characteristic constant for component i and is dependent on pressure, temperature, and the nature of the component mixture.
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Solution of this system of equations allows us to calculate the compositions of the two different phases, which is necessary for designing the separation scheme for the mixture. Each term in the system of equations is linear variables having power of 1 in x or y. A similar system of equations is used to model a stagewise gas-liquid contactor, such as a distillation column, described in Chapter 3. Source: Adapted from Wankat, P. The material balances for each component yield the following system of n equations for stage k :.
V and L represent the molar flow rates of the vapor and liquid stream, respectively. The subscripts for these flow rates represent the stage from which these flows exit. For example, V k and L k are the vapor and liquid flow rates exiting stage k , respectively. The mole fractions are doubly subscripted variables, the first subscript representing the component, the second one the stage. Each stage is assumed to be an equilibrium stage; that is, the exiting vapor and liquid flows are in equilibrium with each other. This allows us to utilize the equilibrium relationships of the form shown by equation 4.
Algebraic equations encountered in chemical engineering can also be polynomial equations ; that is, they can have variable orders greater than one. This equation is an example of a cubic equation of state , V being the volume of the substance under the given conditions of temperature T and pressure P.
Chemical Process Computations | R. Raman | Springer
Constants a , b , c , and d are functions of the system pressure, temperature, number of moles, and fluid properties. These equations of state are further used in thermodynamic calculations involving interconversion between energy and work, and phase equilibrium. It is readily apparent that an accurate equation of state is critical for superior process design and performance.