Material Balances Lecture 1 Biochemical Engineering Review of

Material Balances Lecture 1 Biochemical Engineering

Review of Thermodynamics • System – any matter identified for investigation • Surroundings – the remainder of the universe • Boundary – separates system from surroundings ▫ May be real and tangible or virtual and nominal

Types of System

• Process – causes changes in the system or surroundings • Batch process – operates in a closed system • Semi-batch process – allows either input or output of mass • Fed-batch process – allows input of material to the system but not output • Continuous processs – allows matter to flow in and out of the system

Equilibrium vs Steady-state • Steady-state ▫ Describes a process in which the properties of the system (T, p, V, …) doesn’t vary with time • Equilibrium ▫ Describes a system in which all opposing forces are counter-balanced, leading to insignificant changes in the properties of the system

Law of Conservation of Mass • Given component A, what if Mass in ≠ Mass out? ▫ Something is wrong with the measurements ▫ The system has a leak ▫ Component A is consumed/generated within the system ▫ Component A accumulates in the system

General Mass Balance • For component A Mass in Mass out Mass generated Mass consumed Mass accumulated

Sample Problem A continuous process is set up for treatment of waste water. Each day, 105 kg cellulose and 103 kg bacteria enter the feed stream, while 104 kg cellulose and 1. 5 x 104 kg bacteria leave the effluent. The rate of cellulose digestion by the bacteria is 7 x 104 kg/day. The rate of bacterial growth is 2 x 104 kg/day; the rate of bacterial lysis is 5 x 102 kg/day. Write balances for cellulose and bacteria in the system

Types of Material Balance • Differential Balance ▫ Used for continuous processes ▫ Based on flow rates • Integral Balance ▫ Used for batch, semi-batch and fed-batch ▫ Based on the quantity or mass, usualy over a specified time period

Simplified General Mass Balance: the Steady-state At steady-state, does mass in = mass out? With reaction Without reaction Total mass Yes Total moles No Yes Mass of a molecular specie No Yes Moles of a molecular specie No Yes Mass of an atomic specie Yes Moles of an atomic specie Yes Material

Procedure for material balance calculation 1. Draw a clear process flow diagram 2. Select a set of units and state it clearly 3. Select a basis for calculation and state it clearly 4. State all assumptions applied to the problem 5. Identify which components of the system are involved in reaction

A fermentation slurry containing Streptomyces kanamyceticus cells is filtered using a continuous rotary vacuum filter. Slurry is fed to the filter at the rate of 120 kg/h; 1 kg slurry contains 60 g cell solids. To improve filtration rates, particles of diatomaceous aerth filter aid are added at a rate of 10 kg/h. the concentration of kanamycin in the slurry is 0. 05% by weight. Liquid filtrate is collected at a rate of 112 kg/h; the concentration of the kanamycin in the filtrate is 0. 045% (w/w). Filter cake containing cells and filter aid is removed continuously from the filter cloth. (a) What percentage water is in the filter cake? (b) If the concentration of kanamycin dissolved in the liquid within the filter cake is the same as that in the filtrate, how much kanamycin is absorbed per kg filter aid? 1. Draw a clear process flow diagram 2. Select a set of units and state it clearly 3. Select a basis for calculation and state it clearly 4. State all assumptions applied to the problem 5. Identify which components of the system are involved in reaction

Xanthan gum is produced using Xanthomonas campestris in batch culture. Laboratory experiments have shown that for each gram of glucoses utilized by the bacteria 0. 23 g of oxygen and 0. 01 g ammonia are consumed, while 0. 75 g gum, 0. 09 g cells, and 0. 27 g gaseous CO 2 and 0. 13 g H 2 O are formed. Other components of the system such as phosphate can be neglected. Medium containing glucose and ammonia dissolved in 20, 000 L water is pumped into a stirred fermenter and innoculated with X. campestris. Air is sparged into the fermenter; the total amount of off-gas recovered during the entire batch culture is 1250 kg. because xanthan gum solutions have high viscosity and are difficult to handle, the final gum concentration should not be allowed to exceed 3. 5% wt. (a) How much glucose and ammonia are required? (b) What percentage air is provided? 1. Draw a clear process flow diagram 2. Select a set of units and state it clearly 3. Select a basis for calculation and state it clearly 4. State all assumptions applied to the problem 5. Identify which components of the system are involved in reaction