Lecture 1 Biochemical Engineering 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 Batch process – all materials are provided at the start, and the products are removed only when the process is complete Semi batch – all other process that does not fit in the other three If input and output rates of continuous process is equal, it can continue on indefinitely

Equilibrium vs 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 Mass in = Mass out 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 Cellulose: 2x104 accumulation Bacteria: 5.5x103 accumulation

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 Material At steady-state, does mass in = mass out? With reaction Without reaction Total mass Yes Total moles No Mass of a molecular specie Moles of a molecular specie Mass of an atomic specie Moles of an atomic specie 𝑚𝑎𝑠𝑠 𝑖𝑛+𝑚𝑎𝑠𝑠 𝑔𝑒𝑛𝑒𝑟𝑎𝑡𝑒𝑑=𝑚𝑎𝑠𝑠 𝑜𝑢𝑡+𝑚𝑎𝑠𝑠 𝑐𝑜𝑛𝑠𝑢𝑚𝑒𝑑

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

What percentage water is in the filter cake? 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. What percentage water is in the filter cake? 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? Draw a clear process flow diagram Select a set of units and state it clearly Select a basis for calculation and state it clearly State all assumptions applied to the problem Identify which components of the system are involved in reaction 4.4% 9.6x10-4 kg/kg

How much glucose and ammonia are required? 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 CO2 and 0.13 g H2O 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. How much glucose and ammonia are required? What percentage air is provided? Draw a clear process flow diagram Select a set of units and state it clearly Select a basis for calculation and state it clearly State all assumptions applied to the problem Identify which components of the system are involved in reaction 980 kg glucose; 9.8 kg NH3 25% excess air

Material Balance w/ Recycle, Purge and Bypass