Model and Simulation: Simplifications in Model

Model Simplification:

Continuum: Laws of conservation hold in continuous phase. For dispersed bubble or solid particles in liquid, if the main mechanism is away from the interface of the dispersed and continuous phases, it may be convenient to consider the entire dispersion to be a continuous phase, e.g. study on the pipe wall and pressure loss. If the main mechanism takes place at the gas-liquid interface, continuum is meaningless, e.g. mass transfer between the bubble and liquid.

Combining simple and rigorous models: Two ways to model dispersed bubble in liquid, 1. build rigorous cell model for the dispersed bubble and surrounding liquid, and combine them in a simple manner. 2. Apply simple thin film model at the surface of the bubble and combine with the mass transfer and bubble-size distribution in a rigorous manner.

Uniform Probability Distribution: Useful in averaging the properties assuming the individual entity follow uniform distribution law, e.g. in adsorption, the probability of occupying the empty space on the surface is the same.

Parallel Mechanisms: The mechanism of  heat transfer is conduction, convection and radiation due to molecular motion, bulk flow and infrared radiation. The parallel mechanism allows us to treat different mechanisms separately, but under the assumption that there is no interaction between different mechanisms.

Analogy to Electrical Circuits: Many transport mechanisms are analog to the flow of current in electrical circuits.
Current flow: Ohm's Law;
Heat transfer: Fourier's Law;
Mass transfer: Fick's Law.
(Heat transfer due to radiation is described by Stephan-Boltzman's Law, i.e., the rate of heat transfer is proportional to the difference of the fourth power of the temperature.)

Film Model and Boundary Layer Approximation: The film model uses the assumption that in the small region adjacent to the wall, the variation is much larger than that at the center. Thus the concept of thin film at the wall is developed and accounts for all the variations. The central cylinder is considered with no variation.
But the boundary layer model allows the layer thickness to vary with time and distance. It is more likely an approximation to the reality, the experimental results.

Order of magnitude Approximation: If the ratio of the contribution from one mechanism and that from others is high enough, then the other mechanisms can be neglected to reduce the complexity.

Quasi-Steady State: The assumption for unsteady-state problem, that during a small time interval, the process is at steady-state is known as "quasi-steady state".

Finite and infinite dimensions: Many mathematical equations approach certain value when one or some of its parameters goes to infinity or zero, which is not possible in physical experiments. Thus, it can be assumed that when the parameter value is large or small enough, it is close to infinity or zero.

References:
Verma, Ashok Kumar. 2014. Process Modelling and Simulation in Chemical, Biochemical and Environmental Engineering. CRC Press.