Bertram K. C. Chan’s scientific contributions

Several numerical examples are chosen to illustrate and highlight the application of the R Program for numerical computations in Simultaneous Mass Transfer and Chemical Reactions in typical transport phenomena in Chemical Engineering Science. In the field of science and engineering, advection is the transport of a substance by bulk motion . The properties of that substance are carried with it. The term advection is sometimes considered as a synonym for convection , but technically, convection covers the sum of transport both by diffusion and by advection. R‐package ReacTran contains routines that enable the development of reactive transport models in aquatic systems, porous media, and even idealized organisms. The geometry of the model domain is either one‐dimensional, two‐dimensional, or three‐dimensional.

In partial differential equations (PDE), the function has several independent variables and may also contain their partial derivatives. A first step to solve PDE is to discretize one or more of the independent variables. Functions tran.1D, tran.2D, and tran.3D from the R package ReacTran implement finite difference approximations of the general diffusive–advective transport equation. In a first application, the model is solved to steady state , which retrieves the condition where the concentrations are invariant. In R, steady‐state conditions may be estimated using functions from the package rootSolve, which implement among others a Newton–Raphson algorithm. For one‐dimensional models, steady.1D should be used. The advection equation is not simple to solve numerically: the system is a hyperbolic PDE and interest typically centers on discontinuous “shock” solutions, which are difficult for numerical schemes to solve.

Hatch and Pigford studied the process of simultaneous gas absorption accompanied by chemical reaction, using the system CO 2 –NH 3 –Water. These two gases were mixed and brought into contact with a smooth laminar jet of water. A large number of highly significant industrial systems consist of simultaneous mass transfer operations and chemical reactions, some of these are: absorption of CS 2 in aqueous amine solutions for the manufacture of dithiocarbamates; absorption of O 2 in aqueous solutions of CuCl for the conversion to CuCl 2 and copper oxychloride; and so on. Fick first described the molecular diffusion in an isothermal, and isobaric binary system of components A and B. Mass transfer occurs by molecular diffusion through a fluid layer at phase boundary. Beyond this film, concentration is homogeneous.

Several numerical examples are chosen to illustrate and highlight the application of the R Program for numerical computations in Simultaneous Mass Transfer and Chemical Reactions in typical transport phenomena in Chemical Engineering Science. In the field of science and engineering, advection is the transport of a substance by bulk motion . The properties of that substance are carried with it. The term advection is sometimes considered as a synonym for convection , but technically, convection covers the sum of transport both by diffusion and by advection. The advection equation is the partial differential equation that governs the motion of a conserved scalar field as it is advected by a known velocity vector field. R‐package ReacTran contains routines that enable the development of reactive transport models in aquatic systems, porous media, and even idealized organisms.

Data are facts or figures from which conclusions can be drawn. There are several steps involved in turning data into information, and these steps are known as data processing. This chapter describes data processing and how computers perform these steps efficiently and effectively. It will be indicated that many of these processing activities may be undertaken using R programming, or performed in an R environment with the aid of available R packages – where R functions and datasets are stored. Quality control is a regulatory procedure through which one may measure quality, with pre‐set standards, and then act on any differences. To learn to do statistical analysis and computations, one may start by considering the R programming language as a simple calculator! In epidemiology, after preparing the collected datasets to undertake biostatistical analysis, the first step is to enter the datasets into the R environment.

In many biochemical, biomedical, and chemical processes, in both the chemical industry and in physiological systems, including environmental sciences, mass transfer, accompanied by reversible, complex biochemical, or in chemical reactions in gas–liquid systems, is frequently found. It is well known that many biochemical and chemical processes involve mass transfer of one or more species from the gas phase into the liquid phase. In typical industrial absorption processes, one should consider the absorption of gases into liquids which are agitated such that the dissolved gas is transported from the surface to the interior by convective motions. Consider the absorption of gases into liquids which are in a state of agitation such that the dissolved gases are transported from the surface to the interior by agitated convective motion. In physical absorption, the gas dissolves in the liquid without reacting.