Mathcad Prime Research Articles

Using process simulators in Chemical Engineering education: Is it possible to minimize the “black box” effect?

AbstractSimulators are instrumental to engineers and scientists, in general, and to chemical engineers,more specifically, which enable the optimization and analysis of alternative solutions in a time‐efficient and cost‐effective way. Thus, their integration into Chemical Engineering studies has gained traction over the years in supporting traditional lectures or as the sole tool for knowledge transmission. However, despite their proven benefits in Higher Education, limitations exist, as the application of the tool may result in deficient learning. In fact, the algorithms and design equations that are used to transform inputs into results are not identifiable by the students, thereby instilling a “superficial understanding” of the problem. Thus, the objective of this paper is to provide some guidelines through three simple case studies, which may help minimize the so‐called “black box” effect. Two different state‐of‐the‐art computational tools were used in parallel. Aspen One simulations provided the reference point, which was used by the students to verify the process models built by them with Mathcad Prime. A survey taken by the students then allowed conclusions to be made, which concurred that the experience had been very successful.

Well washing process modelling

The study of the influence of technical and technological factors on the efficiency of well flushing was car-ried out under experimental conditions. The analysis of existing experimental installations is performed with the help of which it is possible to assess the influence of technical and technological factors on the process of well flushing. The laboratory facility for modeling the well flushing process was designed using similarity criteria ob-tained in accordance with the basic provisions of the theory of dimensions. The developed installation allows you to model and study the influence of many factors on the well flushing process due to its compact overall dimen-sions and ease of conducting experiments, namely: the eccentric placement of the drill string; the type of flushing fluid (rheological properties); the size of the rock fraction; the frequency of pulsations to create a pulsating char-acter of the fluid movement; rotation of the drill string; longitudinal movement of the drill string. The main factors of influence and the range of their changes on the efficiency of sludge transportation are determined on the basis of previous studies. An experiment plan is constructed to study the significance of factors on the quality of sludge removal from the well bore using the «Taguchi» plan. Data processing was performed in the software «Mathcad Prime». Variations in factors lead to an improvement in the quality of well flushing, by reducing the area of sludge settling in the wellbore. The flow rate of the washing liquid has the most positive effect on the removal of sludge. The size of the rock fraction and the longitudinal movement of the drill string has the least impact. Pulsa-tion of the washing liquid has a significant impact on the quality of sludge removal, which is a significant and interesting factor from the point of view of further scientific research.

On the integration of Mathcad capabilities into a mass transfer operations course in Chemical Engineering studies

AbstractMass transfer unit operations are of extreme importance to chemical engineers. However, they involve complex and tedious calculations which provoke real fear among the students who end up failing and, sometimes, quitting. The exclusive use of hand calculations in engineering studies is discouraging, old‐fashioned, and a primary source of mistakes. The integration of software packages very much facilitates the calculations and engages the students. Computing skills using the latest technologies are prized by employers and can be critical in a recruitment process. This paper reports an example of the unique capabilities of the Mathcad software for the implementation of more appealing teaching strategies. Unknowns and equations are easily associated with specific process variables and engineering phenomena. Thus, if used conveniently, Mathcad Prime can improve the students’ predisposition to learn.

Determination of the hardness of the weld metal and the metal of the heat affected zone (HAZ) during low-frequency oscillations of the weld pool

Work rele vance. The using of mechanical harmonic oscillations of welding pool or tool are inexpensive and quite simple procedure formation desirable degree of dispersion structure it means weld metal strength. Possibility of oscillations differently applied relative of the surfacing (welding) process axis lets welding seam or surfacing bead formation with certain anizotropy of mechanical properties in given direction.Many works have dedicated of researches of microstructure formation by conditions of periodic action on weld melt. However, the most part of it are devoted mostly researching to influence oscillations with frequency much superior value of 5 Hz and amplitude value range from some microns to 2–3 mm.Purpose of work is getting quantity dependencies which defining hardness value of weld metal and metal of HAZ as a function of technological and oscillations modes parameters.Research methods. For researchers the samples have had prepared and polished to #8 Mirror Finish by ISO (ГОСТ 25593 – 83). The surfacing process in CO2 protection environment had has carried out by alloy wire named G3Si1 by EN 13479 ISO 143341 (ТУ У 322-4-392-96) which diameter1.2 mm. Base metal was common quality carbon steel type Е 235-С by ISO 630:1995, ISO 1052:1982 (ДСТУ 2651:2005). Measurement of hardness (by Vickers) had carried out on hardness tester named LECO M-400 under indenter load1 kgby ISO 6507-1:2007 (ДСТУ ISO 6507-1:2007). Research resultants had treatment by regression analysis methods with application of analytics software package STATISTICA 12 and engineering math software PTC Mathcad Prime 3.1.Results. Regressive models of hardness value as function magnitudes arc current, the surfacing process velocity, amplitude and frequency oscillations have received. Contour plots of depend of hardness value from amplitude and frequency magnitudes were created. Variant of predict of the receiving maximum value hardness weld metal and metal of HAZ at arc current125 Aand the surfacing process speed 14 m/h are presented.Scientific novelty. The experiments were carried out with different amplitude and frequency values which were given through programming step motor.Empirical depends of influence of technological and oscillation modes parameters of certain range on weld metal hardness and metal HAZ hardness values are created.Practical value. An increase possibility of hardness values of weld metal and metal of HAZ due to use weld pool oscillations with frequency value range 2.5–4.5 Hz and amplitude value range 3–7 mm was proven. The magnitudes of amplitude and frequency permitting receives maximum hardness values at optimal values of arc current and the surfacing velocity were obtained.

Mastery of the foundations of mathematical modeling in a technical university

One of the key components of engineering education is the possession of a basic tool for obtaining new fundamental knowledge, scientific research, and designing technical systems – mathematical modeling. The use of tools and capabilities of the engineering application PTC Mathcad Prime 3.1 in mastering the basics of the scientific method of mathematical modeling is a necessary component of the educational process, largely determining its effectiveness, providing a significant increase in students' motivated interest in research work, stimulating their creative self-realization.

SOME FEATURES OF PROGRAMMING IN MATHCAD PRIME

Some distinctive features of programming in the system of computer mathematics Mathcad Prime are considered in the article. Examples of various programs that contribute to understanding the essence of these features are given.

THREE "GREEDY" ALGORITHMS

The article considers three logistic tasks (transportation problem, traveling salesman problem, pursuit problem), by the example of which the essence and features of “greedy” algorithms are shown. For the frst time, a solution was given to a transportation problem in the Mathcad Prime environment using the matrix method using units of measure. Two new applications of the traveling salesman problem have been proposed. The difference scheme for solving the pursuit problem is described.

Mathematical Model of Vacuum Evaporation Using Apparatus with Mechanical Water Vapor Recompression

This article presents mathematical model of evaporation of aqueous solutions of mineral salts on apparatus with mechanical recompression of water vapor and process intensification upon vacuuming. The developed mathematical model is an engineering prediction where all calculations are associated with technological flowchart of evaporator. Predictions according to the mathematical model for evaporator are exemplified for the case of 2% aqueous solution of sodium chloride evaporated to 15 wt % at distillation capacity of 30 kg/h. Engineering predictions were performed consecutively in 5 stages including material calculation of evaporator; estimation of evaporator temperature mode; hydrodynamic and thermal predictions; estimation of heat transfer coefficient. The developed mathematical model was applied to stationary direct flow evaporation using Mathcad Prime software. In order to perform high quality analysis and to verify adequacy of the mathematical model, 12 criteria were selected characterizing evaporation efficiency in evaporator. Advantages of the developed mathematical model were highlighted and substantiated, practical recommendations on its application were given upon efficiency estimation of vacuum evaporation with mechanical recompression of water vapor.

Method of calculation of static regime of rectification columns for optimization of constructive and technological parameters on MathCAD Prime 3.0.

Method of calculation of static regime of rectification columns for optimization of constructive and technological parameters on MathCAD Prime 3.0.

КОМПЬЮТЕРНОЕ ДОКАЗАТЕЛЬСТВО ГИПОТЕЗЫ О ЦЕНТРОИДАХ

This article provides a proof of the "hypothesis about of centroids", which is given in the "Experimental validation of hypotheses in GeoGebra and published in the current issue of the "Сhebyshevskiy sbornik". This hypothesis is formulated as follows: "Let are a non-degenerate triangle from each vertex held the median. Then the original triangle is split into six triangles without common interior points so that their centroids lie on the same ellipse. The proof of the hypothesis is based on symbolic computation, implemented in ve packages of computer mathematics GeoGebra, Mathcad Prime, Maxima, Maple and Mathematica [2-8]. The use of dierent systems of symbolic computation for solving a problem allows to obtain visual material for comparative assessment of these systems. In the nal part of the article oers to consider another statement: "the hypothesis about of circumcenters". It is formulated so: "Let the three cevian intersect inside acute-angled triangle in the circumcenter. Then the original triangle is split into six triangles without common interior points so that their circumcenters lie on the same ellipse. This hypothesis was proposed and conrmed experimentally, using a dynamic model constructed in GeoGebra.

Mathematical simulation of rocket engine with a composite sectional charge

Due to the need to improve the appearance of the solid-propellant rocket engine, we stated the task of developing the methods allowing us to calculate internal ballistics performance of a composite sectional charge of solid propellant. These methods were implemented on a computer in the mathematical package MathCAD Prime 3.0, it has accuracy that is sufficient for technical evaluation of the rocket engine using solid propellant with the sectional charge.

Hydrogen Production From Palmitic Acid Through Autothermal Reforming: Thermodynamic Analysis

This work studies thermodynamic analysis of hydrogen production via autothermal reforming of palmitic acid. A Gibbs free energy minimization method was applied to analyze thermodynamic of syngas production via oxidative reforming of palmitic acid. Equilibrium compositions were estimated at temperature of 800°C, 900°C and 1000°C under atmospheric pressure. Optimal operating temperature and molar feed ratios of; steam to palmitic acid (S/C) and oxygen to palmitic acid (O/C) ranging from 0.5 to 4; were determined. The PTC Mathcad Prime 2.0 is used to calculate enthalpy, entropy and Gibbs free energy. Aspen Plus program was applied for calculation of product yields and heat duty. Maximum yield of 17.88 mole/molePalmitic with S/C of 4 and O/C of 0.5 can be achieved at 1000°C and yield were 7.75 mole/molePalmitic with S/C of 4 and O/C of 4. Production of hydrogen and carbon monoxide increased with increasing temperatures.

“Cloud” functions and templates of engineering calculations for nuclear power plants

The article deals with an important problem of setting up computeraided design calculations of various circuit configurations and power equipment carried out using the templates and standard computer programs available in the Internet. Information about the developed Internetbased technology for carrying out such calculations using the templates accessible in the Mathcad Prime software package is given. The technology is considered taking as an example the solution of two problems relating to the field of nuclear power engineering.