Improved method to converge pressure equalization steps when simulating a cyclic adsorption process

Pressure swing adsorption (PSA) is a mature technique for biogas upgrading. However, it constitutes the most expensive step to obtain fuel-quality bio-methane, particularly in small-scale units. To reduce the cost of upgrading in small-scale plants, we have evaluated different PSA cycles with two and three columns (less than commercial units). An equalization tank was used to perform one asynchronous pressure equalization step and keep the process fed continuous even in the case of using two columns. The effect of the purge step was also evaluated. Carbon molecular sieve was used as adsorbent. The feed composition was 40% CO2/60% CH4 and pressure swinging between 5 and 0.1 bar in the adsorption and blowdown steps, respectively. Four performance indicators (methane purity and recovery, productivity and energy consumption) were used to evaluate the PSA cycles. The mathematical model could predict the experimental PSA performance. Bio-methane with purity higher than 97.5% (specification) and recovery higher than 90% was obtained experimentally using a PSA with two columns and an equalization tank. When a third column is used (implementing an additional pressure equalization), the recovery increases in approx. 4% showing the importance of pressure equalization to reduce the methane slip.

Improved ODE integrator and mass transfer approach for simulating a cyclic adsorption process

This paper presents research into the mechanism involved in the cooling of a plastic thermoformed part after it is formed onto a mold. The intent of this research is to develop a simple and practical mathematical model useful to small thermoforming companies without a large engineering staff that describes the transient heat conduction of the cooling process. The model should also be able to predict the temperature distribution within the thickness of the part during the cooling. This mathematical model, which began with simplified boundary conditions, was then compared to experimental cooling data and modified accordingly to properly fit that data and the actual boundary conditions of the cooling part. The research began by examining the cooling of a series of high molecular weight polyethylene thermoformed side panels for plastic, portable restrooms. These parts where chosen for this preliminary research because of their very simple, flat geometric shape that lends them to being modeled as simple plane walls in transient conduction. The shape of the parts also leads to near constant thickness over the vast majority of the part. Using the model of a plane wall in transient conduction, the governing partial differential equation was solved for two possible boundary conditions on the mold side of the part: constant imposed surface temperature and constant imposed surface heat flux. These two solutions were then compared to experimental data gathered on the temperature profile of the free surface of the part during a production environment. After the experimental data and simple mathematical models were compared the necessary changes to the assumed mold side boundary condition was made to adjust the mathematical model to the experimental data. The research found that the use of simple boundary conditions at the mold side of the part is incorrect. Neither the constant imposed surface temperature nor the imposed surface heat flux boundary conditions fit the data. Initial analysis of the experimental data showed that a time of 30 seconds into the cooling cycle an apparent change in that boundary condition occurs for the part and mold used to gather the data. Further analysis showed that the boundary condition begins as a constant surface heat flux and then changes to an imposed surface temperature that decays exponentially to the initial mold surface temperature. Using this boundary condition, a revised mathematical was developed that match the experimental data very well. The error of the new model compared to the experimental was less than 1.5% for all times during the cooling cycle.

Approximation of a PSA process based on an equivalent continuous countercurrent flow process: Blow-up and blow-down representation

Mathematical spacer grid models for two phase flow

In this paper, an improved mathematical model is presented for the bending analysis of doubly curved functionally graded material (FGM) sandwich rhombic conoids. The mathematical model includes expansion of Taylor\'s series up to the third degree in thickness coordinate and normal curvatures in in-plane displacement fields. The condition of zero-transverse shear strain at upper and lower surface of rhombic conoids is implemented in the present model. The newly introduced feature in the present mathematical model is the simultaneous inclusion of normal curvatures in deformation field and twist curvature in strain-displacement equations. This unique introduction permits the new 2D mathematical model to solve problems of moderately thick and deep doubly curved FGM sandwich rhombic conoids. The distinguishing feature of present shell from the other shells is that maximum transverse deflection does not occur at its center. The proposed new mathematical model is implemented in finite element code written in FORTRAN. The obtained numerical results are compared with the results available in the literature. Once validated, the current model was employed to solve numerous bending problems by varying different parameters like volume fraction indices, skew angles, boundary conditions, thickness scheme, and several geometric parameters.

High-purity (>99.5%) O2 production from air with silver-exchanged titanosilicates (Ag-ETS-10) using multiple single- and dual-stage vacuum swing adsorption (VSA) cycle configurations was investigated through process simulation, and optimization. Model predictions for the Skarstrom cycle were validated through experiments and an O2 purity of 98.3 ± 0.5% with a corresponding recovery of 10.6% was achieved. Oxygen purity-recovery Pareto fronts for the Skarstrom cycle and 6-step cycle with pressure equalization (PE) and heavy product pressurization (HPP) with dry air as the feed were obtained. The optimization predicted 82.0% O2 recovery with a product purity of 99.5% for a 6-step cycle with PE and HPP and dry air feed stream. The effect of nitrogen content in the feed on the performance indicators was also studied. Operating conditions for various cycle configurations were optimized through nondominated sorting genetic algorithm technique to achieve low total energy consumption (592.4 kWh/tonne O2) and high ...

Carbon dioxide removal from flue gas with a two-stage vacuum pressure swing adsorption (VPSA) process, which uses activated carbon (AC) beads as the adsorbent, was investigated both theoretically and experimentally. First, single-column VPSA experiments were studied for CO2/N2 separation with high CO2 feed concentration. Then, a two-stage VPSA process composed two columns for each stage was designed, and the effects of different parameters were investigated. The first-stage VPSA unit operates with a four-step Skarstrom cycle, which includes feed pressurization, adsorption, blowdown, and counter-current purge with N2. For the second-stage VPSA process, a cycle with feed pressurization, adsorption, pressure equalization, blowdown and pressure equalization was employed. With the proposed two-stage VPSA process, a CO2 purity of 95.3% was obtained with 74.4% recovery. The total specific power consumption of the two-stage VPSA process is 723.6 kJ/kg-CO2, while the unit productivity is 0.85 mol-CO2/kg·h.

A mathematical model for simulation of a water table profile between two parallel subsurface drains using fractional derivatives

An equilibrium model for pressure swing adsorption (PSA) process with equalization step is developed by using the method of characteristics. The concentration profiles at the cyclic steady state are obtained by tracking the movement of wave fronts derived from the characteristic lines during the transient cycles. The results of this model compare quite well with the conventional finite difference method, but with less computational effort. Multiple waves in PSA processes are clearly demonstrated by this model. Effects of equalization step on PSA process performances are also analyzed using this model.

Bimetals are in many ways substitutes for scarce metals, while they represent an independent group of materials necessary for the creation of new machines, devices and other various products. The increasing volume of production of bimetals and products made from them requires an increase in their operational characteristics and, accordingly, an increase in the quality of finished products. One of the difficult technological tasks is the connection of aluminum and its alloys with steels of various classes, since there are many problems associated with the quality of the connection of me¬tals with different properties. To improve the reliability and durability of machines and other pro¬ducts made of bimetals, it is necessary to carry out continuous quality control, and the most effective methods are non-destructive testing. Quite promising in terms of simplicity and accessibility is the method of active thermal control, in which the investigated product is subjected to pulsed thermal action by means of a source of thermal loading. The amplitude, shape and time variation of temperature signals serve as informative parameters that allow an operator or an automated system to detect certain defects and evaluate their parameters. With all the availability of pulsed thermal control, the most difficult component is associated with specialized computer programs for processing experimental data and determining the parameters of a delamination defect. The aim of the study is to create a computer model of the thermal state of a bimetallic plate in the presence of an air bubble between the layers and, through computer simulation, to determine the size of defects during active pulse thermal non-destructive testing of steel-aluminum plates. Materials and methods. When performing the work, the methods of mathematical and computer modeling were used. The created software using the development tools of the MATLAB package was based on known methods for obtaining an approximate solution to a boundary value problem on a computer using the finite difference method. Results. A mathematical model has been developed, an algorithm for solving a boundary value problem, and a computer program has been created that allows simulating a pulse thermal control to determine the parameters of a delamination defect in a bimetallic plate. Conclusion. It was found that it is more efficient to measure the temperature difference from the side where the defect is located and the multilayer plate is heated. Heating the plates from the side opposite to the defect and their further cooling showed significantly lower efficiency in terms of obtaining a useful temperature signal. It is shown that in the presence of a defect, the greater the loading heat flux and the defect size, the greater the value of the useful signal determined by the temperature difference on the measured surface.

One of the fundamental problems in simulating the motion of sharp interfaces between immiscible fluids is a description of the transition that occurs when the interfaces merge and reconnect. It is well known that classical methods involving sharp interfaces fail to describe this type of phenomena. Following some previous work in this area, we suggest a physically motivated regularization of the Euler equations which allows topological transitions to occur smoothly. In this model, the sharp interface is replaced by a narrow transition layer across which the fluids may mix. The model describes a flow of a binary mixture, and the internal structure of the interface is determined by both diffusion and motion. An advantage of our regularization is that it automatically yields a continuous description of surface tension, which can play an important role in topological transitions. An additional scalar field is introduced to describe the concentration of one of the fluid components and the resulting system of equations couples the Euler (or Navier–Stokes) and the Cahn–Hilliard equations. The model takes into account weak non–locality (dispersion) associated with an internal length scale and localized dissipation due to mixing. The non–locality introduces a dimensional surface energy; dissipation is added to handle the loss of regularity of solutions to the sharp interface equations and to provide a mechanism for topological changes. In particular, we study a non–trivial limit when both components are incompressible, the pressure is kinematic but the velocity field is non–solenoidal (quasi–incompressibility). To demonstrate the effects of quasi–incompressibility, we analyse the linear stage of spinodal decomposition in one dimension. We show that when the densities of the fluids are not perfectly matched, the evolution of the concentration field causes fluid motion even if the fluids are inviscid. In the limit of infinitely thin and well–separated interfacial layers, an appropriately scaled quasi–incompressible Euler–Cahn–Hilliard system converges to the classical sharp interface model. In order to investigate the behaviour of the model outside the range of parameters where the sharp interface approximation is sufficient, we consider a simple example of a change of topology and show that the model permits the transition to occur without an associated singularity.

The mass transfer zone in nitrogen PSA columns

In the theory of analysis and synthesis of technical systems, mathematical modelling and optimization of multilayer systems containing sources of physical fields occupy an important place. This is due to the fact that their state is described by means of boundary value problems with multidimensional differential equations. To solve the boundary value problems and implement the process of optimizing the technical parameters of the modelled systems, it is necessary to conduct interdisciplinary studies of computational and applied optimization mathematical models. Fulfilment of the conditions for the existence of a single solution to boundary value problems by default is possible only when the object of study is a single-layer material under the action of load sources. If it is necessary to calculate and optimize the technical parameters of a multilayer material subjected to load sources, then it is impossible to immediately guarantee the correctness of the calculated and applied optimization mathematical models, since it is necessary to obtain the conditions for the existence and uniqueness of solutions to boundary value problems with systems of differential equations. Maximizing the technical parameters of load sources and averaging the characteristics of material layers will lead to approximate values of the objective function and technical parameters of the modelled system, which leads to irrational consumption of energy and heat resources and uncontrolled losses, and useless losses of the test material in the technological process. The article presents the conditions for the correctness of multipoint boundary value problems with multidimensional differential equations describing the state of a multilayer material under thermal action. It is advisable to use these studies to substantiate the correctness of other technical and biotechnological systems, which will increase the accuracy of the implementation of applied optimization problems of economic and mathematical modelling.

The cyclic scheduling problem modeled in terms of Cyclic Concurrent Process Systems is considered. The problem can be seen as a kind of Diophantine problem, hence its solvability, i.e. schedulability, plays a pivotal role in many supply-chain problems. In contradiction to the traditionally offered solutions the approach proposed allows one to take into account such behavioral features as transient periods and deadlocks occurrence. So, the contribution’s aim is the modeling framework enabling an evaluation of cyclic scheduling problems solvability, i.e., the declarative approach to reachability problems regarding cyclic steady states determination as well as conditions guaranteeing assumed performance of multimodal processes executed within a concurrent cyclic processes environment.