Conceptual Mathematical Model Research Articles

Development of a Model for Benchmarking of Energy Consumption and CO2 Emission in Cold-end of Olefin Plant

Benchmarking of different process industries, such as petrochemical processes, with respect to energy consumption and CO2 emission, is a fundamental measure while implementing a comprehensive energy plan at the national level. Olefin Plant is one of the process industries that is highly energy intensive and needs to be addressed when looking at petrochemical complexes. In this research, olefin cold-end, which requires heat removal from the process via refrigeration at very low temperatures, has been studied. In sub-ambient processes, shaft work requirement is a dominant factor that causes very high energy cost. A conceptual mathematical model has been developed to facilitate energy benchmarking in olefin cold-end processes. A conceptual model using Pinch analysis is developed to predict energy consumption in refrigeration cycles. To develop the model, the cold-end from five Iranian olefin plants were studied and the effect of different factors such as technology, capacity, feedstock and product types were investigated. The gap between the current level of energy consumption and best practice technology using Pinch analysis was determined. The comparison showed an average potential of 17.7 % reduction in shaft work requirement. Having developed the aforementioned model, there is no need to undertake a full retrofit study for olefin cold-end processes anymore because the model can easily be applied to similar processes and the scope for improvement can be identified. Both time and money associated with extra engineering work can be saved. Application of this model to all olefin’s cold-end processes in Iran showed that there would be 65,838 kW/h potential for energy consumption reduction, which is equivalent to about 382,519 t of CO2 emissions.

The Strategic Decision-Making as a Complex Adaptive System: A Conceptual Scientific Model

A company in a competitive environment that wishes to be a benchmark in the business world needs a management model that enables the development of systemic thinking on the part of its executives. In addition to systemic thinking, it is also necessary that executives (i) are aware that the decision-making processes should be shared, (ii) have bounded rationality, and (iii) exert political influence according to their preferences. In this context, the aim of this paper is to describe a conceptual scientific model for strategic decision-making from rules originating from Complex Adaptive Systems and the following mathematical techniques: Analytic Network Process and Linear Programming. This applied and quantitative study is a theoretical essay developed from an integrative review of the aforementioned concepts and techniques, resulting in the proposition of a scientific and conceptual mathematical model that can be applied to a wide variety of business environments. The results obtained from a hypothetical example (Strategic Operation Management Decision) show that the model is able to rank a set of strategic decisions in the environment of most companies and generate information to minimize the negative effects of shared decisions.

Mechanisms of Formation of Natural Hydrogen Reservoirs in Thermal Aquifers - Impact of Bacteria and Gas Bubble Dynamics

Underground hydrogen reservoirs, whose existence has been confirmed recently by geologists all over the world, represent a new source of renewable energy. Hydrogen is formed as the product of reaction of serpentinization between ferromagnesian minerals of the Mantle and water in the offshore zones of subduction or in continental zones at considerable depth beneath hydrothermal aquifers. Initially dissolved in water, hydrogen can create free gas bubbles when the local concentration of H2 dissolved in water exceeds the equilibrium value. The bubbles raise up and create the gas cap of free hydrogen. This process is significantly influenced by methanogen bacteria inhibiting in aquifers and consuming hydrogen for their metabolism. The reactions initiated by bacteria leads to the appearance of other volatile components as methane. The dimension, the form of the gas cap and the concentration of hydrogen and methane determine the efficiency of gas production and the energy potential of the reservoir. In the present paper we develop the conceptual mathematical model of gas cap formation in hydrogen reservoir. The bacterial activity is described by the equation of population dynamics with specific kinetic functions obtained by the authors by treating experimental data. The formation of free gas is modelled in terms of the formation of oversaturated nuclei, their growth and simultaneous motion of isolated bubbles. As far as the bubbles grow, they stick together and create continuous free gas. Thus, the hydrogen motion consists of two stages: (i) the motion of isolated bubbles, controlled by the equations of ganglion dynamics; and (ii) the motion of continuous gas through water, governed by Darcy’s law. The bubble growth is ensured by the mass exchange with hydrogen dissolved in water, which involves a non-equilibrium in the average hydrogen concentrations. Such a problem of hydrogen raising is solved analytically in simplified situation without bacteria. The problem can be reduced to a system of nonlinear hyperbolic equations, which has either continuous or discontinuous solutions (shock waves) depending on the degree of the non-equilibrium. Multiples deformations of the shocks under gas raising are described. The impact of bacteria is studied numerically by using the open source Basilisk (developed by D’Alembert Institute). We have revealed non trivial scenarios of the appearance of piece-wise constant traveling waves, or auto-oscillations caused by the nonlinear population dynamics. The result obtained enables us to give estimation to the characteristic time of gas cap formation and the evolution of its composition in time.

Why is license plate rationing not a good transport policy?

ABSTRACTLicense plate rationing (LPR) has become an increasingly popular travel demand management strategy in developing countries. This paper aims to show that such a trend is concerning because of the inherent flaws of the policy. Using a conceptual mathematical model that explicitly considers mode choice and user heterogeneity, we prove that LPR is not a first-best policy, even though it can help reduce congestion under certain conditions. There is however no guarantee that LPR can even be a second-best policy: it may never improve the system cost, regardless of its configuration. More important, we show when it does improve the system cost, LPR makes it impossible to maximize the system efficiency by using other complementary policies. Our analysis also reveals unintended consequences of the policy. Notably, a more restrictive LPR could actually make congestion worse when imposed on a rich population that can bypass the policy through acquiring additional cars. Finally, numerical results confirm that LPR is likely regressive in many (if not most) practical cases. Specifically, the wealthier users tend to benefit more from LPR, especially when they can buy additional cars. The regressivity of the policy may be corrected only when LPR is highly restrictive and additional vehicle acquisition is tightly controlled. However, such a correction may only be achieved at the expense of significant welfare losses.

Emulsion flooding for enhanced oil recovery: Filtration model and numerical simulation

Abstract The present paper discusses emulsion flooding laboratory experiments in porous media with the application of the Filtration Theory, and a series of simulation experiments that showed the potential use of emulsions as EOR technologies in Mexican mature fields with approximately 20° API gravity oil and high water cut production. This method is based on the hydrophobization of sandstone rocks and the reconfiguration of water flow patterns, by means of O/W emulsion injections, improving and increasing the oil recovery. Emulsion flooding laboratory experimental tests were performed with Ottawa sand and Berea sandstones. During the oil recovery process, the additional oil recovery was above 25%. The dispersed phase of the emulsion is retained at the pore throats, leading to porous medium impediments described by two mechanisms: (a) pore blockage by size exclusion, and (b) drop retention due to interactions between droplets and pore walls. Both mechanisms cause irreversible permeability reduction. In order to know the general effect on this process, a filtration model describing emulsion flow through porous media was used to obtain filtration parameters. In our work, we describe the use of a well-known mathematical model, which consists of a differential equation system based on the Filtration Theory and a modified Darcy equation that is characterized by three parameters: filter coefficient, flow redistribution and local flow restriction factors. The EOR simulation model by emulsion flooding was created using STARS™ by CMG. The conceptual mathematical model and fitting of the experimental results concerning the oil displacement by water and additional oil displaced by the emulsion show that the wettability change caused by the emulsion is the main recovery mechanism.

Conceptual Model in the Formal Basis of Hierarchical Systems for Mechatronic Design

Hierarchical Systems (HSs) technology is presented to define a conceptual model of an exemplary mechatronic object. The conceptual model suggested contains connected formal descriptions of the designed object structure, its aggregated dynamic representation in its environment, and the environment model. All the descriptions are connected by the coordinator, which performs the design and control tasks on its selection, learning, and self-organization strata. Coherence of the given conceptual model and traditional mathematical models is revealed. It allows easy transfer from the conceptual to the detailed design phase. A conceptual formal model of the design system in the form of the HS coordinator is presented.

Experimental study and first thermodynamic law analysis of a solar water heater system

Abstract The performance of a pilot scale flat plate solar water heater system is investigated theoretically and experimentally. The effect of the operating conditions and characteristic factors of the collector on the system efficiency is studied. A conceptual mathematical model is developed in order to analyze the system behavior in different operating conditions by considering the physical and constructive aspects of the system. The accuracy of the model result is estimated by comparing the model results with the existing experimental data. The highest obtained system thermal efficiency is 45%, and the optimum local values for surface azimuth and tilt angles are obtained at 180 degrees from north and 33 degrees, respectively, for the constructed solar water heater in Isfahan, Iran, with the local latitude of 32 . 6333 ∘ $32.6333^\circ $ N.

Operational goal setting in anthropocentric objects from the viewpoint of the conceptual model called Etap: I. Structures of algorithms for the support of crew decision-making

From the viewpoint of control of modern complex anthropocentric objects, such objects can be adequately described by the conceptual mathematical model called Etap. This model formalizes both the domain of operation of the anthropocentric objects and the set of tasks to be carried out on the object. Operational goal setting is the first phase of the control of an anthropocentric object. In terms of the Etap model, operational goal setting is the change in the typical situation of the current session of the object operation. The proposed operational goal setting algorithm uses a priori information (a specified sequence of typical situations that ensures the accomplishment of the current session of the object operation, a priori specified set of threats that can emerge in the course of the operation session, a knowledge matrix with the terms of linguistic variables for each pair typical situation-threat) and the current data (obtained from the object's crew and onboard measurement system). For the description of the operational goal setting task, the following concepts are used: the crew circumspection, the crew situational awareness, and the crew situational confidence.

Comparison between two different conceptual mathematical models in prediction of direct runoff hydrographs from a small watershed

In the present study, two mathematical models namely (i) Lag and route model and (ii) Muskingum model which are based on unit-step and transfer functions approach were developed for runoff prediction from Shenda park watershed treating the watershed as lumped, linear and time-invariant system. The hydrological data of the study watershed were collected from zonal station of NationalAgricultural Research Project, Shenda Park, Kolhapur (M.S.) for the years 2000 to 2008. Out of twelve single storm events, nine storm events were included in the analysis for parameters estimation and remaining three storm events were considered for prediction purposes. The model parameters, viz. , lag time and (,) and storage co-efficient (K) of Lag and route model were estimated by the methods of cumulants (Singh, 1988) and moments (Nash, 1957) whereas the model parameter storage constant (K) for Muskingum model was estimated by using method suggested by Jawed (1973). Performance evaluation of these two developed model in determining direct runoff hydrograph ordinates were evaluated using various statistical indices such as correlation co-efficient (R), special correlation co-efficient (Rs.), co-efficient of efficiency (CE) and root mean square error (RMSE). The results showed that both the developed model can be used for prediction of the direct run off hydrograph from the study watershed, however, direct runoff hydrographs obtained through Muskingun models are much closer to actual observed direct runoff hydrograph than that of Lag and route model.

Biological and chemical control in copper bioleaching processes: When inoculation would be of any benefit?

Bioleaching of secondary and low-grade copper ores in heaps and dumps today is a well-established technology. However, there is still a strong need to improve the copper leaching rates and recoveries currently reached at plant level in order to improve the economics and broaden the range of application of this technology. In this context, it is important to be able to define the factors which are controlling the rate of copper leaching in different process configurations and at different stages during the operation. This work presents a conceptual mathematical model which can help to define when a bioleaching process is controlled by biological, chemical, or transport phenomena. The model is based on the kinetic analysis of the electrochemical aspects of the microbiological and chemical sub-processes involved in bioleaching. It will facilitate collaboration among biologists, metallurgists and process engineers in the search for innovative developments in the field.

Mathematical modeling of colloid and virus cotransport in porous media: Application to experimental data

A conceptual mathematical model was developed to describe the simultaneous transport (cotransport) of viruses and colloids in three-dimensional, water saturated, homogeneous porous media with uniform flow. The model accounts for the migration of individual virus and colloid particles as well as viruses attached onto colloids. Viruses can be suspended in the aqueous phase, attached onto suspended colloids and the solid matrix, and attached onto colloids previously attached on the solid matrix. Colloids can be suspended in the aqueous phase or attached on the solid matrix. Viruses in all four phases (suspended in the aqueous phase, attached onto suspended colloid particles, attached on the solid matrix, and attached onto colloids previously attached on the solid matrix) may undergo inactivation with different inactivation coefficients. The governing coupled partial differential equations were solved numerically using finite difference methods, which were implemented explicitly or implicitly so that both stability and speed factors were satisfied. Furthermore, the experimental data collected by Syngouna and Chrysikopoulos [1] were satisfactorily fitted by the newly developed cotransport model.

A conceptual model of the microwave channel of information leakage by the power supply circuit

For the construction of the microwave filter devices to prevent information leakage on the supply lines should take into account the impact of external screens. Existing methods for the synthesis filtering devices are based on the mathematical model the two-wire transmission line, excluding the effect of shielding the outer envelope. As a result, the frequency response function of the filter is different from the experimental, which leads to deteriora­tion in the band rejection filter. Proposed as a conceptual mathematical model of the filter element model coupled transmission line. The conceptual model takes into ac­count the effect of shielding the outer shell and increases the accuracy of calculating the filtration devices in the power supply circuit.

Interactive network analysis of the plasma amino acids profile in a mouse model of hyperglycemia

Amino acids are a group of metabolites that are important substrates for protein synthesis, are important as signaling molecules and play central roles as highly connected metabolic hubs, and therefore, there are many reports that describe disease-specific abnormalities in plasma amino acids profile. However, the causes of progression from a healthy control to a manifestation of the plasma amino acid changes remain obscure. Here, we extended the plasma amino acids profile to relationships that have interactive properties, and found remarkable differences in the longitudinal transition of hyperglycemia as a diabetes emergency. What is especially important is to understand pathogenesis for better treatment and early diagnosis of diabetes. In this study, we performed interactive analysis using time course data of the plasma samples of AKITA mice, which develop hyperglycemia. Primarily, we decided to analyze the interactive property of amino acids which had highly significant association with hyperglycemia, namely alanine, glycine, leucine, isoleucine and valine. Next, we inferred the interactive network structure, which reproduces the actual time course within an error allowance of 10% using an S-system model (a conceptual mathematical model for analyzing and simulating networks). The emphasis of this study was altered interactions of plasma amino acids that show stabilizing and destabilizing features in a variety of clinical settings. By performing sensitivity analysis, the most dominant relations in this network were selected; the control paths from glycine to isoleucine in healthy control and from alanine to glycine in hyperglycemia. This result is in good agreement with the biological knowledge regarding branched-chain amino acids, and suggests the biological importance of the effect from alanine to glycine.

New proposed conceptual mathematical models for biomass viability and membrane fouling of membrane bioreactor

The production and accumulation of soluble microbial products (SMP), extracellular polymeric substances (EPS) and colloidal inert compounds within a membrane bioreactor (MBR) may greatly affect the biomass viability and subsequently the permeability of the membrane. This paper aims at presenting new mathematical models of biomass viability and membrane fouling that has been conceptually developed through establishing links between these biomass parameters and operating parameters of the MBR. The proposed models can be used to predict the biomass viability and membrane fouling at any state of operation of MBR. Meanwhile, easily measurable parameters of the proposed model can also serve to estimate SMP/EPS concentration in the supernatant of MBR without the tedious and expensive measurement.

The High Energy Demand of Neuronal Cells Caused by Passive Leak Currents is Not a Waste of Energy

It is estimated that maintenance of the resting potential of neurons consumes between 15% (in gray matter) and 44% (in fully myelinated white matter) of the brain's total energy budget [1]. This poses the intriguing question why evolution has not strived to lower the permeability of passive ion channels to cut the high resting-state energy budget of the brain. Based on a conceptual mathematical model of neuronal ion currents and action potential (AP) firing we demonstrate that a neuron endowed with small leak currents and correspondingly low energy consumption by the Na(+)/K(+)-ATPase in the resting state may indeed recapitulate all features of normal AP firing. However, the activation and inactivation of such a "low-energy-cost neuron" turns out to be extremely sensitive to small fluctuation of Na(+) currents associated with Na(+)-dependent secondary-active transport that is indispensable for the metabolic integrity of the cell and neurotransmitter recycling. We provide evidence that sufficiently large leak currents function as important stabilizers of the membrane potential and thus are required to allow robust AP firing. Our simulations suggest that the energy demand of the Na(+)/K(+)-ATPase needed to counterbalance passive leak currents cannot be significantly dropped below observed values.

Developing an Interactive Intervention Planner - A Systems Engineering Perspective

Intervention planning is crucial for maintenance operations in particle accelerator environments with ionizing radiation, during which the radiation dose received by maintenance workers should be reduced to a minimum. In this context, we discuss the development of a new software tool and the entailed methodology, including the visualization aspects. The software tool integrates interactive exploration of a scene depicting an accelerator facility augmented with residual radiation level simulations, with the visualization of intervention data such as the followed trajectory and maintenance tasks. Its conception allows for future inclusion of measurements performed by mobile robotic devices. In this work, we explore the systems engineering life cycle of the development process of an interactive intervention planner, which includes the needs analysis, specification explicitation, conceptual mathematical modelling, iterative implementation, design and prototype testing and usability testing.

Investigating the Propagation and Death of Information in Human Subpopulation Networks

We introduce a conceptual-mathematical model that simulates the spread of information. We represent the states of the actors in the information flow using compartments. The compartment diagram is translated into a system of coupled ordinary differential equations. The diversity of social groups (subpopulations) is incorporated in the model, and the model is applicable for a heterogeneous community. We determine four possible spots that can be influenced to control the information propagation such as (1) controlling the inflow and outflow of people in each subpopulation, (2) regulating the media of communication, (3) influencing the belief system of the actors, and (4) introducing an antithesis to the circulating information.

Effects of design parameters on performance and cost analysis of combined ultraviolet-biofilter systems treating gaseous chlorobenzene based on mathematical modeling

A conceptual mathematical model was used to evaluate the design parameters of a combined ultraviolet (UV)-biofilter system, and perform a cost analysis. Results showed that the UV light source strength and the gas residence times in the UV system (UVRT) and biofilter (EBRT) had positive effects on the overall chlorobenzene removal efficiency of the system. High ratio of UVRT to EBRT improved the removal efficiency, suggesting that the UV system has a greater effect on the overall performance of the system compared with the biofilter. Analysis of the capital and operating costs showed that the capital costs of the standalone biofilter system were much higher than those of the standalone UV system. However, the biofilter operating costs were lower than those of the UV system. The operating costs of the combined UV-biofilter system increased with increasing UVRT/EBRT ratio, whereas its capital costs decreased.

A Hypothetical Model of Cargo-Selective Rab Recruitment During Organelle Maturation

Rabs constitute a group of small GTPases that confer directionality to intracellular vesicle transport by promoting on the membrane of transport vesicles in the formation of specific protein complexes allowing for efficient fusion with a selected set of target organelles. The molecular mechanism controlling recruitment of the correct Rab at the right time is not fully understood. We propose a model according to which the residence time of a given Rab on the membrane of an organelle is determined by its transient trapping into a Rab effector complex (REC) composed of cargo receptor, SNAREs and further effectors. The stability of REC is controlled by the conformational state of the receptor which may change due to binding and release of cargo or changes in the luminal ion milieu. We use a conceptual mathematical model to calculate temporal changes in the Rab decoration of an organelle brought about by exchange with a cytosolic pool of Rabs or alternatively by budding and uptake of Rab-carrying vesicles. Considering the time-dependent drop in pH as one crucial factor for the conformational change of endocytic cargo receptors, our model provides a good quantitative description of the switch from Rab5 to Rab7 during the early-to-late endosome transition and correctly explains the arrest of this transition at insufficient luminal acidification. Model simulations suggest that a switch from one Rab to another may be continuous or abrupt. We discuss mechanisms, e.g. specific signalling pathways, which may restore an arrested organelle maturation.

Non-Linear Mathematical Model of the Interaction between Tumor and Oncolytic Viruses

A mathematical modeling of tumor therapy with oncolytic viruses is discussed. The model consists of two coupled, deterministic differential equations allowing for cell reproduction and death, and cell infection. The model is one of the conceptual mathematical models of tumor growth that treat a tumor as a dynamic society of interacting cells. In this paper, we obtain an approximate analytical expression of uninfected and infected cell population by solving the non-linear equations using Homotopy analysis method (HAM). Furthermore, the results are compared with the numerical simulation of the problem using Matlab program. The obtained results are valid for the whole solution domain.