Heat factor balance equation

Isothermal Gas Flow in Pipes and Channels Isothermal compressible flow is often encountered in long transport lines, where there is sufficient heat transfer to maintain constant temperature. Velocities and Mach numbers are usually small, yet compressibihty effects are important when the total pressure drop is a large fraction of the absolute pressure. For an ideal gas with p = pM. JKT, integration of the differential form of the momentum or mechanical energy balance equations, assuming a constant fric tion factor/over a length L of a channel of constant cross section and hydraulic diameter D, yields,... 

Axial heat flux parameter Y The parameter Y, which replaces the heat flux shape factor in the CHF correlation, is not only a measure of the nonuniformity of the axial heat flux profile but also a means of converting from the inlet subcooling (AHin) to the local quality, X, form of the correlation via the heat balance equation. It is defined as... 

Subchannel imbalance factor Y The parameter Y was used in the heat balance equation to account for enthalpy transfer between subchannels. It is defined as the fraction of the heat retained in the subchannel and is a measure of this subchannel imbalance relative to that of its neighbors. Thus,... 

Heat and mass balance equations are used in all aspects of process modelling however, what is key to this model is an understanding of the electrolytic process behind the cell. For example, the model must be able to predict current efficiency and k-factor if it is to predict electricity consumption. Most of these electrolytic parameters are calculated using empirical relationships derived from experimental data both from test cells and the full-scale plant. Considering k-factor, this is primarily a function of brine strength and temperature. Figure 20.5 illustrates the experimentally derived function used in the model. 

H2, Cl2, and Br2 are placed in a flask and heated to 1000 K. (a) What molecular species will be present when the reactions come to equilibrium Neglect atomic species. Consult Table 9.1. (b) Write all the equilibrium reactions that are possible for this system. Neglect reactions that are the reverse of reactions already written and reactions differing from the others only by a multiplicative factor. Also ignore reactions that are nonproductive, i.e., ones in which the reactants and products are identical. Choose balanced equations that have the lowest possible, whole-number... 

In a more sophisticated analysis these functions can be found as the solutions of the dynamic and energy balance equations for filling a mold. 0m is the dimensionless temperature of the mold To is the initial temperature of the reactive mixture co = (H2kr,T)/a is the dimensionless factor characterizing the ratio of time scales for heat transfer and the chemical reaction. Other dimensionless variables are as follows ... 

Equation 9.1.46 is the dimensionless energy balance equation for gas-phase, constant-volume semibatch reactors. The correction factor of the heat capacity is... 

In this case mass balance as well as heat balance equations must be formulated in order to compute the effectiveness factor. For this case the effectiveness factor has literally the same definition given by equation (5.22), the difference being that the actual rate of reaction is evaluated at the surface concentration and temperature C, T, while the intrinsic rate (rate without diffusional resistances) is evaluated at the bulk conditions thus reflecting the effect of mass transfer... 

The governing mass and heat balance equations were derived in section 5.1.9 which simulate the concentration and temperature gradient between the bulk fluid and the external surface of the catalyst pellet. The effectiveness factors which represent the ratios of the observed actual rates of reactions to the intrinsic reactions rates where there is no mass and heat transfer resistances are computed for different reactions and different components. 

In a balanced equation, the number of moles of one substance is stoichiometrically equivalent to the number of moles of any other substance. The term stoichiometrically equivalent means that a definite amount of one substance is formed from, produces, or reacts with a definite amount of the other. These quantitative relationships are expressed as stoichiometrically equivalent molar ratios that we use as conversion factors to calculate these amounts. Table 3.3 presents the quantitative information contained in the equation for the combustion of propane, a hydrocarbon fuel used in cooking and water heating ... 

A thermochemical equation shows the balanced equation and its AHrxn- The sign of AH for a forward reaction is opposite that for the reverse reaction. The magnitude of AH depends on the amount and physical state of the substance reacting and the AH per mole of substance. We use the thermochemically equivalent amounts of substance and heat from the balanced equation as conversion factors to find the quantity of heat when a given amount of substance reacts. 

This is the amount of heat released when 1 mole of CI2 reacts (see balanced equation). We are not reacting 1 mole of CI2, however. From the volume and density of CI2, we can calculate grams of CI2. Then, using the molar mass of CI2 as a conversion factor, we can calculate moles of CI2. Combining these two calculations into one step, we find moles of CI2 to be ... 

Looking at the balanced equation, this is the amount of heat released when four moles of Fe react. But, we are reacting 250 g of Fe, not 4 moles. We can convert from grams of Fe to moles of Fe, then use A/7° as a conversion factor to convert to kJ. 

All these factors yield the following heat balance equation for the flow of a polymerizing liquid under specific geometric conditicms, particular, in a cylindrical tube (model of a tubular reactor) ... 

Step 1 is the decomposition of reactants into elements in their standard states. But this is just the opposite of the formation reaction of the reactants, so the enthalpy change of the process is -AHf°(reactants). Similarly, Step 2, the formation of the products from elements in their standard states, has an enthalpy change of AHf°(products). Remember, however, that the formation reaction is defined for the generation of one mole of the compound. Consequently, to use tabulated heats of formation we must multiply by the stoichiometric coefficients from the balanced equation to account for the number of moles of reactants consumed or products generated. Taking these factors into account leads to one of the more useful equations in thermochemistry. 

The form of the heat balance equations for a given calorimeter depends on a number of factors, such as the number of defined domains, the interactions between the domains, and the mutual location of the heat source and temperature sensor. This means that the mathematical form of the equations is related to the thermal and geometrical parameters of the calorimeter and to the location of the sensors and heat... 

Methods of measuring factors in the heat balance equation... 

The final two-dimensional mathematical model thus consists of one partial parabolic differential mass balance equation (3.12) with boundary and initial conditions in (3.14) for each of the j reactions and one partial parabolic differential heat transfer equation (3.15) with boundary conditions in (3.17), (3.18) and initial conditions in (3.20). Simultaneously the pressure drop ordinary differential equation (3.7) and the differential equations for the temperature and pressure in each of the surrounding channels in (3.22) must be integrated. Catalyst effectiveness factors in the catalyst bed must be available in all axial and radial integration points using the methods in Section 3.4. 

This equation also gives a relationship between the mass balance equations for each component (3.32) and the heat balance in (3.34) allowing an analytical solution after insertion of the boundary conditions (3.33) and (3.35) [113]. This allows calculations of temperatures and concentrations in the interior of a catalyst particle from the key component concentrations in the particle and the temperature and concentration at the surface. The next step is to combine this solution with the surface heat and mass flux equations (3.36) and the equation defining the effectiveness factor in Equation (3.37) by use of the surface mass flux relations for the key components [113]. The final equation is ... 

The amount of a substance and the quantity of heat specified by the balanced equation are thermochemically equivalent and act as conversion factors to find the quantity of heat transferred when any amount of the substance reacts. 

Stream properties required for solving material and energy balance equations and other process calculations are predicted from component properties. The properties of petroleum pseudocomponents can be estimated from their boiling points and specific gravities. The component properties include the molecular weight, critical constants, acentric factor, heat of formation, ideal gas enthalpy, latent heat, vapor pressure, and transport properties. These are predicted mainly by empirical correlations based on experimental data. Many of these correlations are documented in the American Petroleum Institute Technical Data Book (API, 1983). 

Abstract. This article describes a hydrodynamic model of collaborative flnids (oil, water) flow in porons media for enhanced oil recovery, which takes into account the influence of temperature, polymer and surfactant concentration changes on water and oil viscosity. For the mathematical description of oil displacement process by polymer and surfactant injection in a porous medium, we used the balance equations for the oil and water phase, the transport equation of the polymer/surfactant/salt and heat transfer equation. Also, consider the change of permeabihty for an aqueous phase, depending on the polymer adsorption and residual resistance factor. Results of the numerical investigation on three-dimensional domain are presented in this article and distributions of pressure, saturation, concentrations of poly mer/surfactant/salt and temperature are determined. The results of polymer/surfactant flooding are verified by comparing with the results obtained from ECLIPSE 100 (Black Oil). The aim of this work is to study the mathematical model of non-isothermal oil displacement by polymer/surfactant flooding, and to show the efficiency of the combined method for oil-recovery. 

Thermal conduction in the solid phase is a key factor, as already mentioned in section 1.2.4. The heat conduction process is accounted for by Fourier s law in the heat balance equation which is thus a second order partial differential equation. An efficient numerical technique is required to avoid "numerical conduction" because the solid temperature gradient is very sharp at the light-off point (see section 3.1). There is no study of Ais numerical problem in the literature. However, Eigenberger (1972) studied the consequences of heat conduction on steady-state multiplicity. He showed that the conduction process is responsible for a reduction of the number of steady state solutions. In the example studied by Eigenberger, the steady-state solution is close to the "highest steady state" (i.e., steady state with the temperature maximum close to reactor inlet) without conduction because "the temperature maximum moves to the front of the reactor, driven by the backward conduction of heat". 

We will select 21 SCFM of air to strip each 1 gpm of water therefore, the air flow to the column will be 1,890 SCFM. Based on the inlet air having 80% relative humidity and the exit air leaving saturated with water vapor at HO F maximum temperature, the liquid effluent temperature will be 108 F by heat balance. The Henry s Law constants are 1,740 atm/mol fraction for the feed liquid and 840 atm/mol fraction for the effluent liquid. The stripping factors from Equation 5-19 at atmospheric pressure are 113 at the column bottom and 278 at the column top. To produce a 0.14 ppm by wt. ethyl benzene effluent will require an average of 6.95 transfer units. 

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