Balance, energy

The balance includes the following contributions glucose, ammonium ions, NaOH consumed, biomass produced, ethanol in the liquid phase and in the gaseous phase and acetate. The enthalpy of combustion of gaseous ethanol was corrected for the heat of vaporization and the enthalpy of combustion of biomass was corrected for the nitrogen content. 

At the end of the experiment there is an excess enthalpy as low as 0.7% (J/J) compared to the glucose consumed (Table 18). A statistical analysis facilitates the interpretation of the errors. The test was performed assuming an error of 1% on the heat measurement and the quantity of added base. Errors on the other 

An energy balance is required to study the heat generation and spatio-temporal evolution of temperature inside a battery. Nonuniform distribution and local excursion of temperature in a battery pack is a safety concern for advanced electric and hybrid vehicles. GeneraHzed energy conservation for temperature distribution in a battery takes the following form [33-35], and can be expressed for each phase, k, within the DNS framework  

We can also consider the mass balance for a particular component in the total mass. Thus, for a component in a chemical reactor, 

In mass balance calculations involving chemical and biochemical systems, it is sometimes more convenient to use the molar units, such as kmol, rather than simple mass units, such as the kilogram. 

A flow of 2000 kgh-1 of aqueous solution of ethanol (10wt% ethanol) from a fermentor is to be separated by continuous distillation into the distillate (90 wt% ethanol) and waste solution (0.5 wt% ethanol). Calculate the amounts of the distillate D (kgh ) and the waste solution W (kgh ). 

Energy balance is an expression of the first law of thermodynamics - that is, the law of the conservation of energy. 

For a nonflow system separated from the surroundings by a boundary, the increase in the total energy of the system is given by  

Provide meaningful experience in solving mass balances for physical and chemical processes. 

Perform energy balance on reactive and nonreactive processes. 

Verify hand calculation results with Hysys, PRO/II, Aspen, and SuperPro Designer. 

At steady state, the energy balance for volume element AV can be written as follows  

Intuitively, Equation 3.9 can be understood as an exothermic reaction heat is released due to the chemical reaction proceeding in the system at the rate R —AHr)AV [ W] this heat, in turn, is partially transported to the environment at the rate AQ and is partially consumed by increasing the temperature of the reaction mixture from T to T + AT. For an endothermic reaction, an analogous reasoning is applied i (—AHr) A V is negative and often causes a temperature suppression (excluding the effect of AQ AT is thus negative). 

The heat flux term, AQ, can often be described with an expression of the following type  

In the previous expression (Equations 3.10 and 3.153), AS denotes the heat transfer area, U is an overall heat transfer coefficient comprising the reactor wall and the stagnant layers (films) inside and outside the reactor, and Tc denotes the temperature of the environment. 

FIGURE 3.10 Energy effects in a volume element A V in a homogeneous tube reactor. 

Apart from material conversions, components q in biomass i can also be converted into energy e via technology j with conversion of V(. Moreover, components q in product p can also be converted into energy e via technology / with conversion of Total energy 

The examination of mixing mechanisms will also deal primarily with the internal mixer, because the energy requirements must be determined quantitatively. A discussion of this subject will be given in Chapter 11. 

Because mixing involves viscous heat generation and simultaneous cooling, heat transfer measurement is a necessary part of calculating the energy balance. 

Precise data gathering requires extensive instrumentation, which becomes prohibitively expensive. However, with reasonable assumptions and approximations, an overall energy balance of the mixing operation may be obtained using relatively simple instrumentation. This work is an example of such a study of the operation of a laboratory Banbury mixer with a powdered rubber compound. 

The characterisation of the mixing results is outside the scope of this work. The emphasis is on the analysis and not on the optimisation of the process. 

A preblended powdered rubber compound was charged into the mixer, instead of separately charging a slab of rubber and carbon black. This was done to minimise the variability in the charging procedure and to avoid gross inhomogeneity at the beginning of the mixing. 

After converting all energy forms to fuel equivalent, these energy forms are leveled on the equal basis and thus we are ready to conduct energy balance. For a chemical process, energy balance is defined as 

Energy supply + Heat of Reaction = Energy export + Energy loss. (3.1) 

Energy input Energy generation Energy output 

Electricity 28.6 MMBtu/h. Process unit Exothermic reaction MMBtu/h MP Steam export 65.5 MMBtu/h 

Boiler feed water 2.9 MMBtu/h Condensate return 12.2 MMBtu/h 

The temperature field and local heat fluxes in the gas phase are governed by the energy balance  

Heat transfer between cell components must also be accounted for, either as boundary conditions of Eq. (5) (boundary heat flows) or as a volumetric heat source (contributing to Q in Eq. (5)). These heat source terms due to interfacial heat transfer occur mainly in two ways [5]  

Between cell component layers and flowing gas streams, e.g., between the anode or anode side of the PEN and the fuel gas stream or betw een the interconnect and the oxidant gas stream. This type of heat transfer is best described in terms of convective heat transfer coefficient h. 

Alternatively, the heat transfer from the fuel gas stream to the oxidant gas stream via a solid layer such as the PEN element or the interconnect may be described in terms of an overall heat transfer coefficient. 

For convective heat transfer at the boundary between a solid layer and a fluid, the following continuity condition may be imposed [6]  

The temperature of the spinning filament is a function of distance from the spinneret and is determined by the energy balance along the spinline. Heat transfer 

The heat transferred by radiation is strongly dependent on the temperature of the spinning filament. The apparent heat transfer coefficient for radiation can be expressed by  

Many theories have been developed to predict the heat transfer coefficients of spimiing filaments. One of the commonly used relationships is given by Kase and Matsuo  

Neglecting the radial temperature variations within the filament, the energy balance of the spiiming filament can be written as  

Consider a section of uniform cylindrical pipe of length L and radius R, inclined upward at an angle 0 to the horizontal, as shown in Fig. 6-2. The steady-state energy balance (or Bernoulli equation) applied to an incompressible fluid flowing in a uniform pipe can be written 

We can write a momentum balance on a cylindrical volume of fluid of radius r, length L, centered on the pipe centerline (see Fig. 6-2) as follows  

Note that from Eq. (6-4) the shear stress is negative (i.e., the fluid outside the cylindrical system of radius r is moving more slowly than that inside the system and hence exerts a force in the — x direction on the fluid in the system, which is bounded by the r surface). However, the stress at the wall (tw) is defined as the force exerted in the +x direction by the fluid on the wall (which is positive). 

Continuity provides a relationship between the volumetric flow rate (Q) passing through a given cross section in the pipe and the local velocity (vx), i.e., 

if the radial dependence of the shear rate (dvx/dr) is known or can be found, the flow rate can be determined directly from Eq. (6-7). Application of this is shown below. 

Example 3 Venturi Flowmeter An incompressible fluid flows through the venturi flowmeter in Fig. 6-7. An equation is needed to relate the flow rate Q to the pressure drop measured by the manometer. This problem can be solved using the mechanical energy balance. In a well-made venturi, viscous losses are negligible, the pressure drop is entirely the result of acceleration into the throat, and the flow rate predicted neglecting losses is quite accurate. The inlet area is A and the throat area is a. 

With control surfaces at 1 and 2 as shown in the figure, Eq. (6-17) in the absence of losses and shaft work gives 

The continuity equation gives V2 = ViAla, and Vi = Q/A. The pressure drop measured by the manometer is p —pz = (pm — p)gAz. Substituting these relations into the energy balance and rearranging, the desired expression for the flow rate is found. 

Example 4 Plane Poiseuille Flow An incompressible Newtonian fluid flows at a steady rate in the x direction between two very large flat plates, as shown in Fig. 6-8. The flow is laminar. The velocity profile is to be found. This example is found in most fluid mechanics textbooks the solution presented here closely follows Denn. 

This problem requires use of the microscopic balance equations because the velocity is to be determined as a function of position. The boundary conditions for this flow result from the no-slip condition. All three velocity components must be zero at the plate surfaces, y = H/2 and y = —HI2. 

The reaction equilibrium calculation requires knowing the temperature of the reactor. Temperature is determined by the oxygen supply and the presence of water in the system. Due to this, it is necessary to establish an initial temperature value for a first estimate of the conversion and the composition of output compounds, and then calculate the real temperature of the system by a global energy balance. 

By the enthalpies balance of the overall reaction (Equation 4.17), and assuming that the gasifier operates in adiabatic mode, the following equation can be derived. It is considered that all streams enter the gasifier at ambient temperature. Also, that the enthalpy of formation of the pure compounds such as O2, N2, and H2 is equal to zero. 

Modeling of Processes and Reactors for Upgrading of Heavy Petroleum 

Assuming that the combustion reaction of vacuum residue (dry basis) with stoichiometric supply of oxygen is complete (Equation 4.62), by Hess s law it is possible to calculate the standard enthalpy of formation (H gy) in kJ/kmol (Equation 4.63) (De Souza-Santos, 2004). The enthalpy of combustion of vacuum residue corresponds to low heating value LHV, whose definition is the heat released when a fuel is burned using stoichiometric supply of oxygen  

The LHV in kJ/kmol can be calculated if HHV (high heating value) is known. HHV is the heat released by complete combustion and stoichiometric of the fuel plus the released heat by condensation of water produced in said combustion. If in reaction (4.62) it is assumed that during combustion all the hydrogen contained in the vacuum residue converts to water, then LHV is determined with 

When we come to model this system it will be particularly useful to work not in terms of the actual temperature T but in terms of the ambient temperature Ta (which is known) and the temperature rise or degree of self-heating, AT = T - Ta. The latter, AT, then becomes our second variable, i.e. we look for dAT/dt. Equation (4.4) can be written as 

Here the form kx(AT) expresses the dependence of the reaction rate constant on the temperature rise. 

The accumulation can be either positive or negative, depending on the relative magnitudes of the input and output. It should be zero with a continuously operated reactor mentioned in the previous section. 

Suppose T = 271.7 as for the PER (or batch) case in Example 5.3. Using Equation 5.12 and the same rate constants as in Example 5.3 gives ioptimai = 2.50 h. The corresponding value for hout is 0.772ain. Recall that Example 5.3 used i = 2 h and gave hom/ 2in = 0.760. Again, the temperature that is best for a fixed volume does not correspond to the volume that is best for a fixed temperature. 

The reader will appreciate that the rules for what maximizes what can be quite complicated to deduce and even to express. The safe way is to write the reactor design equations for the given set of reactions and then to numerically determine the best values for reaction time and temperature. An interior optimum may not exist. When one does exist, it provides a good starting point for the more comprehensive optimization studies discussed in Chapter 6. 

A reasonably general energy balance for a flow reactor can be written in English as 

Enthalpy of input streams - enthalpy of output streams 

This is an integral balance written for the whole system. Each of the additive terms has units of power, joules per second or watts. The various terms deserve discussion. 

MTp = stack solid mass-specific heat product (J/K) 

N (N ) = anode (cathode) total inlet molar flow (mol/s) 

I = total gas components in anode or cathode Qi = convective heat loss (W) 

The first and third terms on the right-hand side of Equation 12.61 are the energy changes as a result of flow into and out of the anode and 

From the time of formation of the Solar System nearly 4.6 x 10 years ago to the present epoch the planets have evolved from newly agglomerated, hot bodies to their current shape and form. This evolutionary process will continue until the Sun reaches the end of its life as a main sequence star and turns into a red giant. 

A planet absorbs sunlight and emits thermal radiation in the infrared. In most cases planets also contain internal heat sources, which are of great interest for the construction of models of the interior and for evolutionary theories. In a steady state. 

In the discussion of the energy balance a number of processes have to be considered  

For the terrestrial planets, only items 4 and 5 are of importance. For the outer planets, all items are of interest, except item 6 which plays a dominant role only on lo, a much smaller one on Europa, and possibly a very small one on Ganymede and Callisto. On Jupiter and Saturn items 1,2,3,4, and 5 contribute to the total infrared emission, the only quantity which can be measured by remote sensing techniques [left term in Eq. (9.4.1)]. On Uranus and Neptvme a metallic hydrogen core is not expected to exist therefore, the radial redistribution of helium caimot take place. However, other processes can conceivably affect the measured helium-to-hydrogen ratio as will be discussed further below. Item 4 is important for all planets. The absorbed solar radiation [first term on the right side of Eq. (9.4.1)] is found by a measurement of the planetary Bond albedo and a knowledge of the radius, the solar constant, and the heliocentric distance of the object. 

On the outer planets the internal heat is found by measuring the thermal emission and subtracting the term representing absorbed solar power. Consequently, careful measurements of the effective planetary temperatures and the Bond albedos are required. The quantities R and D in Eq. (9.4.1) are relatively well known for each planet, as is S. On Earth the internal power is small in comparison with the other terms of Eq. (9.4.1). Thus it would be difficult to find the internal heat by subtracting two almost equal quantities. The terrestrial internal power can be found much more 

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The analysis of the heat exchanger network first identifies sources of heat (termed hot streams) and sinks (termed cold streams) from the material and energy balance. Consider first a very simple problem with just one hot stream (heat source) and one cold stream (heat sink). The initial temperature (termed supply temperature), final temperature (termed target temperature), and enthalpy change of both streams are given in Table 6.1. 

In each shifted temperature interval, calculate a simple energy balance from... 

In Fig. 6.33a. heat Qftjel is taken into the boiler from fuel. An overall energy balance gives... 

The energy cost of the process can be set without having to design the heat exchanger network and utility system. These energy targets cam be calculated directly from the material and energy balance. Thus... 

In addition to being able to predict the energy costs of the heat exchanger network and utilities directly from the material and energy balance, it would be useful to be able to calculate the capital cost, if this is possible. The principal components that contribute to the capital cost of the heat exchanger network are... 

Let us take each of these components in turn and explore whether they can be accounted for from the material and energy balance without having to perform heat exchanger network design. 

Having explored the major degrees of freedom, the material and energy balance is now fixed, and hence the hot and cold streams which contribute to the heat exchanger network are firmly defined. The remaining task is to complete the design of the heat exchanger network. 

Cracking reactions are endothermic the energy balance is obtained by the production of coke that deposits on the catalyst and that is burned in the regenerator. 

Anon. (1983), Assessment of the energy balances and economic consequences of the reduction and elimination of lead in gasoline . Working Group ERGA (Evolutions of Regulations, Global Approach). CONCAWE, La Haye. 

Because densification occurs via tire shrinkage of tliennodynamically unstable pores, densification and microstmcture development can be assessed on tire basis of tire dihedral angle, 0, fonned as a result of tire surface energy balance between tire two solid-vapour and one solid-solid interface at tire pore-grain boundary intersection [, 78, 79 and 80],... 

It should be stressed that although these symmetry considerations may allow one to anticipate barriers on reaction potential energy surfaces, they have nothing to do with the thermodynamic energy differences of such reactions. Symmetry says whether there will be symmetry-imposed barriers above and beyond any thermodynamic energy differences. The enthalpies of formation of reactants and products contain the information about the reaction s overall energy balance. 

For an isothermal system the simultaneous solution of equations 30 and 31, subject to the boundary conditions imposed on the column, provides the expressions for the concentration profiles in both phases. If the system is nonisotherm a1, an energy balance is also required and since, in... 

The selection of a process can be complex, requiring carehil evaluation of the many variables for each appHcation. The hemihydrate process is energy efficient, but this may not be an overriding consideration when energy is readily available from an on-site sulfuric acid plant. The energy balance in the total on-site complex may be the determining factor. 

The conservation of mass gives comparatively Httle useful information until it is combined with the results of the momentum and energy balances. Conservation of Momentum. The general equation for the conservation of momentum is... 

Two approaches to this equation have been employed. (/) The scalar product is formed between the differential vector equation of motion and the vector velocity and the resulting equation is integrated (1). This is the most rigorous approach and for laminar flow yields an expHcit equation for AF in terms of the velocity gradients within the system. (2) The overall energy balance is manipulated by asserting that the local irreversible dissipation of energy is measured by the difference ... 

H. L. MuUer and S. P. Ho, "Economics and Energy Balance of Ethanol as Motor Fuel," paper presented at 1986 SpringAIChE Mational Meeting, New Orleans, La., Apr. 1986. 

An energy balance over a differential length, dx yields... 

Heat Transfer in Rotary Kilns. Heat transfer in rotary kilns occurs by conduction, convection, and radiation. In a highly simplified model, the treatment of radiation can be explained by applying a one-dimensional furnace approximation (19). The gas is assumed to be in plug flow the absorptivity, a, and emissivity, S, of the gas are assumed equal (a = e ) and the presence of water in the soHds is taken into account. Energy balances are performed on both the gas and soHd streams. Parallel or countercurrent kilns can be specified. 

Mass and energy balances are used to evaluate blast furnace performance. Many companies now use sophisticated computeri2ed data acquisition and analysis systems to automatically gather the required data for daily calculation of the mass and heat balances. Typical mass and heat balances are shown in Figure 4 and Table 5, respectively. 

The resulting overall energy balance for the plant at nominal load conditions is shown in Table 3. The primary combustor operates at 760 kPa (7.5 atm) pressure the equivalence ratio is 0.9 the heat loss is about 3.5%. The channel operates in the subsonic mode, in a peak magnetic field of 6 T. AH critical electrical and gas dynamic operating parameters of the channel are within prescribed constraints the magnetic field and electrical loading are tailored to limit the maximum axial electrical field to 2 kV/m, the transverse current density to 0.9 A/cm , and the Hall parameter to 4. The diffuser pressure recovery factor is 0.6. 

Table 3. Overall Energy Balance at 500 MW Nominal Load...

The scientific basis of extractive metallurgy is inorganic physical chemistry, mainly chemical thermodynamics and kinetics (see Thermodynamic properties). Metallurgical engineering reties on basic chemical engineering science, material and energy balances, and heat and mass transport. Metallurgical systems, however, are often complex. Scale-up from the bench to the commercial plant is more difficult than for other chemical processes. 

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