Materials balance

Material balancing Is a method technicians use to determine the exact amount of reactants needed to produce the specified products. This method is used when two or more substances are combined in a chemical process. Reactants must be mixed in the proper proportions to avoid waste. Material balancing provides an operator with the correct reactant ratio. 

ensure that reactant total weight is equal to product total weight, and 

determine relative numbers of reactant atoms or ions. 

Note The relationship between AMUs and other units is 1 AMU = 1 gram, pound, or ton. 

List the reactant elements. List the product elements. Is this chemical equation balanced Na O + 2HOCI - 

Material (mass) balance, the natural outcome from the law of conservation of mass, is a very important and useful concept in chemical engineering calculations. With usual chemical and/or biological systems, we need not consider nuclear reactions that convert mass into energy. 

Let us consider a system that is separated from its surroundings by an imaginary boundary, ihe simplest expression for the total mass balance for the system is as follows  

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. 

A typical material balance is shown in Table 1. The purpose of material balance is to show the following infoimation of a process stream ( ) its total and component flow rates, (2) its operattug conditions (temperature and pressure), (3) its physical properties (density and viscoaty of vapor or/and liquid, and liquid surface tension (for two-phase flow only)), and (4) its name or description. 

Material balance is a useful tool to make sure the unit is mass balanced. It shows what chemicals are in each process stream, and it also provides major infoimation of each process stream. Actual presentation in the table varies mth project. 

Material balance is usually developed using a process simulation computer program to avoid tedious hand calculation. These computer programs are available commercially. Most times, it is a necessity for process engineer to do his/her work. 

Equation 5.1 shows the component balance for biomass i where and x. are the component flow rates and compositions, respectively. Besides, shows the tot flow rate of 

Each biomass i is split into potential technology j with flow rate of as shown  

In technology j, the components of biomass i from flow rate F are then converted to 

The total production rate of primary product p for all technologies j is given as 

primary product p can be distributed to potential technology / for further processing to produce product p. The splitting of primary product p is written as 

Although the residence time of plastic melt in the dehydrochlorination process is very long, the amount of HCl gas evolved is less than in the liquefaction processes of Niigata and Sapporo. This may indicate that PVC and PVDC materials are removed effectively 

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When only the total system composition, pressure, and temperature (or enthalpy) are specified, the problem becomes a flash calculation. This type of problem requires simultaneous solution of the material balance as well as the phase-equilibrium relations. 

An additional separator is now required (Fig. 4.2a). Again, the unreacted FEED is normally recycled, but the BYPRODUCT must be removed to maintain the overall material balance. An additional complication now arises with two separators because the separation sequence can be changed (see Fig. 4.26). We shall consider separation sequencing in detail in the next chapter. 

Consider the single-stage phase split shown in Fig. 3.1a. Overall material balances and component material balances can be written as... 

The amounts of each phase and their compositions are calculated by resolving the equations of phase equilibrium and material balance for each component. For this, the partial fugacities of each constituent are determined ... 

Material balance and properties of the main fractions resulting from primary and secondary fractionation of a 50/50 volume % mixture of Arabian Ligb and heavy crude oil (specific gravity d f = 0.875). 

Proportions correspond to the material balance for catalytic cracking in Figure 10.3 showing streams (l)(2)(3)(4) and (5). 

Keywords compressibility, primary-, secondary- and enhanced oil-recovery, drive mechanisms (solution gas-, gas cap-, water-drive), secondary gas cap, first production date, build-up period, plateau period, production decline, water cut, Darcy s law, recovery factor, sweep efficiency, by-passing of oil, residual oil, relative permeability, production forecasts, offtake rate, coning, cusping, horizontal wells, reservoir simulation, material balance, rate dependent processes, pre-drilling. 

Reservoir engineers describe the relationship between the volume of fluids produced, the compressibility of the fluids and the reservoir pressure using material balance techniques. This approach treats the reservoir system like a tank, filled with oil, water, gas, and reservoir rock in the appropriate volumes, but without regard to the distribution of the fluids (i.e. the detailed movement of fluids inside the system). Material balance uses the PVT properties of the fluids described in Section 5.2.6, and accounts for the variations of fluid properties with pressure. The technique is firstly useful in predicting how reservoir pressure will respond to production. Secondly, material balance can be used to reduce uncertainty in volumetries by measuring reservoir pressure and cumulative production during the producing phase of the field life. An example of the simplest material balance equation for an oil reservoir above the bubble point will be shown In the next section. 

The material balance equation relating produced volume of oil (Np stb) to the pressure drop in the reservoir (AP) is given by ... 

The prediction of the size and permeability of the aquifer is usually difficult, since there is typically little data collected in the water column exploration and appraisal wells are usually targeted at locating oil. Hence the prediction of aquifer response often remains a major uncertainty during reservoir development planning. In order to see the reaction of an aquifer, it is necessary to produce from the oil column, and measure the response in terms of reservoir pressure and fluid contact movement use is made of the material balance technique to determine the contribution to pressure support made by the aquifer. Typically 5% of the STOMP must be produced to measure the response this may take a number of years. 

It is possible that more than one of these drive mechanisms occur simultaneously the most common combination being gas cap drive and natural aquifer drive. Material balance techniques are applied to historic production data to estimate the contribution from each drive mechanism. 

Gas reservoirs are produced by expansion of the gas contained in the reservoir. The high compressibility of the gas relative to the water in the reservoir (either connate water or underlying aquifer) make the gas expansion the dominant drive mechanism. Relative to oil reservoirs, the material balance calculation for gas reservoirs is rather simple. A major challenge in gas field development is to ensure a long sustainable plateau (typically 10 years) to attain a good sales price for the gas the customer usually requires a reliable supply of gas at an agreed rate over many years. The recovery factor for gas reservoirs depends upon how low the abandonment pressure can be reduced, which is why compression facilities are often provided on surface. Typical recovery factors are In the range 50 to 80 percent. 

The primary drive mechanism for gas field production is the expansion of the gas contained in the reservoir. Relative to oil reservoirs, the material balance calculations for gas reservoirs is rather simple the recovery factor is linked to the drop in reservoir pressure in an almost linear manner. The non-linearity is due to the changing z-factor (introduced in Section 5.2.4) as the pressure drops. A plot of (P/ z) against the recovery factor is linear if aquifer influx and pore compaction are negligible. The material balance may therefore be represented by the following plot (often called the P over z plot). 

The subscript i refers to the initial pressure, and the subscript ab refers to the abandonment pressure the pressure at which the reservoir can no longer produce gas to the surface. If the abandonment conditions can be predicted, then an estimate of the recovery factor can be made from the plot. Gp is the cumulative gas produced, and G is the gas initially In place (GIIP). This is an example of the use of PVT properties and reservoir pressure data being used in a material balance calculation as a predictive tool. 

Analytical models using classical reservoir engineering techniques such as material balance, aquifer modelling and displacement calculations can be used in combination with field and laboratory data to estimate recovery factors for specific situations. These methods are most applicable when there is limited data, time and resources, and would be sufficient for most exploration and early appraisal decisions. However, when the development planning stage is reached, it is becoming common practice to build a reservoir simulation model, which allows more sensitivities to be considered in a shorter time frame. The typical sorts of questions addressed by reservoir simulations are listed in Section 8.5. 

Reservoir pressure is measured in selected wells using either permanent or nonpermanent bottom hole pressure gauges or wireline tools in new wells (RFT, MDT, see Section 5.3.5) to determine the profile of the pressure depletion in the reservoir. The pressures indicate the continuity of the reservoir, and the connectivity of sand layers and are used in material balance calculations and in the reservoir simulation model to confirm the volume of the fluids in the reservoir and the natural influx of water from the aquifer. The following example shows an RFT pressure plot from a development well in a field which has been producing for some time. 

The oscillating jet method is not suitable for the study of liquid-air interfaces whose ages are in the range of tenths of a second, and an alternative method is based on the dependence of the shape of a falling column of liquid on its surface tension. Since the hydrostatic head, and hence the linear velocity, increases with h, the distance away from the nozzle, the cross-sectional area of the column must correspondingly decrease as a material balance requirement. The effect of surface tension is to oppose this shrinkage in cross section. The method is discussed in Refs. 110 and 111. A related method makes use of a falling sheet of liquid [112]. 

In unsteady states the situation is less satisfactory, since stoichiometric constraints need no longer be satisfied by the flux vectors. Consequently differential equations representing material balances can be constructed only for binary mixtures, where the flux relations can be solved explicitly for the flux vectors. This severely limits the scope of work on the dynamical equations and their principal field of applicacion--Che theory of stability of steady states. The formulation of unsteady material and enthalpy balances is discussed in Chapter 12, which also includes a brief digression on stability problems. 

Then Che differential material balance (9,6) for substance 1 takes the form... 

Having discussed at some length the formulation and testing of flux models for porous media, we will now review v at Is, perhaps, their most Important application - the formulation of material balances In porous catalyst pellets. 

To reduce the material balance conditions (11,1) to differential equations for the composition and pressure, flux relations must be used to relate the vectors to the gradients of the composition and pressure... 

Combining these with the material balance conditions (11.1) we therefore obtain... 

Solution of the material balance equations gives the pressure and... 

Knowing the solution of the material balance equations It is easy to calcu>... 

The differential material balances contain a large number of physical parameters describing the structure of the porous medium, the physical properties of the gaseous mixture diffusing through it, the kinetics of the chemical reaction and the composition and pressure of the reactant mixture outside the pellet. In such circumstances it Is always valuable to assemble the physical parameters into a smaller number of Independent dimensionless groups, and this Is best done by writing the balance equations themselves in dimensionless form. The relevant equations are (11.20), (11.21), (11.22), (11.23), (11.16) and the expression (11.27) for the effectiveness factor. 

When used in the material balance condition this again gives a single differ-ential equation for but it is not the same as the equation obtained... 

A third approach is suggested by Hugo s formulation of material balances at the limit of bulk diffusion control, described in Section 11.3. Hugo found expressions for the fluxes by combining the stoichiometric conditions and the Stefan-Maxvell relations, and this led to no inconsistencies since there are only n - 1 independent Stefan-Maxwell relations for the n fluxes. An analogous procedure can be followed when the diffusion is of intermediate type, using the dusty gas model equations in the form (5.10) and (5.11). Equations (5.11), which have the following scalar form ... 

The material balance conditions (11.1) may be rewritten in terms of the total flux N and the diffusion fluxes J, when they take the form... 

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