Material balance techniques

It is usually helpful to follow a systematic procedure when tackling material balance problems. One possibility is outlined below. 

Draw and label the process flowsheet—organize information into an easy to understand form. If possible show problem specifications on the flowsheet. Label unknowns with algebraic symbols. 

Select a basis for the calculation—the basis is an amount or flowrate of a particular stream or component in a stream. Other quantities are determined in terms of the basis. E.g. in Example 7.1 the flowrates of product and water were obtained on a basis of 10kgs of feed. It is usually most convenient to choose an amount of feed to the process as a basis. Molar units are preferable if chemical reactions occur, otherwise the units in the problem statement (mass or molar) are probably best. 

Convert units/amounts—as necessary to be consistent with the basis. 

Write material balance equations—for each unit in the process or for the overall process. In the absence of chemical reactions the number of independent equations for each balance is equal to the number of components. 

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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 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. 

SimSim fills the gap between material balance techniques and complex reservoir simulation yet keeping the simplicity and speed of the material balance but providing reservoir simulation like results, i.e. pressure, saturation, hydrocarbons in place and fluid flux distribution within the reservoir. 

S.3 Recycles, Processes in which part of a product stream is separated and recycled back to the feed are very common in the chemical industry. The protoype chemical process in Figure 7.1 shows a recycle stream. Material balance techniques are, in principle, the same as for non-recycle processes. However, because the recycle stream is usually unspecified, a large number of equations may have to be solved simultaneously. 

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. 

The use of the computer in the design of chemical processes requires a framework for depiction and computation completely different from that of traditional CAD/CAM appHcations. Eor this reason, most practitioners use computer-aided process design to designate those approaches that are used to model the performance of individual unit operations, to compute heat and material balances, and to perform thermodynamic and transport analyses. Typical process simulators have, at their core, techniques for the management of massive arrays of data, computational engines to solve sparse matrices, and unit-operation-specific computational subroutines. 

Step 8 Solve the Equations. Many material balances can be stated in terms of simple algebraic expressions. For complex processes, matrix-theory techniques and extensive computer calculations will be needed, especially if there are a large number of equations and parameters, and/or chemical reactions and phase changes involved. 

The material balance around the riser requires the reactor effluent composition. Two techniques are used to obtain this composition. Both techniques require that the coke yield be calculated. 

This section is a general discussion of the techniques used for the preparation of flowsheets from manual calculations. The stream flows and compositions are calculated from material balances combined with the design equations that arise from the process and equipment design constraints. 

The split-fraction coefficients can be estimated by considering the function of the process unit, and by making use of any constraints on the stream flows and compositions that arise from considerations of product quality, safety, phase equilibria, other thermodynamic relationships and general process and mechanical design considerations. The procedure is similar to the techniques used for the manual calculation of material balances discussed in Section 4.3. 

This combined equation represents a differential total material balance of a component, whether present as HA or the reaction product A-, within the reacting phase. The reader is referred to Olander s original paper for a more complete rationale for generating these differential component material balances for systems of reacting species near equilibrium. By using Olander s technique, the system of four differential equations with reaction terms can be simplified significantly to two differential equations with no reaction terms. 

A well-known class of techniques for reducing the number of iterates is the use of tearing (L4). We shall illustrate this procedure by way of an example taken from Carnahan and Christensen (C3). Let us consider the two-loop network shown in Fig. 5 and assume that formulation A is used. To abbreviate the notation let us denote the material balance around vertex i [Eq. (35)] by fi = 0 and the model of the element [Eq. (36)] by fu — 0. Then assuming all external flows and one vertex pressure, p, say, are specified, we have a set of 12 equations that must be solved simultaneously. But if we now assume a value for ql2, the remaining equations may be solved sequentially one at a time to yield the variables in the following... 

A second major estimating technique is the materials balance approach—the original focus of this paper. A chemical engineering standard, the materials balance can reduce to the simple mass balance, as when the measured mass of a chemical in products leaving the plant is subtracted from the raw material entering the plant to yield the loss. This loss is then partitioned among releases to various media or other sinks. If... 

Materials balance—This technique, in principle, is developed to its fullest extent, but it is extraordinarily sensitive to uncertainties in the data it uses. Better characterization of all pathways and chemical reactions would help, as would more accurate measurements of flows through these paths. 

The critical technology development areas are advanced materials, manufacturing techniques, and other advancements that will lower costs, increase durability, and improve reliability and performance for all fuel cell systems and applications. These activities need to address not only core fuel cell stack issues but also balance of plant (BOP) subsystems such as fuel processors hydrogen production, delivery, and storage power electronics sensors and controls air handling equipment and heat exchangers. Research and development areas include ... 

The resultant equations are non-linear and in this general case numerical solution techniques must be used. However, there exists a special case where an analytical solution may be obtained. If the increase in biomass concentration during flow through the reactor is small then an average value for the biomass concentration, independent of the distance Z along the fermenter, may be used. The material balance for the substrate over the reactor element may then be written ... 

The modelling of real food webs can be an exceedingly complicated task but, to illustrate the basic technique, a situation may be defined where a continuous stirred-tank biological reactor contains two species, one the predator, the other the prey. The food for the prey is assumed to enter as the sterile feed stream to the reactor, so that the predator may only consume the prey which grows in the reactor. Material balances can be drawn up for the process in much the same way as has... 

Solution An overall material balance gives ain + bin = aout + bout. The data are obviously imperfect, but they will be accepted as is for this example. The following program fragment uses the random search technique to fit the general form = ka utbnout. 

Nitroso-5-phenyl-l-pentanol dimer was a single product (18 % yield) reported in this work. In view of the poor material balance of the product and the limited techniques used for the isolation (recrystallization) and characterization (UV intensity at 297 nm, IR, and elemental analysis) of the photolysis products, reaffirmation of this frequently cited results by modem instruments would be desirable. 

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