The Basic Problem

When you drive by a chemical plant at night, the most impressive part is the lights. They outline every piece of equipment. When you look more closely, you can often see three types of silhouettes. The tallest are the thin distillation columns, which are described in Chapter 12 and 13. The next tallest are the fat gas absorption columns, which are the subject of this chapter. Ironically, the shortest silhouettes are the chemical reactors, charged with reagents to make the desired products. 

This relative size has a moral while the chemical plant would not exist without the chemical reactors, the biggest expense - the biggest equipment - will often be in the separation equipment. This separation equipment centers on distillation and gas absorption, the two most important unit operations. The analysis and the design of these operations is central to the entire chemical industry. 

I have found that distillation is better understood than gas absorption. I believe that this is because everyone knows that distillation is how you concentrate ethanol from water Distillation is how you turn wine into brandy. In contrast, few know what gas absorption is for. What specific gases are absorbed, anyway What liquids absorb the gases What happens to the liquids afterwards I find this ignorance ironic because of increased environmental concerns. Gas absorption is the chief method for controlling industrial air pollution, yet many with environmental interests remain ignorant of its nature. 

Most gas absorption aims at separation of acidic impurities from mixed gas streams. These acidic impurities include carbon dioxide (CO2), hydrogen sulfide (H2S), sulfur dioxide (SO2), and organic sulfur compounds. The most important of these are CO2 and H2S, which occur at concentrations of five to fifty percent. The organic sulfur 

Process Gases to be removed Common targets (% Acid gas) 

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When viewing effluent treatment methods, it is clear that the basic problem of disposing of waste material safety is, in many cases, not so much solved but moved from one place to another. The fundamental problem is that once waste has been created, it cannot be destroyed. The waste can be concentrated or diluted, its physical or chemical form can be changed, but it cannot be destroyed. 

One of the basic problems in molecular dynamics is how to sample infrequent events. Typically a reaction must pass over a barrier, and effort would be wasted if many trajectories are run that do not reach the reactant channel. 

An alternative to using a superposition of Gaussian functions is to extend the basis set by using Hermite polynomials, that is, hamonic oscillator functions [24]. This provides an orthonormal, in principle complete, basis set along the bajectoiy, and the idea has been taken up by Billing [151,152]. The basic problem with this approach is the slow convergence of the basis set. 

Finding the adequate descriptor for the representation of chemical structures is one of the basic problems in chemical data analysis. Several methods have been developed in the most recent decades for the description of molecules including their chemical or physicochemical properties [1]. 

Rigid Systems. Literature pertaining to the theoretical analysis of the three-plane rigid piping system is voluminous (30). This Hterature is expanding steadily and, as it is becoming more abstract, tends to obscure the basic problem which is the analysis of a three-dimensional statically iadeterminate stmcture. 

The basic problems of the sciences and engineering fall broadly into three categories ... 

The basic problem of design was solved mathematically before any reliable kinetic model was available. As mentioned at start, the existence of solutions—that is, the integration method for reactor performance calculation—gave the first motivation to generate better experimental kinetic results and the models derived from them. 

The major conclusion was that if blowdown is in fact of primary importance, then the current manual system must be improved to enhance blowdown response time. The estimated average activation time of 20 minutes would have to be brought closer to a matter of a few minutes. The basic problem underlying the long response time was a lack of a clear statement of blowdown... 

Now if the function is linear in the parameters, the derivative dyidaj does not contain the parameters, and the resulting set of equations can be solved for the parameters. If, however, the function is nonlinear in the parameters, the derivative contains the parameters, and the equations cannot in general be solved for the parameters. This is the basic problem in nonlinear least-squares regression. 

The consideration of the simple pendulum illustrates the basic problem behind devising a perpetual motion machine. The problem is the fact that energy exists in several forms and is transformed from one form to the other, especially when motion is involved. Even if friction is eliminated, there arc still the electromagnetic radiation and gravitational inter-... 

Using the basic problem for dilute solutions, assume the following conditions for a higher concentration. 

The basic problem of statistical mechanics is to evaluate the sum-over-states in equation 7.2 and obtain Z and F as functions of T and any other variables (such as external magnetic fields) that might appear in %. Any thermodynamic observable of interest can then be obtained in a straightforward manner from equation 7.5. In practice, however, the sum-over-states often turns out to be prohibitively difficult to evaluate. Instead, the physical system is usually replaced with a simpler model system and/or some simplifying approximations are made so that the sum-over-states can be evaluated directly. 

Once HsoS and Hs h are both specified, the basic problem is to once again find a way to compute the sum-over-states appearing in the expression defining the partition function (equation 7.2) ... 

A variation of the basic problem with indistinguishable boxes occurs when the mapping from boxes to figures is required to be one-to-one, that is, when we are not allowed to put the same figure in two different boxes. In that case Pdlya showed that the substitution of the figure generating function must be made, not in the cycle index Z(S but in the expression... 

The second main application of the orbital model lies with ab initio calculations in chemistry (Szabo and Ostlund [1982]). The basic problem is to calculate the energy of an atom, for example, from first principles, without recourse to any experimental facts. The procedure consists in solving the time independent Schrodinger for the atom in question, but unfortunately only... 

The basic problem in regard to the safety of rechargeable metal cells is how to manage the heat generated in a cell when it is abused. The temperature of a cell is determined by the balance between the amount of heat generated in the cell and the heat dissipated outside the cell. Heat is generated in a cell by thermal decomposition and /or the reaction of materials in the cell, as listed below ... 

The approach just outlined is after-the-fact approach to QC all defects caught in this manner are already present in the product being processed. This type of QC will usually catch defects and is necessary, but it does little to correct the basic problem(s) in production. One of the problems with add-on QC of this type is that it constitutes one of the least cost-effective ways of obtaining quality products. Quality must be built into a product from the beginning of the design that follows the FALLO approach (Fig. 1-3) it cannot be inspected into the process. The target is to control quality before a product becomes defective. 

In the search for a better approach, investigators realized that the ignition of a combustible material requires the initiation of exothermic chemical reactions such that the rate of heat generation exceeds the rate of energy loss from the ignition reaction zone. Once this condition is achieved, the reaction rates will continue to accelerate because of the exponential dependence of reaction rate on temperature. The basic problem is then one of critical reaction rates which are determined by local reactant concentrations and local temperatures. This approach is essentially an outgrowth of the bulk thermal-explosion theory reported by Fra nk-Kamenetskii (F2). 

Because of the enormous range of difference approximations to an equation having similar asymptotic properties with respect to a grid step (the same order of accuracy or the number of necessary operations), their numerical realizations resulted in the appearance of different schemes for solving the basic problems in mathematical physics. 

In all the variational methods, the choice of trial function is the basic problem. Here we are concerned with the choice of the trial function for the polarization orbitals in the calculation of polarizabilities or hyperpolarizabilities. Basis sets are usually energy optimized but recently we can find in literature a growing interest in the research of adequate polarization functions (27). 

The basic problems involved in emulsion and foam chemistry are discussed with emphasis on how to solve them and how to correlate the information thus obtained for future use and interpretation. A blending of theoretical and practical knowledge has to be used, and examples are given to illustrate the methods of solving the industrial problems involved. 

The basic problem is to search for the parameter vector k that minimizes S(k) by following an iterative scheme, i.e.,... 

Classic optimization techniques result from application of calculus to the basic problem of finding the maximum or minimum of a function. The techniques themselves have limited application, but they might be useful for problems that are not too complex and do not involve more than a few variables. The concept, however is important. 

This is the basic problem with any attempt to evaluate the overall effectiveness of placebos, as Beecher and the Danish researchers had tried to do. There is not just one placebo effect. Instead, the placebo effect depends on a host of factors. It depends, for example, on the condition being treated, the way in which the placebo is administered, the colour of the placebo, its price, whether it has a recognized brand name and the dose that is prescribed. Studies of the placebo effect reveal that, all else being equal, taking placebo pills four times per day is more effective than taking them only twice a day brand-name placebos are more effective than placebos presented as generic drugs placebo injections are more effective than placebo pills and more expensive placebos are better than cheaper ones.16... 

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