Michelsen

The eigenvalue problem defined by equations (12.56) and (12.37) has been studied by Lee and Luss l79j and, more recently, in considerable detail by Villadsen and Michelsen When - I it is easy to show... 

R. M. Woodby and D. L. Michelsen, Emerging Technologies for Hazardous Waste Treatment Sjmposium, I EC Division of ACS, Atiantic City, N.J., June 4-7,1990. 

Vihadsen, J. V, and M. L. Michelsen. Solution of Differ ential Equation Models by Polynomial Approximation. Prentice Hall, Englewood Cliffs, NJ(1978). 

Flash-drum specifications in addition to (T9, T9) and (T9, adiabatic) are also possible but must be applied with care, as discussed by Michelsen [Comp. Chem. Engng., 17,431 (1993)]. Most computer-aided process design and simulation programs permit a wide variety of flash specifications. 

The development of mathemafical models is described in several of the general references [Giiiochon et al., Rhee et al., Riithven, Riithven et al., Suzuki, Tien, Wankat, and Yang]. See also Finlayson [Numerical Methods for Problems with Moving Front.s, Ravenna Park, Washington, 1992 Holland and Liapis, Computer Methods for Solving Dynamic Separation Problems, McGraw-Hill, New York, 1982 Villadsen and Michelsen, Solution of Differential Equation Models by... 

CMR - Christian Michelsen Research - a Norwegian PSA consulting company, completeness - The degree to which all accidents have been considered. 

Lee, J. H. S, Knystautas, R., and Goroshm, S. 1996. The Testing of Detonation Arresters. Proc. Inti. Symp. On Hazards Prevention and Mitigation of Industrial Explosions, pp. 7.27-7.40. Christian Michelsen Research AS, Bergen, Norway. 

Bakke, J. R., and B. H. Hjertager. 1986a. Quasi-laminar/turbulent combustion modeling, real cloud generation and boundary conditions in the FLACS-ICE code. CMI No. 865402-2. Chr. Michelsen Institute, 1986. Also in Bakke s Ph.D. thesis Numerical simulation of gas explosions in two-dimensional geometries. University of Bergen, Bergen, 1986. 

Michelsen, A., Schmidt, I.K., Jonasson, S., Quarmby, C. and Sleep, D. 1996b Leaf N abundance of subarctic plants provides field evidence that ericoid, ectomycorhizal, and non- and arbus-cular mycorhizal species access different sources of soil nitrogen. Oecologia 105 53-63. 

Michelsen, M.L. Phase Equilibrium Calculations. What is Easy and What is Difficult Computers Chem. Eng, 17,431-439 (1993). 

Hamm, U. Michelsen, J. (2000) Analysis of the organic food market in Europe. Proceedings of the 13th International IFOAM Scientific Conference, Basel, Switzerland, pp 507-510. 

Fredenslund, A., Gmehling, J., Michelsen, M. L., Rasmussen, P. and Prausnitz, J. M. (1977a) Ind. Eng. Chem. Proc. Des. and Dev. 16, 450. Computerized design of multicomponent distillation columns using the UNIFAC group contribution method for calculation of activity coefficients. 

In addition to the three methods described above, nonlinear regression methods or other transform approaches may be used to determine the dispersion parameter. For a more complete treatment of the use of transform methods, consult the articles by Hopkins et al. (15) and Ostergaard and Michelsen (14). 

The differential equation is evaluated at certain collocation points. The collocation points are the roots to an orthogonal polynomial, as first used by Lanczos [Lanczos, C.,/. Math. Phys. 17 123-199 (1938) and Lanczos, C., Applied Analysis, Prentice-Hall (1956)]. A major improvement was proposed by Villadsen and Stewart [Villadsen, J. V., and W. E. Stewart, Chem. Eng. Sci. 22 1483-1501 (1967)], who proposed that the entire solution process be done in terms of the solution at the collocation points rather than the coefficients in the expansion. This method is especially useful for reaction-diffusion problems that frequently arise when modeling chemical reactors. It is highly efficient when the solution is smooth, but the finite difference method is preferred when the solution changes steeply in some region of space. The error decreases very rapidly as N is increased since it is proportional to [1/(1 - N)]N 1. See Finlayson (2003) and Villadsen, J. V., and M. Michelsen, Solution of Differential Equation Models by Polynomial Approximations, Prentice-Hall (1978). 

Michelsen J. (2001) Recent development and political acceptance of organic farming in Europe , Sociologia Ruralis, 41 (1) on Politics, Ideology and Practice of Organic Farming, 3-20. 

Wypych, P. W., and Arnold, P. C., Predicting and Improving Flow Performance in Dense-Phase Pneumatic Transportation, Int. Symp. on the Reliable Flow of Particulate Solids, Organised by the Chr Michelsen Institute, Bergen, Norway (1985a)... 

Dubrow SF, Boardman GD, Michelsen DL (1996) Chemical pretreatment and aerobic-anaerobic degradation of textile dye wastewater. In Reife A, Freeman HS (eds) Environmental chemistry of dyes and pigments. Wiley, New York... 

Westeott BL, Gruhn N, Michelsen L, Lichtenberger D (2000) Experimental observation of non-aufbau behavior photoelectron spectra of vanadyloctaethylporphyrinate and vana-dylphthalocyanine. J Am Chem Soc 122 8083-8089... 

In oil and gas facilities, these effects can be generally related to flame velocity, where this velocity is below 100 m/s (300 ft./s), damage is considered unlikely (Note This is generally within the limits of confinement normally found in offshore facilities). The size of a vapor cloud or plume in which such velocities can occur has been experimentally investigated at the Christian Michelsen Institute (CMI, Norway). The experiments demonstrated that flames need a "run-up" distance of approximately 5.5 meters (18 ft.) to reach damaging speeds. Therefore vapor clouds with dimensions less than this may not cause substantial damage. This is a much over-simplification of the factors and variables involved, but does assume the WCCE of congestion, confinement and gas concentrations. 

---