Incorporating Danckwerts’ boundary conditions into the solution of the stochastic differential equation

Adsorption Measurements of Nitrogen and Methane in Hydrogen-Rich Mixtures at High Pressures

“…The well-known Danckwerts boundary condition, represented by the first line in the preceding of equations, was applied at the inlet of the adsorber. Such conditions allow dispersion effects on the concentration at the inlet and are obtained for cases in which the continuity of the concentration is lost at the origin …”

Various applications of the dispersion model for flow systems with Danckwerts’ boundary conditions

“…This procedure was employed during comparison of results by stochastic modeling and analytical solution of relations analogous to Eq. (1) (Siyakatshana et al, 2005). The next example can be the analytical derivation of Eq.…”

“…In relation to this, previously derived equations will be extended for multi-stage systems. Also an allusion will be made on the 'mathematical' application of the proposed method as used in the context of stochastic modeling of similar processes (Siyakatshana et al, 2005). When denoting resulting (computational) relations, the system of multiple summations will be used to a great extent, which also provides a directive for the creation of corresponding computational subroutines.…”

Modeling an annular flow tubular reactor

“…Siyakatshana et al (2005) incorporated Danckwerts' boundary conditions into the solution of a stochastic axial dispersion model. They obtained E(t) and F(t) curves by setting the axial dispersion parameter equal to 1/2s 2 , which is the instantaneous variance from Eq.…”