The transient startup behavior of a liquid-liquid extraction pulse column

Abstract

The transient startup behavior of _a liquid-liquid extraction pulse column was investigated experimentally and mathematically. The purpose of the research was to develop methods for estimating the transient response curves and times required to reach steady state. Experimental data were obtained on a pulse column 20 feet high and 3 inches in inside diameter. The plate section of the column contained 79 plates spaced % inches apart. A tributyl phosphate/Varsol-nitric acidwater ternary extraction system was used. The column system was operated for approximately 200 hours to obtain the experimental transient response curves. Each run lasted from 4 to 9 hours. Transients were introduced as step changes in the nitric acid feed concentration after the column had been operating under acid free steady state conditions. Raffinate concentration versus time curves were deter­ mined continuously with a continuous electrolytic conductivity detector and recorder. The mathematical transient response curves were obtained from the so­ lution of mathematical models describing the column behavior. Ordinary differential equations were formed by either reducing the partial differ­ ential equations describing the column behavior to finite difference form or by forming transient material balances over finite sections of the col­ umn . Nine different mathematical models or combinations were formed. The partial differential equations describing the system behavior were derived on the basis of plug flow down a packed counter-current ex­ traction column. Longitudinal diffusion and mixing were neglected. The sets of ordinary differential equations were integrated on both analog and digital computers. For the analog computer the equilibrium curve was linearized. For the digital computer the non-linear equilibrium curve was used and expressed in polynomial or tabular form. A modified Runge-Kutta numerical procedure was used in the integration of the sets of equations. The largest number of equations integrated in one set was 128. The response curves from the various mathematical models were com­ pared with those from experimental data. Three of the models produced good estimates of the time required to reach steady state. The dead time portion of the curves was reproduced by two of the material balance models when the column subdivision was sufficiently refined. The models which xere formed by substituting an interlocking finite difference representa­ tion for the height derivative produced curves which oscillated during the dead time period but which reproduced the experimental data fairly well thereafter. The mathematical simulations would have been improved if a longitudi­ nal turbulent diffusion term had been included. The experimental data in­ dicated that significant longitudinal diffusion occurred.