The present work deals with the modeling of the kinetics of essential oils extraction from plant materials by water and steam distillation. The experimental data were obtained by studying the hydrodistillation kinetics of essential oil from juniper berries. The literature data on the kinetics of essential oils hydrodistillation from different plant materials were also included into the modeling. A physical model based on simultaneous washing and diffusion of essential oil from plant materials were developed to describe the kinetics of essential oils hydrodistillation, and two other simpler models were derived from this physical model assuming either instantaneous washing followed by diffusion or diffusion with no washing (i.e., first-order kinetics). The main goal was to compare these models and suggest the optimum ones for water and steam distillation and for different plant materials. All three models described well the experimental kinetic data on water distillation irrespective of the type of distillation equipment and its scale, the type of plant materials and the operational conditions. The most applicable model is the one involving simultaneous washing and diffusion of the essential oil. However, this model was generally inapplicable for steam distillation of essential oils, except for juniper berries. For this hydrodistillation technique, the pseudo first-order model was shown to be the best one. In a few cases, a variation of the essential oil yield with time was observed to be sigmoidal and was modeled by the Boltzmann sigmoid function.

This paper presents kinetics modeling of essential oil hydrodistillation from juniper berries (Juniperus communis L.) by using a non-linear regression methodology. The proposed model has the polynomial-logarithmic form. The initial equation of the proposed non-linear model is q = q??(a?(logt)2 + b?logt + c) and by substituting a1=q??a, b1 = q??b and c1 = q??c, the final equation is obtained as q = a1?(logt)2 + b1?logt + c1. In this equation q is the quantity of the obtained oil at time t, while a1, b1 and c1 are parameters to be determined for each sample. From the final equation it can be seen that the key parameter q?, which presents the maximal oil quantity obtained after infinite time, is already included in parameters a1, b1 and c1. In this way, experimental determination of this parameter is avoided. Using the proposed model with parameters obtained by regression, the values of oil hydrodistillation in time are calculated for each sample and compared to the experimental values. In addition, two kinetic models previously proposed in literature were applied to the same experimental results. The developed model provided better agreements with the experimental values than the two, generally accepted kinetic models of this process. The average values of error measures (RSS, RSE, AIC and MRPD) obtained for our model (0.005; 0.017; ?84.33; 1.65) were generally lower than the corresponding values of the other two models (0.025; 0.041; ?53.20; 3.89) and (0.0035; 0.015; ?86.83; 1.59). Also, parameter estimation for the proposed model was significantly simpler (maximum 2 iterations per sample) using the non-linear regression than that for the existing models (maximum 9 iterations per sample). [Project of the Serbian Ministry of Education, Science and Technological Development, Grant no. TR-35026]

The main problem of hydraulic transport is the resistance generated during the mixture transport through the pipeline. Testing the flow characteristics of mixtures, shown in this paper, are based on the principles of determining the unit energy losses by a mathematical calculation using the non-linear regression-the Levenberg-Marquardt algorithm. Such obtained results allow determining a transport rate in the horizontal pipeline , depending on the mixture bulk density and pipeline diameter. The flotation tailings is mainly used as a filling material in the mine "Trepca"-Stari Trg. According to the grain size distribution, it is a finegrained material of a size of 0.074 mm to 1.2 mm. It is a multicomponent material containing pyrite, pyrrhotine and other heavy metals, and therefore, has a high bulk mass. The average rate of the hydromixture, in which the energy losses reach the minimum value, depends on the pipeline diameter and kinetic bulk density of the mixture. For the test interval of change in the pipeline diameter, shown in this paper (0.168 mm, 0.176 mm, 0.193 mm, and 0.225 mm), and kinetic bulk density of the hydraulic mixture (1-1.6 kg/m 3), this rate ranges from 3-5.5 m/s. The increase of the energy losses in the hydraulic mixture transport increases proportionality with the increase of its kinetic bulk density. The results, presented in this paper, show that the required bulk density of 1.6 kg/m 3 should be accepted as a limit from a point of view of the hydraulic transport cost-efficiency.