Modeling the kinetics of essential oil hydrodistillation from juniper berries (Juniperus communis L.) using non-linear regression

Abstract

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).