NITRATE REMOVAL IN WOODCHIP DENITRIFICATION BIOREACTOR – AN APPROACH COMBINING MATHEMATICAL MODELLING AND PI CONTROL

A mathematical model of nitrate removal in woodchip denitrification bioreactor based on field experiment measurements was developed in this study. The approach of solving inverse problem for nonlinear system of differential convection-reaction equations was applied to optimize the efficiency of nitrate removal depending on bioreactor’s length and flow rate. The approach was realized through the developed algorithm containing a nonlocal condition with an incorporated PI controller. This allowed to adjust flow rate for varying inflow nitrate concentrations by using PI controller. The proposed model can serve as a useful tool for bioreactor design. The main outcome of the model is a mathematical relationship intended for bioreactor length selection when nitrate concentration at the inlet and the flow rate are known. Custom software was developed to solve the system of differential equations aiming to ensure the required nitrate removal efficiency.

Implementasi Rancangan Pembelajaran Berbasis Sharing dan Jumping Task pada Konsep Hukum Kekekalan Massa

The law of conservation of mass is a fundamental law and is related to other chemical materials such as chemical reaction equations so that student's learning obstacles of the law of conservation of mass must be overcome. One of the ways to overcome student's learning obstacles of the law of conservation of mass concept is the implementation of sharing and jumping task based lesson design, which is the aim of this research. The research method used is a qualitative descriptive research method. The research subjects were students of X.1 and X.2 SMA in Bandung and chemistry teacher who collaborate with researcher as team teaching. The data on the implementation of sharing and jumping task based lesson design of the law of conservation of mass was obtained from observations, tests, and interviews. Implementation of sharing and jumping task based lesson design of the law of conservation of mass concept was carried out twice. The result of the first implementation is that the previously identified learning obstacles still appear but in a smaller percentage. After the first implementation of the lesson design, it was revised and implemented in other class. The results of the second implementation can overcome student's learning obstacle who think that the mass of solids is heavier than the mass of liquids, but a small number of students still do not take into account the mass of gases in chemical reactions and do not fully understand the meaning of the law of conservation of mass.

Mathematical model of shallow water self-purification process

The paper covers the model of shallow water self-purification processes. The proposed mathematical model of biological kinetics is based on a system of non-stationary convection-diffusion-reaction equations with nonlinear terms, taking into account the water flow movement, gravitational sedimentation of impurities, microturbulent diffusion, and the detritus decomposition as a result of activity the aerobic and anaerobic bacteria. Discretization is performed on the basis of a linear combination of central and Upwind Leapfrog difference schemes, which makes it possible to increase the solution accuracy of biological kinetics problem at large values of the grid Péclet number (Peh > 2). To solve high-dimensional SLAEs, a modified alternating-triangular method was used.

A priori error estimates for finite element approximations to transient convection-diffusion-reaction equations in fluidized beds

In this work, a priori error estimates for finite element approximations to the governing equations of heat and mass transfer in fluidized beds are derived. These equations are time dependent strongly coupled system of five semilinear convection-diffusion-reaction equations. The a priori error estimates for all the five variables are obtained for the error measured in L ∞(L 2) and L 2 ( E ) ${L}^{2}\left(\mathcal{E}\right)$ , E $\mathcal{E}$ is the energy norm.