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A reactor model to simulate the visbreaking process is developed. The model includes two types of visbreaking reactors: coil and soaker. For the vaporization in the reactor to be taken into account, the vapor–liquid equilibrium (VLE) is first determined, and then the reactor model is solved only with the liquid phase because thermal cracking reactions occurring during visbreaking take place in this phase. The variation of liquid and vapor flow rates are also taken into consideration. A reaction scheme based on nine pseudocomponents and kinetic expressions reported in the literature were used. It was found that VLE affects the prediction of reactor conversion depending on the feedstock and the operating conditions. The residue conversion decreases when VLE is considered, which is due to vaporization diminishing the reactor space available for performing the reactions. The model predicts greater mass fractions of gas and naphtha than the experimental values. This is because the model assumes that they are produced by all pseudocomponents heavier than them. It is anticipated that the proposed model can be used in complex refinery planning studies with more reliability than the empirical models available to date.

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The robust observer design for the online estimation of heat in continuous stirred tank reactors, containing nonstructured uncertainties within its model description as well as noisy temperature measurements, is addressed. The proposed observer contains a sliding-mode term and is designed based on Differential Algebraic technique. The concept of the algebraic observability for a given class of model uncertainty is introduced. It is applied to the uncertainty estimation from noisy temperature measurements providing a simple observer structure which turns out to be robust against output (sensors) noises as well as sustained disturbances. The performance of this observer is shown to be calculated numerically. The obtained results look promising for possible industrial applications.

Experimental studies were developed in a batch reactor (16 dm 3 ), to obtain the kinetic model of Cr(VI) removal by means of an electrochemical process. An overall kinetic model was obtained and experimentally validated in a continuous stirred electrochemical reactor (16 dm 3 ) with synthetic and industrial wastewater. To develop the mathematical model of the continuous reactor in relation to the Cr(VI) and Fe(II) concentration in the solution, a classical mass balance procedure was performed. The Cr(VI) concentration in the electrochemically-treated waters was less than 0.5 mg dm À3. In the electrochemical process the Cr(VI) reduction is caused by the Fe(II) released from the anode due to the electric current applied, by the Fe(II) released for the dissolution (corrosion) of the electrodes due to the acidic media, and by reduction at the cathode. During the process, reduction from Fe(III) to Fe(II) occurs. All of these different reactions cause a diminution in the quantity of sludge generated. Finally, it was found that due to the slow rate of reduction of Cr(VI) during the first part of the process it is necessary to develop a method of control to apply the process in a continuous industrial system.

This article proposes a simple "in-situ" pulse respirometric method for the estimation of four important kinetic and stoichiometric parameters. The method is validated in a suspended biomass nitrifying reactor for the determination of (i) maximum oxygen uptake rate (OUR(ex)max), (ii) oxidation yield (f(E)), (iii) biomass growth yield (f(S)), and (iv) affinity constant (K(S)). OUR(ex)max and f(E) were directly obtained from respirograms. In the presented case study, a minimum substrate pulse of 10 mgNH(4) (+)-N L(-1) was necessary to determine OUR(ex)max which was 61.15 +/- 4.09 mgO(2) L(-1) h(-1) (5 repetitions). A linear correlation (r(2) = 0.93) obtained between OUR(ex)max and the biomass concentration in the reactor suggests that biomass concentration can be estimated from respirometric experiments. The substrate oxidation yield, f(E), was determined along 60 days of continuous operation with an average error of 5.6%. The biomass growth yield was indirectly estimated from the substrate oxidation yield f(E). The average obtained value (0.10 +/- 0.04 mgCOD mg(-1)COD) was in accordance with the f(S) estimation by the traditional COD mass balance method under steady-state conditions (0.09 +/- 0.01). The affinity constant K(S) was indirectly estimated after fitting the ascending part of the respirogram to a theoretical model. An average value of 0.48 +/- 0.08 mgNH(4) (+)-N L(-1) was obtained, which is in the range of affinity constants reported in the literature for the nitrification process (0.16-2 mgNH(4) (+)-N L(-1)).