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Lange and Carson (1984 J. Comput. Assist. Tomogr. 8 306–16) defined image reconstruction for transmission tomography as a maximum likelihood estimation problem and derived an expectation maximization (EM) algorithm to obtain the maximum likelihood image estimate. However, in the maximization step or M-step of the EM algorithm, an approximation is made in the solution which can affect the image quality, particularly in the case of domains with high attenuating material. O'Sullivan and Benac (2007 IEEE Trans. Med. Imaging 26 283–97) reformulated the maximum likelihood problem as a double minimization of an I-divergence to obtain a family of image reconstruction algorithms, called the alternating minimization (AM) algorithm. The AM algorithm increases the log-likelihood function while minimizing the I-divergence. In this work, we implement the AM algorithm for image reconstruction in gamma ray tomography for industrial applications. Experimental gamma ray transmission data obtained with a fan beam geometry gamma ray scanner, and simulated transmission data based on a synthetic phantom, with two phases (water and air) were considered in this study. Image reconstruction was carried out with these data using the AM and the EM algorithms to determine and quantitatively compare the holdup distribution images of the two phases in the phantoms. When compared to the EM algorithm, the AM algorithm shows qualitative and quantitative improvement in the holdup distribution images of the two phases for both the experimental and the simulated gamma ray transmission data.

Advanced non-invasive experiments like computer automated radioactive particle tracking and computed tomography along with computational fluid dynamics (CFD) simulations were performed in mimic anaerobic digesters to visualize their flow pattern and obtain hydrodynamic parameters. The mixing in the digester was provided by sparging gas at three different flow rates. The simulation results in terms of overall flow pattern, location of circulation cells and stagnant regions, trends of liquid velocity profiles, and volume of dead zones agree reasonably well with the experimental data. CFD simulations were also performed on different digester configurations. The effects of changing draft tube size, clearance, and shape of the tank bottoms were calculated to evaluate the effect of digester design on its flow pattern. Changing the draft tube clearance and height had no influence on the flow pattern or dead regions volume. However increasing the draft tube diameter or incorporating a conical bottom design helped in reducing the volume of the dead zones as compared to a flat bottom digester. The simulations showed that the gas flow rate sparged by a single point (0.5 cm diameter) sparger does not have appreciable effect on the flow pattern of the digesters.

The effects of sparger design and gas flow rate on, gas holdup distribution and liquid (slurry) recirculation velocity have been studied in a surrogate anaerobic bioreactor used for treating bovine waste with a conical bottom mixed by gas recirculation. A single orifice sparger (SOS) and a multi-orifice ring sparger (MORS) with the same orifice open area and gas flow rates (hence the same process power input) are compared in this study. The advanced non-invasive techniques of computer automated tomography (CT) and computer automated radioactive particle tracking (CARPT) were employed to determine gas holdup, liquid recirculation velocity, and the poorly mixed zones. Gas flows (Q(g)) ranging of 0.017 x 10(-3) m(3)/s to 0.083 x 10(-3) m(3)/s were used which correspond to draft tube superficial gas velocities ranging from 1.46 x 10(-2) m/s to 7.35 x 10(-2) m/s (based on draft tube diameter). Air was used for the gas, as the molecular weights of air and biogas (consisting mainly of CH(4) and CO(2)) are in the same range (biogas: 28.32-26.08 kg/kmol and air: 28.58 kg/kmol). When compared to the SOS for a given gas flow rate, the MORS gave better gas holdup distribution in the draft tube, enhanced the liquid (slurry) recirculation, and reduced the fraction of the poorly mixed zones. The improved gas holdup distribution in the draft tube was found to have increased the overall liquid velocity. Hence, for the same process power input the MORS system performed better by enhancing the liquid recirculation and reducing the poorly mixed zones.