Corrected kriging update formulae for batch-sequential data assimilation

Recently, a lot of effort has been spent in the efficient computation of kriging predictors when observations are assimilated sequentially. In particular, kriging update formulae enabling significant computational savings were derived. Taking advantage of the previous kriging mean and variance computations helps avoiding a costly matrix inversion when adding one observation to the TeX already available ones. In addition to traditional update formulae taking into account a single new observation, Emery (2009) proposed formulae for the batch-sequential case, i.e. when TeX new observations are simultaneously assimilated. However, the kriging variance and covariance formulae given in Emery (2009) for the batch-sequential case are not correct. In this paper, we fix this issue and establish correct expressions for updated kriging variances and covariances when assimilating observations in parallel. An application in sequential conditional simulation finally shows that coupling update and residual substitution approaches may enable significant speed-ups.

KrigInv: An efficient and user-friendly implementation of batch-sequential inversion strategies based on kriging

Several strategies relying on kriging have recently been proposed for adaptively estimating contour lines and excursion sets of functions under severely limited evaluation budget. The recently released R package KrigInv 3 is presented and offers a sound implementation of various sampling criteria for those kinds of inverse problems. KrigInv is based on the DiceKriging package, and thus benefits from a number of options concerning the underlying kriging models. Six implemented sampling criteria are detailed in a tutorial and illustrated with graphical examples. Different functionalities of KrigInv are gradually explained. Additionally, two recently proposed criteria for batch-sequential inversion are presented, enabling advanced users to distribute function evaluations in parallel on clusters or clouds of machines. Finally, auxiliary problems are discussed. These include the fine tuning of numerical integration and optimization procedures used within the computation and the optimization of the considered criteria.

A potential application of sludge-based catalysts for the anaerobic bio-decolorization of tartrazine dye.

Two highly efficient (K2CO3/sludge carbon and ZnCl2/sludge carbon) solids were prepared by chemical addition following carbonization at 800 °C and were tested for anaerobic reduction of tartrazine dye in a continuous upflow packed-bed biological reactor, and their performance was compared to that of commercial activated carbon (CAC). The chemical and structural information of the solids was subjected to various characterizations in order to understand the mechanism for anaerobic decolorization, and efficiency for SBCZN800 and SBCPC800 materials was 87% and 74%, respectively, at a short space time (τ) of 2.0 min. A first-order kinetic model fitted the experimental points and kinetic constants of 0.40, 0.92 and 1.46 min(-1) were obtained for SBCZN800, SBCPC800 and CAC, respectively. The experimental results revealed that performance of solids in the anaerobic reduction of tartrazine dye can depend on several factors including chemical agents, carbonization, microbial population, chemical groups and surface chemistry. The Langmuir and Freundlich models are successfully described in the batch adsorption data. Based on these observations, a cost-effective sludge-based catalyst can be produced from harmful sewage sludge for the treatment of industrial effluents.

Characterization and performance of carbonaceous materials obtained from exhausted sludges for the anaerobic biodecolorization of the azo dye Acid Orange II.

This work presents the preliminary study of new carbonaceous materials (CMs) obtained from exhausted sludge, their use in the heterogeneous anaerobic process of biodecolorization of azo dyes and the comparison of their performance with one commercial active carbon. The preparation of carbonaceous materials was conducted through chemical activation and carbonization. Chemical activation was carried out through impregnation of sludge-exhausted materials with ZnCl2 and the activation by means of carbonization at different temperatures (400, 600 and 800°C). Their physicochemical and surface characteristics were also investigated. Sludge based carbonaceous (SBC) materials SBC400, SBC600 and SBC800 present values of 13.0, 111.3 and 202.0m(2)/g of surface area. Biodecolorization levels of 76% were achieved for SBC600 and 86% for SBC800 at space time (τ) of 1.0min, similar to that obtained with commercial activated carbons in the continuous anaerobic up-flow packed bed reactor (UPBR). The experimental data fit well to the first order kinetic model and equilibrium data are well represented by the Langmuir isotherm model. Carbonaceous materials show high level of biodecolorization even at very short space times. Results indicate that carbonaceous materials prepared from sludge-exhausted materials have outstanding textural properties and significant degradation capacity for treating textile effluents.