Co-Hydroprocessing of Fossil Middle Distillate and Bio-Derived Durene-Rich Heavy Ends under Hydrotreating Conditions

Methanol-to-gasoline (MTG) and dimethyl ether-to-gasoline (DTG), as industrially approved processes for producing greenhouse gas-neutral gasoline, yield byproducts rich in heavy mono-ring aromatics such as 1,2,4,5-tetramethylbenzene (durene). Due to its tendency to crystallize and the overall poor fuel performance, the heavy fuel fraction is usually further processed using aftertreatment units designed for this purpose. This research article discusses the co-hydroprocessing (HP) of bio-derived heavy gasoline (HG) with fossil middle distillate (MD), drawing on available refinery hydrotreaters. Co-HP experiments were conducted in a laboratory-scale fixed bed reactor using an industrial CoMo/g-Al2O3 catalyst, varying the space-time between 0.7 and 4.0 cm3 Cat h cm3 Feed and the reaction temperature between 340 and 390 °C. In addition to the durene conversion, special attention was paid to the octane and cetane numbers (CN) of gasoline and MD, respectively. A six-lump model with ten parameters was developed to predict relevant fuel yields dependent on the process conditions. Under stable catalyst conditions, C10 aromatic conversions of more than 60% were obtained, while the CN remained close to that of pure MD. Harsh process conditions increased the gasoline yield up to 20% at the cost of MD, while the kerosene yield remained almost constant. With an optimized lumping model, fuel yields could be predicted with an R2 of 0.998. In this study, co-HP heavy aromatic-rich MTG/DTG fuels with fossil MD were proven to be a promising process strategy compared to a stand-alone after-treatment

Discretisation-invariant swaps and higher-moment risk premia

This thesis introduces a general framework for model-free discretisation-invariant swaps. In the first main chapter a novel design for swap contracts is developed where the realised leg is modified such that the fair value is independent of the monitoring partition. An exact swap rate can then be derived from the price aportfolio of vanilla out-of-the-money options without any discrete-monitoring or jump errors. In the second main chapter the P&Ls on discretisation-invariant swaps associated with the variance, skewness and kurtosis of the log return distribution are used as estimators for the corresponding higher-moment risk premia. An empirical study on the S&P 500 investigates the factors determining these risk premia for different sampling frequencies and contract maturities. In the third main chapter the dynamics of conventional and discretisation-invariant variance swaps and variance risk premia are compared in an affine jump-diffusion setting. The ideas presented in this thesis set the ground for many interesting and practically relevant applications

Exact and Parameterized Algorithms for the Independent Cutset Problem

The Independent Cutset problem asks whether there is a set of vertices in a given graph that is both independent and a cutset. Such a problem is $\textsf{NP}$-complete even when the input graph is planar and has maximum degree five. In this paper, we first present a $\mathcal{O}^*(1.4423^{n})$-time algorithm for the problem. We also show how to compute a minimum independent cutset (if any) in the same running time. Since the property of having an independent cutset is MSO$_1$-expressible, our main results are concerned with structural parameterizations for the problem considering parameters that are not bounded by a function of the clique-width of the input. We present $\textsf{FPT}$-time algorithms for the problem considering the following parameters: the dual of the maximum degree, the dual of the solution size, the size of a dominating set (where a dominating set is given as an additional input), the size of an odd cycle transversal, the distance to chordal graphs, and the distance to $P_5$-free graphs. We close by introducing the notion of $\alpha$-domination, which allows us to identify more fixed-parameter tractable and polynomial-time solvable cases.Comment: 20 pages with references and appendi

On Conflict-Free Cuts: Algorithms and Complexity

One way to define the Matching Cut problem is: Given a graph $G$, is there an edge-cut $M$ of $G$ such that $M$ is an independent set in the line graph of $G$? We propose the more general Conflict-Free Cut problem: Together with the graph $G$, we are given a so-called conflict graph $\hat{G}$ on the edges of $G$, and we ask for an edge-cutset $M$ of $G$ that is independent in $\hat{G}$. Since conflict-free settings are popular generalizations of classical optimization problems and Conflict-Free Cut was not considered in the literature so far, we start the study of the problem. We show that the problem is $\textsf{NP}$-complete even when the maximum degree of $G$ is 5 and $\hat{G}$ is 1-regular. The same reduction implies an exponential lower bound on the solvability based on the Exponential Time Hypothesis. We also give parameterized complexity results: We show that the problem is fixed-parameter tractable with the vertex cover number of $G$ as a parameter, and we show $\textsf{W[1]}$-hardness even when $G$ has a feedback vertex set of size one, and the clique cover number of $\hat{G}$ is the parameter. Since the clique cover number of $\hat{G}$ is an upper bound on the independence number of $\hat{G}$ and thus the solution size, this implies $\textsf{W[1]}$-hardness when parameterized by the cut size. We list polynomial-time solvable cases and interesting open problems. At last, we draw a connection to a symmetric variant of SAT.Comment: 13 pages, 3 figure