Dynamics of a Bioreactor with a Bacteria Piecewise-Linear Growth Model in a Methane-Producing Process

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1. Introduction

Currently, anaerobic methods are applied to reduce water contamination problems. With these methods, we can reduce the percentages of chemical oxygen demand (COD) and biological oxygen demand (BOD), which are measurements of water quality. Depuration through anaerobic treatments converts organic matter in wastewater into methane (CH₄—biogas) and carbonic gas (CO₂). Methane can be used as an energetic component because it offers good calorific power, and CO₂ can be recirculated to the bioreactor to improve the percentages of biogas yield, thus decreasing organic loads. Organic loads contain high concentrations of organic matter that originates from water circulation in garbage, which dissolves the elements present in it when running through the waste. The result is an environmentally damaging liquid that contaminates the soil and superficial and subterranean waters in their path. For this reason, leachates, among others, are one of the most significant contaminating agents in a landfill as has been extensively discussed in the literature (see, e.g., [1–3]).

In this paper, we are mainly interested in leachates since our experimental secondary data comes from this sort of wastewaters. The most used systems for leachate treatment are the so-called high-rate systems, such as the UASB reactor (Figure 1). This bioreactor separates different phases: biological (sludge bed), liquid (sludge blanket), and gas (upper section). The wastewater enters the reactor through its lower section and exits through the upper section. The reactor has no filling to support biological growth. The sludge created in the reactor can be divided into two...