When mineral processing separation results, for either constant or varying quality of the feed, can be approximated on the so-called Fuerstenau upgrading plots with the same one-fitting parameter a, then this parameter can be used as a selectivity indicator. If the equation has a form [...], where [...] stands for recovery of non-useful component in tailing while\ksi is the recovery of useful component in the concentrate, then at the same selectivity of upgrading (constant a) the increase of the useful component in the feed \alfa results in an increased amount of this component in both concentrate \beta and tailing [...] while the ratio of [...] to \beta is linearly dependent on \alfa when \epsilon is constant. Thus, at a constant selectivity a and constant \epsilon an increase in \alfa leads to a greater increase of the considered component in the tailing \theta than in the concentrate \beta.

The separation or beneficiation processes are conducted in many devices and concern many various types of minerals and raw materials. The aim of conducting these processes is always to achieve the best possible results allowing as much of the useful component as possible to be obtained by maintaining reasonable costs of the process. Therefore, it is important to have the possibility to monitor the process effects and to have efficient tools to evaluate the course of it. Generally, the ore’s ability to partition into concentrate and tailings is called its efficiency, upgradeability etc. It can be said that there is no unambiguous measure of upgradeability and there are many factors in use which enable to evaluate it qualitatively. Among them are such commonly known parameters as: recovery, losses, yield, upgrading ratio and many others. They are based on three principal parameters that is the average content of the useful component α, the contents of this component in concentrate β and the contents of this component in tailings ϑ. For a given ore (assuming that α = constant), the multi-product separation results can be treated as points of a trajectory located on the surface of factor w in a three dimensional space (β, ϑ, w). The course of the trajectory depends on the ore petrographic and mineralogical properties preparation for the process. For these reasons, searching for optimal (potential) possibilities of the ore is relative, which is presented in the example of Halbich, Fuerstenau and Madej upgrading curves. Such curves are efficient tools to evaluate the course of a separation (beneficiation) process and each of their types allow the effects to be shown in different perspective. Apart from this, they allow also the optimal feed conditions to conduct a certain process with aim of achieving the expected results to be found. Furthermore, the effect of the ore preparation on the flotation results, on the sum of recoveries of the useful component in concentrate and residual recovery in tailings is presented in the paper. The results indicated that any additional contamination of concentrate should be taken into account during the organization of the flotation process. In this way, the results of fractionated flotation have much valuable information to establish the course of the process.

In recent years, more and more attention has been paid to the quality of produced coal size categories for energy purposes. This is important from the perspective of promoting clean coal technologies which aim at changing the perception of coal as a fuel friendly for the environment. This is specifically because hard coal resources in Poland allow the national energy security to be guaranteed on the basis of energy production based on hard coal. Fine coals upgraded at coal processing facilities in the separation process in fine coal jigs are mainly used in energy production from coal. In the article, an analysis of hard coal upgrading in a jig regarding the optimum recovery of a useful fraction in the concentrate (combustible and volatile matter) and non-useful fraction in tailings (ash and sulfur) was conducted. Based on the industrial testing of a fine coal jig, the granulometric and densimetric analysis of the taken samples of concentrate, middlings and tailings of coal was conducted in laboratory conditions. Yields of products were calculated in separated size-fractions of separation products, and ash content and total sulfur content were determined in them. Based on the results of granulometric, densimetric and chemical analyses of the obtained size-fractions, the balance of separation products and appropriate calculations, Fuerstenau upgrading curves which allowed the process to be evaluated and a comparison of the results of hard coal upgrading regarding the optimum recovery of the organic phase in the concentrate and mineral components in tailings to be drawn. The obtained results were evaluated on the basis of different criteria for changing the device’s hydrodynamic operational conditions. The ash content and total sulfur content were analyzed as non-useful substances.

Small and medium-sized enterprises (SMEs) are facing barriers to grow due to the lack of structured procedures for upgrading and allocating the limited resources. To overcome these drawbacks and to improve business capabilities, a structured framework to conduct a comprehensive diagnostic and upgrading study is presented in this paper. The proposed framework involves four phases. First, the external and internal strategic factors, which can affect the enterprises’ performance are evaluated using strategic planning and assessment tools. Second, key upgrade performance indicators are developed and evaluated using multi-attribute rating techniques to guide, evaluate, and track progress of upgrading process. Third, a set of upgrade strategies are generated and evaluated using resource allocation model. Finally, a periodic re-evaluation plan is introduced to monitor the implementation progress. The developed framework for performance evaluation and upgrading is suitable to be used as a structured know-how procedure in manufacturing enterprises and can support entrepreneurs in their strategic decisions. To validate the proposed framework, a data set was collected from a local housecore company. As a result, one package of the efficient frontier strategies that represents the best use of resources was proposed for implementation.

The paper presents results of the field tests on membrane biogas enrichment performed with the application of mobile membrane installation (MMI) with the feed stream up to 10 Nm3/h. The mobile installation equipped with four hollow fibre modules with polyimide type membranes was tested at four different biogas plants. Two of them were using agricultural substrates. The third one was constructed at a municipal wastewater plant and sludge was fermented in a digester and finally in the fourth case biogas was extracted from municipal waste landfill site. Differences in the concentration of bio-methane in feed in all cases were observed and trace compounds were detected as well. High selectivity polyimide membranes, in proper module arrangements, can provide a product of high methane content in all cases. The content of other trace compounds, such as hydrogen sulphide, water vapour and oxygen on the product did not exceed the values stated by standard for a biogas as a vehicle fuel. The traces of hydrogen sulphide and water vapour penetrated faster to the waste stream enriched in carbon dioxide, which could lead to further purification of the product – methane being hold in the retentate (H2O > H2S > CO2 > O2 > CH4 > N2). In the investigated cases, when concentration of N2 was low and concentration of CH4 higher than 50%, it was possible to upgrade methane to concentration above 90% in a two-stage cascade.

To performsimulation ofCH4 andCO2 permeation through polyimide membrane,MATLABwas used. Simulation program has included permeation gaseous mixture with methane contents as observed at field tests in the range of 50 and 60% vol. The mass transport process was estimated for a concurrent hollow fibre membrane module for given pressure and temperature conditions and different values of stage cut. The obtained results show good agreement with the experimental data. The highest degree of methane recovery was obtained with gas concentrating in a cascade with recycling of the retentate.