Solutions of a fractional oscillator by using differential transform method

In this paper, we present an efficient algorithm for solving a fractional oscillator using the differential transform method. The fractional derivatives are described in the Caputo sense. The application of differential transform method, developed for differential equations of integer order, is extended to derive approximate analytical solutions of a fractional oscillator. The method provides the solution in the form of a rapidly convergent series. Numerical examples are used to illustrate the preciseness and effectiveness of the proposed method.     

Computation of Instantaneous Fuel Consumption for the Determination of Combustion Efficiency with Special Reference to Coal Briquette Size

This study comprises of the computation of instantaneous fuel consumptions as a straight means for the interpretation of combustion-related characteristics of coal. The model relies on the determination of the extent of combustion by the calculated fuel combustion amounts at specific instants in order to examine the oxidation behavior and possible influences governed by any variable of interest. In this context, coal briquettes prepared by varying dimensions with and without a volume constraint were evaluated and instantaneous fuel consumptions corresponding to the determined instants were computed for comparison rather than introducing the model with a single experiment. Thus, the influences imposed by the enlargement of the briquette volume as well as by the variations in the compactness of briquettes on the effectiveness and efficiency of combustion reactions were dealt. The applicability of the model was checked by the trends revealed from the view of reaction kinetics in terms of activation energies. At the end of the study, the results deduced on the grounds of instantaneous fuel consumption values were seen to have been in full confirmation by those related to reaction kinetics, showing the applicability of the model in reflecting the particular cases during a combustion reaction.     

An Investigation of WAG Process Using Horizontal Wells

In this study, a comprehensive laboratory investigation was conducted for the recovery of heavy oil from a three-dimensional (3-D) physical model, packed with 18°API gravity crude oil, brine and crushed limestone. A total of 15 experiments were conducted using the 3-D physical model with 30 cm × 30 cm × 6 cm dimensions. Basically, water-alternating gas (WAG) process was used for recovering heavy oil. Three groups of well configurations were mainly used: (i) vertical injection and vertical production wells, (ii) vertical injection and horizontal production wells, and (iii) horizontal injection and horizontal production wells. Base experiments were run with water only and carbondioxide alone and optimum rates for WAG process were determined. In CO₂ injection experiments, vertical injection and horizontal production well configuration supplied a higher recovery (15.06% OOIP) than that of the others. Horizontal injection and horizontal production well configuration gave poor recovery with the same gas rate, while vertical injection and vertical production was better off with a lower gas rate. The volumetric ratio of the water and CO₂ slugs (WAG ratio) was varied 1:3 to 1:10 in order to determine optimum conditions. For water alternating gas injection case at a WAG ratio 1:7, vertical injection and vertical production well configuration gave the highest recovery (21.04% OOIP). Waterflooding reached the best recovery (37.20% OOIP) in vertical injection and vertical production well configuration. Oil production from WAG injection is higher than that obtained from the injection of continuous CO₂ or waterflooding alone.