Amir Ehsan Feili Monfared

Nonlinear heterogeneous reactions are important for simulating dissolution as they involve reactant adsorption, reaction, and product desorption, leading to nonlinear behavior. This study proposes a new curved reaction boundary condition in general form in the lattice Boltzmann framework. This method calculates the unknown distribution functions and the interface concentration using extrapolated distribution functions on actual interface position. Various analytical benchmarks were used to compare this method's accuracy with two available schemes, including Kashani et al. and Huber et al. methods. According to the results, in the simulation of reactant transport on straight and curved surfaces with and without dissolution, errors obtained by the proposed method did not exceed 1.7% in different conditions, while errors of the two other methods were up to 50%. The convergence rate of different methods was determined, and based on the results, the convergence rate of the proposed method was second-order, while the corresponding values for the two other methods were only first-order. The results of different root-finding methods in the proposed method including Bisection, Newton-Raphson, and linear approximation were compared to determine the interface concentration. The results showed that Bisection errors did not exceed 1%. At the same time, using Newton-Raphson and linear approximation led to errors of 12.9% and 25.3%, respectively. The effect of reaction orders on an obstacle dissolved under reactive flows in a channel was investigated. According to the results, in each Damköhler number, increasing the reaction order decreased the dissolution rate; however, increasing the Damköhler number significantly restricted the effect of orders.

The method of volume of fluid is a popular method often used to calculate normal vectors in simulating two-phase flows. This study proposes a new method based on scalar diffusion phenomenon using smoothed profile combined with lattice Boltzmann method. The method is spatially and time-wisely local, which facilitates its parallel implementation. Accuracy and computational time of the proposed method on straight and curved surfaces in single- and multi-obstacle media were compared with four standard methods: Youngs, efficient least-square volume of fluid interface reconstruction algorithm (ELVIRA), Swartz, and coupled volume of fluid and level set (VOSET). In addition, the problems of heterogeneous dissolution of porous media under reaction-controlled and natural conditions were simulated. The results showed that in terms of the calculated angles, the proposed method is 0.4°–1.52° more accurate than the common Youngs method. Additionally, its computational time was about 36% less than that of the Youngs method. Compared with ELVIRA, Swartz, and VOSET, despite their marginal higher accuracy, their computational times were 346%–772% higher. Furthermore, it was shown that the accuracy of ELVIRA and Swartz methods in multi-obstacle media decreases significantly with decrease in gap between the neighboring obstacles. However, for the proposed method, the effect of gap was considerably less significant.

One of the key elements that performs an essential role in the success of an underbalanced drilling operation is the precise prediction of bottom-hole circulating pressure, especially when aerated mud is employed. Employment of complex two-phase flow correlations is the common procedure to predict the multiphase flow pressure gradient. Lack of generality and relatively big errors are the practical problems of such methods threatening the whole underbalanced condition of the operation. In this study, genetic algorithm is used in combination with the adaptive network-based fuzzy inference system to model the case with the optimal cluster center's range of influence for each of the data dimensions. The substantial improvement in the model performance and achievement of a MSE of .0015 showed that the stated combination performs much more accurately than the conventional methods.

Precise prediction of bottomhole circulating pressure (BHCP) is the major concern in the designing stage of an underbalanced drilling (UBD) operation. A successful UBD operation hinges tightly on the accurate control of downhole pressures. In order to predict the pressure gradient, complex two-phase flow correlations are employed and the flow pattern is defined. The problems arising from such methods are the significant errors relative to the nature of a UBD and the need for localization of the parameters or the shift from one correlation to another from case to case. In this study, different types of fuzzy inference systems are developed to construct new models. The resulting average percentage relative error (APE) of 13.83% for a Sugeno model and 13.11% for a Mamdani model indicated that the generated fuzzy models have the capability of precise BHCP prediction with higher accuracies in comparison with the popular mechanistic models.