HIGH-PERFORMANCE INFORMATION TECHNOLOGIES TO STUDY FILTRATION PROCESSES IN MEDIA WITH VARIABLE-SIZED NANOPOROUS PARTICLES

Abstract

This study presents mathematical solutions for the pressure distribution and consolidation coefficient within a nanoporous material characterized by varying compressibility and permeability properties. The mathematical model of nanoporous filtration systems is founded on a phenomenological model developed by the authors. This model encapsulates the intricate dynamics of a two-phase and two-level transport process, known as nanofiltration-consolidation. To solve the defined mathematical problem analytically, the operational Heaviside’s method where employed in composition with Laplace integral and Fourier integral transformations. The application of the finite integral cos Fourier transform allowed to get analytical representations for pressure profiles both in interparticle and intraparticle spaces as a function of particle position within media, particles radius, and total time. To advance understanding of complex nanofiltration processes occurring within media containing nanoporous particles of varied sizes, a specialized software complex has been engineered. The adherence to software development best practices has rendered the software design highly adaptable, allowing for effortless future extensions and improvements. This, in turn, empowers the software with the capacity to seamlessly incorporate new features and enhancements. As a part the simulation phase, a constructed software suite was used to explore the internal kinetics of filtration processes within multidimensional nanoporous particle media. Numerical modelization results reveal insight into internal processes, such as pressure drop within the intraparticle network, leading to a notable deceleration in nanofiltration kinetics, specifically in relation to nanoporous particles of differing sizes. Among them, the consolidation coefficients indicate that particles of the second-type have a less destroyed cellular structure compared to particles of the first-type. The simulated profiles illustrate that liquid pressure experiences rapid drops at the surface of the particles in contrast to the sections closer to the center of the particles. Furthermore, a more substantial overall decline occurs as vary-sized particles approach the media edge. In the other hand, a noticeable slowing down of the liquid pressure drop can be observed in the micropores of the particles.