Sensitivity analysis and bioconvection flow of nanofluid in a porous media with microbial growth: an application of microbial enhanced oil recovery and mineral extraction

Abstract Bioconvection is fast becoming an integral part of heat and mass transfer systems because of the versatility of microbes in engineering processes. The discovery of microbes that are capable of enhancing oil recovery and mineral extraction is a huge milestone in the two industries, as the technology promises cheaper, environmentally sustainable means of extraction, and increased yields. Despite all the foreseen benefits of the technology, there are still major hurdles to overcome in order to fully explore this promising technology. In this paper, a mathematical model is developed to explore the role of microbial activity in oil recovery and mineral extraction. Unlike most existing bioconvection models, the current formulation explicitly embraces microbial growth, capturing reproduction and carrying capacity influences that dynamically change the flow environment. The governing equations, which are described using partial differential equations, are converted into non-dimensional form using similarity variables. The resulting boundary value problem is solved numerically using the overlapping multi-domain spectral method to allow the investigation of the contribution of key parameters on the model. The numerical results reveal that microbial Brownian diffusion improves solute concentration within the boundary layer, enhancing product extraction, whereas superior permeability promotes temperature, solute, and microbial distributions by minimizing the loss of energy. Also, improved microbial growth rate and carrying capacity enhances metabolite production and stabilize bioconvective patterns, with direct relevance to microbial enhanced oil recovery, environmental remediation, and bioreactor design. Sensitivity analysis demonstrates that frictional drag coefficient, heat, mass, and microbial transfer are each dominated by various key parameters, emphasizing the significance of parameter-specific optimization to maximize the performance of the system.