A physicochemical model for transport of mobile forms of occurrence of elements by gas bubbles in porous medium-gas bubble-facilitated transport of metals in the lithosphere is proposed and its corresponding mathematical model is discussed. The physico-chemical model consists of three phases: water with dissolved metallic elements, gas bubbles and solid matrix of the porous medium. In the model the gas bubbles act as carriers to transport the elements in the pore water from the depth in the lithosphere to the Earth's surface. In the process of transportation the elements dissipate in porous rocks and consequently a new kind of geochemical halo-jet halo of dispersion is formed in the rocks. In order to describe the transport and fate of the elements in the porous rocks a nonlinear quasiconvection mathematical model is developed, in which the transport of elements is modeled by a quasiconvection of gas bubbles with the elements and the interaction of elements with the porous medium is represented by a second-order chemical kinetics. A finite difference scheme is provided to solve the nonlinear quasiconvection model. From the numerical solutions a stabilization effect of concentration front in the transportation of elements in the porous medium is discovered. The sensitivities of the stabilization effect to model parameters are analyzed. To verify the reality of the mathematical model, physicochemical modeling experiments are conducted. The obtained experimental data support the proposed model in this work.