A mathematical model of unsteady flows of geofluids in mud volcanic processes

Abstract

Mud volcanoes are widely spread throughout the world. They are located, for example, in Sakhalin, Krasnodar region, and Azerbaijan. In this work, we consider a mathematical model describing the motion and process of eruption of geofluids in a mud volcano. A method for obtaining unique solutions of the nonstationary inverse problem to determine the depth of the location of a volcano root and gas source was suggested for the first time on the basis of this model. The time period between two volcano eruptions and physicomechanical properties of geofluids, water-clayey breccia, and permeability of the supplying pipe are assumed known. Multidisciplinary investigations of mud volcanism allows us to estimate the possibility of existence of gas deposits and its resources in the given region as well as to study the dynamics of the fluid regime in the Earth’s crust. In addition, quantitative and qualitative analysis of the products and periodicities of mud volcano eruptions make it possible to study their influence on the ratio of greenhouse gases in the atmosphere. It is also important to determine the correlation between the seismicity and the manifestation of mud volcanism in a region. Few works exist on the construction of full models of mud volcanism. For example, the authors of [1] give an estimate of the gas source depth for a mud volcano based on the known solution for steady gas motion in a borehole. The authors of [2] present the supplying pipe of a mud volcano as a vertical cylindrical pipe, which is filled with a mud mixture moving in isothermal conditions. The solution of the direct problem is given on the basis of a system of compaction equations. The authors of [3] use a number of relations known from fluid and gas mechanics to estimate gas migration in mud volcano pipes. In this work we assume that mud volcanism is caused by the formation of tectonic fractures. According to the mechanism of descending filtration, a plug of water-clayey breccia is formed from the covering sedimentary layers in the region of fractures, which is supported from below by natural gas flowing from the gas source supplying the mud volcano. The supplying pipe of the volcano is considered a fissured porous medium filled with breccia and gas. In the course of time, unstable balance is established between the water-clayey plug and the gas, which is broken when the gas pressure increases and forces the breccia out. The depths of the location of the volcano root and gas source are determined from the condition of balance, thus we find the solution of the inverse problem. The process of forcing water-clayey breccia out by the gas is considered up to the moment of its eruption, when the gas pressure drops. Then, again the supplying pipe is filled, and the access to the deep gas in the pipe is stopped. Thus, a new eruption is being prepared. The gas that remained in the region of the mixture of breccia and gas would be released to the Earth’s surface through the system of gryphons of the mud volcano.