Diagnosis of the formation damage process using the theory of catastrophe

Abroad area of interdisciplinary research, commonly referred to as nonlinear science, includes nonlinear thermodynamics, catastrophe theory, dynamic chaos theory, and fractal mathematics. This field has produced numerous influential figures, many books, and countless articles. Many popular books have been published on the theory of catastrophes, chaos, and fractals. Systems studied by nonlinear science are usually called complex; their properties are not reducible to those of their components and exhibit newly emerging, or "emergent" features. A catastrophe is an abrupt change that occurs as a sudden response of a system to a gradual change in external conditions. The mathematical description of phenomena associated with sharp and qualitative changes is provided by the theories of singularities and bifurcations. Bifurcations (catastrophes) are discontinuities in systems described by smooth (continuous) functions. This article attempts to make an adaptive operational decision aimed at preventing complications arising from sand production in wells, based on the application of catastrophe theory and mathematical and statistical tools. The influence of sand production on well productivity, particularly the associated plug formation, is a relevant issue and pertinent research focus today. The physical cause of the sand plug's effect is that due to the small cross-section of the wellbore, the sand plug located above the productive horizon acts as a downhole fitting, creating significant resistance to the upward flow. Early diagnosis of the onset of near-wellbore zone damage and the transition of wells to sand-producing status is crucial. In addition, timely control of complications related to sand removal during the complete distortion of the bottomhole zone, when the sand production process is fully established, is of great relevance. The effectiveness of measures to prevent the complications in operation process depends on the validity and efficiency of such control.