PROBABILISTIC ESTIMATION OF WAX COLMATATION PROCESS OF OIL RESERVOIR BOTTOM-HOLE ZONE

Abstract

The wax colmatation process of oil reservoir bottom-hole zone is accompanied by the current well production rate decrease, and it is determined by many factors which are not possible to be taken into account to a considerable extent, neither experimentally, nor theoretically. The aim of the work is to study the probability theory by applying mathematical apparatus. Formation is supposed to consist of an abundance of capillaries, and the wax crystal gets stuck in the capillary with the critical cross-section, and all the crystals, moving after it, sink (accumulate in it). Describing this process in terms of the probability theory, the probability functions of colmatation absence and realization in the form of an exponential law and space coordinate have been obtained. When approaching the well, the pressure gradient rises, temperature differential increases (as a result of the throttling effect), wax crystals are discharged from oil more intensively, i. e. the colmatation depends on the reference radius. The exponential law is generalized by the Weibull’s law, and thereafter, by the Makham’s extended exponential law under such conditions. The functions in time coordinates were recorded analogically. Transition from the abundance of capillaries to the permeability coefficient, recorded for any oil formation intersection at an arbitrary moment of time, has been made in accordance with the law of large numbers. The analysis has shown that an intensive temporal decrease of the permeability coefficient occurs in the reservoir bottom-hole zone, the colmatation zone is extending in space with time, and the permeability coefficient increases nonlinearly when moving away from the well that corresponds to the physical essence of the process. The notion of an average permeability coefficient in the colmatation zone for any moment of time has been introduced and the oil well production rate depending on its
operation time has been calculated by utilizing the Dupuit’s formula with the time varying permeability coefficient and considering the zone-heterogeneous formation. As a result, the process of wax colmatation has been described
for the first time not only in time but also in space coordinate.