CONCENTRATION FIELD OF THE TRACER IN A STRATUM WITH A HYDROFRACTURING CRACK

The authors have presented results on development of a mathematical model of convective evolution of a tracer
marker in natural reservoirs with a hydrofracturing crack with allowance for the leaks from the crack into the
stratum. To construct the pressure field as applied to two-dimensional problems, a quasi-stationary method has
been developed that uses the idea of successive change of steady states. To find the dimensions of the zone of
pressure perturbations in a porous medium, that is formed by the injection of the tracer into the crack, use has been
made of the law of conservation of mass. Dependences have been established of the velocity of motion of the tracer
marker in the hydraulic-fracturing crack and the surrounding porous medium on the parameters of the stratum and
the well.
Dependences have been constructed of the front and back boundaries and the length of the marker in the
crack and the surrounding porous medium on the reservoir parameters of the stratum and time. Formulas have
been determined to compute space–time concentration distributions of the tracer in the stratum with a crack.
On the basis of an analysis of the theory, regularities have been established of the formation of satellite markers
generated by tracer motion in the crack. It has been shown that in low-permeability reservoirs, the length of the
satellite marker is much smaller than its dimensions in the crack

Author:  A. I. Filippov, A. Yu. Davletbaev, R. R. Gareev
Keywords:  mathematical model, convection, tracer marker, concentration field, continuity equation, porous medium, hydraulic-fracturing crack
Page:  1447