 Dear colleagues, first of all, I would like to thank the conference organizers for giving the opportunity to present our work here at this conference. The subject of my presentation is influence of time-delayed reaction on stability of the reaction from propagation in the porous medium and transition to self-oscillating mode of the from propagation. The work is done by Konyukhov and Zavyalov, my colleague from the Moscow Institute of Physics and Technology. I will begin with the experimental results. The aim of the experiment was to study the multi-phase flow in the porous medium accompanied by their guess-producing reaction. Such reactions are used in technological applications. For example, acid is injected into the rocks containing cabinets to improve permeability of the medium. In our experiment, the acetic acid was injected into the porous medium containing sodium b-carbonate. The products of the reaction are sodium acetate, water, and carbon dioxide, which forms Gauss's phase. The skeleton of the porous medium is a mixture of glass spheres, 200 micrometers, and sodium b-carbonate particles. Before the experiment, the skeleton is saturated with mineral oil. After the acid was injected into the porous medium, into the cell, the reaction zone was propagated through the cell from the inlet to outlet boundary. A number of precious sensors were distributed along the cell. A sample of the precious sensors data is shown in this figure and one can estimate the location of the front of the reaction. This is the appearance of the laboratory setup. It's simple. This is the working cell, pumping, and pressure measurement devices. We obtained in this experiment a self-oscillating mode of the reaction of the front propagation when the front pressure saturations oscillates with some frequency. In this figure, the data from one of the precious sensors is shown. We can see oscillations with well-defined frequency. In the figure below, the data of precious sensors during one of the experiments, all precious sensors, is shown. The curve which corresponds to the first precious sensor from the inlet boundary is almost oscillation-free. This important means that the source of the oscillations is the reaction front itself rather than external influence. This picture below, this is time, of course, time. This means from different precious sensors. In this figure, we can see the flow visualization. Figure from one to four corresponds to one oscillation cycle and from five to eight another oscillation cycle. We can see formation and propagation through the reaction zone. We call it secondary wave. This wave is a saturation shock. Fingering instability of the reaction front is also shown. Now we pass to the modeling of this flow. This type of reactions are usually modeled by the first-order kinetics. The reaction rate is a function of concentration of the assay solution. C sub s is equilibrium concentration, and coefficient of the reaction rate is proportional to the area of contact between solid and their liquid phases. When acid is injected into the porous medium, the concentration of the acid decreases in time due to reaction, and the surface of contact decreases too. One can expect that the reaction rate will decrease in time as well. However, special experiments on rapid acid injection have shown that there is a maximum at about one second of the reaction rate. This means that there is a time delay between the penetration of the acid solution into the porous medium and the reaction. We modeled this effect by the introduction of time delay into the kinetic equation. After linearization, we obtain ordinary differential equation, and solution to this equation approximates experimental curves with reasonable accuracy. The possible reason for this behavior is capillary non-equilibrium or transient diffusion effects. This requires further investigation. We have not a clear picture of this phenomenon. Here the balance equations are shown. These equations were closed by the time delay attraction kinetics. Tau is time delay parameter. These equations were solved by using complicit numerical scheme. Here we have the solution for the saturation distance. First time after injection started, the front propagates stably, but after some time interval, we have transition to the self-oscillating mode of the reaction front propagation. This is a stable stage. Here we have oscillations. In the right-hand side of this slide, the number of saturation curves from distance at successive points in time is shown, and we see here the formation of saturation stroke. This is the secondary waves we have seen in the experiment, which propagates during each oscillation cycle. There is a number of dimensionless parameters of this problem, such as concentration of acid, concentration of sodium bicarbonate in the solid phase. The Curler number, we introduced a new parameter time delay, and we have studied the dependence of the solution on this parameter. The question is, how does the time delay influence all the transition to the oscillating mode of the reaction front propagation? The answer is given here in this figure. We can see envelope curves for pressure oscillations at the front of the reaction. The front was defined as a point where the concentration of sodium bicarbonate equals half of its initial value. We see that when time delay increases, the amplitude of oscillations also increases, and the time from propagation from the inlet to outlet boundary decreases with this parameter. In this figure, we can see how the pressure from pressure depends on time. We see oscillations at different values of this parameter, and conclusions. The kinetics of gas-production reaction initiated by injection of acid solution into the oil-saturated porous medium with chemically active skeleton is characterized by the time delay effect. Numerical stimulation has shown that the time delay reaction stimulates instability of the multi-phase flow and transition to the self-oscillating mode of the reaction front propagation. Thank you for your attention. This is a picture taken at the first stage of the processes. The gas-rich zone is the darker one. The lighter is the oil-saturated zone, and the flow direction is the bottom to the atmosphere. The outlet is atmospheric pressure, and the inlet is slightly above to drive the flow. Of course, if there is no gas-production, no oscillations. Maybe we didn't study the dependence on the length of the channel. This is taken into account using the relative permeability of the multi-phase flow.