Abstract Initiation of the in-situ combustion (ISC) may be accompanied by rapid increase of oxygen concentration in the production fluid. This may cause serious damage to the well equipment by corrosion or explosion. The most common method for reducing the risk of incomplete oxygen consumption (and oxygen breakthroughs) is pre-heating of the bottomhole zone with the use of well steam treatment (WST) technology. It is possible to optimize the initiation of ISC process - to minimize amount of injected steam, to achieve maximum air injection rate in a fastest way and to ensure that no oxygen breakthroughs to producing wells will occur during initiation of the ISC process. We propose a method for initiation of ISC based on the developed semi-analytical model. Our approach allows to calculate the increasing air injection rates, from initial value to maximum acceptable value. The method is applied to model prevention of oxygen breakthroughs and to provide fast and safe initiation of an the ISC. Two cases are considered: initiation of ISC in the reservoir with the initial constant temperature and initiation of ISC in the reservoir with the pre-heated zone around injector well. In addition, we develop a method of optimal initiation of ISC after WST that allows to spend a minimum amount of energy and to satisfy the conditions of effective, fast and safe initiation of ISC. The CMG STARS reservoir simulator was used for testing the developed model. The results which were obtained in accordance with the developed semi-analytical model are in full agreement with numerical experiment.

The paper is concerned with the asymptotic behavior of a solution with an inner transition layer (front) in the reaction-diffusion-advection mathematical model to describe an in-situ combustion process.

The dynamics of sharp transition layers in the reaction-diffusion-advection model is numerically studied. The mathematical model qualitatively describes the motion of an oxidizer for the thermogas method of enhanced oil recovery. The influence of permeability heterogeneity on the front shape is considered. The simulation results are compared with the numerical data obtained with the use of the CMG STARS thermohydrodynamic simulator.

Phase and component segregation in lipid membranes was studied by means of mathematical modeling. The time dependence of phase segregation on the lateral diffusion coefficient was calculated. The phase and component segregations were also simulated by multiparticle Monte-Carlo methods, and the phase diagrams of the system were obtained.

For a singularly perturbed parabolic equation in two dimensions, the formation of a solution with a sharp transition layer from a sufficiently general initial function is considered. An asymptotic analysis is used to estimate the time required for the formation of a contrast structure. Numerical results are presented.

The kinetics of photoinduced EPR I signals at different concentrations of ferredoxin was studied on isolated pea chloroplasts. A kinetic model of ferredoxin-dependent electron transport around photosystem I was suggested. A multiparticle model was constructed, which makes it possible to "directly" model the processes of electron transfer in multiprotein complexes and limited diffusion in different compartments of the system (stroma, lumen, and intermembrane space). A comparison of the kinetic and "direct" models revealed an important role of spatial organization of the system in the kinetics of redox turnover of P700.

Electron spin resonance spectroscopy was used to monitor photoinduced changes in the redox state of P700, a photoactive pigment of phctosystemL in isolatedPisum sativum chloroplasts. The kinetics of the ESR signal from P700 (ESR signal I) was recorded at different concentrations of exogenous ferredoxin, ,A kinetic model was developed for ferredoxin-dependent cyclic electron transport around photosystem I. A multiparticle model was built to directly describe electron transfer in multienzyme complexes and restricted diffusion of mobile carriers in individual compartments (stroma, lumen, intramembrane space) of the system. The two models were compared, and a conclusion was made that the spatial organizationof the system plays'a-significant role in shaping the kineticsof redox transitionsof nOD.