This paper examines the process of wormholes formation during hydrochloric acid treatment of well bottom-hole zone in carbonate formations. An algorithm for solving the problem of wormhole formation in a porous medium for a two-dimensional case was developed. Two-scale model (porescale and Darcy’s scale) taking into account convection, diffusion, and chemical reaction were used in this work in order to describe the dissolution of carbonates with hydrochloric acid (hydrochloric acid treatment). The initial distribution of the porosity field was generated as a distribution of random numbers around some mean value. Based on the distribution of the initial porosity field, the initial permeability field of the rock was calculated. The random distribution was used to describe the heterogeneity of the actual rock. The rest of the study parameters were taken from known experiments on the dissolution of carbonate cores. The numerical model was built for solving the system of equations for acid dissolution, and carbonate dissolution modes with hydrochloric acidwere obtained depending on the Damkohler number, Thiele modulus on the pore-scale and Darcy’s scale as a result of this research. Also, the optimal Damkohler numbers (injection rates) were found. The computer code for the problem of the development/growth of wormholes in a porous medium based on the developed algorithm was built using the C++ programming language.

Background: Kazakhstan is one of the largest oil producers in Central Asia, with a significant share of oil and gas projects associated with the Caspian region (primarily, these include the North Caspian Project at Kashagan, the Tengiz oil field, and the port infrastructure of Aktau). Oil spills in marine waters pose a serious ecological threat to the environment, making it essential to develop effective tools for forecasting their spread. Aim: To develop and test parallel algorithms for the simulation of wind-driven sea currents on graphics processing units (GPUs) for oil spill forecasting. Materials and Methods: Three-dimensional hydrodynamic models with parameterized turbulent viscosity were were used. Numerical schemes were implemented in explicit and implicit forms, parallelized along x and y coordinates using the OpenCL library. Computations were performed on the CPU and GPU for both uniform and non-uniform grids. Results: GPU-based computations demonstrated significant acceleration: up to 23 times faster on uniform grids and up to 13 times faster on non-uniform grids. The accuracy computations on a non-uniform grid with 40 nodes was comparable to that of computations on a uniform grid with 500 nodes. Conclusion: Parallel GPU algorithms substantially reduce computation time while maintaining high accuracy in modeling wind-driven currents. This makes them a promising tool for forecasting oil spill dispersion in the Caspian Sea.

The aim of this study has been to conduct a comparative analysis of the deterministic finite difference method and a stochastic approach based on differential equations for modelling one-dimensional diffusion. The explicit finite-difference scheme FTCS and the Euler–Maruyama method for the numerical solution of stochastic differential equations were employed in the study. A comparison of the concentration profiles obtained using both approaches on a grid with the same resolution was carried out. The results show that the stochastic method yields macroscopic profiles close to the reference solution, although these are accompanied by statistical noise, the magnitude of which decreases as the number of particles increases. It was found that limiting the maximum number of particles per cell to 10 already ensures acceptable accuracy whilst significantly saving computational resources. It was concluded that the choice between the methods should be determined by the required smoothness of the solution and the acceptable computational cost: the deterministic method is preferable for problems with smooth fields, whilst the stochastic method is preferable when modelling turbulent processes and complex boundaries.

The Caspian Sea’s unique environment and intense hydrocarbon extraction make it a high-risk, understudied region for oil spill modelling. This review assesses the physical, chemical, and biological processes governing oil spill transport and fate, and evaluates the principal numerical tools available for the Caspian Sea context. The weathering processes are reviewed from foundational formulations to operational implementations. Key research challenges identified include the absence of photo-oxidation from operational models, limited laboratory data for Caspian crude oil types, and simplified biodegradation parameterizations. Hydrodynamic forcing uncertainty, arising from the lack of a dedicated operational ocean model, remains the dominant source of trajectory forecast error. Seven operational oil spill modelling tools and the ROMS hydrodynamic platform are reviewed. Only OSCAR and MIKE 21 have documented applications to the Caspian Sea, representing a significant regional gap. ROMS is identified as the most suitable hydrodynamic platform for future operational forecasting. Finally, the integration of machine learning and deep learning methods, including neural network trajectory prediction and SAR detection, is discussed as a promising frontier for improving forecast accuracy in this data-sparse environment.