My teaching interest includes mathematical and numerical modelling of fluid flow in reservoir rocks, inverse problem theory, uncertainty quantification, numerical optimisation and geostatistics. I currently teach the following courses: 

1. Reservoir Simulation: The course gives the theoretical basis and practical fundamentals for mathematical modelling and numerical simulation of fluid flow in petroleum reservoirs. The governing laws and equations required for the modelling of single-phase and multi-phase flow in porous media, such as mass conservation, Darcy, equation of state, rock compressibility, capillary pressure and relative permeability, are reviewed. By combining these laws and equations, the corresponding partial differential equations are derived. The numerical methods for solving the governing partial differential equations using finite difference methods are presented.

2. Reservoir Characterisation and Modelling: The course has three main components. 1) Data sources, quality and analysis, including spatial analysis. 2) Generating 3D models of reservoir properties - classical gridding and mapping, kriging as a data-driven (variogram) form of classical mapping (estimation) and a means of data integration. Simulation techniques are introduced as a means of assessing uncertainty resulting from heterogeneity. 3) Scaling of grids and property models for the purpose of reservoir simulation is the final topic.

3. Advanced Topics in Numerical Reservoir Simulation: This course reviews the governing PDEs of multi-phase flow in porous media derived with a black-oil phase-behaviour approach, and presents the derivation of the PDEs with a compositional phase-behaviour approach (using both 2-parameter and 3-parameter equation of state). A commonly-used numerical method (finite volume method) for solving the governing PDEs is discussed, and space discretisation (27-point and 7-point) using quadrilateral grids, nonorthogonal (corner-points) and orthogonal (block-centred), is reviewed. An overview of Newton-Raphson linearisation methods in fully-implicit, IMPES and AIM scheme, is given. Iterative linear solvers for sparse matrixes are reviewed, and a few techniques for paralleling and tuning the solvers are discussed. The course, in addition to the fundamentals, covers several practical and special topics in reservoir simulation, such as, placement of deviated and multilateral wells, group controls for constraint handling, local grid refinement and coarsening, miscible and immiscible gas flooding, gas condensate, regionalisation (PVT, equilibrium and SCAL), dual porosity model for naturally fractured rocks, adsorption models, aquifer models, rock compaction/swelling and history matching. 

4. Uncertainty Modelling: The course gives the theoretical basis and practical fundamentals for uncertainty quantification and modelling (forward and backward), inverse problems and numerical optimisation. It outlines the types and sources of uncertainty, and the importance of uncertainty modelling in decision-making processes. The forward propagation of the uncertainty in the parameters of interest using different techniques, such as Monte Carlo simulation and experimental design methods, is discussed, and techniques used for drawing samples (unconditioned or directly conditioned) from multivariate distributions are reviewed. A particular attention is paid to inverse modelling (in linear and nonlinear problems) with a Bayesian approach. Popular calibration algorithms, gradient-based (steepest descent and quasi-Newton) and derivative-free used for approximating/estimating Maximum a Posteriori (MAP) and Maximum Likelihood (ML) are discussed. Gradient computation/approximation techniques in high-dimensional problems are also reviewed. The fundamentals of Markov chain Monte Carlo (MCMC) are discussed, and different techniques used for the approximation (sampling) of posterior probability density function, such as Metropolis–Hastings algorithm, data assimilation (ensemble Kalman filter) and reduced-order-model-assisted and surrogate (metamodel)-assisted algorithms, are presented and discussed. This course also reviews the algorithms and techniques used to optimise noisy single and multi-objective functions (with and without constraints), such as might be found field development and production optimisation under geological uncertainty problems.

5. Data Analytics: The aim of the course is to provide students with a broad overview of machine learning to oil and gas. The theory and fundamentals, as well as understanding data driven methods are covered. Real field examples will equip students to apply data analytics and machine learning methods in petroleum engineering.