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1. Ertekin, Turgay, Jamal H. Abou-Kassen, and Gregory R. King. Basic Applied Reservoir Simulations. Society of Petroleum Engineers, 2001.
2. Aziz, Khalid, and Antonin Settari. Petroleum reservoir simulation. Chapman & Hall, 1979.
3. Peaceman, Donald W. Fundamentals of Numerical Reservoir Simulation. 1977.
4. Crichlow, Henry B. Modern reservoir engineering: a simulation approach. Prentice hall. 1977.

Lectures supported by problem-solving tutorials developing material covered in lectures

Lectures 3 hours/week

Tutorials 1 hour/week

Homework assignments 5 hours/week

Home Reading 3 hours/week

 I. OVERVIEW AND INTRODUCTION - week 1-2
Reservoir simulation in petroleum engineering activity

Reservoir simulation in the sequence of petroleum geoscience and engineering disciplines

The importance of forecasting reservoir performance

Methods that provide a forecast, decline curve analysis, streamline simulation and grid-based simulator

The goals of carrying out reservoir simulation in Petroleum discipline

A review on the data required for reservoir simulation, porosity, permeability, saturation, pressure, relative permeability, capillary pressure, hysteresis of relative permeability and capillary pressure, three-phase relative permeability, well skin, fluid viscosity, formation volume factor, gas solubility and rock compressibility

Reservoir simulation in all stages of petroleum development: exploration, secondary migration and formation of petroleum accumulations, exploration welling, appraisal, depletion, preliminary geological model, data from several wells, well interference, secondary recovery, tracer and breakthrough data.

Direct and inverse problems. Modelling and history matching

Classification of models in reservoir simulation: single phase models, two-phase flows, black oil model, compositional model, thermal model.

Commercial reservoir simulators.

II. TRANSPORT PHENOMENA LAWS IN POROUS MEDIA- weeks 2-3
Mass conservation law, energy conservation law and the conservation of momentum law

Darcy’s law - Isotropic and anisotropic media - extended darcy and equation of state (EoS)

III. NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS - week 4
Discretisation, Taylor series, first and second derivative approximation

Finite difference, implicit and explicit

Jacobi Iterative method, Fauss-Seidel method

Boundary value problem and Initial value problem

Linearisation, Pseudo pressure

IV. SINGLE PHASE FLOW - weeks 5-6
Primary recovery. Depletion (pressure blowdown). Mathematical model.

Example of closed system: flow of gas in reservoirs, 1d, 3d, initial and boundary conditions. Model = mass conservation + EoS + Darcy´s law

Mass conservation law for single-phase flow

Darcy´s law for single-phase flow of Newtonian and non- Newtonian fluids, with gravity, accounting for inertial effects, in anisotropic rocks

Rock compression, Terzhagy eq. Slightly compressible fluid and rock

Compressibility of fluid/rock and pseudo pressure

Formulation of single-phase flow in porous-media, oil reservoirs and gas reservoirs

Analytical model for 1d flow towards well

V. NUMERICAL METHODS FOR A SINGLE PHASE FLOW - week 7
Finite difference methods for single phase flow. First- and second difference quotinets. Grid systems. Treatment of initial and boundary conditions. Steady state flows – elliptic problems. Unsteady state flow of compressible fluids – parabolic problems

VI. TWO PHASE FLOW - week 8
Derivation of basic equations. Small-scale and large scale approximations

Features: relative permeability, capillary pressure, phase viscosities and densities. Compressible and incompressible phases

Formulation of multi-phase flow in porous media, two-phase and three-phase

VII. NUMERICAL METHODS FOR MULTI PHASE FLOW - weeks 9-10
Multiphase displacement – hyperbolic problems. Mixed type problems. Formulation of initial and boundary conditions

Finite difference methods. Matrix solvers. IMPES

Consistency, stability and convergence. Grid orientation effects

VIII. WELL MODELLING - week 11
Well index. Boundary conditions on the well. Pieceman’s condition. Dietz’s factors

Piecemen’s condition. Rarefied grid.

IX. HISTORY MATCHING - week 11-12
Inverse Modelling

Parameterisation, objective funcation formation, and calibration

Tuning Alogorithm

Bayesian formulation and Uncertainty Quantification

Optimisation algorithms

Reparameterisation

Ensamble Kalman Filter

X. ADVANCED RESERVOIR SIMULATION- week 12
Compositional models in petroleum exploration. Secondary migration of oil and gas

Simulationof fractured reservoirs and unconventional resources

Upscaling

Steamline Simulation

Not Applicable

Attendance at lectures is highly recommended.

There will be an in-term tests that will count towards the final assessment.

Dates of the in-term test will be given via MyUni two weeks in advance.

Alternative test dates for students who cannot be present on the date of the test on medical and compassionate grounds can be requested through the Course Coordinator.

Final exam is comprehensive and covers all materials in the course.

Submission of Work for Assessment
Practical and field class exercises should be submitted in hardcopy with a completed copy of the assessment coversheet that is available from the school office. This should be signed to indicate you have read the above university policy statement on plagiarism, collusion and related forms of cheating.

Extensions for Assessment Tasks
Extensions of deadlines for assessment tasks may be allowed for reasonable causes. Such situations would include compassionate and medical grounds of the severity that would justify the awarding of a supplementary examination. Evidence for the grounds must be provided when an extension is requested. Students are required to apply for an extension to the Course Co-ordinator before the assessment task is due. Extensions will not be provided on the grounds of poor prioritising of time.

Penalty for Late Submission of Assessment Tasks
Assessment tasks must be submitted by the stated deadlines. There will be a penalty for late submission of assessment tasks. The submitted work will be marked ‘without prejudice’ and 10% of the obtained mark will be deducted for each working day (or part of a day) that an assessment task is late, up to a maximum penalty of 50% of the mark attained. An examiner may elect not to accept any assessment task that a student wants to submit after that task has been marked and feedback provided to the rest of the class.

Provision of Feedback to Students
Assignments will be returned to students within three-four weeks of their submission.