## PETROENG 3001 - Reservoir Simulation

### North Terrace Campus - Semester 2 - 2019

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. A particular attention is given to the internal and external boundary conditions, and initial conditions. It is also demonstrated how numerical simulation can help us to forecast the reservoir performance in response to different field-development scenarios. The role of input data of reservoir simulators on the accuracy of prediction is another aspect which is reviewed in this course. It is also discussed how to reduce the inherent uncertainties in the input data, using inverse modelling techniques, known as history matching. Through several exercises and assignments, an overview of a commercial reservoir simulator, is given.

• General Course Information
##### Course Details
Course Code PETROENG 3001 Reservoir Simulation Australian School of Petroleum Semester 2 Undergraduate North Terrace Campus 3 Up to 4 hours per week Y MATHS 1012, MATHS 2201, MATHS 2104, PETROENG 2009, MECH ENG 2021, COMP SCI 1201, PETROENG 3025 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. A particular attention is given to the internal and external boundary conditions, and initial conditions. It is also demonstrated how numerical simulation can help us to forecast the reservoir performance in response to different field-development scenarios. The role of input data of reservoir simulators on the accuracy of prediction is another aspect which is reviewed in this course. It is also discussed how to reduce the inherent uncertainties in the input data, using inverse modelling techniques, known as history matching. Through several exercises and assignments, an overview of a commercial reservoir simulator, is given.

##### Course Timetable

The full timetable of all activities for this course can be accessed from Course Planner.

• Learning Outcomes
##### Course Learning Outcomes
On successful completion of this course students will be able to:

 1 Explain the mathematical and computational concepts behind commercial reservoir simulators 2 Explain the physical laws that govern fluid flow in porous media 3 Formulate single-phase and multi-phase flow in petroleum reservoirs 4 Solve the governing partial differential equations using finite difference methods and interpret the potential numerical errors 5 Treat internal and external boundary conditions and initial conditions 6 Explain iterative matrix solvers 7 Write a program for simple problems 8 Use a commercial reservoir simulator for studying the reservoir performance in response to different development strategies 9 Measure the uncertain parameters of reservoir models based on history data 10 Demonstrate the ability to work cooperatively in groups for the assignments

The above course learning outcomes are aligned with the Engineers Australia Stage 1 Competency Standard for the Professional Engineer.
The course is designed to develop the following Elements of Competency: 1.1   1.2   1.3   1.4   1.5   1.6   2.1   2.2   2.3   2.4   3.1   3.2   3.3   3.4   3.5   3.6

This course will provide students with an opportunity to develop the Graduate Attribute(s) specified below:

University Graduate Attribute Course Learning Outcome(s)
Deep discipline knowledge
• informed and infused by cutting edge research, scaffolded throughout their program of studies
• acquired from personal interaction with research active educators, from year 1
• accredited or validated against national or international standards (for relevant programs)
1-9
Critical thinking and problem solving
• steeped in research methods and rigor
• based on empirical evidence and the scientific approach to knowledge development
• demonstrated through appropriate and relevant assessment
3, 4, 8, 10
Teamwork and communication skills
• developed from, with, and via the SGDE
• honed through assessment and practice throughout the program of studies
• encouraged and valued in all aspects of learning
8, 10
• technology savvy
• professional and, where relevant, fully accredited
• forward thinking and well informed
• tested and validated by work based experiences
1, 2, 4, 7-9
Intercultural and ethical competency
• adept at operating in other cultures
• comfortable with different nationalities and social contexts
• able to determine and contribute to desirable social outcomes
• demonstrated by study abroad or with an understanding of indigenous knowledges
10
Self-awareness and emotional intelligence
• a capacity for self-reflection and a willingness to engage in self-appraisal
• open to objective and constructive feedback from supervisors and peers
• able to negotiate difficult social situations, defuse conflict and engage positively in purposeful debate
10
• Learning Resources
##### Required Resources

Not applicable

##### Recommended Resources
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.

• Learning & Teaching Activities
##### Learning & Teaching Modes

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

The information below is provided as a guide to assist students in engaging appropriately with the course requirements.

Lectures 3 hours/week

Tutorials 1 hour/week

Homework assignments 5 hours/week

##### Learning Activities Summary

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

##### Specific Course Requirements

Not Applicable

• Assessment

The University's policy on Assessment for Coursework Programs is based on the following four principles:

1. Assessment must encourage and reinforce learning.
2. Assessment must enable robust and fair judgements about student performance.
3. Assessment practices must be fair and equitable to students and give them the opportunity to demonstrate what they have learned.
4. Assessment must maintain academic standards.

##### Assessment Summary
 Assessment Task Weighting (%) Individual/ Group Formative/ Summative Due (week)* Hurdle criteria Learning outcomes Assignments 30 Individual /Group Summative Weeks 2-12 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. Midterm Exam 10 Individual Summative ~Week 7 1. 2. 3. 4. 5. 6. 9. Final Exam 60 Individual Summative 1. 2. 3. 4. 5. 6. 9. Total 100
* The specific due date for each assessment task will be available on MyUni.

This assessment breakdown complies with the University's Assessment for Coursework Programs Policy.

##### Assessment Related Requirements

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.

##### Assessment Detail

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

##### Submission

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 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.

Grades for your performance in this course will be awarded in accordance with the following scheme:

M10 (Coursework Mark Scheme)
FNS   Fail No Submission
F 1-49 Fail
P 50-64 Pass
C 65-74 Credit
D 75-84 Distinction
HD 85-100 High Distinction
CN   Continuing
NFE   No Formal Examination
RP   Result Pending

Further details of the grades/results can be obtained from Examinations.

Grade Descriptors are available which provide a general guide to the standard of work that is expected at each grade level. More information at Assessment for Coursework Programs.

Final results for this course will be made available through Access Adelaide.

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The University places a high priority on approaches to learning and teaching that enhance the student experience. Feedback is sought from students in a variety of ways including on-going engagement with staff, the use of online discussion boards and the use of Student Experience of Learning and Teaching (SELT) surveys as well as GOS surveys and Program reviews.

SELTs are an important source of information to inform individual teaching practice, decisions about teaching duties, and course and program curriculum design. They enable the University to assess how effectively its learning environments and teaching practices facilitate student engagement and learning outcomes. Under the current SELT Policy (http://www.adelaide.edu.au/policies/101/) course SELTs are mandated and must be conducted at the conclusion of each term/semester/trimester for every course offering. Feedback on issues raised through course SELT surveys is made available to enrolled students through various resources (e.g. MyUni). In addition aggregated course SELT data is available.

• Student Support
• Policies & Guidelines
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