Reservoir Simulation
Numerical reservoir simulation from first principles: the simulation workflow, mass balance, multiphase Darcy flow and the black-oil model, finite-volume discretization and transmissibility, explicit, implicit and IMPES time stepping, Newton-Raphson and preconditioned linear solvers, the Peaceman well model, grid design and upscaling, initialization by equilibration, numerical dispersion and grid effects, history matching and ensemble methods, and probabilistic forecasting for reserves under the SEC rules and SPE-PRMS, applied to a Mission Canyon waterflood pilot in North Dakota.
PET-420 Year 4 3 credits 12 lessons · 3 h 58 min ▶ Video lessons coming soon
Offered by HSM University · Petroleum Engineering
This is the American version of this course. See the Canadian version.
What you'll learn
- Explain what a reservoir simulator does, how a simulation study is organized and when simulation is preferred to material balance or analytical methods.
- Derive the mass balance and multiphase Darcy equations and write the black-oil model in terms of formation volume factors and solution gas-oil ratio.
- Discretize the flow equations with the finite-volume method, calculate harmonic face transmissibilities and solve one-dimensional systems with the Thomas algorithm.
- Compare explicit, implicit, IMPES and adaptive implicit time stepping and calculate explicit stability and saturation throughput limits.
- Describe Newton-Raphson iteration, residuals and Jacobians, and explain how preconditioned Krylov solvers and CPR solve the linear systems.
- Calculate a Peaceman well index and equivalent radius, relate block and bottomhole pressures and choose well controls for history and prediction.
- Design a simulation grid, upscale porosity and permeability with volume-weighted, arithmetic, harmonic, geometric and flow-based methods and describe fractured and unconventional models.
- Initialize a model by gravity-capillary equilibrium, distinguish the free-water level from the oil-water contact and check the initialization.
- Explain upstream weighting, numerical dispersion, grid orientation, mobility ratio and gravity effects on simulated displacements.
- Plan and carry out a history match with an objective function, recognize non-uniqueness and describe assisted and ensemble methods.
- Build forecast cases, quantify uncertainty with ensembles and experimental design, and relate P90, P50 and P10 forecasts to reserves under the SEC rules and SPE-PRMS.
- Integrate the course in a waterflood study that builds, matches and forecasts a pilot model and turns the results into recommendations.
Course content
12 lessons · 3 h 58 min total · final exam
- 1 Why simulate: the simulation workflow 22 min · quiz
- 2 Governing equations and the black-oil model 20 min · quiz
- 3 Finite differences and transmissibility 19 min · quiz
- 4 Time stepping: explicit, implicit and IMPES 20 min · quiz
- 5 Solving the equations: Newton-Raphson and linear solvers 20 min · quiz
- 6 Well models and the Peaceman well index 20 min · quiz
- 7 Building a reservoir model: grids, upscaling and properties 20 min · quiz
- 8 Initialization and equilibration 19 min · quiz
- 9 Two-phase flow, numerical dispersion and grid effects 19 min · quiz
- 10 History matching 20 min · quiz
- 11 Forecasting, uncertainty and reserves 20 min · quiz
- 12 Capstone: simulating the waterflood pilot 19 min · quiz
- E Final exam 20 questions
Requirements
Recommended background. You can start any course at any time.
Description
Numerical reservoir simulation from first principles: the simulation workflow, mass balance, multiphase Darcy flow and the black-oil model, finite-volume discretization and transmissibility, explicit, implicit and IMPES time stepping, Newton-Raphson and preconditioned linear solvers, the Peaceman well model, grid design and upscaling, initialization by equilibration, numerical dispersion and grid effects, history matching and ensemble methods, and probabilistic forecasting for reserves under the SEC rules and SPE-PRMS, applied to a Mission Canyon waterflood pilot in North Dakota.
Part of the Engineering stream, typically taken in year 4.