Numerical Simulation of Fractured Reservoirs

Explore numerical simulation techniques for fractured reservoirs in this comprehensive lecture from the Society for Industrial and Applied Mathematics. Delve into the dual-porosity model, the workhorse of applied fractured reservoir simulation, and learn how to encapsulate fractures in simulation models. Examine the challenges of scale dependency in fractured formations and discover opportunities for single-phase and multi-phase flow modeling. Investigate advanced topics such as unstructured grids for complex fractures, multi-rate dual-porosity modeling, and spontaneous imbibition physics. Gain insights into uncertainty quantification, geomechanics, and the future of fractured reservoir simulation. Enhance your understanding of this critical aspect of reservoir engineering and applied mathematics.

Intro
Fractures are the "highways" for flow and
fractured geological formations
The workhorse of applied fractured reservoir simulation: The dual-porosity model
Encapsulating fractures in a simulation model using the dual-porosity approach
The ingredients of the dual-porosity model
A key simulation challenge: Fractured formations do not have a well-defined REV
Calculating the effective permeability of a fracture network
Scale dependency of average permeability for one single fracture network
Scale-dependency of production forecast for a single fracture network
Opportunity for single-phase flow: A night out with a drunken Scotsman...?
Opportunity for single-phase flow: Probabilistic transport such as CTRW
Opportunities for multi-phase flow: Resolve fractured explicitly with unstructured grids
Modelling complex fractures and geological structures with unstructured grids
Honouring geometry of reservoir-scale faults and fractures with unstructured grids
Fast updating of fracture network with hierarchical or embedded fracture modelling
Taking stock: Where are we now... - Dual-porosity model remains the workhorse for applied Simulations of fractured reservoirs
Parameters driving spontaneous imbibition: Wettability, permeability, matrix surface area
Challenge: Non-uniform matrix saturation and under-prediction of transfer at early time
Opportunity: Use ideas from probabilistic solute transport modelling
Multi-rate dual-porosity modelling - simple in theory and practice
Opportunity: Revisit physics of spontaneous imbibition, a non-linear diffusion problem
Example memory functions that can model diffusion in a matrix block
analytical solution for spontaneous imbibition
Opportunity: Uncertainty quantification, clustering, model ranking, robust optimisation
Opportunity: Geomechanics for fractured reservoirs
Niels Bohr: Prediction is very difficult - especially about the future
Thank you!