Introduction to MRST for Reservoir Simulation

MATLAB Reservoir Simulation Toolbox
(MRST)
by
Rupak
Department of Chemical Engineering
Indian Institute of Technology Guwahati

The MATLAB Reservoir Simulation Toolbox
 A free open-source software for petroleum reservoir:
 reading
 running simulation
 visualization
 MRST is not a primarily a simulator:
 developed as a research tool by researcher at SINTEF Digital.
 can be downloaded and used under GNU General Public License (GPL).
 To download, visit: www.sintef.no/mrst/
 MRST offers black-oil and compositional model capable of simulating industry-standard problems.
 Graphical user interfaces for post-processing simulation results.
April 24, 2025 CL 644: Reservoir Simulation 2

Core Functionality & Add-on Modules
MRST= Core Modules + Add-on Modules

Core Functionality & Add-on Modules
 Core Module
 data structures for creating and manipulating grids.
 petro-physical data
 drive mechanism: gravity, boundary conditions, source terms, and wells
 Automatic differentiations.
 Add-on modules
 discretization : TPFA, MPFA, mimetic etc.
 flow equations and solvers
 workflow tools: coarsening, upscaling, flow diagnostics, visualization
 analysis of large-scale CO2 storage in saline aquifers.
 special models like geomechanics and fractured reservoirs

Overview of Functionality
Grid generation and coarsening
April 24, 2025 Flow Visualization Lab 5
 upr: used to generates the 2D or 3D
Voronoi grid.
 coarsegrid: data structures and
simple coarsening
 agglom: to create an adapted coarse
partition.
 libgeometry: to compute geometric
quantities like cell volumes, areas ,
centroids etc.
 opm_gridprocessing: contains
functionality for reading and
processing the GRID section of
ECLIPSE input data.
 triangle: to create triangular grid

Discretization and solvers for incompressible flow:
 incomp: incompressible, two phase
flow. This module implements two point
flux approximations (TPFA) and
implicit/explicit transport solver.
 mimetic, mfpa, ntpfa, vem implements
consistent discretization.
 adjoint: Implements strategies for
production optimization for
incompressible, two-phase flow

Implicit solvers based on Automatic Differentiation:
The automatic differentiation-object oriented (AD-OO) frame work offers fully implicit simulators from
industry-standard input decks, including computations of adjoints

Workflow tools:
 co2lab: comprehensive tools for large-
scale CO2 storage saline aquifers
 diagnostics: flow diagnostics,
 mrst-gui: interactive visualization
 optimization: solution of optimal control
problems based on AD-OO
 enkf and remso: third-party modules for
EnKF (Ensemble Kalman filter) and
multiple-shooting optimization

Upscaling and multiscale methods
 msrsb is state-of-the art multiscale
solver.
 msfem: implements multiscale finite
elements method on unstructured grids.
 msfvm: Implements the operator
formulation of the multiscale finite-
volume method for incompressible flow
on structured and unstructured grids.
 hfm: implements msrsb this for fracture
models
 upscaling: flow-based single-phase
upscaling.
 steady-state: multiphase upscaling based
on steady state assumptions.

Fractured Media
dfm: discrete fracture models, hfm: hierarchical/embedded fracture models

Downloading and Installing
Download official release from SINTEF Digital official website and extract
mrst-2021b containing all parts of software.
Since MRST is a secondary software you need to activate the software in
MATLAB
 You have to run startup.m script to activate MRST
MRST Package Welcome Message

Exploring Functionality and Getting Help
 To find out what a specific function does, you ca type help function_Name in the
command window

Example of Automatic Differentiation (AD)
We want to compute z = f(x,y) = x3
y and its partial derivatives for the values x=1 and y = 2.
z = f(x,y) = x3
y
𝜕𝑧
𝜕𝑥
=3 𝑥 2 𝑦
𝜕 𝑧
𝜕 𝑦
=𝑥 3
z | x=1,y=2 = 2
𝜕𝑧
𝜕𝑥
| x=1,y =2=6
𝜕 𝑧
𝜕 𝑦
| x=1,y =2=1
Manual
 Independent variables: x, y
 Dependent variable: z
[x,y] = initVariablesADI(1,2);
Independent variables Initialized value of IV
𝜕𝑥
𝜕𝑥
|1,2
𝜕 𝑥
𝜕 𝑦
|1,2
𝜕 𝑦
𝜕 𝑥
|1,2
𝜕 𝑦
𝜕 𝑦
|1,2 𝜕𝑧
𝜕𝑥
|1,2
𝜕 𝑧
𝜕 𝑦
|1,2

Basic Data Structures in a Model
Fluid properties:
fluid = initSingleFluid('mu' , 1*centi*poise , ...
'rho', 1014*kilogram/meter^3);
fluid = initSimpleFluid('mu' , [ 1, 10]*centi*poise , ...
'rho', [1014, 859]*kilogram/meter^3, ...
'n' , [ 2, 2]);
fluid = initCoreyFluid('mu' , [ 1, 10]*centi*poise , ...
'rho', [1014, 859]*kilogram/meter^3, ...
'n' , [ 2, 2] , ...
'sr' , [ 0.2, 0.2] , ...
'kwm', [ 0.85, 0.60]);
Single-Phase Flow
Two-Phase Flow
• Corey model with exponent ‘n’
• Zero residual saturation
• krw=, kro=
Two-Phase Flow
• Corey model with exponent ‘n’
• With residual saturation
• krw=, kro=

Reservoir states:
state = initResSol(G, p0,s0);
state = initResSol(G, W, p0,s0);
• p0 = Initial pressure
• s0 = Initial saturation
• When there are wells in the reservoir
• Additional field ‘wellsol’
• wellSol = initWellSol(W, pw0);
𝑠0=
{ 1, 𝐹𝑜𝑟 𝑠𝑖𝑛𝑔𝑙𝑒− h
𝑝 𝑎𝑠𝑒
[𝑠𝑤 0𝑠𝑜 0], 𝐹𝑜𝑟 𝑡𝑤𝑜− h
𝑝 𝑎𝑠𝑒 𝑓𝑙𝑜𝑤

Fluid sources:
src = addSource(src, cells, rates, ‘sat’, sat)
 src = an empty array (src==[])
 rates = volumetric flow rates of sources
 sat = fluid composition of injected fluids with rate > 0
Example:
src==[]
src = addSource(src, 1,1,[], 100*m3/day, ‘sat’, 1)
Boundary conditions:
bc = addBC(bc, faces, type, values, ‘sat’, sat)
 bc = an empty array (bc==[])
 faces = faces for which the conditions are set
 type = type of boundary condition: pressure or flux
 values = pressure of flux value for the given conditions

Boundary conditions:
bc = pside(bc, G, ‘side’,p)
bc = fluxside(bc, G, ‘side’,flux)
Side argument is a string which one out of the following six alias groups:
• West/Xmin/Left
• East/Xmax/Right
• South/Ymin/Back
• North/Ymax/Front
• Upper/Zmin/Top
• Lower/Zmax/Bottom

Wells:
W = addWell(W, G, rock, cellInx)
W = verticalWell(W, G, rock, I, J, K, 'pn1', pv1, ...)
W = verticalWell(W , G, rock, I, J, K, 'Type', 'rate/bhp', ...
'InnerProduct', well_ip, ...
'Val’,rate/bhp value, 'Radius’, radious of well, ...
'Name', ‘I/P', 'Comp_i', [1, 0],'Sign',1);
 I,J,K=Location of well
 Type = String specifying the well control: rate or bhp
 InnerProduct = Method of consistent discretizations
 Val = Target value of well control
 Radius =Welbore radius in meters
 Name = String giving the name of the well
 Comp_i = Fluid composition for injection well
 Sign = Well type: Production (sign=-1)/Injection (sign=1)

Example:
Problem 1: Quarter five-spot problem
- Flow equations: - .( )=q
∇ 𝐾∇𝑝
- Single-phase incompressible flow
- 2D cartesian grid covering 500× 500 m2
- Two source term at diagonally opposite corners
- Permeability = 100 mD and Porosity = 0.25
- Fluid = Water
Problem 2: Boundary conditions
- The reservoir is 50 m thick and is restricted to a 1 × 1 km2
area.
- The permeability is uniform and anisotropic, with a diagonal (1,000, 300, 10) mD tensor
- the porosity is uniform and equal 0.2
- the reservoir is represented as a 20×20×5 rectangular grid
- Neumann conditions with total inflow of 100 m3
/day on the east boundary
- Dirichlet conditions with fixed pressure of 25 bar on the west boundary

Grids:
 MRST Module: gridProcessing
 Features:
 a common data structures and infrastructures for all types of grids
 all grids are assumed to be unstructured
 nbo grid generator
 several grid factory routines for : regular cartesian grids, rectilinear grids, triangular grids etc.
Regular Cartesian Grid Rectilinear Grid Triangular Grid

Grids:
 Basic files and their functions:
 cartGrid - Construct 2d or 3d Cartesian grid in physical space
 tensorGrid - Construct Cartesian grid with variable physical cell sizes
 tetrahedralGrid - Construct valid grid definition from points and tetrahedron list
 triangleGrid - Construct valid grid definition from points and triangle list
 computeGeometry - Add geometry information (centroids, volumes, areas) to a grid

Parameters:
 MRST Module: params
 Features:
 Data structures for petrophysical properties
 Routines for setting and manipulating : boundary conditions, source/sink, well models etc.
 Basic files and their functions: Rock
 makeRock - Create rock structure from given permeabilty and porosity values
 grdecl2Rock - Extract rock properties from input deck
 permeabilityConverter - Add tensor permeability to GRDECL struct
 permTensor - Expand permeability tensor to full format.
 poreVolume - Compute pore volumes of individual cells in grid.
*GRDECL: Grid section of an ECLIPSE deck

Rock Modelling: Example
 Homogeneous modelling:
 Square 10 × 10 grid model with a uniform porosity of 0.2 and isotropic permeability
equal 200 mD
 The permeability is uniform and anisotropic, with a diagonal (1,000, 100, 10) mD
tensor the porosity is uniform and equal 0.2
 Heterogeneous modelling:
 Generate φ as a Gaussian field and then compute K from the Carman–Kozeny relation

Upscaling
• Also called homogenization
• Replace number of heterogeneous fine grid blocks with one equivalent coarse homogeneous grid
block
• Properties of fine scale model are approximated by that of a coarse model
• It’s an averaging procedure
• Additive properties
 Porosity
 Fluid saturations
• Non-additive properties: Permeability

Why Upscaling?
• First level upscaling :
 Laboratory data interpretation at the scale of reservoir.
• Second level upscaling:
 Scales properties of a fine grid to a coarse grid
 Scale up of geological grid to simulator grid for numerical simulation
• Other example:
 Consideration of first-hand-data distribution.
 Reservoir engineers usually apply a finer local grid in well-denser-area as well as in wellbore
around, and apply a coarser grid in well-thinner-area.

Introduction to MRST for Reservoir Simulation

More Related Content

Similar to Introduction to MRST for Reservoir Simulation (20)

Recently uploaded (20)

Introduction to MRST for Reservoir Simulation