PETREL_6_Upscaling.pdf

Upscaling Geological Models Ammar Agnia

Ammar Agnia Education 

Texas A&M University, MSc. Pet. Eng.



University of Sirte, B.Sc. Pet. Eng.

Work  



(2012-Peresent) Reservoir Engineering Team Lead – Lead – UK (2010-2012) RA - Reservoir Modeling Consortium, College Station, United States. States. (2007-2009) Reservoir Engineer Engineer - Software Support Support and and Implementation, Implementation, Tripoli/Benghazi, Tripol i/Benghazi, Libya.

Upscaling What is upscaling? 

Creating a relationship between a fine-scaled geological grid and the coarser simulation grid (consistency).

Why upscale a grid? 

Size: The average simulator requires a model between 100,000 to one million cells.

Gridding for Simulation Grid requirements:

May conflict !

– Adequate description description of reservoir reservoir structure and initial properties – Sufficient detail to describe change in saturation and pressure with time – Compatibility with mathematical model

Simulation grid sizes are limited by time & computer resources

Millions of Cells

~100,000 Cells

Concept Upscaling allows the Reservoir engineers to create a coarser reservoir model from the fine geomodel to be used in a simulator. simulator. An upscaled grid has: 

reduced number of cells (bigger cells)



zigzag or stair-step type faults (cell orthogonality)



coarser vertical layering.

Upscaling Workflow 1. Coar Coarsen sen the the fine grid in in the XX- and Y-dir -directio ection. n. 2. Make a vertical vertical subdivis subdivision ion of the coarse coarse grid. grid. 3. Quality check the resulting 3D grid (cell volumes volumes and cell angles). 4. Sample properties properties from the fine grid grid into the coarse grid. grid.

Making the Coarse Grid: Three Methods Simple grid:  Simple and fast  For models without faults  Can insert simulation faults. Structural grids:  When the fine grid is made using the structural gridding process. Pillar gridding:  Used to make 3D grids that adapt to faults.

When Do You Use the Simple Grid Approach? If you have non-faulted non-faulted grid…





Use the surfaces that were used to make the fine grid to define horizons. Specify the grid increment and orientation on the Geometry tab.

When do you use the Structural Framework Process? 

If you are building a Stair-stepped faulting grid or if the source (fine) grid is constructed using Structural framework process.

Structural framework

Structural gridding

Stair-stepped grid

Structural Gridding Process

 

Use the structural framework that was used to make the fine grid as input. Specify the grid increment and orientation on the Geometry tab.

When do you use Pillar Gridding Process? If the constructe constructedd fine grid is based based on the fault fault model. model.

In this course, you will use the Pillar gridding process to make a coarse simulation grid.

Pillar Gridding: Overview 1. Create a grid grid adjusted to the the mid-points of the Key pillars. pillars. 2. Extrapolate the pillars to the the top and base base shape points. points. This creates a 3D grid of pillars, represented represented by the top, mid, and base skeleton grids.

Note: Pillars are created at every corner of every grid cell.

Pillar Gridding: Settings When you create a grid with the Pillar gridding process, you are working with the mid skeleton in a 2D window.

Pillar Gridding: Terminolog Terminologyy Boundary: Polygon, boundary segment or part of a boundary. Trends: Guidance for the grid and used as segment divider (where no faults). I and J directions: Use for setting fault in I or J direction. Segments (Regions): Compartment closed by faults or trends.

Pillar Gridding: Cell Shape Make zig-zag zig-zag type faults: faults: Gives Gives a grid with cell cell angle angless close close to 90 deg. angles at cell cell corners are are better better Note: 90 deg angles for simulation.

Pillar Gridding: Cell Shape and Orientation To create a simulation grid with orthogonal cells, the number of trends and directed faults in the grid should be kept to a minimum. 

Use zig-zag faults.



Use trends outside the boundary to get zigzagg fa za faul ults ts and and the the correct grid orientation.

Grid Effects: Grid Orientation 1

Areal cell orientation and permeability permeability anisotropy Flow from cell to cell goes through cell faces not corners

8

6

4

8 timesteps between injector & producer producer,, “Appears” to sweep more oil

5 timesteps between injector & producer 5

7

4 3

5 2

2

3 1

1

Low

High Permeability, mD

Grid Effects: Grid Orientation Flow from cell to cell goes through cell faces, not through corners. The orientation of the grid cells affects the flow.

Grid Effects: Grid Orientation/Correcti Orientation/Correction on Techniques… Areal cell orientation and permeability permeability anisotropy Avoid the temptation to automatically automatically orient orient a simulation grid with the faults! (Try a FrontSim run to examine principal flow directions and orient grid accordingly).

Adds computation time in the Grid section & a more complicated solution for for every 1 timestep

Low

High Permeability, mD

Grid Effects: Grid Orientation/Correctio Orientation/ Correctionn Techniques… Grid orientation sensitivity

Original Orientation

Re-orientated

Grid Effects: Grid Orientation/Correctio Orientation/ Correctionn Techniques… SPE 5734

Grid Effects: Grid Orientation/Correctio Orientation/ Correctionn Techniques… SPE 5734

Note: NINEPOIN keyword selects selects a Ninepo Ninepoint int Tr Transmissib ansmissibility ility option, option, which adds diagonal transmissibility values to the grid as non-neighbor connections in the XY plane. .

Pillar Gridding: Grid Orientation Permeability anisotropy: Avoid the temptation to automatically automatically orient a simulation grid with the faults. Use FrontSim to find flow directions: Set up a simple, one-step simulation on the fine grid.

Note: Flow directions change if a new well is opened or wells are shut down.

Pillar Gridding: Cell Size I and J increment: Gives the average cell size and, hence, the model size.

Note: Cell size specified is an average. Cells vary in size as the t he gridding honors faults.

Grid Effects: Cell size Throughput related problems ECLIPSE has convergence rules limiting the maximum saturation change of a cell in one timestep 

Example: – In a one month timestep, ECLIPSE calculates that oil flowing from Cell 1(large) to Cell 2 (small) is a large proportion of the total volume of Cell 2 – ECLIPSE chops the timestep to 15 days & recalculates – Repeats until the limit is reachedincreasing the simulation time! Cell 1

Cell 2

Grid Effects: Numerical Dispersion

Water Injector

Oil Producer

40% Sw

The Reservoir: 100% Sw (SWU) Water Injector

60% Sw (front edge) Oil Producer

Finite Volume Model: 100% SWAT

80% SWAT

65% SWAT

50% SWAT

Grid Effects: Numerical Dispersion

Grid Effects: Cell orthogonality SPE 92868 Deviated

Reference

Grid Effects: Cell orthogonality • “Non-orthogonality “Non-orthogonality will usually imply that cross terms should be added in the finite difference equations. • Neglecting these terms may lead to errors that are independent of the (Soleng&H (Sole ng&Holden olden 1998) grid spacing.” spacing.” • In cases in which the grid is nonorthogonal, we apply the multi-point (Durlofsky ofsky 2003) flux techniques (Durl

Note: MPFA keyw keyword ord mul multip tipoin ointt flux approximation specifies that multipoint multip oint transmissibil transmissibilities ities are to be used in the discretized flow equations.

Pillar Gridding: Faults Tab Tab Select to Remove Faults 1. Sele Select ct Grid with selec selected ted faults/tren faults/trends. ds. 2. Toggle OFF the All faults check box. box. 3. Sele Select/des ct/deselect elect faults faults in drop-d drop-down own list. 4. Cl Clic ickk Update visible from lists. lists.

Pillar Gridding: Refining the Grid Set the number of cells between two faults. 1. Highli Highlight ght a Tren Trendd (endpo (endpoint intss become yellow). 2. Click Set number of cells on connection.. connection 3. Sp Speci ecify fy the the numb number er of of cells cells..

Edit on Simulation Grids The orthogonality or the cell shapes of any 3D grid can be edited in the process Ed Edit it 3D 3D grid gr id . Visuali isualiz ze fault faults s and/or and/or I- and JJ-Int Intersect ersections ions to be able to grab the pil pillar lars s in the gri grid d and and edit them. Before:

After:

Edit on Simulation Grids The orthogonality or the cell shapes of any 3D grid can be edited in the process Ed Edit it 3D 3D grid gr id . Visuali isualiz ze fault faults s and/or and/or I- and JJ-Int Intersect ersections ions to be able to grab the pil pillar lars s in the gri grid d and and edit them.

Edit on Simulation Grids continued… It is usually best to do the edits After Structural upscaling, and to use the geometrical property Cell Angle to check for orthogonality before and after editing. Before:

After:

Pillar Gridding Result When clic When cl icking king OK OK to the Pil Pillar lar Gri ridding dding dialog, Petrel Petrel will generate a new grid in the Models tab:

Top skeleton skeleton

Mid sk skeleton eleton

Base skeleton

Pillar Gridding Result When clic When cl icking king OK OK to the Pil Pillar lar Gri ridding dding dialog, Petrel Petrel will generate a new grid in the Models tab:

Pillar Gridding Pillar Geometry and Grid Formats Select a simple pillar geometry for simulation grids. Four grid file types for ECLIPSE ECLIPSE:: GSG:: (General Simulation Grid)  GSG includes all pillar geometries and truncated faults (Binary).  .GRDECL .GRDECL:: Linear faults (ASCII).

GRID:: Linear and curved faults  .GRID  .EGRID .EGRID:: Li Line near ar faul faults ts


Vertical Subdivision Capture Main Flow Barriers Simulation results will be different! Stratigraphic Model

Sim Si m Mo Mode dell 3


0


Permeability, mD

1000

Vertical Subdivisi Subdivision: on: Two Two Methods Metho ds Based on input data: Use the Make horizons, horizons, Make zones, zones, and Layering processes. Based on the fine model: Use the Scale up structure process.

Scale Up Structure: Settings for Each Zone 

Specify the type of layering in each zone.



Specify the number of layers in each zone.



(Optional) Combine two zones into one by clicking .



Remember to update the Top and Base horizon of your new zones.

Layering Types of Zone Divisions Specify the number of layers (Proportional), cell thickness (Follow top/Base), or Fractions.

Specify the Zone division. Proportional Follow Base Follow Top Fractions

Follow Base with Reference

Layering: Result Types of Zone Divisions Proportional

Follow base

Follow top

Fractions

Scale Up Structure Settings Other settings:  Collapse main zones if thinner than a given threshold . 

Use the Edit 3D grid process to edit horizon nodes, then re-run using Keep locked nodes unchanged unchanged .

Scale Up Structure: Settings for Each Zone 1. Sp Spec ecififyy the the num numbe berr of of zone zoness in in the the co coar arse se gri grid. d. 2. Click

to delete.

3. Sp Spec ecififyy the the num numbe berr of of lay layer erss in ea each ch zo zone ne..

Use IJK-Faulting for Stair-Stepped Faults Other settings: Select Use IJK faulting to include all faults in the fault model as stair-stepped that are not in the coarse grid.

Workflow 1. Deselect the the faults to be stair-stepped and run Pillar gridding. 2. Run the Scale Scale up structur structure: e: Turn on IJK-faulting.

1 2

3. Re Resu sultlt:: All faults from the the fault model model that were not included in the pillar gridding process are stair-stepped.

3


Quality Check of the Coarse Grid To reduce potential simulation errors, check: 

grid bulk volume



cell angles



cell inside out.

Quality Check of the Coarse Grid: Cell Angles Angles

Quality Check of the Coarse Grid: Bulk Volume 1. The geological geological grid and the the simulation grid grid should have have approximately the same pore volume. 2. At this point, verify verify there is consistency consistency between between the bulk volume volume of the fine and the coarse grid. 3. Comp Compute ute the bulk bulk volume volume for both grids, then compare the total volume.

Quality Check of the Coarse Grid: Cell Inside-Out

Quality Check of the Coarse Grid: ACTNUM 1. Set up the required required property property (Cell_ang (Cell_angle). le). 1

2

2. Righ Right-cli t-click ck and sele select ct Calculator….


Consistency in STOIIP Between the Fine and the Coarse Model You validated the bulk volumes of the models. To make sure you have the same STOIIP in your coarse model as in the fine model, be careful when upscaling NTG and porosity. porosity. Bulk Volume ( A x h) Pore Volume ( BV x NTG x φ) Fluid description ( Bo ; Sw)

Porosity, NTG, and Facies Review the fine grid properties before you start:  Is there a NTG property?  Is there a facies property?  Was the porosity conditioned to the facies model?

Example: Scale Up Porosity In the fine grid, porosity was conditioned to a facies model. Fine model

Porosity assigned to upscaled facies model.

Porosity upscaled using an arithmetic mean.

Porosity upscaled with NTG as weight.

Scale Up Properties Select a grid for samples.

Select the sampling method.

Zone mapping algorithms

Scale Up Properties Select a grid to sample from.

Select the sampling method.

Zone mapping algorithms

Upscal Ups caling ing Pro Proper pertie tiess Sam Sampli pling ng Met Method hodss (1) (1)

All Intersecting cells: Samples all cells in the source grid that overlap each cell in the target grid in 3D.

Source cell center: Samples cells in the source grid whose centers are within the target grid cell.

Upscaling Properties Sampling Methods (2) Zone-mapped layers:

Samples all layers in those columns that are mapped to the layer of the target cell.

Target cell center: Samples the value of the source property located at the center of the target cell.

Why Zone Mapping? mapping ing associ associates ates each layer in the the target target grid with a  Zone mapp range of layers in the source grid.  Restricts search space for the selected sampling algorithm.  Speeds up the Upscaling properties process.

Scale Up Properties: Zone Mapping Using Matching Horizon Names

Open mapping

Scale Up Properties: Zone Mapping Using Geometric Overlap

Close mapping

Sampling Method: Zone Mapping Situation in which Mapping all layers to all layers cannot apply apply.. Fine grid

Coarse grid

Open mapping is a good option in this t his situation.

Scale Up Properties: Select an Algorithm Algorithm for Each Property Click on one of the properties from the fine grid to access the available settings.

Algorithms Averaging (volume-weig (volume-weighted): hted): The coarse grid grid property is computed using the volume of the fine cells as weight. A secondary property property also can can be used as as weight.

Methods: Different Methods for Discrete and Continuous Properties Discrete properties: For facies, it is natural to use the Most of method. Continuous properties: Several available averaging methods. For porosity, porosity, arithmetic mean is the natural choice.

View Results in a Well Section Window Well C7 shows, in order:  Original porosity log.  One

panel with fine scale porosity layering.

 Three

panels with coarse scale porosity layering.

View Results in a Histogram Window

Example: Porosity scaled up using arithmetic mean compared to porosity assigned to a scaled up facies fac ies pro proper perty ty..

Compare Pore Volumes: Use the Calculator to Compute the Pore Volumes Enter the expression for pore volume. Use NTG if appropria appropriate. te. Read the total pore volume on the Statistics tab in the Settings for Pore_volume window.

Throughput Related Problems 1.You can set a threshold value for pore volume 2. 3.Cells with a smaller volume are set inactive.

Best Practice Ideally, the simulation engineer (and petrophysicist?) is involved Ideally, before the geologic model is built 

What is being modeled?



How? – Fine or coarse scale – Non-net rock is explicitly modeled?

 

Be specific, “porosity” is a catch-all catch -all phrase If a cut-off is to be used to define net-to-gross, it must be carefully chosen!

Permeability Upscaling Methods Single-phase Permeability upscaling

Combined analytical

Simple analytical

Flow based

No-Side-Flow BC Arithmetic

Harmonic-Arithmetic Linear BC

Harmonic

Geometric

Power

Arithmetic-Harmonic Adjoint

Half-grid block

Upscaling Permeability Arithmetic Averag Averaging ing

Flow direction

Arithmetic Averagin Averaging: g: I

K

Ai

 d

i

I



Ai k i d i

Assumption is that properties in layers are only moderately different. Sharp contrasts should be eliminated by proper upgridding!

Upscaling Permeability Harmonic Averag Averaging ing Harmonic Averagin Averaging: g: Flow direction

1 I

K

d i

 A

i



d i I

Ai k i

It is similar to the transmissibility calculation for block-to-block flow

Upscaling Permeability Geometric Averag Averaging ing

Geometric Averaging Averaging:: Flow direction

I

N ln K 

 ln k

I

i

Good if a chessboard-type property distribution is given

Scale Up Permeability: The Objective is to Preserve Flow Behavior Fine model

Upscaled models



Permeability determines the flow behavior.



The values in neighboring cells are important when upscaling.

Upscaling of Properties Property up-scaling can be divided into two main categories: 1. 

2.



Averaging The averaging methods can be used for all properties. Chose between various algorithms.

Flow based tensor up-scaling

The flow based tensor up-scaling can be used for permeability per meability as this property may vary directionally directionally..

Algorithms and and Sampling Directional algorithms are available. When you use those methods, a permeability tensor is computed.

Note: Sampling: The methods for computing permeability tensors cannot use volume weighting. The entire source cell is used.

Directional Methods: Input and Output 1 When you choose to use a directional algorithm, the permeability property displays as a folder in the process dialog.

1 2

2 Left-click one one of the directional permeabilities inside the folder. 3 Select the fine grid permeability permeability property property to use as input for the calculations. It can be the same for all directions.

3

4

4 The output output is a coarse grid tensor permeability.

Directional Averaging: How Does it Work? Along the flow direction: The overall permeability is given by the harmonic average. Across the flow direction: The overall permeability is given by the arithmetic average. In a cube of cells: These two rules can be combined to approximate the flow through a coarse cell.

Directional Averaging: Arithmetic-Harmonic All slices of cells cells perpendicular perpendicular to the flow direction are averaged using arithmetic means. The harmonic mean of the slices is assigned as the directional permeability.

Upscaling of Properties Flow Based Tensor Up-scaling What is Flow based tensor Up-scaling? Uses Darcy’s Darcy’s equation equation and a given pressure pressure gradient on the fine fi ne scaled grid cell c ells s in the the I, J and K dir directi ections ons to calculate calc ulate the t he result resulting ing Perm-I Perm-I Perm-J and Perm-K Perm-K in the coarse grid gri d (chose ( chose between XYZ or IJK – Full tensor also calculates the resulting diagonal Permeabilities) Permeabilities )

P1 1

P

vi   K  i P P2

v i Porous rock filled with fluid

More time (and CPU) consuming than other averaging methods use filter settings! filter settings!

Upscaling of Properties Flow Based Tensor Tensor Up-scaling - continued

Permeability is very different from otherr prop othe properti erties es since the effective effect ive permeability of an area is affected by it’s distribution and the orientation in which it is measured Designed for Permeability to keep the flow properties of the coarse simulat simu lation ion grid gri d the same same as for the fine scaled geological grid The average average flow veloci velocity ty in i n the coarse grid gri d will wi ll rema remain in the t he sam same e as in the fine fi ne grid.

Methods Flow based - Diagonal tensor/Full tensor Boundary condition: • used to specify the flow at the boundaries of the coarse cell Input properties – from fine grid • Specify input permeability for each direction • Specify the input porosity

Upscaled – from coarse grid • NOTE: Porosity must be upscaled upscaled before permeability

Upscaling of Properties Boundary conditions Three different boundary conditions are available in PETREL: Open bound boundary ary condition: condition: Flow is permitted through all the cell sides. s ides. A linearly linearly varying pressure field is applied to the boundary nodes. Allows for cross flow between cells Closed bound boundary ary condition: condition: means that you apply a constant pressure to two opposite cell block sides and close all the remaining boundaries. Flow can only follow one direction; I to I, J to J and K to K Closed K boundary condition: Flow not allowed to go through upper and lower cell faces when applying a pressure gradient in I and J direction. But when applying a Pressure gradient in Kdirection flow is allowed to go through I and J outer cell faces.

Open:

Closed:

Upscaling of Properties Skin conditions Adds a number of fine cells outside the area to the upscaled cell. The pressure gradient will be applied over the whole skin zone, not just the cells within the coarse cell. By default, the skin zone is limited by the zone mapping. This can improve flow solution as flow can go around the coarse cell. Using velocity average for the skin zone can cause a smearing effect, but with large variance in permeability, this can avoid a zero solution.

Upscaling Permeability Flow-based Methods Fine Grid

Coarse Grid

Full 3D solution: Computationally most intensive solution Step1: Total flux through the system is Step1: computed in the direction of pressure drop

z

H

k

Inlet

L

z

Outlet

Step2 : The effective permeability is then estimated by solving the same problem with constant permeability chosen to give the same flux.

Discussion – Discussion – Upscaling Permeability Simple analytical (Arithmetic, Geometric, Harmonic, Power). + Simple, fast, and might be sufficient. 



Neglect permeability spatial distribution and variation. Geometric a good choice for chessboard chessboard-type -type permeability distribution.

Combined analytical (Arithmetic-harmonic, Harmonic-arithmetic). + Often efficient and robust. 

Inadequate for random heterogeneity with tortuous flow paths.

Conclu Con clusio sionn - Work Flo Flow w

Advanced method is not necessarily the best method. method. To find the “best best”” upscaling method. Use different upscaling methods. Run the models with simple physics. Compare with the fine scale model Consider sector models and streamline simulation.   



Capillary pressure scaling based on J function (1)





The Leve Leveret rettt J functi function on – – related to permeability, porosity, capillary pressure, interfacial tension, and contact angle. Capillary pressure can be scaled based on J function and other quantities. J

J ( Sw)



Pc Pc ( Sw)

k

 cos 



Sw

Capillary pressure scaling based on J function (2) 



Given J function as a function of water saturation – saturation – J (S) – Defined in the place of Pc (say in SWFN SWFN)) Set interfacial tension (IFT) – Use JFUNC – Use STOW STOW,, STOG for IFT vs. pressure



Given grid block properties: permeability - PERM PERM,, porosity - PORO



Capillary pressure can be scaled as (the contact angle=0): Pc(Sw)=J(Sw) IFT (PORO/PERM)^0.5

Capillary pressure scaling based on J function (3) 

JFUNC scaling can apply to PCOW or/and PCOG (item 1 of JFUNC).



The power for porosity (0.5) can be reset (item 4 of JFUNC).



The power for permeability (0.5) can be reset (item 5 of JFUNC).





The average average permeability permeability [XY - PERM=0.5*( PERM=0.5*(Kx+Ky)] Kx+Ky)] can be reselected (item 6 of JFUNC). JFUNC scaling can be applied to each saturation table (JFUNCR).

Scaling for Capillary Pressure Function J-function in Petrel 1. Select Use J-function for oil-water to activate activate the Leverett Leverett J-fun J-function ction scaling scaling for the water-oil capillary pressure function. 2. Select Use J-function for gas-oil to activate activ ate the Leverett Leverett J-fun J-function ction scaling scaling for the gas-oil capillary pressure function. 3. Select Use correlation for oil-water to oil-water to generate a capillary pressure function 1 using a correlation for mixed-wet reservoir rock. 4. Tuning Tuning factors factors a and b are are used used in the J-function J-fun ction equa equation: tion: J(Sw J(Sw)) = ae(bSw).

3

4

2

J-Function Parameters Parameters that characterize the J-function, such as surface tension t ension and grid properties, are defined in the J-function parameters tab.

Oil-water and oil-gas surface tensions.

Scaling factor for capillary pressure function based on grid block porosity and permeability properties.

Matching initial water saturation Workflow of o f using using SWATINIT SWATINIT (1) 1. Calcul Calculate ate the ini initia tiall water water sat satura uratio tionn in the fin finee grid grid mod model el using J function or HAFWL (height above free water level) function. 2. Upsc Upscal alee wate waterr satu satura ratition on fro from m fine fine gri gridd to coa coarse rse gri gridd by summation: Sw_coarse Sw_co arse = SUM (Sw_fine* (Sw_fine*Porv_ Porv_fine) fine) / Porv_coarse Porv_coarse so that water in place is preserved.

Matching initial water saturation Workflow of o f using using SWATINIT SWATINIT (2) 3. Use Use the the J fun funct ctio ionn or or HAF HAFWL WL fu func nctition on as th thee inp input ut Pc Pcow ow to keep the correct shape. J ( Sw) 

Pc ( Sw)

k

 cos 



Matching initial water saturation Workflow of o f using using SWATINIT SWATINIT (3) 4.

Set SW SWATINIT=SWATi.

5.

Output Outp ut en endd po poin intt cap capililla lary ry pr pres essu sure re,, PCW.

The scal scaled ed Pcow using PCW can be considered the ‘truth’ Pc, as it:  Keeps the shape of the input Pcow curve. Reflects cts the upsca upscaled led prope properties rties,,  Refle e.g., permeability, porosity.  Honors SWATi.

Matching initial water saturation Workflow of o f using using SWATINIT SWATINIT (4) Indication Indic ation of unsua unsuall SW SWA ATi. 6. QC SWATi. 7. Apply ma maximum PC PCW – PPCWMAX. 8. Keep PPCWMAX, does not honor honor SW SWA ATINIT TINIT..

Relative permeability upscaling Pseudo Relative Permeability To model a reservoir with as few blocks as possible, but to obtain the accuracy provided by many more blocks (numerical dispersion).

Relative permeability upscaling Pseudo Relative Permeability Upscale Pseudo Curves in a Pseudo Compositional Oil

Recovery Accuracy Between Fine & Upscaled Coarse Gridded Model

Relative permeability upscaling Pseudo Relative Permeability The purpose of all types of Pseudo Relative Permeability and Capillary Pressure is to adapt the core data to something more consistent with the scale of simulation cells. Some assessment of the physics of the flow processes within the simulation cells is therefore necessary if sensible use of pseudo data is to be made.

Relative permeability upscaling Pseudo Relative Permeability Types of Pseudos: •

Static

•

Wells

•

Vertical Equilibrium

•

Dynamic

Relative permeability upscaling Pseudo Relative Permeability Vertical Equilibrium •

Coates, 1967 and 1971

Pseudos •

Hearn, 1971

•

Jacks and Smith, 1973

•

Kytee and Berr Kyt Berryy, 1975 1975

Upscaling validation

Upscaling validation Upscaled Upsca led mode models ls can be checked checked with: • Streamline simulation: 

Fast Simulation runs with Frontsim



Quantitative Time-of-Flight analysis



Preserving allocation data



Connected pore volume to wells maps

• Evaluate the change in the mismatch: 

Objective function.



History Match Analysis module

Upscaling validation • Heterogeneity indices: 

Dykstra-Parsons coefficient



Shear-rate Heterogeneity index



Dynamic Lorenz coefficient

• Layering analysis: 

Li and Beckner

Upscaling validation with Streamline simulation Additional well information Well patterns Which injectors support which producers?

Breakthrough times Use TOF to estimate in which well is water breaking through first?

Allocation data What is the fraction of flow going from one injector to a particular producer?

Upscaling validation with Streamline simulation No wells/observed data ? Use Frontsim with GEOFLOFS . Using pseudo-wells

Using Flow boundary

Upscaling validation with Streamline simulation 106 cell geolo geological gical model model - FS: 6hrs 120kk cell 120 cell ups upscal caled ed mod model el - FD FD:: 6hrs 6hrs

Water Cut

Upscaling method verified

Pressure

Upscaling validation with Streamline simulation SPE 95759

Upscaling validation with Streamline simulation Quantitative Time-of-Flight analysis TOF is calculated along each streamline based on the equation, TOF=Distance/Darcy Velocity/ Porosity.

Inverse time of flight reported in the PRT file

Upscaling validation with Streamline simulation Quantitative Time-of-Flight analysis

Upscaling validation with Streamline simulation Use allocation data Use allocation data From well I04

Injectors should maintain the same flow pattern and supply to producers

Upscaling validation with Streamline simulation Use allocation data

Upscaling validation with Streamline simulation Compare connected pore volume to wells maps Use Frontsim with GEOFLOFS to generate *.FSCAT file. Use Make/edit surface in Pe Petr trel el

Try to preserve the connected pore volume to wells.

Upscaling validation Upscaling Validation Validation using minimized RMS objective function If any observed data availa ava ilable ble (e.g (e.g DST at least) can be used to evaluate the change in the mismatch by Objective function.

IDEA: If no observed data available, fine grid run results IDEA: can be used as reference data to evaluate the mismatch.

Upscaling validation Upscaling Validation Validation using minimized RMS objective function Quick look on the mismatch change using History Match Analysis module

Upscaling validation Upscaling Validation Validation using minimized RMS objective function Locating mismatch area using History Match Analysis module

TOFSENS restart mnemonic in FrontSim Wu and Datta-Gupta , 2001, SPE 66352

The method is based on DattaGupta’s generalized travel time inversion approach to history matching for sensitivity to permeability • SENS_K is for sensitivity of water cut mismatch to a grid cell permeability.

Upscaling validation Locating mismatch area from time of flight. Trav ravel el tim time e match match 1.0

0.8

t u c - r e t a W

0.6

tcal

tobs

0.4

0.2

Observed Calculated

0.0 0

500

1000

1500

Time, days

2000

2500

Rey. et. al 2008

Upscaling validation Dynamic Lorentz Coefficient

• Schma Schmalz lz and Rahm Rahmee (1950 (1950)) propo proposed sed Loren Lorenzz coef coefficie ficient nt of heterogeneity for characterizing the heterogeneity within a formation. • It relate the cumulative flow capacity to the cumulative storage capacity of the reservoir. When plotted a curved relationship will develop. The greater the deviation of this curve from the 45 degree line the greater the heterogeneity of the system. • Lorenz Heterogeneity plot can used as a measure of how much the upscaling is affecting the heterogeneity description.

Upscaling validation Dynamic Lorentz Coefficient Depositional Scenario

Structure

Petrel

FrontSim

Static Models

(GEOFLOFS)

Facies Petrophysics

Shook and Mitchell, 2009, SPE 124625

Dynamic Lorentz Coefficients*





Upscaling validation Dynamic Lorentz Coefficient The TOF in the PRT file is now complemented by an additional ‘CASENAME_ TOF.TXT’ TOF.TXT’ file that provides: Capacity(flow) vs Volume(PV) information. information.

Capacity(f Capacity(flow) low) and Volume(PV) olume(PV) values needs to be normalized by their total sums

Layering analysis

King, 2007, SPE 124625

Thanks

PETREL_6_Upscaling.pdf

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