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General description of tNavigator

General description of tNavigator

Training Tutorials 2014

Training Tutorials 2014

Rock Flow Dynamics

Rock Flow Dynamics

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2 2

Reservoir simulation tasks

Reservoir simulation tasks

Build

Build

model

model

History Matching

History Matching

Assisted History

Assisted History

Matching

Matching

Expert model Evaluation

Expert model Evaluation

Monitoring

Monitoring

Forecast

Forecast

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2 2

Reservoir simulation tasks

Reservoir simulation tasks

Build

Build

model

model

History Matching

History Matching

Assisted History

Assisted History

Matching

Matching

Expert model Evaluation

Expert model Evaluation

Monitoring

Monitoring

Forecast

Forecast

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tNavigator main window

tNavigator main window

1. Run

1. Run tNavigatortNavigator

2.

2. File. File. OpenOpen  – – o p e n  o p e n E 1E 10 0 m o d e l s0 0 m o d e l s

3.

3. File, File, Open asOpen as - sw- switch itch E300, E300, IMEX, SIMEX, STTARS, MOREARS, MORE

4 . 4 . M a iM a in wn wi n d o w ci n d o w co n t a i n s t h e f o l l o w i n g o p t i o n so n t a i n s t h e f o l l o w i n g o p t i o n s Language: Settings, Language: Settings, Language, English Language, English Parallel: choose core number

Parallel: choose core number for parallel calculations

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Open model

Open model

t N a

t N av i g a t o r r e a d s th e fo l l o wv i g a t o r r e a d s th e fo l l o wi n g d a t ai n g d a t a forformmats ats IMEX, IMEX, STSTARS, ARS, MORE , MORE , E100, E100, E300E300

Default

Default  – –E100E100

To op

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tNavigator documentation

tNavigator documentation

tNavUserManualEnglish.pdf

tNavUserManualEnglish.pdf

User Manual. Physical model description, mathematic

User Manual. Physical model description, mathematic

model, formulas, keywords.

model, formulas, keywords.

tNavUserGuideEnglish.pd

tNavUserGuideEnglish.pdf

f

User

User Guide.

Guide. Description

Description of

of tNavigator

tNavigator graphical

graphical interface

interface

tNavArithmeticManualEnglish.

tNavArithmeticManualEnglish.

pdf

pdf

Arithmetic manual (User Arithmetic

Arithmetic manual (User Arithmetic

 – 

 – 

  unique tNavigator

  unique tNavigator

module. One can add and edit user maps, user cuts, user

module. One can add and edit user maps, user cuts, user

graphs and model data file).

graphs and model data file).

release_notes_eng.pdf

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Open model

1. File. Op en

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3D visualization

Visualization panel Options Report panel Time slider

tNavigator can: Visualize the mo del before and d urin g calculation s (Maps, 2D and 3D m a p s ); S t o p c a l c u l at i o n s , ed i t th e m o d e l a n d r u n c a l c u l at i o n s a g a i n .

Press on the block to see the value of map parameter in this block

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Maps

2D map

Histogram 3D map

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Maps List

Initial maps  – depth, porosity, block size along X, Y, Z axis, permeability along X, Y, Z axis, transmissibility multipliers, etc.

Calculated maps  – pressure, saturation of oil, water, gas, ternary saturation diagram, reciprocal of formation volume factor for water, oil, gas, reciprocal of viscosity for water, oil, gas, etc.

Resources  – Oil in place, Mobile Oil in Place, Mass Mobile Oil in Place, Gas in Place, etc.

Regions  – Pvtnum (PVT regions), Satnum (saturation regions),

FIPnum (Fluid-in-Place regions), Eqlnum (equilibration regions), etc.

User Cuts and User Maps  – maps and cuts that can be created via User Arithmetics.

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3D visualization

To rotate map  – hold left mouse button and move the mouse To move map  – hold right mouse button and move the mouse To scale map  – roll mouse wheel

Default view  – press left + right mouse click

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Block statistics

R i g h t m o u s e c l ic k o n b l o c k o n 2 D o r 3 D m a p , c h o o s e B l o c k s t a t is t i c s (size, por osity, p ermeability, r e g i o n s t o w h i c h b l o c k c o r re s p o n d s e t c .)

Press top left angle of table to s elect it Ctrl+C, Ctrl+V (to co py and expor t to Excel)

Change the block  – Select X, Y, Z

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Palette

Vertical palette

1. The parameter values of properties on the map correspond to the colors on palette 2 . V er t i c a l c o l o r p a l et t e is m a r k e d b y h o r i z o n t al li n e s an d n u m b e r s

3 . I n th e fi g u r e th e d e f a u l t p a l et t e (r e d , b l u e, g r e en , y e l lo w , r e d ) 4 . T h e c o l o r c h an g e s ev e n ly b e tw e en t h e tw o c o l o r s

5 . T o c h an g e P al e t te p r o p e rt i e s - ri g h t m o u s e c l i c k o n t h e p a l et t e

Green color  – value 0.4922 of oil saturation

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Discrete palette

1 . R i g h t m o u s e c li c k o n p a le tt e. Set Discr ete Palette 2. Dis cr et e   a n d C o n t i n u o u s p a l et t e

• Discrete palette : c o l o r o n t h e m a p c o r r e s p o n d s t o t h e p a r am e t e r v al u e s f r o m m i n i m u m

( s p e c if i e d in th e p a l et t e o n th e h o r i z o n t a l li n e at th e b o t t o m o f th e c o l o r ) to a m a x i m u m ( in t h e p a l e tt e o n th e h o r i z o n t a l li n e at th e to p o f th i s c o l o r )

• C o n t i n u o u s p a l et t e  : e ac h p a r am e t e r v a l u e c o rr e s p o n d s to t h e c o l o r to n e

3 . B a c k t o c o n t i n u o u s p a l e tt e - ri g h t m o u s e c l i c k o n p a l et t e a n d Set Contin uou s Palette

Discrete palette Continuous palette Discrete palette: green color corresponds to the parameter

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Logarithmical palette

1 . C a lc u l a t e d M a p s . R e l. P e r m o f W at e r

2 . R i g h t m o u s e c l ic k o n t h e p a le tt e . Log arithm ical palette 3. L og ar it hm i cal   a n d defaul t p alette

• Log arithm ical palette: L o g a r i t h m i c a l d i s t r i b u t i o n o f c o l o r s ( d i f f er e n t c o l o r to n e s f o r s m a l l

parameter values)

• Default palette: linear distribu tion of colo rs

Logarithmical palette Default palette

Green color  – parameter value 0.0005 Green color  – parameter value 0.1501 In any palette, you can add a new color or remove the color (right mouse click on the color)

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Distance between blocks

1. 3D map s. P r e s s D i s t an c e b e t w e e n tw o s p e c i f i ed b l o c k s

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Map statistics

1 . M a p s . R e s er v e s . M o b i l e O il in P l a c e (Ma s s ) 2. M ap s t at is ti cs

3. Map statistics: Entries (active block s), Sum , Mean (average), RMS (Root Mean Square), M i n i m u m , M a x i m u m v a l u e o f p a r a m e t e r fo r t h i s m a p

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Cut to select reservoir top layers

1. U ser c ut s . C ut

2 . In M a p ar i th m e ti c c o m m a n d li n e « K <6 » (5 top layers in Z direction w ill be selected).  A p p l y  . 3. Red co lo r  – c u t is t r u e fo r th e s e b l o c k s , b l u e   – c u t i s fa l s e

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Map statistics with Cut

1. Retu rn to Maps. Reserves. Mobile Oil in Place (Mass) 2. Tic k Use Cut . Cut.

3 . 5 to p lay e r s o f th e re s er v o i r ar e v i s u al i ze d

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One model in several windows

Press C r e at e n e w w i n d o w t o o p e n s e v e r al w i n d o w s w i t h y o u r m o d e l :

• In d i f f e r e n t w i n d o w s y o u c a n a n a l y ze : 2D a n d 3 D m a p s , g r ap h s , h i s t o g r a m s • Yo u c a n o p e n n e w w i n d o w s b e f o r e o r d u r i n g c a l c u l at i o n s

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2D maps

Layer: layer number in Z-axis direction (IJ), X-Z-axis

(JK), Y-axis (IK)

Sum: of all vertical layers

Avg (average): of all vertical layers

Rms (variance): variation of all vertical layers

D r o p d o w n m e n u fo r 2 D m a p s :

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2D map Density

Mobile Oil in Place Density

k  b k  k 

i

 j

 j

i

dz 

 j

i

map

 j

i

map

density

)

,

,

(

)

,

,

(

*

)

)

,

,

(

(

)

,

,

(

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,

(

i

 j

map

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,

,

(

i

 j

dz 

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,

,

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i

 j

b

-- Value of map in th e bloc k (i, j, k);

-- Sum of the vertical colu m n for (i, j). If Cut is enable then the sum will inc lude b l o c k s f o r w h i c h t h i s c u t is t r u e ;

-- Value DZ (block size along Z) of th e block (i, j, k); -- Volume o f the blo ck (i, j, k) at current p ressur e.

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2D map Concentration

Mobile Oil in Place Concentration

k  b k 

 j

i

ntg 

 j

i

 j

i

map

 j

i

map

ion

concentrat 

)

,

,

(

*

)

,

,

(

)

,

,

(

)

,

,

(

)

,

,

(

i

 j

b

ntg 

ntg 

b

 *

-- Volume of th e block (i, j, k) at current press ure;

-- Is specified via the corr espon ding k eywo rd NTG (net to gro ss value);

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3D slicing

1. Un ch ec k al l 2. Ti ck lay er s y o u w a n t to v i s u a l i ze 3. Ch oo se U n i o n  o r Intersection  o f la y e r s Tick layers 3D slicing

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Histogram

1. Maps. Initial Maps. Poro sity. Histog ram

2 . T h e h e i g h t o f th e c o l u m n - the number of blocks with the values of porosity (or other parameter) i n th i s r a n g e

• Total number of active blocks (Entries); • Sum of porosity values for all blocks (Sum);

• Mean (average value of porosity for blocks) (Mean); • RMS (porosity variance) (RMS  – root mean square).

 Values (the  height of the column corresponds to the

number of blocks with the values of   porosity in the range)

  Percent (the height of the column corresponds to the

number of blocks per cent with the values of  porosity in the range)

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2D Histogram

The dependence of the porosity (Poro) on the permeability of the cells in the direction of the axis X (PermX)

1 . T w o - d i m e n s i o n a l h i s t o g ra m v i s u a l i ze s th e r el a t io n s h i p b e t w e e n th e t w o p a r am e t e rs 2 . W e s et t h e p a r am e t e rs t h a t w i l l b e d i s p l a y e d al o n g t h e a x e s X an d Y (  p o r o   - poros ity,

p e r m x   - permeability in X direction )

3 . 2 D h i s to g r a m - v i s u al iz at i o n o f th e ir d e p en d e n c e

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Run and stop calculations

1. R un c a lc u lat io n s a n d S t o p

2 . R u n c a lc u l at i o n s to t h e s p ec i f ie d ti m e s t ep (  Goto Step  ). Cal c u lat io n s w ill s to p at t h is s t e p

3 . W h e n y o u r eo p e n t h e m o d e l c al c u l at i o n c an b e r u n f r o m a n y p r e v i o u s l y c a l c u l a t ed s t e p 4 . P lay b ac k r es u l ts  – A u t o p l a y b a c k o f c a l c u l a t ed s t e p s ( s t e p b y s t e p c h a n g e s o n t h e

map s, graphs, tables) 

Run calculations to step, Enter step number

Calculated steps are underlined with a red line Time slider

Stop Run calculations

Playback results

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Calculations. Easy restarts

1 . In t e ra c ti v it y in th e c a l c u la ti o n . Y o u c a n s t o p   the calculation, witho ut w aiting till the end, if, for examp le, there is big difference between histor y and calculation data.

2. R es t ar t c al c u la ti o n  – m o v e ti m e th e s l i d e r to th e ti m e s t e p , w h i c h r e q u i r e s a r e c a l c u l a t io n , a n d r u n th e c a l c u l at i o n a g a i n

Stop calculations Time slider

Red vertical line  – current calculation step

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Create profile (vertical section)

1 . C r ea te p r o f il e

2 . U s e m o u s e c l i c ks t o m a k e p r o f i le li n e ( t h e li n e o f p r o f i l e g o e s t h r o u g h b l o c k c e n t e rs ! T o m a k e th e s t r a i g h t li n e u s e C r o s s - s e c t io n b u t t o n (further in this cou rse))

3. A pp ly. Ok

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Profile. Bubble Maps

1 . 2 D M ap . P r of il e

2. Tic k B u b b l e M ap s . A c c u m u l a t ed B u b b l e M a p s

3 . N e ar th e c i r c l e th e r e a r e v al u e s o f a c c u m u l a t ed o i l , w a t er , w a t e r in j ec t i o n 4 . S iz e o f b u b b l e m a p s is c h an g e d v i a s l i d er

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Profile. Bubble Maps

1 . 2 D M ap . P ro f il e

2. Tic k Bub ble Maps. State Bu bble Maps

3 . N e ar th e c i r c l e th e r e a r e v a l u e s o f c u r r e n t o i l r a t e , w a t e r r a t e, w a t er in j e c t i o n r a t e 4 . S iz e o f b u b b l e m a p s is c h an g e d v i a s l i d er

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User Bubble Maps

1. 2D m ap s. Su m

2 . Ti c k B u b b l e M ap s . C u s to m

3. B u b bl e M ap 1: Liqu id Total, Oil total 4. Ty pe - Calculated

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Grid properties along the profile

1 . G r ap h s . P ro f il e In f o 2 . P r o f il es . P r o f il e 1

3 . T h e o p t i o n o f p r o c es s i n g al o n g t h e p r o f i le : A v g

4. P ro p er ti es : Pressure and Saturation of Oil (on the pictu re)

The horizontal block numbers are in the order they are along the profile. Vertical: to the selected parameters there is the average value for blocks values (along the axis Z), the sum value of the blocks values (along the axis Z) or the value of the layer (layer number is selected from the drop down menu).

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Cross-section (horizontal)

1 . C r o s s -s e c ti o n . H o r iz o n ta l C r o s s -S ec t i o n 2 . H o l d le ft m o u s e b u t to n ( an d m o v e y el l o w s p h e r e) to m o v e t h e h o r i zo n t a l s e c ti o n p l an e 3 . O r en t er s ec t i o n d e p t h in m e te r s 4. A pp ly. Ok  –C r o s s - s e c t io n 1 is m a d e Cross section

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Cross-section (horizontal) on 2D map

1 . 2 D m a p . C r os s s ec t io n

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Cross-section (vertical section  – straight line)

1 . C r o s s -s e c ti o n . Ve r ti c al C r o s s -S ec t i o n 2. A d d C r os s -S ec ti on i n t h e d r o p d o w n m e n u

3 . M ak e 2 m o u s e c li c k s o n t h e m ap  – the plane will be created

4 . H o l d ri g h t m o u s e b u t t o n (a n d m o v e y e ll o w s p h e r e) to m o v e th e s ec t i o n p l an e 5 . O r en t er s e c ti o n b l o c k c o o r d in a t es in m e te r s

6. A pp ly. Ok  –C r o s s - s e c t io n 2 is m a d e 7 . 2 D m a p . C ro s s s ec t io n  2

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Switch from well on map to well graphs

D o u b l e c l i c k o n b l o c k w i t h w e l l c o n n e c t i o n  – s w i t c h t o w e l l g r a p h s (  Rates  )

Double click on well

Oil rate (red) and water rate (blue)

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Well graphs Synchronization

A u t o S y n c  – s y n c h r o n i z a ti o n o f w e l l g r a p h s in d i f f e r en t w i n d o w s

I f w e ll is s e l ec t e d in o n e w i n d o w t h e g r a p h fo r th i s w e l l w i l l b e s e l ec t e d in a n o t h e r w i n d o w automatically

Oil rate. Well PROD_0_1

Bulk pressure. Well PROD_0_1

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Graphs in tNavigator

Table Time Step

Press «Reset» to disable all parameters

Objects (connections, wells, groups, reservoir, FIP regions)

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Graphs. Export to Excel

1 . C li c k u p pe r le ft c o r n er t o s el ec t a ta b le (o r Ctrl+A (select all), Ctrl+C  (co py ), Ctrl+V (paste)) OR

2. Press E x p o rt  ( g r e e n a r r o w   ) to s av e th e tab le. Sp ec if y ex ten s io n .x ls to s av e Ex c el -f ile 

Press to select all table

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Graphs list

• Rates  (oil, water, gas, etc.); • Total (oil, water, gas, etc.);

• R e s o u rc e s  (current and original oil in place, water, gas, …) • A n a l y t i c s   (water cut, gas-oil r atio, water-oil ratio …);

• P r e s s u r e  ( BHP, bulk pressure, …) • Flow B etween FIPs; 

• Run Statistics (num ber of iterations, total calculation time …); • C r o s s p l o t s   (dependence between param eters);

• Hist vs Calc  (histo rical and c alculation data for wells); • Well Profile ( p ar a m e t e r v a l u es fo r w e l l c o n n e c t i o n s ) ; • Well Section

• U s e r A r i t h m e t i c (user graphs);

• B l o c k I n f o (parameter values in block s: press ure, saturation, etc.); • Profile Info (graphs fo r Profile (vertical section));

• Pressure/Temperatur e Slices ( fo r t h e r m a l m o d e l s );

• U n i f i ed A d a p t a t i o n R e s u l t s (historic al and calcu lation data table for w ells); • C o m p a ri s o n o f R e s u l t s ( if 2 o r m o r e m o d e l s r e s u l t s a r e lo ad e d to th e m o d e l );   • A q u i f e r g ra p h s  ;

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Graph types

1. Object  –o n e o f t h e f o l l o w i n g : c o n n e c t i o n , w e l l , g r o u p o f w e l ls , r e g i o n , r e s e rv o i r  . G r ap h s o f v a r i o u s p a r a m e t e r s a s ti m e f u n c t i o n ( in t e r v a l num ber) can be built sim ultaneous ly for selected object (one!).

Objects

Parameters

Switch graphs type

2. Param eter  –one (!) parameter of the follow ing: accu mu lative rates, r a t es , in j e c t i o n , p r e s s u r e , w e l l p r o d u c t i v i t y, g r o u p p r o d u c t i v i t y, re g i o n s c r o s s f l o w s . G r a p h o f v a l u e s f o r a n y n u m b e r o f w e l ls a n d s e l e c t ed

p e r f o ra t ed in t e r v a l s as ti m e fu n c t i o n ( t i m e s t e p n u m b e r ) c a n b e b u i l t fo r this parameter.

3. Step . A n y n u m b e r o f p a r a m e t er s f o r a n y n u m b e r o f o b j e c t s c a n b e calculated for any tim e step. Place time slider to c onc erned interval to select time point.

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Object graph type

Object  – o n e o f t h e f o l l o w i n g : c o n n e c t i o n , w e l l , g r o u p o f w e l l s , r eg i o n , r e s e rv o i r  . Graphs o f v a r i o u s p a ra m e t e r s a s ti m e fu n c t i o n c a n b e b u i l t s i m u l t a n eo u s l y fo r s e l ec t e d o b j e c t ( o n e !) . Injector Producer Shut Stop

Injector (previously - producer) Switch well status:

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Parameter graph types: Separate (graphs for all objects in the window), Sum (sum of the parameter for all selected objects), Average (average of the parameter for all selected objects), Active Average (well is active at the time step if it works on current time step)

43

Parameter graph type

Parameter  – one (!) parameter of th e follow ing: accu mu lative rates, rates, injection, pressu re, w e l l p r o d u c t i v i t y, g r o u p p r o d u c t i v i t y . G r a p h o f v a l u es fo r a n y n u m b e r o f w e l ls a n d s e l ec t e d p e r f o ra t ed in t e r v a l s a s ti m e fu n c t i o n ( t i m e s t e p n u m b e r ) c a n b e b u i l t fo r t h i s p a r a m e t e r.

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Step graph type

Step. A n y n u m b e r o f p a r a m e t e r s fo r a n y n u m b e r o f o b j e c t s c an b e c a l c u l a t ed fo r a n y ti m e s t e p . M o v e ti m e s l i d e r to o b t a i n d a t a fo r th e ti m e s t e p y o u n e e d .

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User Selection

1 . R ig h t m o u s e c l ic k o n g r ap h n am e , A d d t o U s e r S e l ec t i o n  . Only graph s that user selects 2. Go to User Selection t o s e e g r a p h s

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Well filter

W h e n y o u u s e Well filter ( o n th e r i g h t p a n e l ): o n l y w e l l s fr o m f i l t er w i l l b e v i s u a l i z ed o n a l l m a p s a n d g r a p h s

Tick wells Select well groups

All reservoir wells

Wells with filter

Use Well filter

Deselect all: No wells will be visualized

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tNavigator History Matching Tools

HM tables

and graphs

Unified History

Matching Results

Graphs, Plots:

Historical vs

Calculation values

Bubble Maps:

residuals

Properties

Editing

See the course 4-1 HowToEditRelPermMULT

Move RP points in GUI, Convert RP to Corey correlation and

change SWL, SWCR, KRORW values, etc.

Edit MULTX, MULTY,

MULTZ maps

Create any new map

Assisted

History

Matching

See the course 8-1 HowToUseHistoryMatching

Tornado, Latin

Hybercube, Grid Search, Differential Evolution,

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Unified History Matching Table

1 . O p en an d c al c u lat e BRUGGE_var/BRUGGE_var_1.DATA 2 . G r ap h s . Un i f i ed H i s t o r y Ma t c h in g R e s u lt s

3 . H i s t o ri c a l a n d c a l c u l a te d v a l u es o f p a r a m e t e rs f o r w e l l s : Oi l t o t al , W a te r to t a l , G a s To t a l , Liqu id Total, Rates, water cu t, water injection etc.

4 . D a ta is u p d a t ed a t ea c h t i m e s t ep . A t t h e e n d o f t h e c al c u l a t io n m o v e t i m e s l i d e r t o th e d e s i r e d step and analyze the HM table at this step.

Absolute Residual = Hist.  – Calc. Relative Residual = |Hist.  – Calc.| *100%

Hist.

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Sorting History Matching table

HM table data can be s o r t e d b y a s c e n d i n g o r d e s c e n d i n g p a r a m e t er values. L e f t -c l i c k t o h e a d er o f c o l u m n t h a t s h o u l d b e s o r t e d

Sort Descending historical value of the Oil Total

Sort Ascending relative residual Oil Total

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Graphs:

1. Graphs. Totals (Rates, etc…) 2. G r ou p s (F ie ld , W el ls , e tc )

3. Tic k Oil to tal, Oil Total (H), Water Total, Water Total (H), Liqu id Total, Liquid Total (H) 4. (H)  – m e an s h i s t o ri c a l v a l u e

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Graph: historical and calculated values

1 . G r ap h s . H is t v s Ca lc (BRUGGE_var/BRUGGE_var_1.DATA) 2. X-ax is  – calcu lated valu e, Y-axis  – histor ical value

3 . G r ee n b i s ec t o r lin e  – c a l c u l a t ed v a l u e o f p a r am e t e r is e q u a l to h i s t o r i c a l fo r th e w e l l s o n th i s li n e 4. To ler an c e  – Red lines  – 1 0 % d e v i a t i o n fr o m t h e b i s e c t o r ( f o r w e l l d e v i at i o n b e t w e e n c a l c u l a t ed

and his torical value is valid)

Calculated and historical oil total for wells don’t match (residual in more than 10%)

Red wells in the table and graph

Calculated oil rate is equal to historical oil rate at this time step (between red lines)

Green wells in the table and graph. To see Green wells tick off  – Hide Matched

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Graph: historical and calculated values

1 . To l er an c e c an b e c h a n ge d f o r h i g h r a t e w e l ls a n d m i d d l e r a t e w e l l s in d e p e n d e n t l y (5 % f o r h i g h r a t es a n d 1 0 % fo r m i d d l e r a t e s o n th e p i c t u r e )

2. Sq uar e  – w e l ls w i t h m i d d l e r a t e

3. A r ou n d s qu ar e – w e l l s w i t h h i g h r a t e

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Residual Bubble Maps

1 . 2 D M ap . A v g (o r S Um )

2. Tic k Bub ble Maps. Residual Map

3 . S el e c t p ar a m e t e r ( Oi l To t a l o n t h e p i c t u re )

4 . N e ar t h e c i r c l e th e r e a r e v a l u e s o f O i l t o t al r es i d u a l 5 . M o v e tim e s l i d er to s e e r es i d u al s o n e ac h ti m e s t ep

6. R ed c o lo r o f ci rc le (hist v alue > cacl), b l u e c o l o r (hist value < c alc)

Tick off Relative residuals to see Absolute residuals bubble maps

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Historical vs Calculated Bubble Maps

1. B u b bl e M ap s . C us to m

2 . B u b b l e M ap 1 : O i l R at e , O i l R at e , Ty p e H y s t o ri c a l + C al c u l a t ed 3 . B u b b l e M ap 2: N on e , N o n e  

4. Red co lo r (calcu lated oil rate), b l u e c o l o r (historic al oil rate)

References

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