ResSimModSol

8/9/2019 ResSimModSol

1/25

Model Solutions to Examination

1

; ; ; ;

; ; ; ;

; ; ; ;

; ; ; ;

y y y y

y y y y

y y y y

y y y y

Date:

1. Complete the sections above but do not seal until the examination is finished.

2. Insert in box on right the numbers of the questions attempted.

3. Start each question on a new page.

4. Rough working should be confined to left hand pages.

5. This book must be handed in entire with the top corner sealed.

6. Additional books must bear the name of the candidate, be sealed and be affixed tothe first book by means of a tag provided

Subject:

INSTRUCTIONS TO CANDIDATES

8 Pages

PLEASE READ EXAMINATION REGULATIONS ON BACK COVER

No. Mk.

N A M E : R E G I S T R A T I O N N O . :

C O U R S E : Y E A R : S I G N A T U R E : C o m p l e t e t h i s s e c t i o n b u t

d o n o t

s e a l u n t i l t h e e x a m i n a t i o n

i s f i n i s h e d

Reservoir Simulation


2/252

Answer Notes

# => indicates one of several possible answers which are equally acceptable.

[…] => extra information good but not essential for full marks - may get bonus.


3/25


3

Q1Q1Q1Q1Q1 (i)# 1. To perform broad scooping calculations which examine different

development options e.g. waterflooding, gas flooding etc.

# 2. To extend initial material balance calculations by examining

some other spatial factor such as well-placement or aquifer effect.

(ii)

# 1. To assess additional field management options such as infill drilling,

pressure blowdown etc.

# 2. To take the improved history match model which can be developed

after same development twice and to use this to assess various IORstrategies e.g. gas injection, WAG or chemical flooding.

Q2Q2Q2Q2Q2

(i)

# Because of its inherent simplicity you would virtually always apply

single material balance to assess your field performance - to see if DP

decline tallies with estimated field size, sources of influx and

production.

(ii)

Would be used when a more complex development strategy requiring

spatial information is essential e.g. well placement, assessment of shale

effects, gravity segregation etc.


4/254

Q3Q3Q3Q3Q3(#) Because it is the only tool we have to tackle complex reservoir

development/flow problems which extends material balance. Clearly, it

is much better than simple material balance alone.

Q4Q4Q4Q4Q4

(i)The shale continuity strongly affects the hi/lo permeability layer

vertical communication (both pressure and fluid flow). Thus, it will

affect the effective k v/k h (lower or zero for continuous shales) and

will strongly influence gravity slumping of water in a waterflood. In

the situation above with high k on top, some vertical communication will

help recovery.

(ii)

Set up a simple 2D cross sectional model with , say, 50 blocks in the x -

direction and 10 vertical grid blocks - 5 in each layer. Run waterflood

cases with and without shales - and some in-between cases with

transmissibility modifiers set beween T z = 0.0 Æ 0.01 Æ 0.1 Æ 0.5 Æ 1.0.

Compare water saturation fronts and recoveries as fraction of pv

water throughput. Result will allow us to assess the effects of the

shales in the waterflood.

(iii)

Different


5/25


5

The high perm massive sand would have a small scale k v/k h ~1 which

would result in a similar larger scale value. In the laminated sands, the

“small” scale (say core plug scale) would have a low k v/k h of say 0.1 to

0.01 and this would result in a correspondingly lower k v/k h at the grid

block scale.

(iv)

Well

Gas

Oiland

Water

Oiland

Water

Gas

= perforations

Gas Coning It is the drawdown of the highly mobile (low mg) gas into

the perforations. Pattern is shown here in figure. Causes high GOR

production at a level well above the solution gas value.


6/256

Set up a near-well r/z geometry fine grid - possibly 50 layers and

set reservoir near-well rock properties e.g. Layering, T z modifiers,

Rel. perms. etc.

Perform simulations to look at issues such as effect of rate, vertical

communication, gas/oil/water Rel. perms. etc…

Generally needs a fine Dr, Dz grid, often finer near the well where

most rapid changes of S g and pressure with time occur.

(v)1. The geometry would be different: r/z for coning and cartesian or

corner point for full field.

2. The fineness of the grid would be different. Very fine for near-

well; much coarser for full field.

# (Dimensionality too 2D vs. 3D)


7/25


7

Q5Q5Q5Q5Q5

(i)

(ii)

Numerical dispersion is the artificial spreading of saturation fronts

due to the numerical grid block structure in the simulation. It arises

because we take large grids to represent moving fronts. It can be

improved by refining the grid (globally or locally) or by using improvednumerical methods.

(iii)

P

Fluid tends toflow along (parallel)

to the grids

L

P

Wells same distanceapart in Figs A and B

LII

Fig A Fig B

I = injector ; P = producer


8/258

(iv)

The injected fluid tends to flow parallel with the grid from the

injector (I) to the producer (P) - see previous page. This means that

early breakthrough and poorer recoveries are seen in A then in B

above. i.e.

%00IPProducer

Fig B

Pv or Time

Actual RecoveryFig A

Q6Q6Q6Q6Q6

(i)


9/25


10/2510

/ X (V+1) - X(V)/ < small number TOL. [Methods such as the Jacobi, LSOR,

etc. are examples of this].

Q7Q7Q7Q7Q7

mo mo

mw

In block (i, j), then material balancecan be applied for each phase (e.g.oil and water) for 2-phase flow.

i, j

Mass

Accumulation of=

Amount that-

Amount that

oil over time flows in over flows out over

D t D t D t

But amount that flows in/out is given by the pressure differences

between blocks i.e.

Q A k k S

P Poil i j i j ro o

o i

o oij i j ( , ) ( , ). . ( )

- Æ-

Ê Ë Á

ˆ ¯ ˜

-( )-112

1 m

Thus the two phase Darcy Law supplies the relation for volumetric flow

rate and pressure in the grid block. These volumetric flows can be

converted to MASS flows (x by density) and then put into the material


11/25


11

balance equation to obtain Æ a conservation equation and in pressure

equation for oil and water.

\ Material Balance + Darcy’s Law => 2-phase Flow Equation.

Q8Q8Q8Q8Q8

(i)

(ii)

(a) V x yo = D D D z S of

(b)


12/2512

(iii)

#

Q9Q9Q9Q9Q9

1. The black oil model essentially treats a phase (o,w,g) as the basicconserved unit or “pseudo component”

2. Compositional models are based more correctly on the conservation

of components (CH 4, C10, H2O etc.) - the black oil model simply treats

gas dissolution in oil through R so - gas solubility

3. The compositional models incorporate a full PVT description of the

oil whereas the black oil model relies on the simple R so type treatment.


13/25


13

(iii)

(iv) # (a) Waterflood calculations in a low GOR - say 30 ∞ API - oil reservoir

with pressure maintenance.

# (b) CO2 injection in a - say 36 ∞ API - light oil system [Condensate

system - gas recycling etc…]

Q10Q10Q10Q10Q10

(i)

Upscaling in a waterflood essentially means getting the correct

(effective) parameters (-e.g. rel. perm.) for the larger scale grid blocks

which will reproduce a “correct” fine grid model.

(ii)

“Rock” relative permeabilities are meant to be the intrinsic

representative properties of a representative piece of reservoir rock

at the “small” (i.e. core plug) scale.

Pseudo rel. perms. are effective properties at the “larger” (usually

gridblock) scale which incorporate other effects and artefactsartefactsartefactsartefactsartefacts (e.g.


14/2514

numerical dispersion, heterogeneity etc..) in addition to the intrinsic

“rock” rel. perms.

(iii)

MethodologyMethodologyMethodologyMethodologyMethodology

This is a geologically consistent approach to the task of upscaling. i.e.data collection, sedimentological framework,…

[The function of the methodology is to get the geologically + fluid]

mechanically “right” answer.

Techniques?Techniques?Techniques?Techniques?Techniques?These refer to the actual mathematical algorithm to go from a fine

grid Æ coarse grid. E.g. Kyte and Berry, Stone’s method, two phase

tensors etc…

[N.B. This just needs to reproduce the fine grid result - even if it is

WRONG - at the coarse scale]


15/25


15

Q11Q11Q11Q11Q11

(i)

(ii)

It takes a lag distance of about the “range” to see the field variability

(standard dev. - i.e. ~ 100mD) of the field.


16/2516

(iii)

lag

1

Q12Q12Q12Q12Q12

(i)

(ii)

The effective permeability is clearly the harmonic (thickness -

weighted) average as follows:


17/25


17

(iii)The k eff in the randomised model would be between the two answers

in (i) and (ii) above (the answer in (ii) being the lower).

e.g. Strictly in a randomised distribution of permeability the average

value tends to the geometric average (k g) in 2D

kg - is less than the arithmetic (along layer) answer.

kg - is greater than the harmonic (across layer) answer.

Q13Q13Q13Q13Q13

(i)

Note - we take the same contour values (c= 0.1, 0.5, 0.8) in all sketches

below.


18/2518

(ii)

(iii)

(iv)


19/25


20/25


21/25


21

2m

~50cm

Tabular cross-bedding

Bottom sets

or climbing ripples

Para-sequence/sequence-stacks of bedforms

Eroded/? top setse.g.

(ii)• Para sequence - sequence scale

• At parasequence - sequence - also bed form influence

• Para sequence - bed form

• Lamina set - bed form

Q16Q16Q16Q16Q16

(a) There is a double peak - the bimodality probably arises from the

lower perm plugs from deltaic sands, and the higher permeability plugs

from the fluvial channel.


22/2522

(b)

A

A

B

B

Tightly laminateddeltaic sands

Crossbeddesfluvialchannel-stacked crossbeds

2 Scale pseudo-isation - inclined cross bed pseudo - bedform pseudo

laminated sandpseudo

Q17Q17Q17Q17Q17

(i) (a)

hi lo hi lo hi lo

Sw

CAPILLARY DOMINATED

Spontaneous water inhibition into the LOW k laminae occurs inPc-dominated flow. This traps oil in the HIGH k laminae behind thefront where it is well above "residual" but it can't move because theRel. Perm. to oil in the low k water-filled laminae is so low.

HIGH "remaining"oil in hi k

Slow Flow

Water flow direction High water Sw inLOW perms in awater-wet system


23/25


24/2524

Along

Across

(b) The levels of “remaining” oil can be vastly different in laminar

systems which, in simulation/upscaling, moves the pseudo rel. perm. end

points. (see above).


25/25


Documents

ResSimModSol