Lecture 2-B Practical Welltest Analysis

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Practical Welltest

Analysis

Advanced Reservoir Engineering

Hassan Bahrami Hassan Bahrami

2013 2013

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Pressure vs Time in Transient Tests

•• Wellbore effectWellbore effect

•• Reservoir responseReservoir response

•• Boundary effectBoundary effect

Pressure Pressure Time Time Pi Pi

Pressure propagation, radial into formation Pressure propagation, radial into formation

Boundary effect

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Wellbore storage analysis

T

Taking Logarithm of aking Logarithm of the equation:the equation:

General form of equation

General form of equation for WBS effect:for WBS effect:

For pressure data related to For pressure data related to wellbore storage region

wellbore storage region::

•

• Plot of Plot of PP vs. time in avs. time in a Log-logLog-log

plot, results in a

plot, results in a unit slopeunit slope lineline

•

• Plot of Plot of P’P’ : dp/d[ln(t)]: dp/d[ln(t)] vs.vs.

time in a

time in a Log-logLog-log plot, results inplot, results in a

a unit slopeunit slope lineline

tt ΔP ΔP  cc  cc)) (( ]] [[ L L )) 1 1 (( P) P) Log(

Log(   og og t t  Log Log

cc)) (( ]] [[ L L 1 1 t))] t))] P)/d(ln( P)/d(ln( Log[d(

Log[d(   og og t t  Log Log

And by taking the derivatives : And by taking the derivatives :

Log(dt) Log(dt) P P P’ P’ Log(dP) Log(dP) +1 +1 slope slope

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Pressure Draw-Down Test Analysis

Time

Flow rate

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Pressure Derivative Method / Drawdown Test = m (log[ b m

3 .

2 t)

(ln

d

P)

(

d

  

]

3 .

2 log[

]

[

log

0 ]

t)

(ln

d

P)

(

d

[

t

m

Log

     P’ P P t]) + )) t ln( -) t P1)/(ln( -(P2 : P'  ₂  ₁ RF P & P’_r t

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Permeability and Skin from Pressure

derivative

m IARF ) log( * ) * 3 . 2 ( 1hr P RF m t RF P      h m B Q k o * ) * 3 . 2 ( * * * 6 . 162   ] 23 . 3 ) log( ) * 3 . 2 ( [ * 1513 . 1  1  ₂   w t hr r c k m P S  P & P’_r t

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Pressure Build-Up Analysis

Pwf Pws

t=0 Pi

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Pressure Derivative Method / Build-Up Test = m (log[ tp+ b

m

t

_p

2 .

3 )

t

(ln

d

P)

(

d

    

]

3 .

2 log[

]

t

[

log

0 ]

t])

t)/

(

(ln[

d

P)

(

d

[

m

t

Log

p          P t / t ]) + t]) t)/ ( (ln[ d P) ( d '       p t P

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h m B Q k o * ) * 3 . 2 ( 6 . 162   ] 23 . 3 ) log( ) 1 log( * 3 . 2 [ * 1513 . 1  1    ₂   w t p p hr r c k t t m P S 

Permeability and Skin from Pressure

derivative

m ) ) 1 ( log( * ) * 3 . 2 ( 1 p RF RF p RF hr t t t t m P P         P & P’_r t

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Well Models

• Hydraulic (Vertical) Fracture – Infinite conductivity

– Finite (low) conductivity

• Partial completed/perforated

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Infinite-Conductivity or Uniform Flux

Vertical (Hydraulic) Fracture

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Infinite-Conductivity or Uniform Flux Vertical (Hydraulic) Fracture

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Finite-Conductivity Vertical

(Hydraulic) Fracture

+1/4

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Limited Entry Response

-1/2

K_r K_s

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Horizontal wells

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Question: Flow regimes in Slanted wells? Plot a typical P and P’ curves vs time for the following case.

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Layered Reservoirs (Dual Permeability Model)

Welltest analysis using IARF line provides average permeability and skin for multi-layered systems

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Multi-Layered Reservoirs

Welltest Analysis

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Naturally fractured Reservoirs

Dual porosity Dual permeability Model

e

bulk volum

Matrix

volume

d

Matrix voi

φ

_m 

e

bulk volum

Total

volume

void

Fracture

φ

_f 

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Dual Porosity - Dual Permeability Reservoirs

Naturally Fractured Reservoirs (NFRs) _{Fracture radial} flow Total system radial flow K_m, PHI_m K_f, PHI_f

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Fracture Parameters

2 w f m

r

K

   m m f f f f C C C . . .       ) / 1 / 1 / 1 ( 4 a X 2  aY 2  a Z 2   K Permeability C Compressibility rw Wellbore radius  Porosity

a Fracture spacing (block size)

 Shape factor

 Interporosity flow coefficient

 Fracture storativity f fracture m matrix Image Logs Petrophysical Logs a b

Image Logs may provide fracture aperture (b) and

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NFRs welltest analysis

SPE 104056 2 w m f

r

K







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Question: Predict flow regimes for the following case, and make plot of P&P’ vs time on Log-Log plot

water injection

Perf

Heavy Oil (API 15) Water

(Salinity 20000 PPM)

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Type of Boundaries

• Fault ( Sealing fault – Leaky fault )

• Closed Systems (No flow Boundary)

• Constant Pressure Boundary

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Effect of Fault

• Fault:

In early time: DP = m1 * log(Dt) + b In late time: DP = m2 * log(Dt) + b Where : m2 = 2 * m1

• Closed Systems : DP = m * Dt + b Result:

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Constant Pressure Boundary

– Aquifer – Gas cap

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Question: Predict flow regimes

Well

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Question:

Provide your interpretation on the pressure build-up data given below.

-Well model?

-Reservoir model? -Boundary model?

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Welltest Analysis Using ECRIN

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Production time

Production rate

60 1000 24 0

60 hrs production with 1000 STBD oil rate, followed by 24 hrs build-up

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60 1000

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Flow Regimes Prediction

using

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Results

1

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How to remove grids:

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Example of different time steps

5 hrs 20 hrs