Lecture 2-B Practical Welltest Analysis

Advanced Reservoir Engineering

Practical Welltest Analysis

Hassan Bahrami 2013

Pressure vs Time in Transient Tests • Wellbore effect • Reservoir response • Boundary effect

Pressure Pi Pressure propagation, radial into formation Boundary effect

Time

Wellbore storage analysis General form of equation for WBS effect:

ΔP  c t

Taking Logarithm of the equation:

Log( P)  (1) Log [t ]  Log (c)

And by taking the derivatives :

Log[d( P)/d(ln(t))]  1 Log [t ]  Log (c)

For pressure data related to

Log(dP)

wellbore storage region: region: •

Plot of P vs. time in a Log-log

P +1 slope

plot, results in a unit slope line •

Plot of  P’ : dp/d[ln(t)] vs.

P’

time in a Log-log plot, results in a unit slope line

Log(dt)

Pressure Draw-Down Test Analysis

Flow rate

Pressure

Time

Pressure Derivative Method / Drawdown Test

P = m (log[ t]) + b P

d (P) d (lnt)



2.3m

P & P’r 

RF t

 Log [

d (P) d (lnt)

]  0 log [t ]  log[ 2.3m] P': (P2 - P1)/(ln(t 2 ) - ln(t1 ))

P’

Permeability and Skin from Pressure derivative  P  1hr    P   RF   (2.3 * m) * log( t RF  )

P & P’r 

IARF

m

k  

162.6 * Q *  * Bo (2.3 * m) * h

t

S   1.1513 *[

 P  1hr 

(2.3 * m)

 log(

k   ct r w

2

)  3.23]

Pressure Build-Up Analysis

Pi Pwf  t=0

t=tp

Pws

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

d ( P) t  p  t d (ln ) t



2.3m

d (P)  Log [  ]  0 log [ t ]  log[ 2.3m] d (ln[(t  p  t)/t])

 P '  

d (P) d (ln[(t  p

 t)/t])

Permeability and Skin from Pressure derivative

 P  1hr    P   RF   ( 2.3 * m) * log(

P & P’r 

m

t

k  

162.6Q  Bo (2.3 * m) * h

S   1.1513 *[

 P  1hr 

2.3 * m

 log(

t  p

1

t  p

)  log(

k 

 ct r w

2

)  3.23]

t  p  t  RF  t  RF  (1  t  p )

)

Well Models

Well Models • Hydraulic (Vertical) Fracture  – Infinite conductivity  – Finite (low) conductivity

• Partial completed/perforated

• Horizontal well

Infinite-Conductivity or Uniform Flux Vertical (Hydraulic) Fracture

Infinite-Conductivity or Uniform Flux Vertical (Hydraulic) Fracture

+1/2

Example of Linear Flow Regime Analysis

Finite-Conductivity Vertical (Hydraulic) Fracture

+1/2 +1/4

Example of Finite Conductivity Response

Partial Completion (Limited Entry)

Example of Spherical Flow Regime Analysis

Limited Entry Response

-1/2

Ks

Kr 

Horizontal wells

Horizontal wells

0 slope

+1/2 slope

0 slope

Multi-lateral wells

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

Reservoir Models

Homogeneous Reservoirs

Composite Systems

Gas-Condensate Reservoirs

Layered Reservoirs (Dual Permeability Model)

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

Welltest in 2-Layered Reservoirs

Welltest in 2-Layered Reservoirs

Welltest in 2-Layered Reservoirs

Welltest in 2-Layered Reservoirs

Multi-Layered Reservoirs Welltest Analysis

Naturally fractured Reservoirs

φm φ f 





Matrix void volume Matrix bulk volume Fracture void volume Total  bulk volume

Dual porosity Dual permeability Model

Dual Porosity - Dual Permeability Reservoirs Km, PHIm

Kf , PHIf 

Naturally Fractured Reservoirs

(NFRs)

Fracture radial flow

Total system radial flow

Fracture Parameters Image Logs

 



 K m

  

   4 (1/ a X 

 K   f   2



1/ aY 

2

2

  

r w 

2

1/ a Z  )

K C rw  a   

Permeability Compressibility Wellbore radius Porosity Fracture spacing (block size) Shape factor  Interporosity flow coefficient Fracture storativity

f m

fracture matrix

  f  .C  f     f  .C  f     m .C m Petrophysical Logs

a

b Image Logs may provide fracture aperture (b) and fracture spacing (a)

NFRs welltest analysis

 K  f      SPE 104056

 K m  

r w2

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)

Boundary Models

Type of Boundaries • Fault ( Sealing fault – Leaky fault )

• Closed Systems (No flow Boundary)

• Constant Pressure Boundary (Aquifer - Gas Cap)

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: Log [ dP/d[log(Dt)] ] vs Log (Dt)

Slope: +1

Effect of Fault

Leaky Fault

Closed System: No flow boundary

Constant Pressure Boundary  – Aquifer   – Gas cap

Question: Predict flow regimes

Well

Boundary

Question: Provide your interpretation on the pressure build-up data given below. -Well model? -Reservoir model? -Boundary model?

Welltest Analysis Using ECRIN

Hassan Bahrami

60 24

1000 0

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

60 1000

Flow Regimes Prediction using Ecrin Numerical

 Add girds, then double click on well location

Results 1

2

How to remove grids:

Right click:

Example of different time steps 5 hrs

20 hrs

Linear & Elliptical flow

Gradually changing to radial flow