09 - Flow Regimes and the Diagnostic Plot

Flow Regim es and the Diagnostic Plot

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Flow Regimes and the Diagnostic Plot

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April 2000

Flow Regim es and the Diagnostic Plot

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The Diagnostic Plot Instructional Objectives 1. Identif Identify y time time regions. regions. 2. Identif Identify y flow flow regime regimes. s. 3. List List factors factors that that affect affect pressur pressure e response in early time. 4. List List boundarie boundaries s that affect affect pressure pressure response in late time.

Upon completion of this section, the student should be able to: 1. Identify the early, middle, middle, and late time regions regions on a diagnostic diagnostic plot. 2. Identify the the following following flow regimes regimes from their characteristic characteristic shape on a diagnostic plot: volumetric/PSS/recharge behavior, radial flow, linear flow, bilinear flow, spherical flow. 3. List 3 things things that may affect the pressure response response during during the early time region. 4. List 3 types of boundaries boundaries that may may affect the pressure response during the late time region.

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Flow Regimes and the Diagnostic Plot

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The Diagnostic Plot    i   s   p  ,   e   v    i    t   a   v    i   r   e    d  ,   e   g   n   a    h   c   e   r   u   s   s   e   r    P

Elapsed time, hrs

The diagnostic plot is a log-log plot of pressure change and pressure derivative on the vertical axis vs. test time on the horizontal axis. The pressure derivative is defined as the derivative of pressure with respect to the natural logarithm of time. • Pressure change vs. time  – Flow test  –

∆p = pi − p wf Buildup test ∆p = p ws − p wf (∆t = 0 )

• Pressure derivative  – Change in pressure per unit fractional change in time  – Mathematically,

t

∂∆p ∂∆p = ∂t ∂ ln(t )

 – Has units of pressure, can be plotted together with pressure on same graph

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April 2000

Flow Regimes and the Diagnostic Plot

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Time Regions on the Diagnostic Plot    i   s   p  ,   e   v    i    t   a   v    i   r   e    d  ,   e   g   n   a    h   c   e   r   u   s   s   e   r    P

Early-time region

Middletime region

Late-time region

Elapsed time, hrs

Early-time region: wellbore and near-wellbore effects. These effects include wellbore storage, skin factor, partial penetration, phase redistribution, and finite- and infinite-conductivity hydraulic fractures. Middle time region: infinite-acting reservoir behavior. A homogeneous reservoir will give a horizontal derivative response during the middle time region. Data during this region provide the best estimate of reservoir permeability. Late-time region: boundary effects. There are a large number of different types of boundaries that may affect the pressure response, including sealing faults, closed reservoirs, and gas/water, oil/water, and gas/oil contacts.

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Flow Regimes and the Diagnostic Plot

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Flow Regimes • Common geometric shapes • Different flow patterns may appear at different times in a single test • Flow regimes follow sequence within model

• Common geometric shapes occur in many different reservoir models • A single reservoir model may exhibit different flow patterns at different times - Flow regimes occur in a specific sequence for a given model • Flow Regimes - Volumetric behavior - Radial flow - Linear flow - Bilinear flow - Spherical flow

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April 2000

Flow Regimes and the Diagnostic Plot

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Volumetric Behavior

Volumetric behavior occurs when the wellbore, the reservoir, or part of the reservoir acts like a tank. Perhaps the most common occurrence of volumetric behavior is in wellbore storage, although it is not limited to WBS. Volumetric behavior can occur during either a flow test or a buildup test. However, if it occurs during a buildup test, it indicates that whatever part of the reservoir acts like a tank is being recharged from somewhere else. During a flow test, volumetric behavior may indicate a closed reservoir. •Causes  – Wellbore storage  – Pseudosteady state  – Recharge

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Flow Regimes and the Diagnostic Plot

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Volumetric Behavior Wellbore Storage PseudosteadyState Flow

General Form

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∆ p =

 pi −  pwf  =

qBt 

24C 

0.0744qBt 

φ ct hr e2

+

 141.2qB µ     r e   3 ln  − + s  kh    r w   4 

∆ p = mV t  + bV 

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Flow Regimes and the Diagnostic Plot

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Volumetric Behavior ∆ p = mV t  + bV 

General Form

Derivative

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t 

∂∆ p ∂ (mV t  + bV  ) = t  ∂t  ∂t  = mV t 

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Flow Regimes and the Diagnostic Plot

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Volumetric Behavior

  e   v    i    t   a   v    i   r   e    d  ,   e   g   n   a    h   c   e   r   u   s   s   e   r    P

1

1 Time

Volumetric behavior is recognized on the diagnostic plot by the pressure derivative following a unit-slope line, where the line moves one log cycle vertically for each log cycle of horizontal movement. The pressure change may or may not follow the same unit slope line. During wellbore storage, typically the pressure change and the pressure derivative will lie on top of each other. During pseudosteady-state flow or recharge, the pressure and derivative will not coincide. • Shape of derivative  – Unit slope line

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Flow Regimes and the Diagnostic Plot

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Radial Flow

Radial flow occurs in many common situations. Data within the radial flow regime can be used to estimate formation permeability and skin factor. • Causes of radial flow - Vertical well - Fractured well after transient has moved beyond tips of fracture - Horizontal well before transient reaches top and bottom of zone - Horizontal well after transient has moved beyond ends of wellbore

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Flow Regimes and the Diagnostic Plot

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Radial Flow

Vertical Well

General Form

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∆ p =

162.6qB µ   kh

   kt      − 3.23 + 0.869s  log 2   φµ ct r w   

∆ p = m log (t ) + b

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Flow Regimes and the Diagnostic Plot

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Radial Flow General Form

∆ p = m log (t ) + b

t  Derivative

∂∆ p ∂ (m log(t ) + b ) = t  ∂t  ∂t  =

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m

2.303

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Flow Regimes and the Diagnostic Plot

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Radial Flow

  e   v    i    t   a   v    i   r   e    d  ,   e   g   n   a    h   c   e   r   u   s   s   e   r    P

Time

On the diagnostic plot, radial flow is recognized by the horizontal derivative.

• Shape of Derivative - Horizontal

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Flow Regimes and the Diagnostic Plot

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Linear Flow

Linear flow is also quite common, occurring in channel reservoirs, hydraulically fractured wells, and horizontal wells. From data within the linear flow regime, we can estimate channel width or fracture half-length, if we know the permeability. Or, we can estimate the permeability perpendicular to a horizontal well if we know how much of the well is open to flow. • Causes of linear flow - Well with a high-conductivity fracture - Well in a channel reservoir (reservoir with parallel no-flow boundaries) - Horizontal well

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Flow Regimes and the Diagnostic Plot

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Linear Flow 12

Channel

16.26qB µ    kt      ∆ p =  khw  φµ ct  

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Hydraulic Fracture

General Form

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∆ p =

4.064qB µ    kt    khL f 

   φµ c    t  

∆ p = m Lt 1 2 + b L

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Flow Regimes and the Diagnostic Plot

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Linear Flow General Form

Derivative

∆ p = m Lt 1 2 + b L

(

∂∆ p ∂ m Lt 1 2 + b L = t  t  ∂t  ∂t  =

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1 2

)

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m Lt 

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Flow Regimes and the Diagnostic Plot

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Linear Flow   e   v    i    t   a   v    i   r   e    d  ,   e   g   n   a    h   c   e   r   u   s   s   e   r    P

1

2

Time

The linear flow regime is recognized on the diagnostic plot by the derivative following a half-slope line. The half-slope line moves one log cycle vertically for each two log-cycles of horizontal movement. The pressure change may or may not also follow a half-slope line. In an undamaged hydraulically fractured well, the pressure change typically follows a half-slope line. In a channel reservoir, a hydraulically fractured well with damage, or a horizontal well, the pressure change will approach the half-slope line from above.

• Shape of Derivative - ½ slope

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April 2000

Flow Regimes and the Diagnostic Plot

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Bilinear Flow

Bilinear flow occurs primarily in low-conductivity hydraulically fractured wells. From this flow regime, we can estimate fracture conductivity wk f. • Causes of bilinear flow - Well with a low-conductivity fracture (common) - Fractured or horizontal well in a transient dual porosity reservoir (rare but theoretically possible)

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Flow Regimes and the Diagnostic Plot

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Bilinear Flow 12

Hydraulic Fracture

44.1qB µ    1    ∆ p =  wk  f   h    

General Form

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  t       φµ c k     t   

∆ p = m B t 1 4 + b B

Wkf=fracture conducivity, md-ft

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April 2000

Flow Regimes and the Diagnostic Plot

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Bilinear Flow General Form

Derivative

∆ p = m Bt 1 4 + b B

(

∂∆ p ∂ m Bt 1 4 + b B = t  t  ∂t  ∂t  =

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1 4

)

14

m Bt 

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Flow Regimes and the Diagnostic Plot

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Bilinear Flow   e   v    i    t   a   v    i   r   e    d  ,   e   g   n   a    h   c   e   r   u   s   s   e   r    P

1

4 Time

The bilinear flow regime is recognized on the diagnostic plot by the derivative following a quarter-slope line. The quarter-slope line moves one log cycle vertically for every four log-cycles of horizontal movement. The pressure change may or may not also follow a quarter-slope line. In an undamaged hydraulically fractured well, the pressure change typically follows the quarter-slope line as soon as wellbore storage effects have ended. In a hydraulically fractured well with damage, the pressure change will approach the quarterslope line from above. This flow regjme is easily confused with the linear flow regime. Particular attention should be paid to the slope of the derivative to distinguish these two flow regimes. • Shape of Derivative - ¼ slope

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Flow Regimes and the Diagnostic Plot

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Spherical Flow

Spherical flow occurs when the pressure transient is free to propagate in three dimensions. This can occur for wells that penetrate only a short distance into the pay zone, or in wells that have only a limited number of perforations open to flow. This flow regime also commonly occurs during wireline formation tests. From data in the spherical flow regime, we can estimate the geometric mean permeability. • Causes of spherical flow

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Vertical well with only a few perforations open

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Vertical well with only a small part of the zone perforated

-

Some wireline formation test tools

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Flow Regimes and the Diagnostic Plot

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Spherical Flow  

Spherical Probe (RFT)

 pi −  pwf  =

q µ  

1− 4π kr  p 

 

General Form

  φµ ct r p2  kt 

   

∆ p = bS  − mS t −1 2

Nomenclature The Repeat Formation Tester (RFT) probe equation uses SI units:

NExT

ct

-

Total compressibility, Pa-1

k

-

Permeability, m2

pi

-

Initial pressure, Pa

pwf

-

Probe pressure, Pa

q

-

Flow rate, m3 /s

rp

-

Probe radius, m

t

-

Time, s

φ

-

Porosity, fraction

µ

-

Viscosity, Pa•s

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Flow Regimes and the Diagnostic Plot

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RFT Units • Nomenclature • The Repeat Formation Tester (RFT) probe equation uses SI units: • ct Total compressibility, Pa-1 • k Permeability, m2 • pi Initial pressure, Pa • pwf Probe pressure, Pa • q Flow rate, m3/s • rp Probe radius, m • t Time, s Porosity, fraction • φ • µ Viscosity, Pa•s

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Flow Regimes and the Diagnostic Plot

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Spherical Flow General Form

Derivative

∆ p = bS  − mS t −1 2

(

∂∆ p ∂ bS  − mS t −1 2 = t  t  ∂t  ∂t  =

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1 2

)

−1 2

mS t 

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Flow Regimes and the Diagnostic Plot

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Spherical Flow

  e   v    i    t   a   v    i   r   e    d  ,   e   g   n   a    h   c   e   r   u   s   s   e   r    P

1

2 Time

The spherical flow regime is recognized on the diagnostic plot by the derivative following a negative half-slope line. The pressure change approaches a horizontal line from below. The pressure change during spherical flow will never exhibit a straight line with the same slope as the derivative. Spherical flow can occur during either a drawdown or a buildup test. • Shape of Derivative -

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Negative ½ slope

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Flow Regimes and the Diagnostic Plot

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Flow Regimes on the Diagnostic Plot    i   s   p  ,   e   v    i    t   a   v    i   r   e    d  ,   e   g   n   a    h   c   e   r   u   s   s   e   r    P

Wellbore storage

Radial flow Spherical flow

Recharge?

Elapsed time, hrs

Indication of flow regime - One of the biggest advantages of the diagnostic plot is the ability to identify flow regimes. The slope of the derivative plot is a direct indication of the flow regime. After radial flow period, it can be noticed a very definitive bounded reservoir behavior. A unit slope at late times indicates that kh/u is different out in the reservoir we have two zones with different mobilities

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April 2000

Flow Regimes and the Diagnostic Plot

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Exercise 1 Flow Regimes and the Diagnostic Plot FLOWREGM.WTD (Diagnostic Plot) 1000

100    i   s   p  ,   e   g   n   a    h   c   e   r   u   s   s   e   r   p    d   e    t   s   u    j    d    A

10

1

0.1

0.01 0.0001

0.001

0.01

0.1

1

10

100

1000

10000

Radial equivalent adjusted t ime, hr

Identify the flow regimes. WELLBORE STORAGE & LINEAR FLOW ARE ALMOST THE ONLY PERIODS EASY TO IDENTIFY….!!.A HIGH SKIN ALSO IS PRESENT. THE LAST PERIOD INDICATES CONSTANT PRESSURE AT THE BOUNDARY THE RADIAL FLOW PERIOD IS VERY DIFFICULT TO DEFINE A WELL NEAR THE CENTER OF A LONG CLOSED RECTANGLE WITH A HIGH SKIN MIGHT REPRODUCE THIS BEHAVIOR BUT IT DOES NOT MEAN THAT IT IS THE ONLY MODEL THAT CAN REPRODUCE THE BEHAVIOR OF THIS WELL TEST…..INTEGRATED WELL TEST INTERPRETATION IS THE ANSWER…

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Flow Regimes and the Diagnostic Plot

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1. Stewart, G. and Wittmann, M.: “Interpretation of the Pressure Response of the Repeat Formation Tester,” paper SPE 8362 presented at the 1979 SPE Annual Technical Conference and Exhibition, Las Vegas, September 23-26. 2. Smolen, J. J., and Litsey, L. R.: “Formation Evaluation Using Wireline Formation Tester Pressure Data,” JPT (January 1979) 25-32.

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April 2000