09 - Flow Regimes and the Diagnostic Plot

Flow Regimes and the Diagnostic Plot 1

NExT April 2000

Flow Regimes and the Diagnostic Plot


NExT April 2000

The Diagnostic PlotInstructional Objectives

1. Identify time regions.

2. Identify flow regimes.

3. List factors that affect pressure response in early time.

4. List boundaries that affect pressure response in late time.

Upon completion of this section, the student should be able to:

1. Identify the early, middle, and late time regions on a diagnostic plot.

2. Identify the following flow regimes from their characteristic shape on a diagnostic plot: volumetric/PSS/recharge behavior, radial flow, linear flow, bilinear flow, spherical flow.

3. List 3 things that may affect the pressure response during the early time region.

4. List 3 types of boundaries that may affect the pressure responseduring the late time region.


NExT April 2000

The Diagnostic Plot

Elapsed time, hrs

Pre

ssur

e ch

ange

, der

ivat

ive,

psi

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 -

Buildup test -

Pressure derivative

Change in pressure per unit fractional change in time

Mathematically,

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

wfi ppp =( )0tppp wfws ==

( )tlnp

tp

t

=


NExT April 2000

Time Regions on the Diagnostic Plot

Elapsed time, hrs

Early-timeregion

Middle-time

region

Late-timeregionP

ress

ure

chan

ge, d

eriv

ativ

e,ps

i

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 responseduring 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.


NExT April 2000

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


NExT April 2000

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


NExT April 2000

Volumetric Behavior

VV btmp +=General Form

Wellbore Storage

Pseudosteady-State Flow

C

qBtp

24=

+

+= s

r

r

kh

qB

hrc

qBtpp

w

e

etwfi 4

3ln

2.1410744.02


NExT April 2000

Volumetric Behavior

VV btmp +=General Form

Derivative ( )

tmt

btmt

t

pt

V

VV

=

+=


NExT April 2000

Volumetric Behavior

Time

Pre

ssur

e ch

ange

, der

ivat

ive

1

1

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


NExT April 2000

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


NExT April 2000

Radial Flow

+

= s

rc

kt

kh

qBp

wt

869.023.3log6.162

2

( ) btmp += log

Vertical Well

General Form


NExT April 2000

Radial Flow

( ) btmp += logGeneral Form

( )( )

303.2

log

mt

btmt

t

pt

=

+=

Derivative


NExT April 2000

Radial Flow

Time

Pre

ssur

e ch

ange

, der

ivat

ive

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

Shape of Derivative- Horizontal


NExT April 2000

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 channelwidth 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


NExT April 2000

Linear Flow

2126.16

=

tc

kt

khw

qBp

21064.4

=

tf c

kt

khL

qBp

Channel

Hydraulic Fracture

LL btmp +=21General Form


NExT April 2000

Linear Flow

LL btmp +=21General Form

Derivative( )

21

21

2

1tm

t

btmt

t

pt

L

LL

=

+=


NExT April 2000

Linear Flow

Time

Pre

ssur

e ch

ange

, der

ivat

ive

2

1

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- slope


NExT April 2000

Bilinear Flow

Bilinear flow occurs primarily in low-conductivity hydraulically fractured wells.

From this flow regime, we can estimate fracture conductivity wkf.

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)


NExT April 2000

Bilinear Flow

412111.44

=

kc

t

wkh

qBp

tf Hydraulic

Fracture

General Form BB btmp +=41

Wkf=fracture conducivity, md-ft


NExT April 2000

Bilinear Flow

General Form BB btmp +=41

Derivative( )

41

41

4

1tm

t

btmt

t

pt

B

BB

=

+=


NExT April 2000

Bilinear Flow

Time

Pre

ssur

e ch

ange

, der

ivat

ive

4

1

The bilinear flow regime is recognized on the diagnostic plot bythe 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 quarter-slope 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- slope


NExT April 2000

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

- Vertical well with only a few perforations open

- Vertical well with only a small part of the zone perforated

- Some wireline formation test tools


NExT April 2000

Spherical Flow

General Form

=

kt

rc

kr

qpp pt

pwfi

2

14

Spherical Probe (RFT)

21= tmbp SS

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 - Viscosity, Pas


NExT April 2000

RFT Units

Nomenclature The Repeat Formation Tester (RFT) probe equation us es

SI units: ct - Total compressibility, Pa -1

k - Permeability, m 2 p i - Initial pressure, Pa pwf - Probe pressure, Pa q - Flow rate, m 3/s rp - Probe radius, m t - Time, s - Porosity, fraction - Viscosity, Pas


NExT April 2000

Spherical Flow

21= tmbp SSGeneral Form

Derivative( )

21

21

2

1

=

=

tm

t

tmbt

t

pt

S

SS


NExT April 2000

Spherical Flow

Time

Pre

ssur

e ch

ange

, der

ivat

ive

1

2

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

- Negative slope


NExT April 2000

Flow Regimes on the Diagnostic Plot

Wellborestorage Spherical flow

Radialflow

Recharge?

Elapsed time, hrs

Pre

ssur

e ch

ange

, der

ivat

ive,

psi

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 indicatesthat kh/u is different out in the reservoir we have two zones with different mobilities


NExT April 2000

Exercise 1Flow Regimes and the Diagnostic Plot

FLOWREGM.WTD (Diagnostic Plot)

0.01

0.1

1

10

100

1000

0.0001 0.001 0.01 0.1 1 10 100 1000 10000

Adj

uste

d pr

essu

re c

hang

e, p

si

Radial equivalent adjusted time, 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


NExT April 2000

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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09 - Flow Regimes and the Diagnostic Plot

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