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Well Testing and Analysis Infinite Acting Reservoirs and Analysis. Model Response First Drawdown after Stabilisation. Presentation Outline. First Drawdown. Pressure Drawdown Response Pressure Drawdown Analysis Type Curves. Pressure. Prof Peter Behrenbruch Prof Pavel Bedrikovetsky.

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Well Testing and Analysis

Infinite Acting Reservoirs and Analysis

Model Response

First Drawdown after Stabilisation

Presentation Outline

First Drawdown

  • Pressure Drawdown Response

  • Pressure Drawdown Analysis

  • Type Curves

Pressure

Prof Peter Behrenbruch

Prof Pavel Bedrikovetsky

Time from start of drawdown

Ref: Gringarten


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Pressure Drawdown Response


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Drawdown Response - General Solution

Example of pD(tD) Function

Example: Interference Test in an Infinite Reservoir with Homogeneous Behaviour

Ref: Gringarten


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Infinitive Reservoir, General Line Source Solution

104

105

106

107

108

109

10

Dimensionless Parameters

1

10-1

Valid for

10-2

10-1

103

104

1

10

102


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Drawdown Type Curves

Example of Independent Variables*

Dimensionless parameters, non-unique match

Independent variables, unique match

Ref: Gringarten

* oilfield units


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Pressure Drawdown Analysis


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Pressure Transient Analysis

Logarithmic Approximation of Pressure Drawdown

at the wellbore

valid for

or

and in field units

where


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Single Rate Transient Drawdown Analysis

Including Afterflow and Skin

Analysis Plot (Drawdown)

Equations (field units)

Wellbore Storage Effects

Slope m

is negative

10-1

1

10

102

Time (hrs)


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Identification of Correct Analysis for Semi-log Analysis

Log-log Drawdown Response and 1½ Log Cycle Rule


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Semi-log (Horner) Analysis


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Type Curves


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Wellbore Storage (1)

Rate Response


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Wellbore Storage (2)

Pressure Response


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Wellbore Storage (3)

Characteristic on Log-log Plot: 45o Slope

45o slope


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Drawdown Type Curves

Examples of Independent Variables*

Ramey

Gringarten

* oilfiled units

Ref: Gringarten


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Analysis Process

Model Identification, Parameter Calculation, Model Verification

Ref: Gringarten


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Drawdown Type Curves

Examples of Dimensionless Variables*

* oilfiled units

Ref: Gringarten


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Log-log Analysis

Ref: Gringarten


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Model Response in the First Drawdown

Ref: Gringarten


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Type Curve Matching (2)

Gringarten Curves

Ref: Gringarten


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Type Curve Matching (3)

Summary of Analysis Results

Match point:

kh

C

Type curve selected:

S


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Type Curve Matching

Datum Shifting

3.21


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Derivative Type Curve

3.1


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p, psi

Infinite Acting Radial Flow

Straight Line on Semilog Plot

Flat Region on Derivative Plot

Time, hrs

pd

td/cd


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Dp, psi

Wellbore Storage

Unit Slope Line on Log-log Plot

Unit Slope Line plus Hump* on

Derivative Plot

pd

* The hump on a derivative plot is characteristic

of a damaged well (positive skin)


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