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1

Well Test Analysis

Test Design

te

c

tkr

..948.

=

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2

Log-Log Plot(Diagnostic Plot)

Characteristic Slopes

Slope Line Definition

0 Radial Flow

1 Wellbore Storage

1/2 Linear Flow

1/4 Bi-Linear Flow

-1/2 Spherical Flow

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Fully Completed Vertical Well

Assumptions

The entire reservoir interval contributes to the flow into the well.

The model handles homogeneous, dual-porosity and radial composite reservoirs.

The outer boundary may be finite or infinite.

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Diagnostic Plot

0 S1 S

Behavior At early time, response is dominated by the wellbore

storage. If the wellbore storage effect is constant with time, the response is characterized by a unity slope on the pressure curve and the pressure derivative curve.

In case of variable storage, a different behavior may be seen.

Later, the influence of skin and reservoir storativitycreates a hump in the derivative.

At late time, an infinite-acting radial flow pattern develops, characterized by stabilization (flattening) of the pressure derivative curve at a level that depends on the k * h product.

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5

Partial Completion

Assumptions

The interval over which the reservoir flows into the well is shorter than the reservoir thickness, due to a partial completion.

The model handles wellbore storage and skin, and it assumes a reservoir of infinite extent.

The model handles homogeneous and dual-porosity reservoirs.

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Diagnostic Plot

- 0.5 S

Behavior

At early time, after the wellbore storage effects are seen, the flow is spherical or hemispherical, depending on the position of the flowing interval.

Hemispherical flow develops when one of the vertical no-flow boundaries is much closer than the other to the flowing interval. Either of these two flow regimes is characterized by a 0.5 slope on the log-log plot of the pressure derivative.

At late time, the flow is radial cylindrical. The behavior is like that of a fully completed well in an infinite reservoir with a skin equal to the total skin of the system.

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Partial completion with gas cap or aquifer

Assumptions

The interval over which the reservoir flows into the well is shorter than the reservoir thickness, due to a partial completion.

Either the top or the bottom of the reservoir is a constant pressure boundary (gas cap or aquifer).

The model assumes a reservoir of infinite extent. The model handles homogeneous and dual-

porosity reservoirs.

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8

Diagnostic Plot

Behavior

At early time, after the wellbore storage effects are seen, the flow is spherical or hemispherical, depending on the position of the flowing interval. Either of these two flow regimes is characterized by a 0.5 slope on the log-log plot of the pressure derivative.

When the influence of the constant pressure boundary is felt, the pressure stabilizes and the pressure derivative curve plunges.

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Infinite conductivity vertical fracture

Assumption

The well is hydraulically fractured over the entire reservoir interval.

Fracture conductivity is infinite. The pressure is uniform along the fracture. This model handles the presence of skin on the

fracture face. The reservoir is of infinite extent. This model handles homogeneous and dual-

porosity reservoirs.

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Diagnostic Plot

0.5 S

Behavior

At early time, after the wellbore storage effects are seen, response is dominated by linear flow from the formation into the fracture. The linear flow is perpendicular to the fracture and is characterized by a 0.5 slope on the log-log plot of the pressure derivative.

At late time, the behavior is like that of a fully completed infinite reservoir with a low or negative value for skin. An infinite-acting radial flow pattern may develop.

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Two-Porosity Reservoir

Assumptions

The reservoir comprises two distinct types of porosity: matrix and fissures. The matrix may be in the form of blocks, slabs, or spheres. Three choices of flow models are provided to describe the flow between the matrix and the fissures.

The flow from the matrix goes only into the fissures. Only the fissures flow into the wellbore.

The two-porosity model can be applied to all types of inner and outer boundary conditions, except when otherwise noted.

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Diagnostic Plot

Behavior

At early time, only the fissures contribute to the flow, and a homogeneous reservoir response may be observed, corresponding to the storativity and permeability of the fissures.

A transition period develops, during which the interporosity flow starts. It is marked by a valley in the derivative. The shape of this valley depends on the choice of interporosity flow model.

Later, the interporosity flow reaches a steady state. A homogeneous reservoir response, corresponding to the total storativity (fissures + matrix) and the fissure permeability, may be observed.

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Radial Composite Reservoir

Assumptions

The reservoir comprises two concentric zones, centered on the well, of different mobility and/or storativity.

The model handles a full completion with skin. The outer boundary can be any of three types:

Infinite Constant pressure circle No-flow circle

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Diagnostic Plot

Behavior

At early time, before the outer zone is seen, the response corresponds to an infinite acting system with the properties of the inner zone.

When the influence of the outer zone is seen, the pressure derivative varies until it reaches a plateau.

At late time the behavior is like that of a homogeneous system with the properties of the outer zone, with the appropriate outer boundary effects.

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Single Sealing Fault

Assumptions

A single linear sealing fault, located some distance away from the well, limits the reservoir extent in one direction.

The model handles full completion in homogenous and dual-porosity reservoirs.

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Diagnostic Plot

m

2m

Behavior

At early time, before the boundary is seen, the response corresponds to that of an infinite system.

When the influence of the fault is seen, the pressure derivative increases until it doubles, and then stays constant.

At late time the behavior is like that of an infinite system with a permeability equal to half of the reservoir permeability.

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Single Constant-Pressure Boundary

Assumptions

A single linear, constant-pressure boundary, some distance away from the well, limits the reservoir extent in one direction.

The model handles full completion in homogenous and dual-porosity reservoirs.

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Diagnostic Plot

Behavior

At early time, before the boundary is seen, the response corresponds to that of an infinite system.

At late time, when the influence of the constant-pressure boundary is seen, the pressure stabilizes, and the pressure derivative curve plunges.

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Parallel Sealing Faults

Assumptions

Parallel, linear, sealing faults (no-flow boundaries), located some distance away from the well, limit the reservoir extent.

The model handles full completion in homogenous and dual-porosity reservoirs.

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Diagnostic Plot

0.5 S

Behavior

At early time, before the first boundary is seen, the response corresponds to that of an infinite system.

At late time, when the influence of both faults is seen, a linear flow condition exists in the reservoir. During linear flow, the pressure derivative curve follows a straight line of slope 0.5 on a log-log plot.

If the L1 and L2 are large and much different, a doubling of the level of the plateau from the level of the first plateau in the derivative plot may be seen. The plateaus indicate infinite-acting radial flow, and the doubling of the level is due to the influence of the nearer fault.

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Intersecting Faults

Assumptions

Two intersecting, linear, sealing boundaries, located some distance away from the well, limit the reservoir to a sector with an angle theta. The reservoir is infinite in the outward direction of the sector.

The model handles a full completion, with wellbore storage and skin.

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Diagnostic Plot

m

m

360'

=

m

m

Behavior

At early time, before the first boundary is seen, the response corresponds to that of an infinite system.

When the influence of the closest fault is seen, the pressure behavior may resemble that of a well near one sealing fault.

Then when the vertex is reached, the reservoir is limited on two sides, and the behavior is like that of an infinite system with a permeability equal to theta/360 times the reservoir permeability.

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Partially Sealing Fault

Assumptions

A linear partially sealing fault, located some distance away from the well, offers some resistance to the flow.

The reservoir is infinite in all directions. The reservoir parameters are the same on both

sides of the fault. The model handles a full completion.

This model allows only homogeneous reservoirs.

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Diagnostic Plot

Behavior

At early time, before the fault is seen, the response corresponds to that of an infinite system.

When the influence of the fault is seen, the pressure derivative starts to increase, and goes back to its initial value after a long time. The duration and the rise of the deviation from the plateau depend on the value of alpha.

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Closed Circle

Assumptions

A circle, centered on the well, limits the reservoir extent with a no-flow boundary.

The model handles a full completion, with wellbore storage and skin.

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Diagnostic Plot

1 S

Behavior

At early time, before the circular boundary is seen, the response corresponds to that of an infinite system.

When the influence of the closed circle is seen, the system goes into a pseudo steady state. For a drawdown, this type of flow is characterized on the log-log plot by a unity slope on the pressure derivative curve. In a buildup, the pressure stabilizes and the derivative curve plunges.

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Constant Pressure Circle

Assumptions

A circle, centered on the well, is at a constant pressure.

The model handles a full completion, with wellbore storage and skin.

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Diagnostic Plot

Behavior

At early time, before the constant pressure circle is seen, the response corresponds to that of an infinite system.

At late time, when the influence of the constant pressure circle is seen, the pressure stabilizes and the pressure derivative curve plunges.

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Closed Rectangle

Assumptions

The well is within a rectangle formed by four no-flow boundaries.

The model handles a full completion, with wellbore storage and skin.

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Diagnostic Plot

0.5 S

1 S

Behavior

At early time, before the first boundary is seen, the response corresponds to that of an infinite system.

At late time, the effect of the boundaries will increase the pressure derivative: If the well is near the boundary, behavior like that of a

single sealing fault may be observed. If the well is near a corner of the rectangle, the behavior of

two intersecting sealing faults may be observed. Ultimately, the behavior is like that of a closed circle

and a pseudo-steady state flow, characterized by a unity slope, may be observed on the log-log plot of the pressure derivative.

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Constant Pressure and Mixed-

Boundary Rectangles

Assumptions

The well is within a rectangle formed by four boundaries.

One or more of the rectangle boundaries are constant pressure boundaries. The others are no-flow boundaries.

The model handles a full completion, with wellbore storage and skin.

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Diagnostic Plot

Behavior

At early time, before the first boundary is seen, the response corresponds to that of an infinite system.

At late time, the effect of the boundaries is seen, according to their distance from the well. The behavior of a sealing fault, intersecting faults, or parallel sealing faults may develop, depending on the model geometry.

When the influence of the constant pressure boundary is felt, the pressure stabilizes and the derivative curve plunges. That effect will mask any later behavior.

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Case Study

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-1/2 S

Partial Penetration

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Log-Log PlotDe

lta m

(p) / D

elta

Q

(psi2

/cp

(*1E-

06) /

MM

scf/d

ay)

0.001

0.01

0.1

1

10

100

Elapsed Time (hours)0.001 0.01 0.1 1 10 100

Quick Match ResultsPartial penetrationInf initely actingConstant compressibilityCs = 0.054 bbl/psiK = 77 mdkh = 8085 md.ftS = -3 Kz = 0.9 mdhtop = 0 f thp = 32 f tD = 1.050e-004 1/(Mscf/day)Pi = 4072.7472 psiaPi(d) = 4086.0168 psia

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N

31 20 00

31 19 00

31 18 00

31 14 00 31 15 00 31 16 00 31 17 00

1 Km.

31 21 00

31 17 00

959 000

958 000

957 000

956 000

955 000

954 000

953 000

636 000 637 000 638 000 639 000 640 000 641 000 642 000 643 000

W.K-1

m2 m

Single Fault