Christine A. Ehlig-Economides, Peter Hegeman SchlumbergerOilfield Services

Houston

Sven Vik SagaPetroleum A.S.

Sandvika, Norway

With a few simple guidelines, industry professionals, especially those who are not well-testing experts, can know more about well-test interpretation, and thus make more appropriate decisions for well tests. Today's well tests frequently provide much more than permeability, skin, and extrapolated pressure.

Most managers, geoscientists, and petroleum engineers rely on specialists to interpret pressure-transient data from well tests. At times, however, valuable test results are overlooked when modem analysis techniques are not used to interpret the acquired data.

This first in a series of three articles addresses what to expect from a well test interpretation. The second part will show how to design a test, and manage well site data acquisition to ensure optimum results. The concluding part will illustrate these concepts in two successful cases.

### VIEWING DATA

To illustrate what to expect from a well test and how to recognize visually what information can be obtained from pressure-transient data, an exercise is offered in Fig. 1. For maximum usefulness, go to Fig. 1 now. Complete the exercise, and then return to the text al this point.

The pressure-transient data in Fig. 1 offer the means to quantify important well and reservoir parameters. Using a relatively easy procedure, data such as these can be visually evaluated to determine Bell test progress (thanks to real-time surface data readout) and/or what reservoir parameters to expect from in-depth interpretation.

The first step is to make a log-log plot with square log cycles of the pressure change, p, and its derivative-vs.-elapsed time, t. To compute the derivative, follow the procedure given in the accompanying computation box. The derivative is a must.

Next, use the flow regime identification (FRID) tool (Fig. 2) to look for typical flow regimes within the log-log plot. For a better understanding, practice using this tool to solve the exercise in Fig. 1. Do this by making an enlarged copy of the Fig. 1 plots, and a transparency copy of the FRID tool. The ease of identifying flow regimes with this overlay method is evident with a bit of practice.

Flow regimes, which appear as simple patterns in pressure derivative data, are important because each regime represents a streamline geometry for flow in the formation being tested. Thus, for each flow regime there is a set of well and/or reservoir parameters that can be calculated using only that portion of the transient data exhibiting the characteristic pattern.

Eight flow regime patterns are commonly observed in well test data. These are radial, spherical, linear, bilinear, compression/expansion steady state, dual porosity/permeability, and slope doubling.

### RADIAL FLOW

The most important flow regime is radial flow, which is recognized as an extended constant or flat trend in the derivative (that is, it appears neither as the upper part of a "hump" nor the lower part of a "valley" trend).

Radial-flow geometry is described as streamlines concerning to a circular cylinder, as in Fig. 3. In fully completed wells, the cylinder may represent the portion of the well bore intersecting the entire formation (Fig. 3b).

In partially penetrated formations or partially, completed wells, radial flow may be restricted in early time to only the fraction of the formation thickness that has flow directly into the well bore (Fig. 3a).

When wells have been hydraulically fractured (Fig. 3c) or horizontally completed (Fig. 3e), the effective radius for radial flow is enlarged. Horizontal wells also may exhibit early time radial flow along the well bore (Fig. 3d).

Finally, if a well is located near a flow barrier, such as a fault, pressure-transient response may exhibit radial flow to the well, followed by radial flow to the well plus its image across the boundary (Fig. 30.

Radial flow can be detected in all but one of the quiz examples in Fig. 1.

Applying the FRID tool to Well A (Fig. 4), radial flow is found in late time, while the first part of the response follows a unit (45) slope, which is labeled well bore storage.

For Well B (Fig. 4), radial flow can be identified twice. As highlighted, radial flow is first seen after a negative half-slope derivative trend, which is called spherical flow, and and at a lower level following a transition from the first radial-flow portion.

The two radial-flow regimes of Well B can be explained by the open-hole log in Fig. 5. this log shows two formation zones separated by a low-permeability shale. For the first radial flow, the streamlines are limited to the lower layer I. Later, cross flow occurs between the two layers, and the streamlines for the late time radial float, exist in both the lower and upper layers, I and II.

There is no evidence of radial flow in Well C (Fig. 6). However, for Well D (Fig. 6) radial flow is identified before a positive half-slope derivative trend, which is recognized as linear flow.

When the flat derivative trend has a very short duration, as in Well D, its association with radial flow is confirmed only when the subsequent analysis provides reservoir parameters that are consistent with external information. Well D was tested with downhole shut-in and is known to be in a high-permeability fault block with no evidence of natural fractures.

Formation permeability and skin can be determined whenever radial flow occurs. If radial flow occurs in late time, the average reservoir pressure also can be computed.

For Well A (Fig. 4) radial flow is observed in late time and, therefore, one can calculate permeability, skin, and extrapolated pressure (P *).

For Well B (Fig. 4) the two flat derivative trends, the second at a lower level than the first, suggest that the first radial flow occurs only in the lower layer, while the second radial-flow trend represents flow in both layers.

Permeability and skin calculated from the first radial flow characterize the lower layer. If the late time radial flow is assumed to be from both layers, the total permeability-thickness (kh) for the two layers can be determined from this trend, as well as the extrapolated pressure for the two layers. Then, knowing permeability of the lower layer and the combined layers, one can solve for upper-layer permeability.

Because the first radial flow occurs after a spherical flow trend, the skin determined for the lower layer can be decomposed to quantify the damage along the limited entry once the spherical-flow regime is analyzed. The skin determined from the late-time radial flow includes the effect of producing the upper layer from perforations in the lower layer. This necessarily inhibits productivity and the well was subsequently completed in the upper layer.

For Well D (Fig. 6) the upward departure of the derivative from the radial-flow trend indicates reservoir boundaries. Permeability and skin can be determined from the part of the data identified with radial flow. However, because there is a late-time departure from the flat derivative trend, p* cannot be determined in the conventional manner.

The conventional analysis of a build-up test with a Horner plot can be performed only on the data portion exhibiting the flat derivative trend. Because this trend does not appear for Well C (Fig. 6) there is no need to make the Homer analysis. Moreover, if Horner analysis is performed on the data, incorrect values for the permeability, skin, and p* will be determined.

As with many well tests, Wells A to D offer the means to determine additional parameters besides permeability and skin. To realize what can be learned from these tests, it is necessary to be familiar with spherical and linear-flow regimes, both of which are commonly observed in transient data.

### SPHERICAL FLOW

Spherical flow occurs when flow streamlines converge to a point, as in Fig. 7. This flow regime occurs for the partially completed formation and the partially penetrated well.

For partial penetration or partial completion near the upper or lower bed boundary, the nearer bed imposes a hemispherical flow regime. Both spherical and hemispherical flow are seen on the derivative as a negative half-slope. Whenever this appears, spherical permeability can be determined, which in turn yields a value for the vertical permeability, kv, if the horizontal permeability, kh, can be quantified from a radial-flow regime seen in another portion of

the data.

The importance of vertical permeability to predict gas or water coning, or horizontal well performance, has highlighted the need for quantifying this parameters A drill stem test conducted when only a small portion of the formation has been drilled (or perforated) may yield both vertical and horizontal permeability, thus enabling optimized completion engineering or providing, a rationale for drilling or not drilling a horizontal well.

Well B is an example of a drill stem test that yielded vertical and horizontal permeabilities for the lower layer. These permeabilities were derived from the portion of the data exhibiting the spherical-flow (negative half-slope) trend in Fig. 4.

The reason for the spherical flow in early time is evident from the open hole log (Fig. 5) that shows only a few feet of perforations (near 12,400 ft) into the middle of the lower layer, as in

Fig. 7.

Frequently negative half-slope behavior is observed in well tests that indicate a high skin factor. A complete analysis may provide vertical Permeability and decomposition of the skin into components that indicate the amount of skin due to the limited entry and the amount due to damage along the actively flowing interval.

In turn, the treatable portion of the damage can be determined, and the cost effectiveness of damage removal and/or reperforating to improve well productivity can be evaluated.

### LINEAR FLOW

Linear-flow streamline geometry consists of strictly parallel-flow vectors. Linear flow is exhibited in the derivative as a positive half-slope trend. Fig. 7 shows why this flow regime is evident in vertically fractured and horizontal wells, or in a well producing from an elongated reservoir.

Because the streamlines converge to a plane, the parameters associated with this flow recime are formation permeability in the direction of the streamlines, and the flow area normal to the streamlines.

When formation permeability-thickness is known from another flow regime, one can determine the flow-area width. This provides fracture half-length of a vertically fractured well, the effective production length of a horizontal well, or the width of an elongated reservoir.

Alternatively, if flow-area width is known, combining linear-flow data with radial-flow data (in any order) can provide the principle values (k, and k,) for directional permeability in the bedding plane.

In an anisotropic formation, horizontal well productivity is enhanced by drilling in the direction normal to maximum horizontal permeability.

Well C is a water-injection well exhibiting linear flow (Fig. 6). Although no radial flow is evident, the time of the departure from linear flow, as marked on the figure, coupled with an analysis of the data that follows the half-slope derivative trend, provides two independent indicators of both formation permeability and fracture half-length. Thus both can be quantified.

A subtle rise in the derivative after the departure from linear flow suggests a boundary which in this case was interpreted as a fault.

Linear flow is identified in Well D using the FRID tool (Fig. 6). Well D is not hydraulically fractured, and seismic data suggest that it is located between two sealing faults. Thus, the linear flow is explained by streamlines such as in Fig. 7. Because the linear flow is preceded by radial flow, both permeability and the distance between the faults can be determined from this test.

### BILINEAR FLOW

Hydraulically fractured wells may exhibit bilinear flow instead of, or in addition to, linear flow. This flow regime occurs because pressure drop in the fracture itself accounts for parallel streamlines in the fracture while, at the same time, the streamlines in the formation are parallel in the direction normal to the fracture face (Fig. 7).

Because the two linear-flow patterns occur simultaneously in normal directions, this flow regime is termed bilinear. The derivative trend for this flow regime has a positive quarter-slope.

When the formation permeability is known independently, the fracture conductivity, kfw, can be determined from this flow regime. Bilinear flow is not seen in Fig. 1.

### COMPRESSION/EXPANSION

The derivative of a compression/expansion flow appears as a unit slope trend whenever the volume containing the pressure disturbance"is not changing with time, and pressures at all points within this volume vary in the same manner.

This volume can be limited by a portion or all of the well . bore, a bounded commingled reservoir zone, or a bounded reservoir. If the well bore is the limiting factor, the flow regime is called well bore storage. If the limiting factor is the entire drainage volume for the well, this behavior is called a pseudosteady state.

When one or more unit slope trends precede a stabilized-radial-flow derivative, this probably represents well bore storage effects. The transition from the well bore storage unit slope trend to another flow regime usually appears as a "hump," as in Fig. 4.

The well bore storage response is limited effectively to the well bore volume. Hence, it provides very little information about the reservoir. Further, a predominance of well bore storage may mask important early time responses that would otherwise characterize near-well bore features, including partial penetration or a finite damage radius.

This flow regime is minimized by shutting in the well near the producing interval. This can reduce the portion of the data dominated by well bore storage behavior by two or more logarithmic cycles in time. In some wells tested without downhole shut-in, well bore storage effects have lasted several days.

After radial flow occurs, a unit slope trend that is not the final observed behavior may appear because of a zone producing into one.or more other zones commingled in the well bore. This behavior is accompanied by cross flow in the well bore, and occurs when commingled zones are differentially depleted.

When the unit slope occurs as the last observed trend, as in Fig. 8, the assumption is that the entire reservoir volume contained in the well drainage is at pseudosteady-state conditions. The late time unit slope behavior due to pseudosteady state is only observed during drawdown, as indicated on the FRID tool. When the unit slope is seen after radial flow, the zone (or reservoir) volume can be determined and possibly the shape can be described.

### STEADY STATE

Steady state implies that pressures in the well drainage volume are not varying in time at any point, and the pressure gradient between any two points in the reservoir is constant. This condition may occur in an injection/production pattern, or when the pressure in the well drainage volume is maintained by adjacent gas cap or aquifer expansion.

During steady-state flow, the tendency for a constant pressure results in a steeply failing derivative, as shown in Fig. 8. In build-up and falloff tests, a steeply falling derivative may represent either pseudosteady or steady state.

### DUAL POROSITY/PERMEABILITY

Dual porosity/permeability behavior occurs when reservoir rocks contain distributed internal heterogeneities that have highly contrasting flow characteristics. Examples are naturally fractured or highly laminated formations.

The derivative for this case (Fig. 8) may look like a valley shaped trend or like the plot labeled dual porosity or permeability.

This feature may come and go during any one of the flow regimes already described, or during a transition from one flow regime to another. From this flow regime, parameters associated with internal heterogeneity are determined. These included interporosity flow transmissibility, relative storativity of the contrasted heterogeneities, or geometric factors.

### SLOPE DOUBLING

Slope doubling describes two successive radial-flow regimes, with the second being at a level exactly twice that of the first (Fig. 8). This behavior is frequently Explained by a sealing fault, but, because of the curve similarity, slope doubling also can be due to dual porosity/permeability heterogeneity, particularly in laminated reservoirs.

When slope doubling is caused by a sealing fault, distance between the well and fault can be determine .

### QUIZ ANSWERS

The correct answers to the Fig. 1 exercise are:

- Well I with interpretation 2
- Well B with 3
- Well C with 1
- Well D with 4.

### ACKNOWLEDGMENTS

The authors thank Saga Petroleum A.S. for use of the data in Fig. 1, and Schlumberger's management for supporting this three-part series.

*Copyright 1994 Oil & Gas Journal. All Rights Reserved.*