MULTILAYERED WELL ANALYSIS

Most oil and gas wells produce from sedimentary formations, which by their nature are stratigraphic.

Therefore it is of interest to determine the effects of the separate layers on the pressure transient observed during a well test. In some cases the layers have no discernible influence, in other cases there is an effect that changes the appearance of the well test data.

Figure 7.7

Figure 7.8

There are two principle types of reservoir layering, depending on whether the layers are in pressure communication with each other within the formation. If the layers are hydraulically separated within the formation (by shales for example) then they are connected only by the open wellbore -- this reservoir model is known as commingled layers as in Fig. 7.7. If the layers are in hydraulic communication within the reservoir (as well as through the wellbore) the layers are said to experience crossflow as in Fig. 7.8. The pressure transient responses of these two flow models are slightly different.

If we consider the boundary condition on the flowing well for a particular layer j, in the absence of a skin effect the individual layer flow rate qj can be written:

(7.12) From this equation it can be seen firstly that the flow rate from each

layer will be proportional to the layer transmissivity kh/m, and secondly that since the pressure in the wellbore is the same for each layer then the pressure gradient in the formation will also be the same for each layer. Assuming the pressures were the same in all layers before flow to the wellbore started, then in the absence of skin effect there will be no pressure difference between layers at any time -- whether the well is commingled or has formation crossflow. The principle difference between commingled and crossflow models therefore is seen to originate only in the presence of a skin effect.

Much of the interest in multilayered well test analysis is stimulated by the desire to estimate individual layer permeabilities and skin factors.

However, it is impossible to do this unless individual layer flow rates are known. Layered well test analysis therefore falls into two categories: (a) tests in which only total flow rate is known, for which only average permeability and skin factor can be estimated, and (b) tests in which the layer flow rates are measured during the test, for which layer properties can be estimated.

7.2.1 Tests without Flow Measurements

A test with multiple layers frequently looks no different from a normal single layer test; an example is shown in Fig. 7.9. In this example there are two layers of equal thickness, one

with a permeability of 169.9 md and the other with a permeability of 8.495 md (a factor of 20 difference). The permeability estimate from a match to the well test is 89.2 md, which is exactly the thickness-weighted average of the two.

(7.13) In this case, 0.5(169.9 + 8.495) = 89.19.

Figure 7.9

Figure 7.10

In other cases in which one layer is much thicker than the other, or where one layer has a larger skin than the other, the response can look like a dual porosity response. Fig. 7.10

shows an example where one layer has a permeability of 9182 md and a thickness of 0.23 feet and the other has a permeability of 9.182 md (a factor of 1000 difference) and a thickness of 23 feet (a factor of 100 difference). The thick low permeability zone also has a porosity twice that of the thin high permeability zone, and the high permeability zone has a smaller skin factor. Even with these significant contrasts, the deviation of the well test from uniform single layer response is extremely modest. This kind of behavior can only be seen in formations with crossflow, a commingled reservoir will not show such an effect except perhaps in unlikely situations such as where the layers produce from different drainage areas.

In summary, the pressure transient response of a multilayered well usually looks entirely conventional, and normal (single layer) analysis methods can be used to interpret the data. However, it is important to note that the permeability estimate that is obtained is the thickness-weighted average, which may be very different from any of the layer permeabilities. For example, in the well test shown in Fig. 7.10, the two layer permeabilities are 9182 md for 0.23 feet and 9.182 md for 23 feet, however the permeability estimated from the well test is 100 md using a total thickness of 23.23 feet. To determine individual layer properties,

it is necessary to know the individual layer flow rates.

7.2.2 Tests with Flow Rate Measurement

Testing of multilayered reservoirs has been a focus of innovation in the field of well test analysis over the past decade or so. Earlier work considered special cases in which traditional approaches had been found to work, however starting with the work by Dogru and Seinfeld (1979) the inherent ill-posedness came to be understood. Prijambodo, Raghavan and Reynolds (1985) and Ehlig-Economides and Joseph (1987) investigated the effects of crossflow between layers and the influence of individual layer skin. Kuchuk, Karakas and Ayestaran (1986) described the application of nonlinear regression to the interpretation of multilayered well tests, but added the important emphasis on the need to determine individual layer flow rates.

Since it is impractical to measure flow rates continuously at all depths, Kuchuk, Karakas and Ayestaran (1986) proposed a testing method in which the well is flowed at a series of different (wellhead) rates with the flow rate measured at the top of a different layer unit in each period.

The separate layer responses are then combined using convolution, and the total response matched using nonlinear regression. This approach was developed further by Ehlig-Economides (1993) who described

the desuperposition of the individual flow rate changes to make the individual layer responses resemble normal single layer behavior. This approach is similar in concept to rate-normalization as described in 3.7 Desuperposition. The procedure can be used either for graphical the Properties of Stratified Reservoirs", paper SPE 7694 presented at the 1979 SPE Symposium on Reservoir Simulation, Denver, CO, Feb. 1-2 (1979).

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"Horizontal Well Testing in the Gulf of Guinea", Oil Field Review, (April 1992), 42-48.

Ehlig-Economides, C.A., and Joseph, J.: "A New Test for Determination of Individual Layer Properties in a Multilayered Reservoir", SPE Formation Evaluation, (Sept. 1987), 261-271.

Ehlig-Economides, C.A.: "Model Diagnosis for Layered Reservoirs", SPE Formation Evaluation, (Sept. 1993), 215-224.

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Kuchuk, F.J., Goode, P.A., Brice, B.W., Sherrard, D.W., and Thambynayagam, M.: "Pressure Transient Analysis for Horizontal Wells", J. Pet. Tech., (Aug.

1990), 974-984; Trans., AIME, 289.

Kuchuk, F.J., Karakas, M., and Ayestaran, L.: "Well Testing and Analysis Techniques for Layered Reservoirs", SPE Formation Evaluation, (Aug. 1986), 342-354.

Prijambodo, R., Raghavan, R., and Reynolds, A.C.: "Well Test Analysis for Wells Producing Layered Reservoirs with Crossflow", Soc. Pet.

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