The drawdown test consists of flowing a well at a constant rate following a shut-in period. The shut-in period should be sufficiently long for the reservoir pressure to have stabilized. The basis for the drawdown test is found in Eq. (8.40),

which predicts the pressure at any radius, r, as a function of time for a given reservoir flow system during the transient period. If r = rw, then p (r, t) will be the pressure at the wellbore. For a given reservoir system, pi, q, m, B, k, h, f, ct, and rw are constant, and Eq. (8.40) can be written as

where,

pwf = flowing well pressure in psia

b = constant

t = time in hrs

Equation (8.56) suggests that a plot of pwf versus t on semilog graph paper would yield a straight line with slope m through the early time data that correspond with the transient time period. This is providing that the assumptions inherent in the derivation of Eq. (8.40) are met. These assumptions are the following:

1. Laminar, horizontal flow in a homogeneous reservoir.

2. Reservoir and fluid properties, k, f, h, ct, m, and B are independent of pressure.

3. Single-phase liquid flow in the transient time region.

4. Negligible pressure gradients.

The expression for the slope, Eq. (8.56), can be rearranged to solve for the capacity, kh, of the drainage area of the flowing well. If the thickness is known, then the average permeability can be obtained by Eq. (8.57):

As for Productivity Index:

The ratio of the rate of production, expressed in STB/day for liquid flow, to the pressure drawdown at the midpoint of the producing interval, is called the productivity index, symbol J.

The PI is a measure of the well potential, or the ability of the well to produce, and is a commonly measured well property. To calculate J from a production test, it is necessary to flow the well a sufficiently long time to reach pseudosteady-state flow. Only during this flow regime will the difference between and pwf be constant. It was pointed out in Section 3 that once the pseudosteady-state period had been reached, then the pressure changes at every point in the reservoir at the same rate. This is not true for the other periods, and a calculation of productivity index during other periods would not be accurate.

In some wells, the PI remains constant over a wide variation in flow rate such that the flow rate is directly proportional to the bottom-hole pressure drawdown. In other wells, at higher flow rates the linearity fails, and the PI index declines, as shown in Fig. 8.15. The cause of this decline may be (a) turbulence at increased rates of flow, (b) decrease in the permeability to oil due to presence of free gas caused by the drop in pressure at the well bore, (c) increase in oil viscosity with pressure drop below bubble point, and/or (d) reduction in permeability due to formation compressibility.

In depletion reservoirs, the productivity indicies of the wells decline as depletion proceeds, owing to the increase in oil viscosity as gas is released from solution and to the decrease in the permeability of the rock to oil as the oil saturation decreases. Since each of these factors may change from a few to several-fold during depletion, the PI may decline to a small fraction of the initial value. Also, as the permeability to oil decreases, there is a corresponding increase in the permeability to gas, which results in rising gas-oil ratios. The maximum rate at which a well can produce depends on the productivity index at prevailing reservoir conditions and on the available pressure drawdown. If the producing bottom-hole pressure is maintained near zero by keeping the well “pumped off,” then the available drawdown is the prevailing reservoir pressure, and the maximum rate is .

Fig. 8.15. Decline in productivity index at higher flow rates.

In wells producing water, the PI, which is based on dry oil production, declines as the water cut increases because of the decrease in oil permeability, even though there is no substantial drop in reservoir pressure. In the study of these “water wells,” it is sometimes useful to place the PI on the basis of total flow, including both oil and water, where in some cases the water cut may rise to 99% or more.

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