Ejercicio De Drowdown

Drawdown test (Libro Advanced reservoir Engineering, autor Tarek Ahmed y Paul D. Mckinney )

A pressure drawdown test is simply a series of bottom-hole pressure measurements made during a period of flow at constant producing rate. Usually the well is shut in prior to the flow test for a period of time sufficient to allow the pressure to equalize throughout the formation, i.e., to reach static pressure. A schematic of the ideal flow rate and pressure history is shown in Figure 1.32. The fundamental objectives of drawdown testing are to obtain the average permeability, k, of the reservoir rock within the drainage area of the well, and to assess the degree of damage of stimulation induced in the vicinity of the wellbore through drilling and completion practices. Other objectives are to determine the pore volume and to detect reservoir inhomogeneities within the drainage area of the well. When a well is flowing at a constant rate of Qo under the unsteady-state condition, the pressure behavior of the well will act as if it exists in an infinite-size reservoir. The pressure behavior during this period is described by Equation 1.2.134 as:

where:

k = permeability, md

t = time, hours

rw = wellbore radius, ft

s = skin factor

The above expression can be written as:

This relationship is essentially an equation of a straight line and can be expressed as:

and the slope m is given by:

Equation 1.3.1 suggests that a plot of pwf versus time t on semilog graph paper would yield a straight line with a slope min psi/cycle. This semilog straight-line portion of the drawdown data, as shown in Figure 1.33, can also be expressed in another convenient form by employing the definition of the slope:

Notice that Equation 1.3.2 can also be rearranged to determine the capacity kh of the drainage area of the well. If the thickness is known, then the average permeability is given by:

where:

k = average permeability, md

|m| = absolute value of slope, psi/cycle

Clearly, kh/μ or k/μ may also be estimated.

The skin effect can be obtained by rearranging Equation 1.3.1 as:

or, more conveniently, if selecting pwf = p1 hr which is found on the extension of the straight line at t = 1 hr, then:

Where |m| is the absolute value of the slope m. In Equation 1.2.3, p1 hr must be obtained from the semilog straight line. If the pressure data measured at 1 hour does not fall on that line, the line must be extrapolated to 1 hour and the extrapolated value of p1 hr must be used in Equation 1.3.3. This procedure is necessary to avoid calculating an incorrect skin by using a wellbore-storage-influenced pressure. Figure 1.33 illustrates the extrapolation to p1 hr. Note that the additional pressure drop due to the skin was expressed previously by Equation 1.2.130 as:

This additional pressure drop can be equivalently written in terms of the semilog straight-line slope m by combining the above expression with that of Equation 1.3.3 to give:

Another physically meaningful characterization of the skin factor is the flow coefficient E as defined by the ratio of the well actual or observed productivity index Jactual and its ideal productivity index Jideal . The ideal productivity index Jideal is the value obtained with no alternation of permeability around the wellbore. Mathematically, the flow coefficient is given by:

where p is the average pressure in the well drainage area. If the drawdown test is long enough, the bottom-hole pressure will deviate from the semilog straight line and make the transition frominfinite acting to pseudosteady state. The rate of pressure decline during the pseudosteady-state flow is defined by Equation 1.2.116 as:

Under this condition, the pressure will decline at a constant rate at any point in the reservoir including the bottom-hole flowing pressure pwf . That is:

This expression suggests that during the semisteady-state flow, a plot of pwf vs. t on a Cartesian scale would produce a straight line with a negative slope of m\ that is defined by:

where:

m\= slope of the Cartesian straight line

during the pseudosteady state, psi/hr

q = flow rate, bbl/day

A = drainage area, ft2

Example 1.24a Estimate the oil permeability and skin factor from the drawdown data of Figure 1.34.

The following reservoir data are available:

h = 130 ft, φ = 20 %, rw = 0. 25 ft,

pi = 1154 psi, Qo = 348 STB/D, m = −22 psi/cycle

Bo = 1. 14 bbl/STB, μo = 3. 93 cp, ct = 8. 74 × 10−6 psi−1

Assuming that the wellbore storage effect is not significant, calculate:

● the permeability;

● the skin factor;

● the additional pressure drop due to the skin.

Solution

Step 1. From Figure 1.34, calculate p1 hr:

p1 hr = 954 psi

Step 2. Determine the slope of the transient flow line:

m = −22 psi/cycle

Step 3. Calculate the permeability by applying Equation 1.3.2:

Step 4. Solve for the skin factor s by using Equation 1.3.3:

Step

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