Kelompok I.docx

1.1 Well Testing and the Ideal Reservoir Model A well test, in its simplest form, consists of disturbing the reservoir by producing from or injecting into a well at a controlled flow rate for a period of time and measuring the pressure response at the production or injection well, or at some nearby observation well. The pressure response, which depends on the rock and fluid properties beyond the wellbore, is then used to describe the unknown reservoir system. The "Ideal" Reservoir Model We shall describe the reservoir’s pressure response to flow during a test by considering the very simplest reservoir model; one with single-phase, radial flow in a homogeneous, isotropic reservoir with an "outer boundary "that may be considered "infinite," and a constant flow rate at the wellbore ("inner boundary") ( Figure 1 , Schematic of the ideal reservoir). All flow occurs radially through a horizontal reservoir between impermeable upper and lower reservoir boundaries.

Figure 1

The well fully penetrates the reservoir vertically and is fully perforated. The reservoir rock and fluid properties are assumed to be uniform throughout the reservoir and the fluid properties are assumed to be independent of pressure. In reality no reservoir satisfies all of these assumptions; however, we can compare the actual reservoir response with the ideal case for equivalency or divergence. We may refer to this model as the ideal reservoir model and use it to describe the simplest expected pressure response during well testing.

Reservoir Pressure Response During a Drawdown Test With an ideal model, we can show that if the reservoir pressure is initially constant throughout and equal to pi, and the well is opened to flow at constant rate along its full wellbore thickness, a pressure transient will move out radially from each point in the wellbore with time. A specific example, which we shall refer to as the base case, is shown in Figure 1 (The Base Case: The pressure transients in an ideal transient radial flow from a wellbore during a drawdown test).

Figure 1

Near the wellbore the pressure transient response, through the reservoir moves radially away from the well. This movement is rapid initially, but as it spreads out further from the wellbore and contacts progressively larger reservoir volume, it slows in its radial advance. Fluid movement takes place in those regions of the reservoir where the pressure has fallen below the original reservoir pressure. Even though the production rate at the well is constant, the flux rate will be different at each radius because the cross-sectional area exposed to radial flow at each radius differs. A test that involves opening the well to flow at a constant rate is called a drawdown test. The pressure response is a form of pressure transient, and our interpretation of it comprises one aspect of pressure transient analysis. If we solve the equations that describe transient radial flow into the wellbore for our "ideal" reservoir model, it is then possible to specify the pressure distribution in our reservoir as a function of time. Radius of Investigation The radius of investigation is the maximum radius at which a significant pressure disturbance has been propagated. Its approximate position at any given time can be calculated using the expression

(2.1) For the drawdown test pressure response shown in Figure 1 (The base case), we have plotted the radius of investigation versus time in Figure 2 (The effect-of-mobility ratio: the radius investigation versus flow time during a drawdown test).

Figure 2

Now, if we reduce the permeability to the flowing fluid by a factor of five, or increase the viscosity of the flowing fluid by a factor of five, or make changes in each such that the ratio k/ (mobility) is reduced by a factor of five, we will obtain Curve I in Figure 2 . Of course, this assumes that the porosity and fluid compressibility remain constant. With this change in magnitude in either of the variables, the rate of movement of the pressure transient into the reservoir is reduced. Conversely, if the mobility is increased by a factor of five from the base case, we obtain Curve II and note that the pressure transient moves more rapidly into the reservoir. As we see from Equation 2.1, reductions in reservoir porosity or rock/fluid compressibility will also shift the base-case curve upward. Increases in these properties will shift the curve downward. There are two important conclusions that can be drawn from this information: first, we note that if a well test is intended to investigate a certain distance into the reservoir, the required duration of the test will depend upon the relative values of permeability, fluid viscosity, porosity, and total compressibility. Equation 2.1 implies that if the mobility of one reservoir is five times less than that of another, the former must be tested five times longer if the same radius is to be

investigated in both cases. This assumes, of course, that the porosity and fluid compressibility are the same in both cases. The second conclusion we may draw for our ideal reservoir system is that the radius of investigation does not depend upon the production rate. The pressure transient will move outward to the same distance in the same period of time whether the production rate is high or low. (The rate affects only the magnitude of the pressure response.) Considering the conclusion in isolation, then, we need not conduct flow tests at high rates. However, the production rate should be constant throughout the test and should be such that we can accurately measure the pressure response with the tools we have available. We observe, then, that the radius of investigation concept provides a guide for well-test design. Variables That Affect the Shape of the Pressure Transient During a Drawdown Test We should look once again at the shape of the pressure transient as it moves outward in the reservoir and see what properties will cause it to change. Let us consider the base case ( Figure 1 ) and see what happens as we change one variable at a time. The results are given in Figure 3 (The effect of mobility on pressure transients during a drawdown test)

Figure 3

and Figure 4 (The effect of production rate on pressure transients during a drawdown test).

Figure 4

We begin by changing the mobility ratio. In Figure 3 we see that if the permeability is reduced or the viscosity increased so that the mobility (k/ ) is reduced by a factor of five, the pressure transient does not move as far into the reservoir as we expected, but has a larger pressure drop within the radius that it penetrates. The production, then, must come from a smaller radius, and, because of the lower mobility, the pressure gradients are greater. Consequently, the pressures at the wellbore during a test will be lower for a low-mobility reservoir system. The converse is also true. Let us now consider a change in production rate. In Figure 4 we see that such a change does not affect the radius of investigation as we might expect, but does change the pressure profile. At higher flow rates the pressure profile is steeper because higher pressure gradients are needed to satisfy the production rate. The converse is also true. Pressure Transients During a Drawdown Test in a Finite Reservoir It is helpful to see how the pressure profiles change in a reservoir that is not "infinite." To do so we must modify our theoretical model to show a finite volume reservoir with an impermeable barrier. Let us use an enclosing no-flow outer boundary with an outer radius of re. No flow takes place across this outer radius. In Figure 5 (The effect of a finite reservoir outer boundary on pressure transients)

Figure 5

we see that the presence of a finite outer boundary with an outer radius of re will not affect the pressure profile until the radius of investigation reaches re, but that thereafter the pressure profile drops more rapidly. This occurs because, in the finite case, all of the production must come from the finite reservoir volume. In effect, as we see in Figure 6 (The reflection of a pressure profile at a sealing fault)

Figure 6 and Figure 7 (The reflected pressure profile reaches wellbore) the pressure transient, upon reaching the barrier, is reflected back toward the wellbore.

Figure 7

In Figure 6 the reflection has not reached the wellbore; in Figure 7 it has. Prior to the pressure transient reaching the finite outer boundary, we have what is referred to as transient flow conditions. However, once the radius of investigation reaches the finite outer boundary we have the onset of what is referred to as pseudosteady-state (quasi-steady state) flow, and, with it, the beginning of "stabilized" flow. By stabilized or pseudosteady-state flow we mean that the rate of pressure change with time at any given radius is constant. Between the two flow periods is a transitional flow period. We may use the knowledge that stabilized flow has begun to estimate the limits of the reservoir (reservoir limit test).

Reservoir Pressure Response During a Drawdown-Buildup Test Sequence

Because it is often difficult to maintain a constant production rate during a drawdown test and because the mathematics involved are easy to interpret, we normally allow a well to produce for a period of time, then shut it in (production goes to zero) and observe the buildup in pressure at the wellbore. This constitutes a pressure buildup test, which is the most common type of well test. The pressure distribution in the reservoir is shown in Figure 1 .

Figure 1

Note that the well is shut in at t = t4 and that the pressure builds up thereafter. In buildup tests, except for the early influence of decaying well rates on pressure response, the majority of test data relate to a condition where the rate is zero and thus not changing.

Injectivity and Falloff Tests

Rather than cause a well to be produced at a constant rate as we do for a drawdown test, we may inject fluid into it at a constant rate. This is especially applicable for wells that are used for fluid injection. The test is referred to as an injectivity test. The pressure profile for this test, as shown in Figure 1 , is the mirror image of what occurs during a drawdown test, provided that the only change is in the direction of flow—from out to in.

Figure 1

(We assume that fluid property changes with pressure are not significant.) In a manner parallel to the buildup test, we may stop injection into the well after a period of time and measure the pressure falloff with time (the falloff test). Again, we will have a series of pressure profiles that will constitute mirror images to the drawdown-buildup sequence (see Figure 2 ).

Figure 2

Analysis of results follows procedures similar to drawdown-buildup testing.