Chapter 7 well test analysis

A transient test is essentially conducted by creating a pressure disturbance in the reservoir and recording the pressure response at the wellbore, i.e., bottom-hole flowing pressure pwf,

Vietnam National University - Ho Chi Minh City

University of Technology

Faculty of Geology & Petroleum Engineering

Department of Drilling - Production Engineering

References

Chapter 7

Well Test Analysis

Transient Well Testing

Pressure transient testing is designed to provide the engineer with a quantitative analysis of the reservoir properties A transient test is essentially conducted by creating a pressure disturbance in the reservoir and recording the pressure response

at the wellbore, i.e., bottom-hole flowing pressure pwf, as a function of time

Drawdown test

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

Drawdown test

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

pwf = a + m log(t) where:

kh



 

Drawdown test

Drawdown test

Equation suggests that a plot of pwf versus time t on semilog

graph paper would yield a straight line with a slope m in

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:

● the skin factor;

● the additional pressure drop due to the skin

Pressure buildup test

Pressure buildup analysis

describes the buildup in

wellbore pressure with time

after a well has been shut in

One of the principal objectives

of this analysis is to determine

the static reservoir pressure

without waiting weeks or

months for the pressure in the

entire reservoir to stabilize

Pressure buildup test

Two widely used methods are discussed below; these are:

(1) the Horner plot;

(2) the Miller–Dyes–Hutchinson method

pws = wellbore pressure during

shut in, psi

Horner plot

The first contribution results

from increasing the rate from

0 to Qo and is in effect over the

entire time period tp + Δt,

Horner plot

The second contribution

results from decreasing the

rate from Qo to 0 at tp, i.e.,

shut-in time, thus:

o t w

Q B p

Horner plot

where:

pi = initial reservoir pressure, psi

pws = sand face pressure during pressure buildup, psi

tp = flowing time before shut-in, hours

Qo = stabilized well flow rate before shut-in, STB/day

t = shut-in time, hours





162.6Q B o o o m

kh





Horner plot

referred to as the Horner

plot, is illustrated in Figure

Note that on the Horner

plot, the scale of time ratio

(tp + Δt)/Δt increases from

right to left It is observed

from Equation 1.3.6 that pws

= pi when the time ratio is

means that the initial

reservoir pressure, pi, can

extrapolating the Horner

plot straight line to (tp +

Δt)/Δt = 1

Example

Table 2.2 shows the pressure buildup data

from an oil well with an estimated drainage

radius of 2,640 ft Before shut-in the well

had produced at a stabilized rate of 4900

STB/D for 310 hours Know reservoir data

● the average permeability k;

● the skin factor;

● the additional pressure drop due to skin

Applying the above mathematical assumption to Equation 2.11, gives: 𝑝𝑤𝑠 = 𝑝∗ − 𝑚 log 𝑡𝑝 − log ∆𝑡

or: 𝑝𝑤𝑠 = 𝑝∗ − 𝑚 log 𝑡𝑝 + 𝑚 log ∆𝑡

This expression indicates that a plot of p ws vs log(∆t) would

produce a semilog straight line with a positive slope of +m that is

Miller–Dyes–Hutchinson method

The semilog straight-line slope m has the same value as of the

Horner plot This plot is commonly called the

Miller-Dyes-Hutchinson (MDH) plot The false pressure p * may be estimated from the MDH plot by using:

𝑝∗ = 𝑝1ℎ𝑟 + 𝑚𝑙𝑜𝑔(𝑡𝑝 + 1) (2.12) Where 𝑝1ℎ𝑟 is read from the semilog straight-line plot at ∆t = 1 hour

Type Curves

 Introduction

 Type Curve Approach

 Gringarten Type Curve

The reservoir and well parameters, such as permeability and skin, can then be calculated from the dimensionless parameters defining that type curve

Introduction

The dimensionless variable pD

Taking the logarithm of both sides of this equation gives:

For a constant flow rate, Equation indicates that the logarithm of

dimensionless pressure drop, log(pD), will differ from the

logarithm of the actual pressure drop, log(p), by a constant

Introduction

Similarly, the dimensionless time tD

Taking the logarithm of both sides of this equation gives:

2

0.0002637 log( )D log( ) log

Introduction

Hence, a graph of log(p) vs

log(t) will have an identical

shape (i.e., parallel) to a graph

of log(pD) vs log(tD), although

the curve will be shifted by

log[kh/(141.2QBμ)] vertically in

log[0.0002637k/(ϕμc t r w 2)]

horizontally in time This

concept is illustrated in Figure

1.46

Introduction

Taking the logarithm of both sides of this equation, gives:

Equations 1.4.3 and 1.4.5 indicate that a graph of log(p) vs log(t) will have an identical shape (i.e., parallel) to a graph of log(pD) vs

log(tD/rD2), although the curve will be shifted by

log(0.0002637k/ϕμc t r 2) horizontally in time When these two curves are moved relative to each other until they coincide or

“match,” the vertical and horizontal movements, in mathematical terms, are given by:

Type Curve Approach Step 1 Select the proper type curve, e.g., Figure 1.47

Step 2 Place tracing paper over Figure 1.47 and construct a log-log

scale having the same dimensions as those of the type curve This can

be achieved by tracing the major and minor grid lines from the type curve to the tracing paper

Step 3 Plot the well test data in terms of p vs t on the tracing paper

Step 4 Overlay the tracing paper on the type curve and slide the actual

data plot, keeping the x and y axes of both graphs parallel, until the

actual data point curve coincides or matches the type curve

Step 5 Select any arbitrary point match point MP, such as an

intersection of major grid lines, and record (Δp)MP and (t)MP from the

actual data plot and the corresponding values of (pD)MP and (tD/r D 2)MPfrom the type curve

Step 6 Using the match point, calculate the properties of the reservoir

Gringarten Type Curve

D

t p

C



1 ln( ) 0.80901 2 2

Gringarten Type Curve

or, equivalently:

Equation 1.4.8 describes the pressure behavior of a well with a wellbore storage and a skin in a homogeneous reservoir during the transient (infinite-acting) flow period Gringarten et al (1979) expressed the above equation in the graphical type curve format shown in Figure 1.49 In this figure, the dimensionless

pressure pD is plotted on a log-log scale versus dimensionless

time group t /C The resulting curves, characterized by the

s D

Gringarten Type Curve

Gringarten Type Curve

There are three dimensionless groups that Gringarten et al used when developing the type curve:

(1) dimensionless pressure pD;

(2) dimensionless ratio tD/CD;

(3) dimensionless characterization group CDe2s

The above three dimensionless parameters are defined mathematically for both the drawdown and buildup tests as follows

Gringarten Type Curve

Gringarten Type Curve

0.0002637

0.8396

t w D

Gringarten Type Curve

Equations 1.4.10 and 1.4.12 indicate that a plot of the actual

drawdown data of log(p) vs log(t) will produce a parallel curve that has an identical shape to a plot of log(pD) vs log(tD/CD) When displacing the actual plot, vertically and horizontally, to find a dimensionless curve that coincides or closely fits the actual data, these displacements are given by the constants of Equations 1.4.9 and 1.4.11 as:

Gringarten Type Curve

For drawdown

Dimensionless characterization group CDe2s

When the match is achieved, the dimensionless group CDe2s

describing the matched curve is recorded

2

5.615 2

Gringarten Type Curve

For buildup

All type curve solutions are obtained for the drawdown solution

Therefore, these type curves cannot be used for buildup tests without restriction or modification The only restriction is that

the flow period, i.e., tp, before shut-in must be somewhat large However, Agarwal (1980) empirically found that by plotting the

buildup data pws − pwf at t = 0 versus “equivalent time” Δteinstead of the shut-in time t, on a log–log scale, the type curve

analysis can be made without the requirement of a long drawdown flowing period before shut-in Agarwal introduced

the equivalent time Δte as defined by:

Gringarten Type Curve

Gringarten Type Curve

Gringarten Type Curve