Part_5_Semilog Analysis for Oil Wells

Semilog Analysis for Oil Wells - WTA 1

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Upon completion of this section, the student should be able to:p p

1. Analyze a constant-rate drawdown test using semilog analysis.

a. Identify the data that correspond to the middle time region on the diagnostic plot.

b. Calculate permeability and skin factor from a semilog graph.

2. Analyze a buildup test following a constant-rate flow period using the Horner method.

a. Calculate the Horner pseudo-producing time for variable rate production.

b. List the conditions that must be satisfied for the Horner pseudo-producing time to be applicable without referring to the text.

c. Identify the data that correspond to the middle time region on the diagnostic plot.

d. Calculate permeability, skin factor, and initial pressure from a Horner graph for a buildup test in a well in an infinite acting

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Horner graph for a buildup test in a well in an infinite-acting reservoir.


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Note that the skin factor affects the pressure response only within p p ythe altered zone. The pressure profile at points beyond the radius of the altered zone is not affected by the skin factor.We have already seen that the additional pressure drop due to skin at the wellbore can be calculated from the flow rate and fluid and rock properties.We can modify the Ei-function solution to apply for 2 cases: 1) at the wellbore, and (2) beyond the altered zone.

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Neither of these expressions is valid within the altered zone.pNeither of these expressions is valid until after the logarithmic approximation to the Ei-function becomes applicable throughout the altered zone.

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When < 0 01 we may use the logarithmicrc948 2wtφμWhen < 0.01, we may use the logarithmic

approximation to the Ei-function in the equations given in the

previous slide.

ktwtφμ

This expression may be written in the same form as the equation

of a straight line.y~pwf

( ) x~tlog10

m~kh

qB6.162 μ−

b~s869.023.3klogkh

qB6.162p 210i⎥⎥⎤

⎢⎢⎡

+−⎟⎟⎞

⎜⎜⎛μ

−

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rckh 2wt ⎥⎦⎢⎣⎟⎠

⎜⎝ φμ


A graph of pwf vs. log10(t) should fall on a straight line.g p pwf g10( ) g

Slope m allows us to estimate permeability.

Intercept b (which is usually referred to as p1hr), allows us to estimate skin factor s.

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Slope mp

(t1, pwf1), (t2, pwf2) are any two points on the straight line portion of the graph.

( ) ( )110210

12

loglog ttpp

m wfwf

−−

=

Normally, t1 and t2 are chosen to be powers of 10.For best accuracy, pick points several log cycles apart.

The point p1hr is the pressure on the best straight line through the data at a time of 1 hr. It may be necessary to extrapolate the straight line to a time of 1 hr to read p1hr.In a real test, all, some, or none of the data points may fall on a straight line of the correct slope.This “correct semilog straight line” corresponds to the data identified as the middle-time region on the diagnostic plot based

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on pressure-derivative as shown in the next slide.


( ) ( )110210

12

loglog ttpp

m wfwf

−−

=

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The data summarized below were recorded during a pressure drawdown test from an oil well. Estimate the effective permeability to oil and the skin factor using the graphical analysis technique for a constant-rate flow test.

q = 250 STB/D pi = 4 412 psiaq 250 STB/D pi 4,412 psiah = 46 ft φ = 12%rw = 0.365 ft B = 1.136 RB/STBct = 17 x 10-6 psi-1 μ = 0.8 cp

Pressure Drawdown Test Data for Exercise 10

t pwf t pwf 2 3510.3 18 3414.5 3 3492.7 24 3402.0 4 3480 1 30 3392 34 3480.1 30 3392.36 3462.4 36 3384.3 8 3449.9 48 3371.8 10 3440.2 60 3362.1 12 3432.2 72 3354.1

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15 3422.5


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Consider the rate history for an idealized buildup test. A well is y pproduced at rate q for a time tp, then is shut in for a buildup test. The rate history can be represented as the algebraic sum of two different constant rate flow periods – one at rate q, beginning at t = 0, and another at rate -q, beginning at Δt = 0.

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The pressure response for the rate history shown on the previous p p y pslide can also be obtained by adding the pressure responses from each of the two rate flow histories.

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The second term on the RHS of this equation gives the pressure q g pchange due to production at constant rate q beginning at t = 0.

The third term on the RHS of this equation gives the pressure change due to injection at constant rate q beginning at t = tp, or Δt = 0.

This equation can be simplified by canceling terms within the square brackets, as shown on the next slide.

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As with the drawdown equation, this equation may also be written q , q yin the same form as the equation of a straight line.

y~pws

x~tt

log p10 ⎟⎟

⎞⎜⎜⎛ Δ+

xt

log10 ⎟⎟⎠

⎜⎜⎝ Δ

m~kh

qB6.162 μ−

b~pi

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The quantity is called the Horner time ratio.t

ttp

ΔΔ+

q y

A graph of pws vs. should fall on a straight line

tΔ

⎟⎟⎠

⎞⎜⎜⎝

⎛ΔΔ+t

ttlog p

10

Slope m of the resulting straight line allows us to estimate permeability

Intercept b at = 0 or = 1 gives us the initial pressure pi.

⎟⎟⎠

⎞⎜⎜⎝

⎛ΔΔ+

ttt

log p10 ⎟⎟

⎠

⎞⎜⎜⎝

⎛ΔΔ+

tttp

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The slope m is obtained from .tttt

ppm 1ws2ws

⎟⎞

⎜⎛ Δ+

⎟⎞

⎜⎛ Δ+

−=

( , pws1) and ( , pws2) are any two points on the

straight line portion of the graph.

Normally and are chosen to be powers of 10

ttt

logt

ttlog

1

p10

2

p10 ⎟⎟

⎠

⎞⎜⎜⎝

⎛ΔΔ+

−⎟⎟⎠

⎞⎜⎜⎝

⎛ΔΔ+

1

p

ttt⎟⎟⎠

⎞⎜⎜⎝

⎛ΔΔ+

2

p

ttt⎟⎟⎠

⎞⎜⎜⎝

⎛ΔΔ+

p

ttt⎟⎟⎠

⎞⎜⎜⎝

⎛ΔΔ+ p

ttt⎟⎟⎠

⎞⎜⎜⎝

⎛ΔΔ+

Normally and are chosen to be powers of 10.

For best accuracy, pick points several log cycles apart (Why?)

In a real test, all, some, or none of the data may fall on a straight line of the correct slope. This “correct semilog straight line” corresponds to the data identified as the middle-time region on the

1t ⎟⎠

⎜⎝ Δ

2t ⎟⎠

⎜⎝ Δ

diagnostic plot.Note that the HTR on the x-axis decreases from left to right, so that shut-in time increases from left to right. You may also see Horner plots drawn with HTR increasing from left to right. When this is the case, be aware that shut-in time increases from right to left, as h i th t lid

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shown in the next slide.


.tttt

ppm 1ws2ws

⎟⎞

⎜⎛ Δ+

⎟⎞

⎜⎛ Δ+

−=

ttt

logt

ttlog

1

p10

2

p10 ⎟⎟

⎠

⎞⎜⎜⎝

⎛ΔΔ+

−⎟⎟⎠

⎞⎜⎜⎝

⎛ΔΔ+

1

p

ttt⎟⎟⎠

⎞⎜⎜⎝

⎛ΔΔ+

2

p

ttt⎟⎟⎠

⎞⎜⎜⎝

⎛ΔΔ+

p

ttt⎟⎟⎠

⎞⎜⎜⎝

⎛ΔΔ+ p

ttt⎟⎟⎠

⎞⎜⎜⎝

⎛ΔΔ+

1t ⎟⎠

⎜⎝ Δ

2t ⎟⎠

⎜⎝ Δ

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To estimate the skin factor from a buildup test, we have to know p ,the flowing bottomhole pressure at the instant of shutin, pwf.

The point p1hr is the pressure on the best straight line through the data at a shut-in time of 1 hour. It may be necessary to extrapolate the straight line to a Horner time ratio corresponding p g p gto a shut-in time of 1 hour in order to read p1hr.

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*Wells are almost never produced at exactly constant rate prior to p y pshut-in.

*Variations in rate prior to shut-in can be accounted for in many cases by the use of the Horner pseudoproducing time approximation. When this approximation is used, the buildup analysis is performed by treating the well as if it had produced at y y grate qlast for a time tp.

*This approximation applies when the well produced at rate qlastfor a period at least 10x as long as the duration of the shut-in period.

*If the last rate q is lower than the average production rate theIf the last rate qlast is lower than the average production rate, the Horner pseudoproducing time will be longer than the actual elapsed production time.

*The Horner pseudoproducing time preserves material balance. That is, a well producing at a constant rate qlast for a time tp will produce exactly the same amount of fluid as the actual variable

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produce exactly the same amount of fluid as the actual variable rate history.

*qlas must be stabilized……….!!!


A pressure buildup test was conducted on a well early in the lifeof an oil reservoir having the properties summarized below. Thewell was produced at a constant rate of 80 STB/D for 999 hoursprior to being shut in. Determine the effective permeability to oil,the original reservoir pressure and skin factorthe original reservoir pressure, and skin factor.

μ = 2.95 cp ct = 15 x 10-6 psi-1rw = 0.25 ft h = 32 ftφ = 15% B = 1.25 RB/STBq = 80 STB/D tp = 999 hrspwf = 1847.8 psia

Pressure Buildup Test Datat HTR pws t HTR pws

2 2615.1 18 2662.56 5 8 66 53 2623.9 24 2668.64 2630.1 30 2673.36 2638.9 36 2677.18 2645.1 48 2683.1

10 2649.9 60 2687.7

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12 2653.8 72 2691.415 2658.6

Semilog Analysis for Oil Wells - PTT Interpretation and Analysis 32

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Part_5_Semilog Analysis for Oil Wells

Documents

oil wells wta

semilog graph

wt semilog analysis

correct semilog straight

best straight line

straight line portion

horner graph

altered zone