inflow limitations.doc

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3 Inflow limitations

3.1 Changing the flow conditions around the well.

During the drilling is rock is crushed and fluid filtrate seeps into the reservoir around the well.During the completion is well exposed to various measures, such as: perforating, setting of sand

screen, or injection of acid. An overview of changes in formation around the well, formation

damage, because of the intrusion of various fluids, physic-chemical reactions formation minerals

and mechanical blocks are provided by Krueger/1986 /. During the production, the pressuredecreases and flow erosion can happen. Since all produced fluid must flow through the area around

the well, the changes here have a great effect on productivity.

Changes around the well can often be rectified, for example, by re-perforating, affecting with acid,

or hydraulic fracturing. This can yield major productivity gains. Therefore, it is important to be

able to identify any changes around the well, or preferably avoid such in the first place.

A classic way to quantify the effect of change in the flow conditions is by the flow effectiveness:the relationship between actual production and non-profit rate, as it would have been without the

changes around the well

oo J

J

q

qE == (3-1)

E: the flow efficiency (-)q : actual production

qo: production in the same well pressure, without the flow changes

Figure 3-1 illustrates a hypothetical case in which the filtrate from the drilling fluid has

entered the formation and reduced permeability in a zone closest to the well. As a result,

when the well pressure at a given production will be: pw, while it without any loss of

permeability would have been: pow. If the drift of the affects zone follows Darcy's law,and we know the intrusion radius: rd, and permeability: kd, we can expect out into the

currents strong. But this is not possible to measure this in real life wells.


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Figure 3.1 Inflow with reduced permeability of the well

Van Everding / 1953 / found a way to determine the pressure loss due to changes around the well,according to analysis of the transient pressure response. He introduced the concept of skin

pressure: ps, and represented by a dimensionless skin factor

Shk2

Bqp ooos

= (3-2)

S : dimensionless skin factorps: skin pressure loss (extra pressure because of the flow changes)

3.2 Estimating skin factor


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Skin factor may be estimated by comparing the transient response under the pressure and

flow of eviction.

Figure 3.2 shows the flow toward the well, after start-up as we see the full influx rate

quickly established around the well and gradually for plants across the reservoir. Reduced

permeability just around the well will therefore almost immediately provide an additionalpressure; skin pressure loss.

Figure 3.2 Transient, radial flow to the well

When the well is closed, the influx almost immediately be zero just around the well. Skin pressure

loss due to reduced permeability just around the well will then also disappear. Farther out in the

reservoir will flow to continue any longer, and cause the pressure building. Skinpressure loss inother words, does the production, but not at the press building. We can thus find skin pressure loss

by comparing the transient pressure response in manufacturing and building.

The total press response by transient production is expressed by (2-20), by adding the skin pressure

as a constant part

( ) swo

oooiw p

rc

tk

hk

Bqptp +

+=

2

4ln

4

(3-3)


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If we produce through a period of time: t, and then close the well, we can express response to

pressure by add (superpose) pressure response to production: qo in the period: tp + t h; and press

response for injection: - qo, during the period : t

( ) ( )t

tt

hk

Bqpttptp

pooo

ipww

++=+= ln

4

(3-4)

tp: time from production to eviction

t : time of eviction

The pressure response before the eviction (3-3), and of eviction (3-4) is outlined in Figure

3.3. By comparing these, we can estimate the skin pressure loss


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Figure 3.3 Pressure structure with and without skin

3.3 Productivity index for vertical wells with skin

Skin pressure loss amounts to an addition to the calculated pressure for the assumed

homogeneous reservoir

s

w

eoooRw p

4

3

r

rln

hk2

Bqpp

+

+=

(3-5)

By combining (3-2) and (3-5), we can express the pseudo steady productivity index for

vertical wells with skin

+

=

=

S43

rrlnB

hk2

pp

qJ

w

eoo

o

wR

ops

(3-6)

the flow just around the well is the same for steady and pseudo-steady wells. The steady

productivity index is therefore

+

=S

r

rB

hkJ

w

eoo

ost

2

1ln

2

(3-7)

We see that the productivity index with skin (3-6), (3-7), which remain constant, so that

in flow characteristics, we continue to be linear. This means that the measurements ofstabilized well pressure at different rates can not distinguish between the skin and the

general low permeability. The distinction is important, because a skin often can be

removed. There is less we can do if the permeability is low in the reservoir.

3.4 Factorsthat determine the skin factor and the flow

efficiency

If we know how the flow conditions around the well is, we will be able to calculate skin

factor and the flow efficiency. Such calculation gives an idea about how the changes of

various parameters affecting the well productivity.

If we are based on a homogeneous permeability reduction as illustrated in Figure 3-1, we

can set up the following relations for the pressure loss between the intrusion radius, rd,

and the well:


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- expressed by the actual permeability of the invaded zone

( )w

d

d

ooowd

r

rln

hk2

Bqpp

=

- expressed by the unaffected permeability, plus skin factor

( ) Shk2

Bq

r

rln

hk2

Bqppp ooo

w

dooos

o

wd

+=+

Since the expressions above describes the same pressure drop, we can put them equal. Itprovides the following link between skin factor and the permeability of the invaded zone

w

d

d r

r

k

kS ln1

= (3-8)

The result above is of little use to the prediction. But it indicates how the skin factor

depends on the permeability and invasion. in other words Skin factor quantify, changes

around the well; affected by: production rate, fluid properties , approximately height andouter boundary conditions.

For radial geometry and pseudo steady conditions, we can express your ideas with andwithout skin factor by equation (3-6). The connection between the flow efficiency (3-1)

and skin factor will then be

Sr

r

rr

E

w

e

w

e

+

=

4

3ln

4

3ln

(3-9)

In other words, flow efficiencydepends on both the skin factor and distance to the outerboundary: re

Equation (3-9) indicates that there is no linear relationship between skin factor and the

flow efficiency.

3.5 Geometric skin

Perforation, sands cores and other completion choices can change the flow conditions inthe well, even if they do not change the flow properties in rock. This is often called

geometric skin.


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3.5.1 Perforation skin

Perforation means that a shoot holes through the feeding cemented pipe, into the rock.The flow would then be radial, until it is approaching the trengings the depth of the

perforation, and then flow against each perforation channel as outlined in Figure 3.4

below

Figure 3.4 To the flow of perforated, and to open well

The classic way to study the effect of perforation channels is from the electrical analog

models.Typically, a salt mixture (such as copper sulfate) represents the reservoir, a plastic pipe

represent wall of the well, and the copper strings out from the plastic pipe, to representperforation channels. The electric power will then represent the fluid power, tension

represent the pressure, and conductivity of electrolytes and copper stringsrepresents permeability in rock and perforation channels. Figure 3.5 shows a graphic

illustration of perforation skin, based on such measurements


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Figure 3.5, graphical representation of skin from the perforation

3.5.2 Skin due to the partial completion

With the partial completion, we understand that the well is only completed over parts of

the productive reservoir, as shown in Figure 3.6. This may have occurred because oferrors. Or it may be intentional, for example, to avoid consolidated party.


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Figure 3.6 Flow convergence of partial completion

Muskat / 1937 / showed that the steady production capacity, with the partial completion

could approach that

( ) ( )

( ) ( )

=

ew

oo

we

o

r

h4ln

h~

125.01h~

875.01

h~

125.0h~

875.0ln

r

h4ln2

h~

2

1B

kh2

pp

q

(3-10)

there: h

hh

p=~

and ( ) is gamma function:

=0

1)( dxexn xn

Skin factor can be expressed from the solutions (3-10) above

( ) ( )( ) ( )hhhh

hr

h

h

hS

w

~125.01

~875.01

~125.0

~875.0

ln~2

14ln~

~1

= (3-11)

At the approach of the gamma function, (3-11) becomes


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( ) ( )( ) ( )hh

hh

hr

h

h

hS

w

~125.0

~875.0

~125.01

~875.01

ln~2

14ln~

~1

(3-12)

By the variety area: { }99.005.0~

== hhh p , which corresponds to skin factor:

{ }070=S , are estimates from(3-11), and simplification (3-12) almost coincide

3.5.3 Skin because of gravel packing

Many wells are equipped with different types of gravel packages, to support the formation and

prevent the flow of sand particles in the well. Gravel size is selected so that the packing

accompany to drop the very small particles through but keep bigger back. If all the particles were

stopped, gravel packing company would soon be close.

Gravel packages generally have very high permeability, but when the gravel stops particles from

the formation, the flow channels gradually become closer. the currents move through the pack arealso often so great that it gives extra 2.-order pressure loss.

One consequence of that gravel pack filled with the formation of particles, is that the flowproperties through the packing (permeability and turbulence factor) match better with the flow

characteristics in formation, than with the original flow properties of gravel pack. Unneland /

2001 / provides an overview of the principles, experience and correlation to predict the flowresistance because of gravel packages. The work is primarily related to internal gravel seals on the

Gullfaks field.

3.5.4 Skin because of the wellbore inclination

Reservoir layer is often not horizontal. Wells that are drilled vertically will often be angled inrelation to the reservoir. A lot of wells are also in output punk drilled with a certain inclination. At

the moderate slant will do influx be radial to a certain distance from the well, and then depart as

indicated in Figure 3.7. It may therefore be reasonable to quantify pressure discrepancy as ageometric skin.


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Figur 3.7 Flow towards an inclined well

Cinco-Ley & al / 1975 / calculated productivity of inclined wells (by source-sink

method). From the numerical results, they produced the following skin factor correlation

w

C

r

hS

100

log

5641

10

865.106.2

=

.. for : < 75o (3-13)

: inclination angle (degrees)

h : height of the reservoir( m )

rw : well radius ( m )

This geometric skin factor is used to correct the productivity formulas for vertical wells,

for the slant in relation to the reservoir. Figure 3.8 illustrates (3-13).


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Figure 3.8 Skin factor for the slant, according to Cinco-Ley's correlation

We see that the skin is a negative factor: slant enhances productivity by providing longer-

perforated interval. At the large slant, the negative skin pressure loss will dominate theproductivity index. This means that the productivity index that differs very much from

the radial, as assumed in the point of output.Estimation methods dominated by empirical correlation veil the relationships between theparameters, decision-making and productivity. It may therefore be sensible to limit the

use of Cinco-Ley's correlation to less than 45o, so that the skin is not the negative factor is

far too large. Productivity index of greater inclination should rather be based on the

formula horizontal wells, as shown in Chapter 5.

3.7 Deviation from linear Inflow performance

At sufficiently high flow rates, the inflow characteristics

are not linear. The pressure loss will almost always be

greater than predicted from a constant productivity index.

Below, we quantify flow mechanisms that provide such a

discrepancy.


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3.7.1 Second order pressure loss

Darcys equation implies proportionality between flow

velocity and pressure gradient. Similar relations are used

for other engineering applications, such as: Ohm's law ofelectric resistance, Hooks elasticity law, Fourier's heat

flow law. However such relations are often not applicable at

high rate, or large load..

Forchheimer (1901) proposed a relationship that can be seen

as Darcys equation with a 2.order adjustment

vvvkdr

dp o

+= (6-1)

: Second-order constant, "turbulence factor" (m-1)

From Forchheimer equation (6-1), we can predict therelationship between pressure loss and rate. By assuming

radial and steady-state influx, we get the following

solution

( ) ( ) ooe

22

2

ooo

eooe qq

r

1

r

1

h4

Bq

r

rln

kh2

Brprp

+

=

(6-2)

The first part of (6-2) corresponds to Darcys law. The

second part is independent of viscosity and increases with

the square of flow rate, corresponding to turbulent flow

resistance in pipes. Truly turbulent flow does not occur in

porous media under normal circumstances; the pore channels

are too narrow and flow speed too low. But the flow changes

velocity and direction through the pores. For complicated

pore geometry we can expect relatively large -factor. Forrelatively straight and smooth flow channels, we can expect

little -factor.

Figure 3.9 illustrates 2.order pressure profile with low

viscosity and high production. The figure shows significant

pressure loss near the well. Further out the flow speed is

so small that 2.order pressure loss is negligible.


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Figure 3.9 Pressure profile according to Forchheimer

equation.

Figure 3.9 shows that the deviation from Darcys equation

occurs close to the well. Flow will hear be very close to

steady-state. there (near the wellbore). This will hold even

if the conditions further out is pseudo-steady-state, or

even transient. Thus, the well pressure can be expressed as

21ooRw Fqq

Jpp = (6-3)

By matching the (6-2) and (6-3), we get the following

relation for 2.order pressure loss parameter

w

oo

rh

BF

1

422

2

= (6-4)

Figure 3.10 illustrates 2.order inflow characteristics,

estimated from (6-3), for the same parameters which formed

the basis for Figure 6-1: [J=1.01 . 10-8 Sm3/s/Pa, F=1.14 . 109Pa/(Sm3/s)2 ] .


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Figure 3.10 Second order inflow characteristics

Estimate of 2.order inflow performance from measured data.

We can estimate 2.order inflow performance from measuredwell pressure and production rates. For graphical estimation

it is practical to express (6-3) as

o

o

wR FqJq

ppy +=

=

1(6-5)

Figure 3.11 shows pressures and production rates plotted

according to (6-5). If a straight line can be drawn through

the data points, the slope is equal to: F and the

intersection with the y-axis corresponds to: 1 / J


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Figure 3.11 Graphical estimate of 2.order flow parameters

The points shown in Figure 6.3 are "simulated measurements"

and the straight line is adapted visually. The intersection

with the y-axis provides the estimate: 1 / J = 0.0115,

productivity index: J = 87 Sm3/d/bar (Estimation of "F " isleft to the reader)

Turbulence factor correlated to the rock parameters

The -factor is often correlated to porosity andpermeability. The correlation by Tek & al (1962), Katz &

Coats (1968) is illustrated in Figure 3.12

( )75.025.1

9

k

103048.0/5.5

= (6-6)

k : permeability (mD)

: porosity ( - )

: turbulence factor (m-1)


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Figure 3.12 Correlation of --factor in natural rockSecond-order pressure losses in gravel packs

By gravel packing, we understand that the granular material

is placed between the rock and well to prevent flow of

reservoir fines into the well. The flow rate through such

gravel packs is often so high that it may give significantly

pressure loss.

Experience shows that -factor for gravel pack correspondsbetter to the permeability of the reservoir rock than the

permeability of the gravel. This is explained by that the

production will transport fines from the formation into the

sand pack. Unneland (2001) provides an overview of different

correlations and -factor for gravel pack and comparisonwith data for North Sea fields.

3.7.2 Flow below saturation pressure.

Physical mechanismsWhen the pressure falls below the saturation, gas is

released. This leads to a number of changes in fluid

behavior and flow conditions:


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- The total flow volume gets larger

- Viscosity of oil becomes larger because of less dissolved

gas

- gas and oil fill pores and will therefore have different

permeabilities

- Density difference may make gas will filter upwards

Such changes affect the pressure loss, as illustrated in fig

3.13

Figure 3.13 Inflow below saturation pressure

Vogels inflow performance

Vogel (1968) performed numerical simulations with pressures

below saturation. By systematizing numerical results he

found that the inflow performance could be expressed by the

following non-dimensional relationship


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2

s

w

s

w

max

o

p

p8.0

p

p2.01

q

q

=

(6-8)

qmax : Extrapolated production capacity at zero pressure well

ps : Reservoir pressure at saturationVogels characteristics curve (6-8) shows that the

productivity index decreases with decreasing well pressure.

The comparable dimensionless inflow performance for constant

productivity index reads

s

w

*

o

p

p1

q

q= (6-9)

From (6-9) follows that the comparable production capacity

at zero well pressure: q* =JpRMarshall B. Standing observed that at saturation pressure

(6-8) and (6-9) should provide the same productivity index.Thus, the gradients of (6-8) and (6-9) should be equal at

saturation pressure, as illustrated in Figure 3.14. This

gives the following relationship

max

* q8.1q = (6-10)


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