spe-31087-ms selection of screen slot with to prevent plugging and sand production
TRANSCRIPT
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SPE 31 87
Society of Petroleum Engineers
Selection of Screen Slot Width to Prevent Plugging and Sand Production
P.
Markestad, SPE, and 0 Christie, RF Rogaland Research, and Aa. Espedal, SPE, Statoil,
and
0.
R0rvik, SPE, Saga Petroleum as;
Copyright, 1996, Society of Petroleum Engineers, Inc.
This paper was prepared for presentation at the SPE Formation D amage Control Symposium
held
in
Lafayette, U.S.A., 14-15 February, 1996.
This paper was selected for presentation be an SPE Program committee following review of
information contained in an abstract submitted by the author(s).
C_ontents
of the
pap.er
as
presented have not been reviewed by the society of Petroleum Eng1neers and.are subject to
correction by the author(s). The materi.al, as
~ r e s ~ n t e d
does not necessanly reflect and
position of the society of Petroleum Engineers, off1cers or members. Papers
p r e s e ~ t e
at
SPE meetings are subject to publication review by Editorial Committees of the
soc1ety
of
Petroleum Engineers. Permission to copy is restricted to an abstract of no.t more
t h ~ n
300
words. Illustrations
may
not be copied. The abstract should con a1n. con.splcuous
acknowledgement of where and by whom the paper was presented. Wnte L1branan SPE,
P.O. Box 833836, Richardson, TX 75083-3836, U.S.A., f ax (+1) 214-952-9435.
bstract
A numerical model has been developed that addresses both
plugging of, and sand production through single wrapped
screens. The model was developed on the basis of a fractal
model for the particle size distribution of reservoir sands. A
database of sand types from the North Sea and Haltenbanken
areas was established. Principal component analysis was
used to reduce the number of significant variables in the
database, and to provide a basis for a prediction model for
critical slot widths. A series of laboratory experiments were
performed, and four critical slot widths were identified for
each sand type, defining a safe design interval for screen slot
width. A mathematical model was developed that can be
used to predict the critical slot widths for other sand types
from the area.
Introduction
Single, wire wrapped screens with keystone shaped wire
have been used to control sand production in oil and gas
wells since the 1930 s. They have the advantage over
prepacked screens in that they do not become p l ~ g g e as
easily by drilling mud. Furthermore they functiOn as a
surface filter, where the plugging material is easily removed,
whereas prepacked screens are depth filters where plugging
material tends to get trapped inside the prepack.
Single wrapped screens do, however, have a reputation
for being susceptible to plugging and/or sand production
when designed according to the various traditional criteria
(Refs. 1 and 2). This indicates that the design criteria for
single wrapped screen completions should be revised.
Sand control with screens is basically a function of the
relationship between particle size and screen slot width. The
pioneering work was published by Coberly (Ref.3) in 1937.
Coberly concluded that spherical particles could generally be
retained when the slot width was 2.5 times the particle
diameter or smaller. He also stated that in a mixture
of
particles of different size, the sand control properties of a
155
screen depends on the largest particles in the mixture. He
suggested that screen completions should be designed with
screen slots that were 2 times wider than the
1
of the
formation sand. He did not address the problem of screens
becoming plugged by fines from the formation sand. This
criterion has been used in California, while slot widths equal
to d
1
has been used on the U.S. Gulf Coast area (Ref. 4).
In this paper it is shown that the design criterion
suggested by Coberly, or any other criteria based on a single
point on the particle size distribution curve, can not
adequately describe either sand production or plugging of
single wrapped screen. Instead a method is developed where a
more complete description
of
the particle size distribution is
used
to
predict the plugging and sand control properties
of
single wrapped screens.
The study described in this paper has been limited to one
screen type, single wrapped screens, and erosion of the
screens have not been considered. An extension
of
the study
is
currently being planned that will include alternative screen
designs, and also compare the susceptibility of the various
screen types to erosion.
Description of the particle size distribution
In a traditional presentation of the results from a sieve
analysis, the accumulated mass percentage of particles larger
than a certain diameter is plotted on a semi-logarithmic
scale.
Since the particle distribution is plotted as a function
of
particle mass, the distribution function will emphasise the
largest particles. When the purpose is to describe plugging
of screen slots, it is more relevant to concentrate on the
smaller particles. It is obvious that a particle matrix with
zero porosity will be able to plug a screen slot completely
as long as it contains particles large enough to be retained
by the slot.
Such a particle mixture must consist of large particles
with smaller particles that fit into the pores between the
large particles, still smaller particles that fit into the pores
between the small particles, and so on down to the
molecular level (Fig. 1). Finally, mathematical speaking,
there will be an infinite number of infinitely small particles
with an infinitely small total volume. This type of particle
size distribution is described by Kaye in Ref. 5. The
function is based on the number
of
particles instead of
particle mass. The accumulated number of particles larger
than a certain diameter is described by the p ower function
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SELECTION OF SCREEN SLOT WIDTH TO PREVENT
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SPE 31 87
N d;;,di)=K
r I)
In a logarithmic plot this distribution will be represented
as a straight line with the slope
f.
The constant K is a
proportionality constant that depends on the size of the
sample. It is not important for the sand properties.
This function is also called a fractal particle size
ditribution, and the exponent
f
of eq. 1) is equal to the
fractal dimension of the sand matrix.
Theoretical arguments, that are beyond the scope of this
paper, indicate that a particle distribution with
2db the
smaller grains more than fill up the pore space between the
larger grains, and one can expect the sand to be relatively
stable. Smaller grains can not move through the matrix of
larger grains, e.g. during fluid flow through the matrix.
Also,
if
dk is not too small, this part
of
the sand taken
separately will have a finite porosity and permeability since
it is filled with connected pores of approximate size
dk.
The situation is the opposite in the part with grains
smaller than dk and f2 would make a stable,
permeable surrounding for the screen. The part with f
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SPE 31087
P
MARKESTAD 0 CHRISTIE AA. ESPEDAL 0 R0RVIK
3
on PCJ
and
PC
are fine and badly sorted, while sands with
high scores on
PCJ
and
PC
are coarse and well sorted.
It was found that these two principal components were
the most important ones for describing plugging and sand
control
of
single wrapped screens. The first component,
PCJ
explained 48% of the variation in the data and
PC2
explained 24%, in total 72% of the total variance for the
first 2 principal components.
The principal component analysis effectively reduces the
number of variables from 9
to 2
A total
of
5 sand types were chosen for laboratory
testing. The sand types and their database entries are shown
in Table 1. They were chosen on the basis of their scores
on PC1 and PC2 as illustrated in Fig. 2. Partic le size
distribution curves are shown in Figs. 3,4 and 5
The principal component analysis showed that there were
no
typical variation in the particle size distribution between
the various North Sea fields. Neither were there any
significant regional difference between the North Sea and the
Haltenbanken.
Experimental
procedures
Identification
of main experimental parameters.
In a typical North Sea sandstone reservoir, the variation in
both particle size and distribution is large. The permeability
often varies by a factor
of
100 within the reservoir. Thus,
design criteria that specifies one single optimum slot width
for each sand type are not very useful because it will be very
difficult to chose which sand to use
as
a basis for the design.
It would be more relevant
to
define a range of acceptable slot
widths for each sand type, and then attempt
to
select a screen
that will fit into this range for all the sand types in the
completed interval.
This approach was adopted in the present study. Four
slot widths were determined for each sand type:
d the largest slot size where severe plugging was
frequently observed.
d the smallest slot size where no plugging was
observed.
d the largest slot size where sand production did not
occur.
d the smallest slot size where continuous sand
production did occur.
The d and d slot widths should be considered as
extreme lower and upper limits that should not normally
be
exceeded, while d and d are lower and upper limits for
an
ideal screen design.
The other parameters that were recorded during the
experiments were:
Amount
of
produced sand and sand production mode
(initial, intermittent, continuous)
Permeability ratio and skin factor for each sand type, slot
width and flow rate
Nature of plugging (permanent or removable)
Particle size distribution of produced sand.
Experimental
set
up. The screen filtration experiments
were performed in a radial flow cell as illustrated in
Figs. 6 and 7. The experimental set-up consisted of an
adjustable pump, a radial flow cell representing a 22.5
section of a well with a 7 5 screen, a sand trap and a fluid
reservoir. The radial cell was fitted with 2 differential
157
pressures sensors. One measures the differential pressures
created by flow through 150 mm
of
sand pack well away
from the screen. The other measures the differential pressure
across the screen and 5 em of sand adjacent to the screen.
The positions
of
the differential pressure measuring points
is illustrated in Fig. 6.
The concept
of
using a flow cell filled with loose,
unstressed sand was chosen because it was felt that this
would represent the worst case situation for sand production.
Differential pressures and flow rates as indicated in
Fig.
7 were logged on a computer running a data
acquisition program. Sand production was measured in a
graduated cylinder placed below the sand trap.
The actual particle size distribution of the formation sand
was approximated by mixing a range
of
sands with known
particle size distribution. The cell was flooded with single
phase, synthetic seawater during all the tests since this
represents a worst case situation with no capillary forces.
Test procedures.
Each sand was tested against screens
with slot widths ranging from
100
to
800 microns.
Each test .consisted of two parts. Initially the cell was
completely filled with sand and oriented with the screen at
the bottom. In this situation the screen was always in direct
contact with the sand. This corresponds
to
a well where the
annulus outside the screen is completely filled with sand.
In the second part of the test the cell was oriented with
the screen on top, and
3 4
em of sand was removed. This
was done
to
simulate an annulus that is not completely
filled with sand.
In
this situation liquid flowing towards the
screen will fluidize the sand and lift it towards the screen.
Fluid flow through the sand typically caused some
separation
of
fine material. Both sand production and
plugging did occur more easily in this situation.
Experimental results
The critical slot widths, determined from the experiments are
presented in Table
2
Discussion
General
flow
properties.
A sand control screen will
necessarily restrict the fluid flow into the well to some
degree, even when it
is
functioning
as
intended. Intuitively,
one should expect that the degree of flow restriction would
be a function of the screen slot width, the particle size
distribution of the sand, and maybe the rate
of
flow through
the screen. This turned out not
to
be the case, however, as
the skin factor varied unsystematically between 0.0 and 0.5
for all the sands and screen slot widths. Even
if
the
permeability of the sand varied from 0.2 Darcy for All to
20 Darcy forB
19
This can not be considered
to
be a serious
flow restriction, and it can be concluded that single screen
completions will not significantly restrict well production
as
long
as
they function
as
intended.
The slot area
is
typically only 5-10% of the total screen
area. Fluid flow will converge
on
the slots, and the fluid
velocity will increase
by
a factor
of
10 20 through the
slots, depending on the slot width and the width
of
the
wrapped wire. The converging flow results in a differential
pressure that is higher than expected from the Darcy
equation, where it appears as the observed skin factor. In
this way the flow properties
of
the screen is very dependent
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SELECTION OF SCREEN SLOT WIDTH TO PREVENT
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SP 31087
on the permeability
of
a thin layer
of
sand immediately next
to the screen.
If
the permeability
of
this layer is decreased by
contamination by fine particles, the skin factor will be high.
If the finer particles are produced away from this sand layer,
the skin factor will be low
or
negative. This conclusion is
supported by Runar Mfl)ller in Ref. 6. He showed that the
fines content
of
the layer of sand next to a screen tends to
become reduced with time, resulting in a small and often
negative skin factor.
Plugging
of single wrapped
screens. Plugging was
defined as a situation where the differential pressure across
the screen is more than two times as high as expected from
the Darcy equation.
Plugging
was
never
observed in the screen
down
position. In the screen up position, representing an annulus
which is not completely filled with loose sand, plugging
occurred to some degree for all the tested sand types except
for
All. The
severity
of
the plugging, and the width
of
the
slots that can be
plugged
depends on the particle size
distribution of the sand. Plugging was more likely to occur
when the flow was started suddenly at a relatively high rate.
Plugging in the screen up position was initiated by the
following mechanism: When fluid was flowing towards the
screen, the finest fraction of particles from the sand was
separated from the bulk of the sand and transported towards
the screen. These particles formed a filter cake along the
screen slots with a
much
lower permeability than the bulk
sand, restricting flow through the screen slots. This process
was typical for situations where the flow was initiated
suddenly, corresponding to a well that is brought on stream
suddenly at a high rate.
When the rate of flow was increased gradually, the first
particles that were separated from the bulk of the sand tended
to be small enough to pass through the screens. As the fluid
velocity increased, particles large enough to be retained by
the screen was lifted. But since most of the fines had already
been
produced
the resulting filtercake
did
not
have a
sufficiently low permeability to significantly restrict the
flow through the slots.
This mechanism can also explain why plugging was not
observed for the
All.
This sand has a very high fines
content, dominating the permeability of the bulk sand which
is very low. A filtercake consisting of the finest fraction of
the sand will not have a permeability that is significantly
different from the permeability
of
the bulk sand, and thus do
not reduce productivity through the screens.
The
filter
cake
that formed along the slots when they
became plugged, was generally thin and could be easily
removed.
I t
would often fall
off
by gravity alone if left
without fluid flow for some time. But some particles were
able to invade the slots and got trapped there. There are
however, no indications from the differential pressure
measurements that the trapped particles reduce the overall
flow efficiency of the screens.
Sand control properties
of
single screens. In
Table 3 the results from the present study are compared
with Coberly s criterion of
d
1
(Ref. 3) and with the
Gulf
Coast criterion of ld O (Ref. 4 .
It
is clear that sand is
generally produced through
much
narrower slots than 2
times the
d
1
of the sand.
The
d
1
diameters are very similar
for the A 11, B 10 and C31 sands,
but
the largest sand free
158
slot width, d , varied from 100
micron
for
All
to
400
micron for B 10. In all the tests the risk of sand production
is underestimated by the Coberly criterion, while the
Gulf
Coast criterion both over and underestimates it. The results
presented in
Table
3
clearly show that other parameters
than
d
1
must be important when choosing the slot width
of
sand control screens.
Prediction of critical slot widths. A mathematical
model for prediction of the critical slot widths was fitted to
the experimental data by the least squares method. Several
models, both using the principal components and various
combinations
of
the
9
original variables in the database,
were tested against the experimental data.
The
best results
were achieved with the following model
dail =
f o
fJ/1 J t J12t 2
(2)
Here dcrit is the predicted critical slot width,
{3
0
, ..
2
is a
set
of
constants, and t
and t
2
are the score values,
or
co
ordinates, on the first
two
principal components.
The
predicted values are compared with the observed values from
the laboratory experiments in
Table 4. The
difference
between the observed and predicted values are less than 50
microns which is approximately ha lf the typical step of 100
micron between two consecutive screen sizes. This indicates
that the accuracy of the prediction model is equal
or
better
than the accuracy
of
the experiments.
The
accuracy
of
the
prediction model cannot be evaluated statistically because of
the limited number of experiments. Two more sand types
have been tested to verify the model, however,
and
the
observed results are very similar to the predicted critical slot
widths.
The
predicted values for the critical
slot
widths are
plotted as a function of PC
1
and
PC2
in Figs. 8 to 11.
From
Figs. 8 and 9
one
can
see that
the risk of
screens being plugged is high for fine sands and for coarse
sands with a large fraction
of
fine material. As expected, the
risk
of
plugging the screens is low for coarse, well sorted
sands. But the risk of plugging is also reduced for fine sands
with a high fines content. This is
maybe
surprising, but it
means that the original permeability of these sands are so
low that it is in the same range as the permeabi lity of the
filter cake.
In
Fig. 10 one can
observe
that sand control is a
function both of the particle size and the degree of sorting
and content of small particles. For fine sands, a low score
on PC2, indicating a badly sorted sand with a lot of fines,
will increase the risk
of
sand production. But for coarse sand
with high scores on
PCI
a low score on
PC2
will reduce
the risk of sand production.
Once the data from the principal component analysis and
the set
of
constants (from eq. 2) for the critical slot widths
are known, the prediction model is easily implemented in a
standard spreadsheet. A simple, user-friendly
computer
program for the design of screen slot widths is currently
being developed.
Screen
design. The screens
for
a completion will
typically have to be ordered long before the well is actually
drilled through the reservoir, and the screen slot width will
have to be based
on
samples from other wells in the area.
For
this reason, the ideal solution
would
be to identify a
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SPE
31087
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0.
CHRISTIE AA. ESPEDAL
0.
R0RVIK
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typical screen slot width in advance that could be used for
the whole reservoir with small variations.
A possible method to achieve this is presented in
Fig.
12.
Here the critical slot widths are plotted for all the
samples from Field A. Screen slot width design is then a
matter
of
drawing a straight, horizontal line through the
graph that intersects the critical slot width curves
as
seldom
as possible. A possible solution is shown in Fig.
12.
By this method one can:
Find the optimal screen slot width for a reservoir or part
of
a reservoir.
Identify
sand
types that are well suited to screen
completions.
Identify sand types that may cause problems for the
chosen screen size.
From Fig.
12
one can see that the All and A12 may
cause sand production through the suggested slot width of
250 micron. In this case it is known from the laboratory
testing that the All sand will require a 100 micron screen,
and it may be necessary to reduce the screen size across the
A11 sand. In general, when such potential problem sands are
identified, it will be necessary to go back and study the cotes
and find out whether these sands are typical for the reservoir,
whether they strong or weak, and whether they are likely to
produce at all.
Conclusions
1. No sand types have been identified during the reported
work that are not suited to screen completions. For all the
sand types tested it has been possible to identify an interval
of
screen slot widths that will neither be plugged nor
produce sand. The width
of the design interval varies as a
function of the particle size distribution of the sand.
2. A well functioning screen represents a skin factor
of
less than 0.5.
3. The risk
of
sand production is increased in a situation
corresponding to an open annulus, partially filled with sand.
Plugging
of
screens by formation sand has only been
observed in this situation.
4. The risk
of
plugging the screen is decreased when the
fluid flow velocity through the screen is increased gradually.
This corresponds to bringing a well on stream slowly.
5. Design crite ria for screen slot width based on one
single point on the particle distribution curve can not
accurately predict neither plugging
of
the screens nor sand
production through the screens.
6. By introducing a fractal description for the particle
size
distribution of
the formation sand,
and
using
multivariate analysis, it has been possible to develop a
quantitative method for design of screen slot widths. The
method identifies a safe interval
of
slot widths where
plugging and sand production are not likely to occur.
7. The prediction model is applicable to sands from the
North Sea area and Haltenbanken, and can easily be extended
to other areas.
8. A method is proposed, where the prediction model
can be used to design screen completions for specific
reservoirs or parts
of reservoirs.
Nomenclature
159
dx = x -percentile diameter is here defined
as
the
theoretical sieve size that will retain
percent of the particles by weight.
N d d . = number of particles
l
K
= proportionality constant
f
=
exponent
of particle size
distribution
function (and fractal dimension
of
sand
matrix)
el l
d4ofd90
dcrir=
critical slot widths
d , d_, d ord++)
0
,
12
=
constants in the prediction model
ti
= score value,
or
co-ordinate, on principal
component i
cknowledgements
We would like to thank Saga Petroleum as and Statoil for
the permission to publish the material; Bjarne Aas
of
RF
Rogaland Research for helpful review comments; and Jorunn
0vsthus
of
RF for her accurate laboratory work.
References
1. Penberthy, W. L. and Shaugnessy, C. M.: Sand
Control,
SPE, 1992
2. Sparlin, D. D. and Hagen, R. W.,
Selection and
design of sand control methods,
Course Manual,
ICCI, 1991
3. Coberly, C. J.: Selec tion
of
screen openings for
unconsolidated sands ,
Drill.
and
Prod. Prac.,
API,
1937.
4. Suman, G.
0.
Ellis, R. C. and Snyder, R. E.,
Sand
Control
Handbook,
Gulf Publishing Company,
Houston, 1985
5. Kaye, Brian H., Fractal dimensions in data space;
New descriptors for fineparticle systems,
Particle and
particle system characterization,
Vol4 No 10, 1993
6. M ISller, R.:
The influence
of
formation grain size
distribution on production through a
sand
screen,
Thesis, Stavanger College, 1994
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Table
Sand
A11
810
C31
815
819
SELECTION OF SCREEN SLOT WIDTH TO PREVENT PLUGGING
AND SAND PRODUCTION
1 - Characterisation of the particle
size distribution
of the
d 10
[micron]
213
219
249
475
491
d 40
d 50 d 90
ell
f1
f2
[micron] [micron] [micron]
109 89
38
2.91
-3.22 -8.86
136 126 68 1.99
-1.12 -6.49
210 197 131
1.61
-0.45
-9.23
340 316 169
2.01
-2.20 -7.99
353 329 197 1.79
-0.78 -8.41
Table 2- Experimentally determined
critical
slot widths micron)
Sand
d
d
d
d
A11
0*
100 100 200
810
100 250 250 300
C31
0*
200 400 600
815 200 300
600 800
819
0*
100 500 800
were set equal to 0 when severe plugging o the 100
micron slot was not observed.
Table
3-The experimental
data
compared
with
the Coberly
and Gulf Coast criteria
Sand
d1o
2d o
d
d
Gulf
Coast)
Coi:JOOy)
A11 213
427 100 200
810
219 439 250 300
C31
249 498
400 600
815 475
949 600 800
819 491
982 500 800
160
tested
lnt1
[micron]
173
104
152
379
306
SPE
31087
sands
ln t2
[ ]
18.47
60.87
84.55
29.25
59.59
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SPE 31087
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MARKESTAD,
0.
CHRISTIE,
AA.
ESPEDAL, 0. R0RVIK
Table 4 Predicted critical
slot widths
compared with experimental
results
d
d
d
d
Sand
Measured Predicted Measured Predicted Measured Predicted Measured
Predicted
A11
810
C31
815
819
values values
values values values
values values values
0
6 100
100
100
93 200
185
100 79
250 249
250
273
300
351
0
21
200 201
400
377
600 550
200
205 300
300
600
594 800 787
0
-11 **
100 100 500
512 800 827
d
were set equal to 0 when severe plugging
of
the 100 micron slot was not observed.
Negative slot widths are artefacts
of
the prediction model.
C31
++
q.
t '+
++
++
+
:\:
/ 8 1 9
::t
N
u
ll
t
++
t
-1
++
815
2
3
A11
4
4
2 4
PC1
7
-1
2
3
4
Fig. 1 lllustration
in
2 dimensions of fractal
particle
structure with porosity
equal to zero.
Fig.2 AII the sand types in the database plotted
by
their scores on PC1
and
PC2
161
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SELECTION OF SCREEN SLOT WIDTH TO PREVENT PLUGGING
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A 11
100
100
10
10
0.1
0.1
z
0.01
L--- ' ------ ' --L-. .L. . . . . J .. . . . .L. . .L. . J . . . .L_---- --- ' --- ' - . . . . . .. .__. . . . . . ._L.J .. . J 0.001
10
100
1000
Particle
size
micron)
Fig. 3-The fractal particle
size
distribution
curve for the
A sand.
819
100
n
10
10
i
0
0.1
0.1
e
0.01
I
z
0.001
L _ _ _l____j__L_..J........I.....L...J....Ll...-_ ___..L._L-...JL....L.....J.....J.....LU 0.0001
100
1000
Particle size mi cron)
Fig. 4-The fractal particle size distribution
curve for
the 815
sand.
100
100
~ ~ ~ ~ ~ ~ ~ ~ ~ ~ -
80
-
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