Vol.3, No.2, 120-123 (2011) Natural Science
Copyright © 2011 SciRes. OPEN ACCESS
A new method of temporary plugging based on
andreasen equation
Yuxue Sun, Yanyu Qin*, Qiming Li
Petroleum Engineering Department, Northeast Petroleum University, Daqing, China; *Corresponding Author: qinyanyu3737@126.com
Received 7 December 2010; revised 10 January 2011; accepted 13 January 2011.
Based on the fractal nature of pore size in
sandstone and grindingbody within a certain
range and the Andreasen equation in theory,
using the optimization theory of traditional tem-
porary plugging agent for reference, we estab-
lished a new temporary plugging method for
reservoir protection. This new method empha-
sizes on the formulation and optimization of
solid filling particles and softening particles. It
is good in easy operation and strong applicabil-
ity. Indoor experiments with the natural core
from Hailaer area were conducted using this
new method. Compared with traditional meth-
ods, the filtration reduced significantly and the
permeability recovery was improved greatly,
which verified the rationality of this new method.
Keywords: Temporary Plugging Technology;
Formation Damage Prevention; Andreasen
In the early 1990sbased on “1/3 bridging rule” pub-
lished by Abrams, Luo Pingya and Luo Xiangdong pro-
posed “temporary plugging technology”, which showed
more effective through field application [1]. But the par-
ticle size selection of temporary plugging agent used in
the technology was only base on whether the median
diameter of temporary plugging agent matched the av-
erage pore throat diameter, which ignored many other
factors in actual reservoir, such as complex pore throat
structurecomprehensive size distribution and big pore
throat that contributes more to the reservoir permeability.
Many scholars both at home and abroad have studied
this problem in theory [2,3] Cui Yingchun et al. enriched
the temporary plugging technology of fractal and Yan
Jienian et al. enriched “the D90 rule” based on “Ideal
Packing Theory”. These two types of technology have
achieved good results and have been proved its accuracy
by field experiment.
However, the current temporary plugging methods
also have some defects, such as, the distribution of tem-
porary plugging particle size is narrow, and temporary
plugging particles are mostly rigid. Thus there is greatly
space to be increased. Based on previous theoretical ba-
sis, through optimizing, this paper choose 3 different
kind of rigid temporary plugging particles and 1 kind of
softening temporary plugging particle to mix together,
then achieve a better filling effect [4,5].
As for formation protecting drilling fluid, “Ideal
Packing Theory” means adding temporary plugging
agent particles of continuous diameter size in accordance
with the pore throat size to seal both the various pore
throat in reservoir and the pore among plugging particles
“Ideal Packing Theory” is base on fractal theory and
holds that the pore in sandstone is self-similar in a cer-
tain extentwhich has been confirmed by scholars home
and abroad. At present, the main ingredient of conven-
tional granular temporary plugging agents used in Chi-
nese oil field is organic or anorganic material, most of
which is made by grinding [7].
2.1. Horsfield Model
This model assumes that all particles is spherical, and
spherical particles stacked at the same time have the
same size. According to the order of accumulation, they
are named as first balls, second balls, and by analogy,
the following particles are stacked according to the
six-party arrangement rules, of which the air voids is
25.94%; second balls just enter surplus space of first
time balls accumulation, other balls are also stacked. The
corresponding computational results are showed in Ta-
ble 1. As a result, if the diameter distribution is appro-
priate, the air voids can be reduced to an ideal level.
Y. X. Sun et al. / Natural Science 3 (2011) 120-123
Copyright © 2011 SciRes. OPEN ACCESS
Table 1. Results of Horsfield filling.
Filling state Ball radius Relative number
of balls Air voids
1st balls r1 1 0.2594
2nd balls 0.414r1 1 0.2070
3rd balls 0.225r1 2 0.190
4th balls 0.177r1 8 0.158
5th balls 0.116r1 8 0.149
Filling materials Tiny Numerous 0.039
2.2. Andreasen Equation
Particles made by grinding are not uniform, but of
varying sizes. Its distribution rule can not be described
with Euclidean geometry. It has been proved to satisfy
the fractal geometric property and keep the self-similar
trait within a certain scope after studying. The mathe-
matics foundation of this theory originates from An-
dreasen equation [8].
 
where U(Dp) is cumulative sieve percentage, Dp is cur-
rent particle size, Dpl is maximum particle size, q is
fuller index.
Andreasen thinks that various kinds of distributing air
voids decreases with the minishing of distribution mod-
ule q; when q is within 0.33~0.50, air voids is minimum;
when q is less than 1/3, it is meaningless. This equation
is consistent with the well-known G-S equation.
3.1. Proposal of the Method
At present, the particle size distribution characteristics
of conventional granular temporary plugging agent used
in field is relatively standard. The range of the particle
size is very narrow, which generally cannot meet the
requirement of temporary plugging. The solution is to
mix granular temporary plugging agent of three different
particle size distributions according to a certain mixing
ratio, which will make the temporary plugging effects
dramatically increase, but when the granular temporary
plugging agent is under the action of the positive differ-
ential pressure, the particles can only make bridge effect
in the pore throat or in the fracture, so it is difficult to
form effective seal by deformation. Meanwhile, the fra-
gility of granular temporary plugging agent leads it li-
able to be ground finely during long cycle process, and
then invade into the deep reservoir, so only when there is
high solid content in the drilling fluid, can it make a
temporary plugging effect. In addition, either triple fill-
ing or quadruple filling, and no matter how to adjust the
particle size and gradation, it can not achieve zero filling
of air void in accordance with Horsfield filling model.
Therefore, beside formulating and optimizing three kinds
of solid temporary plugging agents, this method also use
soften deformational particles to completely seal reservoir.
3.2. Step of Optimization
Choose representative sample for casting rock
slice analysis or mercury injection experiments,
and then measure maximum pore throat diameter
in the reservoir.
Draw the distribution graph of pore throat size
changing with granular accumulative total volume
percentage when fuller index q equal 1/3 and 1/2,
in which the enclosed area surrounded by the two
curves is the area with minimum air void. If the
cumulative distribution curve of the optimized
temporary plugging particle is fell on the area with
minimum air void, the sealing effect will become
better along with the higher efficiency of particle
Based on 1/3~1/4 filling rules and other require-
ments (such as fluorescence, solubility, etc.), opti-
mize softening deformational particles whose av-
erage grain diameter meet the requirements.
4.1. Establishment of Model
Verify the above theory and method through indoor
experiment. The experimental cores are from the natural
cores in Hailaer area, of which the maximum pore throat
diameter of the reservoir is 26.5 μm (i.e. d90), which is
tested by mercury injection experiments. Make cumula-
tive distribution curve template when the fuller index q
equal 1/3 and 1/2, as is shown in Figure 1. This curve
template is used for subsequent optimization of tempo-
rary plugging agent. Making blended temporary plug-
ging curve between the two curves in template, then we
get minimal porosity.
Take several kinds of normal rigid temporary plug-
ging particles from field and use laser particle size ana-
lyzer to test particles size. The size distribution of rigid
temporary plugging particles is showed in Table 2.
There are seven kinds of different temporary plugging
agent in the table, including five kinds CaCO3 passing
through sieves of different diameter; WC-1C is a kind of
calcium, SAS is a softening shape-shifting particles; d10
means ten percent particle size is less than the value, d20
etc. is with the similar meaning.
Y. X. Sun et al. / Natural Science 3 (2011) 120-123
Copyright © 2011 SciRes. OPEN ACCESS
0510 15 20 2530
Cumulative Volume Percentage (%
Figure 1. Template of cumulative distribution curve.
Table 2. Size distribution of rigid temporary plugging particles
and flexible particles.
CaCO3 passing through sieves of
different sizes
Agent 0.050 0.030 0.025 0.015 0.005
d10 0.36 0.48 0.96 1.14 0.47 11.4 1.25
d20 2.41 2.74 2.88 2.50 1.66 18.8 3.66
d30 8.22 7.39 8.64 4.93 2.17 32.666.52
d40 9.66 8.44 10.21 5.86 3.27 41.589.88
d50 14.67 11.25 12.32 7.24 4.40 48.3412.34
d60 20.16 17.64 15.45 12.40 7.25 59.6618.16
d70 28.69 22.33 20.66 16.21 9.33 77.8222.31
d80 34.60 25.62 22.34 18.31 12.54 106.3526.57
d90 41.57 30.28 25.66 19.67 14.86 141.6032.50
d100 76.88 59.00 52.10 40.17 28.00 250.0046.60
By calculation and optimization experiment, We made
the corresponding curve, and the filling curve is as Fig-
ure 2 shows. When temporary plugging proportion is
0.030 mm : 0.025 mm: 0.005 mm = 25% : 45% : 30%,
the curve is between that of q = 1/2 and q = 1/3, then we
obtain the best proportion and the air voids is minimal.
Considering the annular shearing wear of granular
temporary plugging agent and the purpose of realizing
zero air voids, we chose SAS, whose average particle
size is 12.34 μm and maximum diameter is 32.5 μm, as
the preferred softening deformational particles in this
experiment according to the optimization rule. By con-
ducting formulation experiment with the above four tem-
porary plugging particles, the completely filling curve is
as Figure 3 shows. When the proportion of formulation
is 0.030 mm : 0.025 mm : 0.005 mm: SAS = 20% : 45% :
25% : 10%, the curve is between that of q = 1/2 and q =
1/3, then we obtain the best proportion and the air voids
is minimal.
4.2. Evaluating Test of Effect
4.2.1. Filtration Experiment
By means of choosing organic silicon drilling fluid
and adding proper amount of optimal shielding tempo-
rary plugging agent in it, we measured the API filtration
and high temperature and high pressure filtration (85
/3.5 MPa) to evaluate the sealing effect of this temporary
plugging method.
Experimental data is showed in Table 3. The formula
051015 20 25 30
Accumulated Particles (%)
Rigid Particles
Figure 2. Filling state of rigid temporary plugging particles.
0510 15 20 25 30
Accumulated Particles ()
Figure 3. Filling state of formulated rigid temporary plugging
Y. X. Sun et al. / Natural Science 3 (2011) 120-123
Copyright © 2011 SciRes. OPEN ACCESS
is as follow.
6bentonite + 0.5soda +0.2KPA + (0.7-0.1)
ammonium salt+(0.5-1)BTM-2+1.5CMJ-2+1 .5
It can be seen from Table 3 that both the API filtration
and HTHP filtration drops after adding temporary plug-
ging agent, where which is added the temporary plug-
ging agent based on Andreasen equation drops the most.
This shows that the new temporary plugging method
based on Ideal Packing Theory is obviously superior to
the traditional temporary plugging method.
4.2.2. Dynamic Pollution Experiment
The experimental cores are from the representative
natural cores in Hailaer area, and the experimental
process is in accordance with the People’s Republic of
China Petroleum Industry Standard SY/T6540-2002.
Polluting the selected cores by base mud, 1/3 bridging
rule, temporary plugging and new temporary plugging
method respectively, we got the measured permeability
recovery which is showed in Figure 4. It can be seen
from Figure 4 that the permeability recovery after pollu-
tion by drilling fluid without shielding temporary plug-
ging technology was only 47.20, and the permeability
recovery was greatly improved after temporary plugging.
Especially the formulated drilling fluid adopting new
temporary plugging method, its permeability recovery
was as high as 90.8. Thus, the new temporary plug-
ging method has a high protection effect for oil layers.
New temporary plugging method based on Andreasen
equation strictly satisfy mathematical theory, at the same
time it considers the fractal characteristics of reservoir
pore and grindingbody, and it puts mathematical knowl-
edge into oil industry excellently.
This temporary plugging method is easy to operate,
fully taking into consideration of the pore filling of var-
ious sizes in reservoirs and the pore filling among tem-
porary plugging particles. It also achieves filling with
minimal air voids by means of formulating and optimiz-
ing of rigid particles and softening particles
The indoor experiments present that the filtration has
Table 3. Rheological property and filter loss of drilling fluid
with Temporary Plugging Agent.
0 (Pa
(mPa·s) (mL) (mL)
Mud 54 32 5 22 4.3 10.1
Mud +5A 59 37 7.522 2.1 6.3
Mud +5B 62 40 9 22 3.2 9.3
Mud1/3 BridgingTemporary
New Method
of Temporary
Permeability Recovery (%
Figure 4. Permeability recovery after pollution by drilling
significantly reduced after adopting new temporary plug-
ging method based on Andreasen equation and the per-
meability recovery was greatly improved. This shows
that the new temporary plugging method has more ideal
effect for protecting reservoirs.
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