A new method of temporary plugging based on andreasen equation

doi:10.4236/ns.2011.32017

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Vol.3, No.2, 120-123 (2011) Natural Science

http://dx.doi.org/10.4236/ns.2011.32017

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: [email protected]

Received 7 December 2010; revised 10 January 2011; accepted 13 January 2011.

ABSTRACT

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

Equation

1. INTRODUCTION

In the early 1990s，based 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

structure，comprehensive 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].

2. THEORETICAL FOUNDATION

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

[6].

“Ideal Packing Theory” is base on fractal theory and

holds that the pore in sandstone is self-similar in a cer-

tain extent，which 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

121

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].

 

pppl

UDD D

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. A NEW METHOD OF TEMPORARY

PLUGGING TECHNOLOGY

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

accumulation.

• 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. INDOOR EXPRIMENT

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

122

100

120

0510 15 20 2530

Dp(μm)

Cumulative Volume Percentage (%

)

q=1/2

q=1/3

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

Temporary

Plugging

Agent 0.050 0.030 0.025 0.015 0.005

WC-1C SAS

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

100

120

051015 20 25 30

Dp(μm)

Accumulated Particles (%)

q=1/2

Rigid Particles

q=1/3

Figure 2. Filling state of rigid temporary plugging particles.

100

120

0510 15 20 25 30

Dp(μm)

Accumulated Particles (％)

q=1/2

Formulated

q=1/3

Figure 3. Filling state of formulated rigid temporary plugging

particles.

Y. X. Sun et al. / Natural Science 3 (2011) 120-123

123

is as follow.

6％bentonite + 0.5％soda +0.2％KPA + (0.7％-0.1％)

ammonium salt+(0.5％-1％)BTM-2+1.5％CMJ-2+1 .5％

PA-1

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.

5. CONCLUSIONS

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.

YPPV FL FLHTHP

Temporary

Plugging

Agent

φ60

φ30

0 (Pa

)

(mPa·s) (mL) (mL)

Mud 54 32 5 22 4.3 10.1

Mud +5％A 59 37 7.522 2.1 6.3

Mud +5％B 62 40 9 22 3.2 9.3

20%

40%

60%

80%

100%

Mud1/3 BridgingTemporary

Plugging

New Method

of Temporary

Plugging

Permeability Recovery (%

)

Figure 4. Permeability recovery after pollution by drilling

fluid.

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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