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