Page 214 - Formation Damage during Improved Oil Recovery Fundamentals and Applications

188 Bin Yuan and Rouzbeh G. Moghanloo

Without nanoparticles pretreatment:
" #
2 2
μ r U
σ cr;initial 5 1 2 w FP φð1 2 S or Þ (4.7a)
2φð12S or Þr P F ei y
With arbitrary amounts of nanoparticles usage to coat rock grains:

2
2 0 1 3
2
μ r U
6 B w FP C 7
σ cr;j 5 12 B C 7
6
4 @ 128πr FP n N k B T 2κh K NP C NP A 5
2φð1-S or Þr P y F ei 1 e
κ 11K NP C NP ðς GS 2ς NP Þς FP
3φð12S or Þ
(4.7b)
With maximum amounts of nanoparticles to cover the surfaces of
rock grains:
2
2 0 1 3
2
μ r U
6 B w FP C 7
128πr FP n N k B T
σ cr;max 5 1 2 @4 A 5
2φð1-S or Þr P yðF ei 1 e 2κh ðς GS 2ς NP Þς FP
κ
3 φð12 S or Þ
(4.7c)
Yuan and Moghanloo (2017b) developed analytical solutions (Eq. (4.8))
to explain the experimental results of Arab and Pourafshary (2013) and eval-
uated the effectiveness of nanofluid pretreatment to prevent fines migration
and the associated damage to the porous medium’s permeability. Fig. 4.5
presents the effluent history of fines concentration with and without differ-
ent types of nanofluids to treat mobile fines. Inferred from Fig. 4.5,Al 2 O 3 -
based nanoparticle is confirmed as the best type of nanoparticle to reduce
fines migration from Arab’s laboratory experimental results. By applying
Eq. (4.8) to match with the experimental results in Fig. 4.5,the finesattach-
ment and straining rates can be enhanced most significantly with Al 2 O 3 -
based nanoparticles, which indicates the optimal type of nanoparticles to
control fines migration (Yuan et al., 2018b):

ð
C FP;eff L λ a 1λ s Þ11 1
ð
5exp 2 λ a 1λ s ÞLx D 2 t D 2x D Þ 1 (4.8)
ð
ð
C FP;inj L λ a 1λ s Þ t cr 21ð Þ ð λ a 1λ s ÞL
As shown in Fig. 4.6, before the breakthrough of nanoparticles, about
t D1 5 1:0, there are no changes to effluent-fines concentration, which
3
3
remains the same as the initial condition (C FP;initial 5 0:02 m =m ).