Page 212 - Formation Damage during Improved Oil Recovery Fundamentals and Applications

186 Bin Yuan and Rouzbeh G. Moghanloo

Without nanoparticles utilization to enhance fines attachment:

2
μ r U 2
σ cr;initial 5 1 2 ð w FP Þ φð1 2 S or Þ (4.6a)
2φð12S or Þr P F ei y
With arbitrary amounts of nanoparticles adsorption onto fine particles
as the coinjection continues:

2
2 0 1 3
2
μ r U
6 B C 7
σ cr;i 5 12 B w FP C 7 φð12S or Þ
6
h
4 @ i A 5
2φð1-S or Þr P y F ei 1 128πr FP n N k B T 2κh 11K NP C NP ðς FP 2ς NP Þς GS
e
K NP C NP
κ
(4.6b)
With the maximum nanoparticles adsorption onto fine particles
finally:
2
" ! #
2
μ r U
σ cr;max 5 1 2 w FP φð1 2 S or Þ (4.6c)
2φð1-S or Þr P yðF ei 1 128πr FP n N k B T 2κh ðς FP 2ς NP Þς GS
e
κ
As the coinjection of nanoparticles and fines continues, the transport
phenomenon of nanoparticles and fines passing through porous media
was analyzed by Yuan et al. (2016; 2017a,b). For both nanoparticles and
fines concentrations profiles along 1-D permeable medium in Fig. 4.4A,
there are four different-state regions progressing from (Yuan et al.,
2018b): (1) injection-condition region; (2) spreading-wave region; (3)
constant-state region; to (4) initial-condition region. Meanwhile, a genu-
ine shock “nanoparticle absorption front” connecting the constant-state
region and the initial-condition region occurs to maintain the physical
integrity of the analytical solutions (Moghanloo, 2012; Noh and Lake,
2004). The existence of coinjected nanoparticles leads to a “concave”
profile in Fig. 4.4A that indicates the reduced amounts of mobile fines in
the carrier fluid. Also, in Fig. 4.4B, the performance of nanoparticles to
control fines migration are quantified as the coinjection continues. Prior
to the breakthrough of the injected mixture, the reduced amounts of
effluent fines (differences between dashed line and solid line) increase as
time progresses. Following the arrival of the injection condition, the
attachment ability of fine particles onto rock grains has already reached
the maximum limit; meaning that, from that point in time, no more fines
control by nanoparticles can be realized.