Primary Drainage
Firstly, the primary drainage process was studied. The decane was forced to enter the single square pore model with unequal arms from the top-right channel. A body force of 10−5, which is equivalent to pressure gradient, was imposed along the entry channel direction to mimic the pressure in the experiments [73]. As can be seen in Figure 6.17, in both experimental and simulation results, although the entry fluid reached the top-left channel having the smallest width, the filling fluid did not enter due to the high capillary pressure. The filling fluid chose the furthest channel, which has
the largest width, to fill first. The capillary filling law holds in this case: the channel with lowest capillary pressure will be filled first. The LB simulation predicted the primary drainage in the micro-models accurately, quite good agreements were achieved. According to Figure 6.17, we can see that, not only the filling order was recovered properly, but also that the curvature of interface and details of fluid distribution matched the experimental results well. Two bubbles caused by snap-off in the left-bottom and right bottom corner of pore were captured by the LB simulation. However, the volume of bubbles in the simulation is slightly bigger than that in experiments; this deviation might be caused by the neglect of density contrast and compress- ibility of the air/decane system. Generally, we think the agreements is quite satisfactory.
Figure 6.17.: Snapshots of primary drainage of decane in a single junction micro-model, experiments results and the lattice Boltzmann simulations. The experimental data and simulation results are shown together for easier comparison. The left black-white snapshots are experimental data, the colour snapshots were obtained from the LB simulation.
Spontaneous Imbibition
In both micro-models, the wetting phase (decane) has spontaneously im- bibed into the model from the top right corner (the single junction micro- model) and bottom right corner (the Berea micro-model). According to the capillary entry pressure rules used by network modelling, the fluid should enter the smallest channel which has the highest capillary pressure first; however, in our study, this is not the case. The results for the single junction micro-model and the Berea micro-model obtained by experiments and the parallel lattice Boltzmann simulation are shown in Figure 6.18 and Figure 6.20 respectively. The snapshots are taken from the top of the micro-models (Z direction). The black-white snapshots are experimental data, the light grey and dark grey represent decane and air respectively, the interface is shown in dark black. The lattice Boltzmann simulations are shown with colours: the red, blue and green represent decane, air and PMMA base respectively.
Figure 6.18.: Snapshots of spontaneous imbibition of decane in a single junc- tion micro-model with equal arms. The left black-white snap- shots are experimental data, the colour snapshots are obtained from the LB simulation.
Figure 6.19.: Sequential snapshots of spontaneous imbibition of decane in a single junction micro-model with unequal arms.
Figure 6.20.: Snapshots of spontaneous imbibition of decane in a Berea sandstone micro-model
first, then top left and bottom left corner which is not consistent with the filling rule used in network modelling (Figure 6.18.3, 6.18.4). In network modelling, the fluid should imbibe into all the other channels simultane- ously. We think this inconsistency was caused by the asymmetry of the experimental micro-model. As a result, we slightly revised the geometry for the LB simulation to break the symmetry. The width of the bottom right channel is one lattice smaller than all the other channels, and the bottom left corner of the squared pore was one lattice smaller than the other cor- ners. It should be noted that after the modification on the geometry, the width of the top left and bottom left channel is the same. According to the filling rules of network modelling the decane should enter two channels simultaneously; however, both the experiment and simulation showed that the decane imbibes into the top left channel first as a result of interface con- tact with the top left corner in advance (Figure 6.18.5,6.18.6). According to Figure 6.19, the capillary filling law broke again. The decane fills first not the narrowest channel, which has the highest capillary pressure, but the nearest channel that the filling fluid reached first. The results of the LB simulation and the experiments show very good agreements, almost all the main process and interface movements were captured by the LB simulation.
For the imbibition in the Berea sandstone micro-model (Figure 6.20), the results from the experiment and the LB simulation showed excellent agree- ment. It can be observed that the decane imbibes from the bottom right corner and enters the nearest top right channel first. After that it entered the top left channel which has the highest capillary pressure. This result supported again our hypothesis, for the case of imbibition, the local geom- etry of the network model junction determines the filling sequence, rather than the capillary pressure of the channels.
Although the agreement of displacement of interfaces between the sim- ulations and the experiments are quite satisfying, the time scales did not match well. This is due to the neglect of density ratio between decane and air. The approximation of density ratio equal to 1 is based on the assump- tion of a low Reynolds number. However, the Reynolds number increases dramatically when the interface of decane touches the solid wall. As a re-
ratio is presumably no longer negligible.