Validation of model predictions of pore-scale fluid distributions during two-phase flow

Pore-scale two-phase flow modeling is an important technology to study a rock's relative permeability behavior. To investigate if these models are predictive, the calculated pore-scale fluid distributions which determine the relative permeability need to be validated. In this work, we introduce a methodology to quantitatively compare models to experimental fluid distributions in flow experiments visualized with microcomputed tomography. First, we analyzed five repeated drainage-imbibition experiments on a single sample. In these experiments, the exact fluid distributions were not fully repeatable on a pore-by-pore basis, while the global properties of the fluid distribution were. Then two fractional flow experiments were used to validate a quasistatic pore network model. The model correctly predicted the fluid present in more than 75% of pores and throats in drainage and imbibition. To quantify what this means for the relevant global properties of the fluid distribution, we compare the main flow paths and the connectivity across the different pore sizes in the modeled and experimental fluid distributions. These essential topology characteristics matched well for drainage simulations, but not for imbibition. This suggests that the pore-filling rules in the network model we used need to be improved to make reliable predictions of imbibition. The presented analysis illustrates the potential of our methodology to systematically and robustly test two-phase flow models to aid in model development and calibration.

Figure 1

(a) Detail of a slice through a micro-CT image of experiment ${\mathrm{SSE}}_B$, during flooding of brine (fractional flow 1). Overlayed are the inscribed spheres in the pores, determined from a dry scan. Red spheres are segmented as oil-filled, blue ones as brine-filled. Each sphere corresponds to a pore in the pore network model simulations. (b) A plot of the average gray value versus the 10th-percentile gray value of each sphere in the micro-CT image of experiment ${\mathrm{SSE}}_B$ shown in (a). Because oil-filled pores have lower average and 10th-percentile gray values, automatic clustering of the points in this plot allows to identify oil-filled and brine-filled spheres (red and blue dots, respectively).

Figure 2

A slice through the Bentheimer sample from the experiment presented by Andrew et al. [31, 32], color-coded with the frequency of voxels being filled with ${\mathrm{CO}}_2$ or brine in five repeated experiments. Red voxels are filled with ${\mathrm{CO}}_2$ in every experiment, blue voxels are always filled with brine. Some pores are filled with a different fluid in the repeated experiments and are assigned an intermediate color accordingly. Green represents the largest uncertainty.

Figure 3

(a) In five repeats of an unsteady-state imbibition experiment [31, 32], the small pores of the Bentheimer sample always remained filled with brine, while the largest pores nearly always contained supercritical ${\mathrm{CO}}_2$. The pores with intermediate radii contained supercritical ${\mathrm{CO}}_2$ in some experiments and brine in others, due to variability in the experiment. (b) The probability of a pore to contain brine after imbibition thus depends on its radius. The standard deviation of the filling state of the pores over five imbibition experiments shows that there is significant variability in the filling states of intermediate pore sizes, even though residual nonwetting phase saturations and cluster sizes do not vary strongly.

Figure 4

Oil-filling and filling discrepancies (frequency of network elements filled differently in the model and the experiment) for (a) pores and (b) throats in experiment ${\mathrm{SSE}}_A$.

Figure 5

Oil-filling and filling discrepancies (frequency of network elements filled differently in the model and the experiment) for (a) pores and (b) throats in experiment ${\mathrm{SSE}}_B$.

Figure 6

Collection of widest percolating oil paths from each input and output pore for (a) the experimental and (b) the modeled fluid distributions in experiment ${\mathrm{SSE}}_A$ and (c) the throat size distributions of these paths.

Figure 7

Analysis of (a) minimum and (b) average and standard deviation of the throat sizes in a persistence analysis of the WPOP in experiment ${\mathrm{SSE}}_A$ (removing the widest path and calculating the second widest, and so on) shows that the oil phase in the experiment is more disconnected than in the model. (c) This is confirmed by the connectivity function in terms of the normalized Euler number of the oil network, which decreases faster and to a lower minimum for the experiment.

Figure 8

Brine-filling and filling discrepancies (frequency of network elements filled differently in the model and the experiment) for (a) pores and (b) throats as a function of their radii after imbibition in experiment ${\mathrm{SSE}}_A$. Simulations were performed with contact angles randomly distributed between ${15}^{\circ }$ and ${45}^{\circ }$.

Figure 9

Brine-filling and filling discrepancies (frequency of network elements filled differently in the model and the experiment) for (a) pores and (b) throats as a function of their radii after imbibition in experiment ${\mathrm{SSE}}_B$. Simulations were performed with contact angles randomly distributed between ${15}^{\circ }$ and ${45}^{\circ }$.

Figure 10

The probability that a pore in (a) experiment ${\mathrm{SSE}}_A$ and (b) experiment ${\mathrm{SSE}}_B$ is filled with brine after imbibition, compared to predictions from simulations with contact angles randomly distributed between ${15}^{\circ }$ and ${45}^{\circ }$ and between ${15}^{\circ }$ and ${25}^{\circ }$. The gray area is the $2\sigma$ confidence interval on the experiment, inferred from repeated experiments discussed in Sec. 3a.

Figure 11

Connectivity analysis of the oil phase after imbibition in experiment ${\mathrm{SSE}}_A$: (a) the cluster size distribution and (b) the connectivity function in simulations performed with advancing contact angles between ${15}^{\circ }$ and ${25}^{\circ }$ match the experiment better than simulations with advancing contact angles between ${15}^{\circ }$ and ${45}^{\circ }$, yet still show discrepancies.

Figure 12

Connectivity analysis of the oil phase after imbibition in experiment ${\mathrm{SSE}}_B$: (a) the cluster size distribution and (b) the connectivity function in simulations performed with advancing contact angles between ${15}^{\circ }$ and ${25}^{\circ }$ match the experiment better than simulations with advancing contact angles between ${15}^{\circ }$ and ${45}^{\circ }$.

Figure 13

Gray value histogram of the investigated image.

Figure 14

(a) Porosity variation and (b) permeability variation in function of segmentation parameters detailed in Table 3. Permeability values were obtained using PNM simulations.