Direct simulation of multiphase flow on pore-space images Mosayeb Shams Supervised by Prof. Martin Blunt Dr. Branko Bijeljic January 2016

Outlook Motivation Background Experimental analysis of snap-off Direct simulation analysis of snap-off Conclusion and future work

Motivation Capillary trapping by imbibition happens in carbon-dioxide storage and oil recovery mechanisms. Pore space geometry plays a key role in both quantity and distribution of residual fluids during imbibition. A thorough understanding of the relationship between multiphase flow displacement mechanism and pore space structure is necessary Direct two-phase flow simulation on micro-CT images to analyse snap-off events as a function of pore structure

Pore space extraction work flow Big picture Pore-network modelling: Computational efficient Significant loss of information on the pore geometry Direct modelling: High simulation time Capturing more detailed information on the pore geometry Pore space extraction work flow

Basic concept: Liquid-Liquid interactions Young-Laplace equation: 𝑃 𝑐 =∆𝑃= 𝑃 𝐿2 − 𝑃 𝐿1 =𝜎𝐾=𝜎 1 𝑅 𝑡 + 1 𝑅 𝑠

Basic concept: Solid-Liquid interactions Young’s equation: 𝜎 𝑆 𝐿 2 = 𝜎 𝑆 𝐿 1 + 𝜎 𝐿 1 𝐿 2 cos 𝜃 𝑐

Modeling: Mathematical Navier-Stokes equations: Continuum surface force (CSF): Color function:

Modelling: Numerical Discretization and solving the PDEs: Finite Volume Method Capturing interface position: Volume of Fluid method Surface tension forces: Filtered Surface Force (FSF) model (Raeini 2013)

Capillary trapping - Experimental measurments Imaging fluid displacement and measuring residual non-wetting phase in carbonate samples are carried out by Andrew et all (2014) Ketton rock sample is drained with supercritical CO2, and then imbibed by brine under in situ conditions (50C and 10 MPa) Some statistical analysis of snap-off trapping has been carried out on the CO2 ganglia by Mohammed Al Geer.

Anomalous ganglia Criterion: in a multi-pore ganglion all inner throats are mostly larger than adjacent throats Multi-pore ganglion: A single ganglion that occupies more that one pore Anomalous ganglion: a multi-pore ganglion that has at least one inner throat which is smaller than one of the adjacent throats A rendered 3D realization of a multi-pore ganglion (By Mohammed Al Geer)

Statistics of pore-throat geometry Throat size vs contraction ratio (By Mohammed Al Geer)

Studied ganglia Ganglia distribution at a 2×2×2 mm subset of the core Multi-pore ganglia Multi-pore ganglia with anomaly

Adjacent pore radius (µm) Analysis of ganglion 72 Throat # Throat radius (µm) Adjacent pore radius (µm) Ratio rp/rt Remarks 214 31.60 72.40 2.29 Outer 259 20.90 102.03 4.88 262 19.99 57.73 2.89 315 22.63 71.19 3.15 365 35.51 61.90 1.74 393 27.14 52.52 1.94 467 29.13 2.45 554 29.35 48.05 1.64 360 17.67 57.37 3.27 Inner 481 39.18 1.82 A comparison between all inner (blue) and adjacent throats (red) at ganglion 72 (By Mohammed Al Geer)

Adjacent pore radius (µm) Analysis of ganglion 15 Throat # Throat radius (µm) Adjacent pore radius (µm) Ratio rp/rt Remarks 92 24.73 83.38 3.37 Outer 326 20.90 64.38 3.07 327 20.29 51.07 2.52 Inner A comparison between all inner (blue) and adjacent throats (red) at ganglion 15 (By Mohammed Al Geer)

Direct simulation of individual throats In order to take into account the local pore topology on snap-off, images of the pore space around the anomalous adjacent throats are cropped and taken as input geometry The criterion for snap-off phenomenon in direct simulation is snap-off Pc Ganglion 15 Throat 326 Ganglion 15 Throat 327 Ganglion 15 Throat 92

Direct simulation analysis of ganglion 15 Example simulation - throat 327: indicator function showing water-layer growth

Capillary pressure vs time for individual throats Snap-off Pc=366 Snap-off Pc=23 Snap-off Pc=162

Snap-off pressure of individual throats for 15 The outer throats (92,326), which are larger than the inner (327), are snapped off first , but 327 is not snapped off because of lower snap-off pressure

Snap-off pressure of individual throats for 72 Direct simulation shows that the inner throat, 360, does not snap off because of having a large negative snap-off pressure in comparison to the adjacent throats.

Snap-off pressure of individual throats for 72

Summary of simulations on individual throats 3 out of 7 ganglia with anomalous cases (15, 72 and 178) have already been resolved using direct simulation on individual throats. For the 4 unresolved cases we have recently started to run simulations on whole ganglion to account for non-local effects.