In the name of God Pore-Scale Modeling of Three-Phase Flow in Mixed-Wet Systems Mohammad Piri Martin Blunt Centre for Petroleum Studies Department of Earth Science and Engineering Imperial College, London

Outline  Why pore-scale modeling of three-phase flow?  Pore-scale configurations  How we model displacement  Comparison with experimental data: Two-phase water-wet Three-phase water-wet  Prediction of three-phase mixed-wet behavior

Why three-phase flow?  Gas injection  Depressurisation below the bubble point  Solution gas drive  Gravity drainage Three-phase flow in the following situations: Characterized by low oil saturations and huge uncertainty in relative permeability – experiments are difficult and empirical models are uncertain.

Network we use A realization of Berea sandstone (Statoil) UNSW, Australia 12,349 pores and 26,146 throats with square, circular or triangular cross-section.

 The network has a disordered topology – can be based on direct analysis of real pore spaces.  State-of the art physics: wettability alteration, flow in corners and layers.  Track saturation paths for any type of three- phase displacement and predict relative permeability and capillary pressure.  Potential use as a predictive tool or to construct/validate empirical three-phase models.  Could be coupled to larger-scale simulation directly. Our pore network model

Configuration EConfiguration FConfiguration G Configuration H Configuration C Configuration D Configuration A Configuration B Two and three-phase configurations Gas Water Oil

Configuration J Configuration K Configuration I Configuration L Configuration NConfiguration M Configuration O Configuration P Two and three-phase configurations (Cont.) Gas Water Oil

Example displacement sequence Configuration C Configuration A Configuration B Configuration E Configuration G Primary DrainageWater Flooding Gas Injection Configuration I Layer Collapsing Gas Injection Gas Water Oil

How to simulate displacement 1. A displacement is a change from one configuration to another. 2. A capillary pressure for every possible displacement is calculated. 3. We assume quasi-static displacement. 4. We choose a displacement (what phase displaces what) and perform the displacement that occurs at the lowest invading phase pressure. 5. Check for trapping. 6. Repeat the process, while tracking a specified saturation path.

Primary drainage prediction Two-phase primary drainage – water-wet Experimental data from Oak – SPE Experiment Prediction

Waterflood prediction Two-phase waterflooding – water-wet Oil/water contact angle from 30 o – 80 o Data from Oak – SPE 20183

Three-Phase Saturation Paths Three-phase steady state experiments – water-wet Oil/water contact angle from 30 o – 80 o. Track saturations. Data from Oak – SPE SwSw SoSo SgSg

Three-phase oil relative permeabilities Measured and predicted oil relative permeabilities for four experiments – gas into oil and water.

Three-phase gas relative permeabilities Measured and predicted gas relative permeabilities for four experiments – gas into oil and water.

Three-phase water relative permeabilities Measured and predicted water relative permeabilities for two experiments – gas into oil and water.

Comparison of predictions Measured and predicted oil relative permeabilities compared to Stone 1 and saturation-weighted interpolation. Network model Stone 1 (crosses) Saturation-weighted interpolation (triangles)

Mixed-wet predictions - oil Study the effect of wettability on three-phase relative permeability. Gas injection into oil and water at fixed oil/water capillary pressure. Water-wet and ‘oil-wet.’ Water-wet Oil-wet

Mixed-wet predictions - gas Water-wet Oil-wet Oil-wet gas relative permeability is lower than the water-wet case, since it is no longer non-wetting to water.

Mixed-wet predictions – water Water-wet Oil-wet Oil-wet water relative permeability is very low. Poor connectivity of water after waterflooding.

 Couple pore scale network model to a 3D simulator to capture displacement paths  Incorporation of multiple displacements Future Work

Conclusions  Developed a definitive three-phase network model  Successfully predicts data from water-wet and mixed-wet two-phase, and water-wet three- phase experiments  Predicts mixed-wet three-phase properties – some surprises  Where next? Extensive validation for a range of reservoir samples