In the name of God Three-Phase Flow in Mixed-Wet Porous Media Mohammad Piri Prof. Martin Blunt Petroleum Eng. and Rock Mechanics (PERM) Research Group Department of Earth Science and Engineering Imperial College

Acknowledgments  Enterprise Oil  Statoil  Shell  BHP  Gas de France  PDVSA – Intevep  Schlumberger  Japan National Oil Corporation (JNOC)  Department of Trade and Industry (DTI) We Thank the Members of the Imperial College Consortium on Pore-Scale Modelling for Their Generous and Continued Support of our Research:

Outline  Why Three-Phase Flow and Physically-Based Network Modelling ?  Model We Use  Three-Phase Physics Layer Formation Wettability and Contact Angles Three-Phase Generic Configurations Network of Displacements for Every Type of Possible Two and Three Phase Processes – Example, Water-Wet System  Network Modelling and Some of Its Complications How to Choose the Right Displacement at Each Time? Single, Double and Multiple Displacements and Their Volume Errors Relative Permeability Computation Connectivity and Clustering and How Important They Are !  Three-Phase Results  Applications, Future Works and Conclusions

Why Three_Phase Flow ?  Gas Injection in Oil Reservoirs  Depressurisation  Solution Gas Drive  Gravity Drainage  Thermal Flooding  Steam Injection  NAPL Migration in the Unsaturated Zone  NAPL Flow in the Saturated Zone in the Presence of Gas We Face with Three Phase Systems at Following Processes:

 Very Difficult to to Measure 3-Phase Relative Permeabilities Particularly for Whole Range of O/W, G/W Permeabilities Particularly for Whole Range of O/W, G/W and G/O Contact Angles and G/O Contact Angles  Empirical Correlations have Little or No Physical Basis  Enormously Reduces the Uncertainty Associated with the Assessment of Gas Injection Projects Assessment of Gas Injection Projects  Significantly Improves our Understanding of Three-Phase Physics for the Design of Recovery Processes Physics for the Design of Recovery Processes Guide to Construct New Empirical Models  Guide to Construct New Empirical Models  Directly in a Dynamic Up-scaling Approach Why Physically-Based Three-Phase Network Models ?

A Realization of Berea Sandstone (Statoil’s Network)  Porosity = %  Cube Size = 3 mm*3mm*3mm  No. of Pores=12349  No. of Throats=26146  Coordination Number=1 to 19  Pores Inscribed Radius= 3.62 to (um)  Throats Inscribed Radius= 0.90 to (um)  Clay Volume=5.7%  Triangular Shape (Irregular & Equilateral)=92.27 %  Rectangular Shape=6.51 %  Circular Shape=1.22 % Model We Use

Configuration EConfiguration FConfiguration G Configuration H Configuration C Configuration D Configuration A Configuration B Two and Three-Phase Generic Configurations Gas Water Oil

Configuration J Configuration K Configuration I Configuration L Configuration NConfiguration M Configuration o Configuration P Two and Three-Phase Generic Configurations (Cont.) Gas Water Oil

WF= Water Flooding GI = Gas Injection PD = Primary Drainage OI = Oil Injection / = OR C D E A B F G H K J I LMN F E O P C D WF PD WF GI WF GI GI/OI GI GI/WF GI OI WF/OI OI WF/OI WF WF/OI GI/WF WF/OI WF GI/WF WF GI/WF WF GI A B CE G I Displacements Network

PD,WF and GI in Strongly Water-Wet Systems 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 Choose Right Disp. Each Time? 1. A capillary pressure between any two phases is defined as: 2. The capillary pressure required to do Piston-Like, Snap-off or Layer Collapsing events that leads to configuration change is calculated using pore inscribed radius, right contact angle, corner angle(s) and interfacial tension. 3. Calculated capillary pressures are placed in one of six following sorted lists corresponding to what phase displaces what phase : Water to Gas, Water to Oil, Gas to Oil, Gas to Water, Oil to Water, Oil to Gas 4. In every list we favour the event that needs lower pressure of displacing phase. This corresponds to the event with the lowest capillary pressure in Drainage processes and the highest capillary pressure in Imbibition processes. 5. During injection of phase I, it displaces either phase J or K at each time (i.e. event). To find which of these should be done at every time: 5-A) Find the most favourable event in I to J and I to K lists 5-B) Between the two most favourable events the one that needs lower I pressure is favoured

How to Choose Right Disp. Each Time? Example: Gas injection after water flooding in a strongly oil-wet system: Pcgw1 Pcgw2 Pcgw3. Pcgwn Pcgo1 Pcgo2 Pcgo3. Pcgon Pg1=Pw+Pcgw1 Pcgw = Pg - Pw Pgn=Po+Pcgon Pcgo = Pg - Po Gas Invasion into Oil Imbibition Process Gas Invasion into water Drainage Process If Pg1<Pgn do G/W Else do G/O Ascending

Single Displacements 1.Both Displacing and Displaced Phases Need to be Connected to Either Inlet or Outlet 2.There is no Volume Error Gas Injection into Oil in a Strongly Water-wet System (Drainage Process) Gas Oil

Double Displacements and Volume Error 1.Only the First and the Third Phases are Connected to Either Inlet or Outlet in the case of Double Displacements 2.There is Volume Error that Needs to be Dealt With 3.Multiple Displacements Involving More Than One Intermediate Stage are Also Possible if Two Phases are Trapped. Gas Injection into Oil in a Strongly Oil-wet System Gas into Water is an Imbibition Process Water into Oil is a Drainage Process Gas Oil Water = Circular Cross Section

 Test for Trapping of all Three Phases  Use Theoretical and Empirical Expressions to Calculate Layer, Corner and Centre Conductance Relative Permeability Pore I Pore J (I) (II)

Connectivity and Clustering (Cont.) Inlet Outlet Cluster is Connected * Dead End Periodic Boundary Condition

Cluster Connectivity (Cont.) The pore that displacement is happening in it Clusters with different phases surrounding the pore Using phase connectivity could be very time consuming because: 1.For every single displacement connectivity of both displacing and displaced phases need to be checked 2.For double and multiple displacements we need to define the trapped and connected clusters 3.It is necessary to know the connectivity of all the site-phases in the network in order to calculate the relative permeabilities How can we deal with this?

Before displacement 1 Check whether the pore allows clusters with the same fluids to be connected to each other through its sites 2 If yes store “ Connected “ else “ Not-Connected “ After displacement 4Check whether the pore allows clusters with the same fluids to get connected to each other through its sites 5If yes store “ Connected “ else “ Not-Connected “ 6Compare the connection of clusters with same fluids before and after the displacement and decide whether to check the continuity of clusters to inlet or outlet, based on the type of displacement and their flags before the displacements. Cluster Connectivity (Cont.)

Sw (frac.) Kro Krw Dr. Paal-Eric Oeren Mohammad Piri Per Valvatne Two-Phase Results Reassuring that Three Independent Codes Give the Same Results. Pcow Sw (frac.)

Tertiary Gas Injection, Strongly Water-wet System

Tertiary Gas Injection, Strongly Water-wet System (Cont.)

Tertiary Gas Injection, Strongly Water-wet System (Cont.)

Tertiary Gas Injection, Strongly Oil-wet System

Tertiary Gas Injection, Strongly Oil-wet System

WAG Flooding, Water-wet System Effects of Initial Oil Saturation on Second Water Flooding

WAG Flooding, Water-wet System

 WAG Flooding  Gas Injection into Different Soi  Secondary vs. Tertiary Gas Injection Applications

 Couple Pore Scale Network Model to 3D Simulator to Capture a Physically Based Kr for the Correct Displacement Path  Solution Gas Drive Future Work

Conclusions  Three-Phase Model  Relative Permeability and Capillary Pressure Results  Working on Coupling a Pore-Scale Network Model with Larger-Scale Simulation and Including More Physics