Oil fragmentation, interfacial surface transport and flow structure maps for two-phase flow in porous media

Transcription

1 Oil fragmentation, interfacial surface transport and flow structure maps for two-phase flow in porous media Marios Valavanides Dept. of Civil Engineering, TEI Athens, Greece DEFI 2016 Dynamics of Evolving Fluid Interfaces Gathering physico-chemical and flow properties October 12-13, 13, 2016, Lyon, France

2 Abstract In general, macroscopic 2-ph flows in p.m. form mixtures of connected- and disconnected-oil flows. Oil ganglion dynamics and drop traffic flow modes have been systematically observed during flow within model pore networks [1,2].as well as in real porous media [3,4]. Τhe flow structure shows a significant and systematic mutation [1] from practically no oil-flow, to large and small oil ganglion dynamics, to drop traffic and connected pathway flow mixtures, depending on the flow conditions and on the physicochemical, size and network configuration of the oil-water-porous medium system. As a consequence, the flow description needs to be reappraised by developing a more efficient, true-to-mechanism modelling. The mechanistic model DeProF for immiscible, steady-state 2-ph flow in pore networks [5], accounts the pore-scale mechanisms and the network-wide cooperative effects. The sources of non-linearity, mainly caused by the motion of populations of oil/water interfaces, are modelled satisfactorily and their effect is projected in the macroscopic scale by combining effective medium theory with appropriate expressions for pore-to-macro scale consistency of the mass transport of individual phases. Based on the concept of decomposition into prototype flows, DeProF detects all the physically admissible flow configurations. The latter form an ergodic ensemble defining the average macroscopic flow configuration. Reduced pressure gradient and relative permeabilities are estimated as ensemble averages. DeProF can be used as a simulation tool as it has revealed many latent critical characteristic properties of the flow structure. Its predictions have been recently validated by a major retrospective examination of independent laboratory studies [6]. Implementation of the DeProF algorithm, produces key bulk and interfacial physical quantities, fully describing the interstitial flow pattern [5] : ganglion size and ganglion velocity distribution, fractions of mobilized/stranded populations, specific (per unit volume of porous medium) surface, velocity and volume fractions of mobilized and stranded interfaces, oil fragmentation, etc. Extensive DeProF simulations have been carried out to derive maps describing the dependence of the flow structure on the true independent variables, the capillary number, Ca, and the flowrate ratio, r,. The simulations span 5 orders of magnitude in Ca (-8<logCa<-4 ) and r (-2<logr<2). Five systems with various -favourable and unfavourable- viscosity ratios have been examined. Trends in the oil/water interface transport properties are compared to energy efficiency trends and the loci of optimum operating conditions. In general, the variables describing the interstitial flow structure, are significantly more sensitive to r than Ca alterations. In addition, the aforementioned discrepancy becomes pronounced with viscosity disparity. This is attributed to the effect of the interstitial balance between capillarity and bulk viscosity. The maps have been used in a supplementary work, whereby the spatiotemporal distribution of interface-adhering tracers is predicted for indicative flow geometries during EOR interventions [7].

3 Applications of 2φFPM2 Oil Industry Upstream - Downstream Enhanced Oil Recovery (EOR) Secondary & Tertiary oil displacement in reservoirs to recover trapped oil (50% original oil in place) Use of displacing media: CO2, water + liquid, WAG, polymers, nitrogen, foams, in-place combustion gas etc CO 2 sequestration Modern petrochemical plant - TAMOIL plant located in Switzerland, including a Fluid Catalytic Cracking unit for the valorization of heavy crude oil charges Charpentier Chem.Eng.J. 2007

4 Applications of 2φFPM2 Soil remediation Problem Remedy Typical DNAPL migration processes [from Kamon et al Engineering Geology 70 (2003)] In-situ soil flushing process [from Khan et al J Env Management 71 (2004)]

5 The phenomenology of the examined process: Immiscible, steady-state two-phase flow in pore networks /media

6 Statement of the SS2φFPM Problem Steady-State Two-phase Flow in Porous Media A q w q w q o q o Homogeneous Porous medium i ( P ) z o w θ Fractional Flow Theory U i = k µ i k i r ( P i ) i= o, w z In Conventional Fractional Flow Theory But in reality k i r k = i r = k i r k i r ( S, ) i x pm 0 0 ( Ca, r; κ, θ, θ, ) A R x pm

7 Basic phenomenology of SS2φFPM Steady-State Two-phase Flow in Porous Media Fractional Flow U i = k µ i k i r ( i P ) i= o, w z Wyckoff, R.D., Botset, H.G., The Flow of GasLiquid Mixtures Through Unconsolidated Sands. Physics 7, 325 (doi: / )

8 Flow Regimes during Steady-State 2-Ph Flow in PM Experimental Study (1). (Avraam & Payatakes, JFM, 293, , 1995) Large Ganglion Dynamics (LGD) Drop Traffic Flow (DTF) Small Ganglion Dynamics (SGD) Connected Pathway Flow (CPF)

9 Disconnected-oil flow In pore network models

10 Flow Regimes during Steady-State 2-Ph Flow in PM Experimental Study (2) (Avraam & Payatakes, JFM, 293, , 1995) Small Ganglion Dynamics (SGD) Drop Traffic Flow (DTF)

11 Disconnected Flow in PM - Recent Experimental Studies Steady-State Two-Phase Flow in Porous Media: Statistics and Transport Properties Glass-bead pore model. Initial transient stage prior to settling of steady-state flow conditions. Tallakstad et al. PRL Tallakstad et al. PRE Mean pressure difference P L during steady state as a function of Ca. A power law dependence

12 Disconnected-oil flow In real porous media

13 Disconnected Flow in PM - Recent Experimental Studies usingµct Oil ganglia dynamics in natural porous media during surfactant flooding captured by ultra-fast x-ray microtomography 3D images sequence of the imbibition & surfactant injection process in a the Bentheimer sandstone. Mmineral phase removed, transparent blue brine & red oil phase. Time series of interfaces relaxation & trapping event spontaneous imbibition / 3s time intervals / 5 µm resolution Youssef et al. SCA

14 Disconnected Flow in PM - Recent Experimental Studies using µct Real-time 3D imaging of Haines jumps in porous media flow Snap-off and coalescence S.Berg et al. PNAS 110(10) 2013 Snap-off (middle/bottom) & coalescence (top) events during imbibition S. Berg et al. SCA

15 Disconnected Flow in PM - Recent Experimental Studies using µct Trickle flow hydrodynamic multiplicity: Experimental observations and pore-scale capillary mechanism Van der Merwe & Nicol, ChemEngSci

16 The DeProF model essentials

17 DeProF A True-to-mechanism Theoretical Model For Steady-State Two-Phase Flow in Porous Media (SS2φFPM) Modeling essentials Decomposition into 3 Prototype Flows: Connected-oil Pathway Flow (CPF) & Disconnected Oil Flow (DOF) DOF= Ganglion Dynamics (GD) + Drop Traffic Flow (DTF) Physicochemical characteristics of oil/water/p.m. Dynamic wettability (flow dependent contact angles) Mobilization & stranding probabilities for disconnected oil Accounting of unit cell Conductivities for all flow configurations Implementation of Effective Medium Theory Hierarchical modeling / Scale-up pore-to- core -to-field scales Physically admissible configurations & ergodicity principles

18 Reappraise the ss 2ph pm independent variables The DeProF model architecture Process l, x (Pore network) (Oil & water) q o, q pm µ θ o, µ w, γow, θa, w ( Pumps ) R System param. x pm κ, θ Α, θ R Operational par. Ca, r DeProF mech/stic model algorithm RESULT The macroscopic rheological state equation: x = x ( Ca, r; κ, θ,, ) A θ R x pm Reduced Macrosocpic Pressure Gradient x P = z γ ow k Ca And k ro, k rw Relative Permeabilities! Interstitial physical characteristics of SS 2φ flow in pm S w, β, ω, Flow arrangement variables (FAV) η ο,cpf, η o,g Oil flow rates in CPF & DOF (GD) U ow,dof Flowrate of o/w interfaces f OF, Coefficient of oil fragmentation, ξ ow,d Flowrate of o/w interface through DTF n G Ganglion size distribution Energy utilization factor f EU

19 U w = q w A Decomposition into Prototype Flows DeProF Externally imposed system parameters: V A βv S o,cpf =1 S o,dof CPF U o,dof U o,cpf { Ca, r; κ, θ 0 A, θ, } DTF GD 0 R x pm U o = A q o DOF=GD&DTF U w,dof CPF GD&DTF ω V GD V DOF The following variables are introduced: Flow Arrangement Variables (FAV): {S w, β, ω} Prototype Flow Variables: {U, S} U = {U o,cpf, U o,dof, U w,dof } S = {S o,dof, S o,d, S o,g } Prototype Flow Interlocking Condition: (SSFD2φPM) o P z w P = z P = z γ = ow Ca x k IPOR2016 M. Valavanides: Effective, two-phase flow characterization of pore network structures

20 DOF modelling - microscopic scale (1) l DTF domain j DTF cell q D / C q w uc i k G q uc GD domain C D / qo Ganglion Cells G u 5 GD domain reduced cell-conductances: G b q uc, n µ w b g jik, n = b,g = 3 A jik + B G G p Ca jik,n l χ u n ( x) b jik A b n B u G n ( x) b : C,G, E,G or X,G b n 1, : reduced effects of bulk phases & interphases : reduced ganglion velocity, χ G :tortuosity of ganglion spine DTF domain reduced cell-conductances: ( U, S) D D A jik + D q uc µ w jik = D D = 3 p σ m 1 D jik l + B D jik, ( U S) g 2 χ Ca 1

21 DOF modelling - microscopic scale (2) Criterion of Mobilization of Ganglia & Droplets J min, j 0 θ A j l ( ) J θ α 0 A j i D V n J θ α Configuration I (Droplet invading throat) ( ) 0 R P L ji θ ji J dr,i i 0 θ R Configuration II (Droplet in throat) ( ) J θ α 0 A D V n J ( θ ) i α 0 R L G n Ganglion mobilization condition: + p P z ( y) dy 2 γ [ J ( θ ) J ( θ )] ow dr,i 0 R min, j j,i= 1,...,5 0 A 2 2 Droplet mobilization condition: p P z ( y) dy 2 γ [ J ( θ ) J ( θ )] l ow α R α A α { I,II} Ganglia & droplets, as members of a dense population, can move even e at Ca << 10-5

22 The DeProF model predictions based on simulations for 2ph flows in pore networks

23 The Domain of Physically Admissible Solutions (PAS) (in DeProF theory) For each set (Ca, r) of system parameter values the 2φ flow visits a continuum of physically admissible flow configurations represented by (S w,β,ω) the PAS domain (cloud of red balls). The PAS domain is a canonical ensemble ω r= 2.5 κ=1.45 Ca= A unique set of values for S w, β and ω (black balls) are obtained by averaging over the PAS domain. The volume of the PAS domain (red cloud) is a measure of the process number of degrees of freedom and S w 0,8 β of the process contribution to configurational entropy.

24 Benchmark: DeProF model ( ) vs experiment ( ) Reduced Mechanical Power Dissipation, W Effect of Ca=µ w U w /γ ow &κ=µ o /µ w No adjustable parameters No interpolation W CPF W D W G W W exp 10 3 κ = 1.45 Ca = κ = 1.45 Ca = r W CPF + W G + W D = W 10 3 κ = r Ca = Avraam & Payatakes, JFM, 293 (1995) Valavanides & Payatakes, CMWR XIII, (2000) κ = 3.35 Ca = r r

25 10000 Reduced mechanical power dissipation of the total flow W 3D κ=1.45 Reduced pressure gradient x Ca (x10-6 ) Ca (x10-6 ) W = 1Φ W W = W kµ γ ( Ca) 2 ow w x = p z γ k Ca ow

26 Flow arrangement variables (FAV) 3D 0,8 S w 0,8 β κ=1.45 0,5 ω Ca (x10-6 ) Ca (x10-6 ) , Ca (x10-6 ) Oil saturation, S w Connected-oil saturation, β (pm volume fraction occupied by the connected oil) ganglia saturation of the DOF cells, ω (ganglion cells over all the DOF region cells)

27 Macroscopic interstitial flow variables

28 Operational efficiency aspects of SS2φFPM (efficiency = m 3 /s of recovered oil per kw spent in pumps) (revealed by DeProF model predictions)

29 Energy utilization factor (f EU = r/w) & Optimum Operating Conditions (OOC) f EU = {flow rate of oil} / {mechanical power supplied to the system} 0,15 0,15 r/w 0,10 κ=1.45 2D r/w 0,10 κ=1.45 3D ,5 0,5 Ca (x10-6 ) 1,5 2, ,5 0,5 Ca (x10-6 ) 1,5 2,0 For any Ca=const, Locus r*(ca) : f EU (Ca, r*)=max[f EU =(Ca, r)] r*(ca) Optimum Operating Conditions (OOC)

30 Energy utilization factor (f EU = r/w) Effect of viscosity ratio, κ 3D 0,15 r/w 0,15 r/w 0,15 r/w 0,10 κ=0.66 3D 0,10 κ=1.45 3D 0,10 κ=3.35 3D Ca (x10-6 ) ,5 0,5 1,5 2, Ca (x10-6 ) ,5 0,5 1,5 2, Ca (x10-6 ) ,5 0,5 1,5 2,0 κ=0.66 κ=1.45 κ=3.35 f EU = {flow rate of oil} /{mechanical power supplied to the system}

31 Optimum Operating Conds in ss2φfpm: Reveal of latent experimental evidence: OOC are latent in k rj (S w ) diagrams! Valavanides et al. (2016) J. Pet. Sci. Eng

32 Extensive DeProF model simulations spanning: 5 orders in Ca: -8<logCa<-4 5 orders in r : -2<logr<2 and 5 viscosity ratio values: κ=µ o /µ w ={0,33, 7, 0, 1,45, 3,00}

33 -4>logCa>-8 Incr. o/w viscosity ratio, κ=µo/µw Specific (pupmv) o/w surface, Aow Reduced o/w interface superficial velocity, Uow,DOF DEFI2016 M.S. Valavanides: Oil fragmentation, interfacial surface transport and flow structure maps for 2ph flow in pm

34 -4>logCa>-8 Incr. o/w viscosity ratio, κ=µ o /µ w Coefficient of oil fragmentation, f OF Fraction of o/w interface transport through DTF, ξ ow,d

35 -4>logCa>-8 Incr. o/w viscosity ratio, κ=µ o /µ w Water saturation, S w 0,8 S w κ=0,33 0,8 S w κ=7 0,8 Sw κ=0 0,8 S w κ=1,50 0,8 S w κ=3, Connected-oil pathway flow (CPF) vol. fraction, β 0,8 β κ=0,33 0,8 β κ=7 0,8 β κ=0 0,8 β κ=1,50 0,8 β κ=3, Drop traffic flow (DTF) vol. fraction in DOF, ω 0,8 ω κ=0,33 0,8 ω κ=7 0,8 ω κ=0 0,8 ω κ=1,50 0,8 ω κ=3, DEFI2016 M.S. Valavanides: Oil fragmentation, interfacial surface transport and flow structure maps for 2ph flow in pm

36 Energy efficiency (oil output per kw spent), f EU =r/w 0,5 f EU =r/w κ=0,33 0,5 f EU =r/w κ=7 0,5 f EU =r/w κ=0 0,5 f EU =r/w κ=1,50 0,5 f EU =r/w κ=3,00 0,3 0,3 0,3 0,3 0,3 0,1 0,1 0,1 0,1 0, >logCa>-8 Incr. o/w viscosity ratio, κ=µ o /µ w

37 Universal, operational Efficiency Map for ss2φfpm

38 CONCLUSIONS Two-phase flow in p.m. is burdened (as well as blessed ) with: oil disconnection and capillarity effects that restrain or inhibit -to a certain extent- the superficial transport of o & w (predominates within the low-end flow regime) the bulk phase viscosities of oil & water (predominates within the high-end flow regime) Detailed /analytic examination of the flow unveils a remarkable internal adaptability with universal characteristic (flow mutation) and well defined underlying mechanisms Process engineers can take advantage of the natural intrinsic characteristics of 2φ flow in p.m., namely the multitude of internal flows that act as - potentially beneficial- degrees of freedom against the imposed macroscopic constraints. Process engineers can judge where to set the balance between capillarity or viscosity (order of magnitude benefit in process efficiency) especially in artificial pore networks

39 Thank you ImproDeProF project ImproDeDeproF project team: C.Tsakiroglou, V. Burganos, C. Aggelopoulos, D. Avraam (ICE/HT-FORTH), T. Daras (T.U. Crete), C. Paraskeva (U. Patras) G. Kamvyssas, E.Skouras (TEI Patras)

40 back-up slides

41 Transformation of relative permeability data reveals operational efficiency aspects of SS rel. perm. diagrams In steady-state conds, oil/water flowrate ratio (=λ, the mobility ratio) r = q q o w = U U o w = k k ro rw µ µ o w = 1 κ k k ro rw (1) Energy utilization factor ( oil flowrate per kw spent ) f EU r = W = k ro κ 1 ( r+ 1) = k rw r = k r+ 1 ro k k ro rw +κ 1 (2) where W κ=µ o /µ w W k µ γ w ( Ca) 2 ow : oil/water viscosity ratio : reduced mech. power dissipation (over equiv. 1ph flow)

42 Operational Efficiency Map for ss2φfpm k rw, k ro, f EU Constant Ca 1 as logr + log κ S w 0 logr k ro k rw asymptote ( ) 2 * f EU = 1 + κ 1 f EU (r*) r x =1/κ f EU (r,ca 3 ) r*(ca) as logr - S w 1 0 Ca=Ca 1 Ca=Ca 2 Ca=Ca 3 d= log r * Ca * = log r Ca ( ) log r ( ) + logκ asymptote Ca r * = 1/ κ = 1/ ( + κ) S * w 1