DYNAMICS OF CAPILLARY FLOW AND TRANSPORT PROPERTIES IN CARBONATE SEDIMENTARY FORMATION BY TIME-CONTROLLED POROSIMETRY

Transcription

1 SCA4-44 /5 DYNAMICS OF CAPILLARY FLOW AND TRANSPORT PROPERTIES IN CARBONATE SEDIMENTARY FORMATION BY TIME-CONTROLLED POROSIMETRY A. Cerepi, Institut EGID-Bordeaux 3, Université Mihel de Montaigne,, allée Daguin, 3367, Pessa, edex, Frane, Tel : (33) 5 57, Fax : (33) 5 57 This paper was prepared for presentation at the International Symposium of the Soiety of Core Analyst held in Abu Dhabi, UAE, 5-9 Otober, 4 ABSTRACT The dynamis of apillary flow in porous media at the pore-sale and the absolute permeability are alulated from time-ontrolled porosimetry data. The study of the flow regime in Hg-air displaements obtained in merury porosimetry show that the main flow regime is a apillary regime. An extended Washburn equation proposed by Sorbie et al. has already been used to analyse the dynamis of apillary flow, the pore filling time and the relative filling order of large and small pores. This method was applied to different alareous porous materials haraterized by different textures. INTRODUCTION Capillary fluid flow through porous media has been the fous of many studies during this last deade beause of its importane as a proess in nature and in different porous materials suh as oil filled and water wet reservoirs, soils and fratured roks [-4]. We determine apillary flow dynamis in porous media at the pore-sale and aim to propose a method for alulating the permeability from time dependene of different physial properties. For that, we used the merury porosimetry. Washburn (9) linked to Laplae's equation by using a apillary model where the porous medium is simulated by a bundle of onial or ylindrial apillary tubes: γ osθ P= R () where P is the apillary pressure; R is the average pore-throat size; γ is the interfaial tension; θ is the angle between merury menisus. Here, we have used a dynamial analysis proedure of Hg-injetion urve, the so-alled time-ontrolled merury invasion. It allows us to determine the pore-sale omplexity from time-ontrolled porosimetry data and to analyse the new parameters whih haraterize the urves of apillary pressure and volume against time. Four main rok-types are used in study (Figure ): Texture I (mudstone-wakestone with mud-supported texture), Texture II (pakstone with grain-supported texture), Texture III (pakstone-grainstone with grain-supported texture), Texture IV (grainstone).

2 SCA4-44 /5 Figure. Definition of the four rok-textures used in this study. EXPERIMENTAL PROCEDURE The experimental devie onsists a Carlo-Erba Series porosimeter, a data aquisition unit, and a miroomputer PC onneted to a printer. To give a physial interpretation of the phenomena, data are analysed following two urves: V(t) and P (t) (Figure ). Merury volume versus time: V(t). During the merury intrusion in porous media, the volume rate versus time shows two apillary flow dynamis (Figure ). A rapid rate of merury invasion AB (between and B, where a signifiant hange of the slope is observed, orresponding to the transition between rapid to slow injetion rate). The rapid rate of merury injetion versus time an be represented by a straight-line : V = Q t + β where Q =dv /dt is the slope of the urve, β is a onstant and t is time. A slow rate of merury invasion BC between t o and t f (total saturation of sample) defined by V= Q t + β where Q =dv /dt is the slope of the urve, β is a onstant and t is time. Capillary pressure versus time: P (t). During the merury intrusion, the apillary pressure evolves following Haines jump (Figure ). Some authors noted the same phenomena in slow drainage. The apillary number Ca and the visosity ratio M haraterize the Hg-air flow regime. Three major flow regimes are defined [5]: visous fingering, stable displaement and apillary fingering. In our ase and by taking into aount the experimental onditions (for merury : µ =.55-3 Pa s, γ =.48 N/m, θ =4 ; for air : µ =.8-3 Pa s), Ca varies with time as follows:

3 SCA4-44 3/5 Ca = α Q A Q () t [, t ] () t [ t, t ] f () µ where α = is a onstant (for the Hg-air system is α =.45); Q (t) and γ osθ Q (t) are injetion rates for rapid and slow kinetis with Q (t) >> Q (t) ; A is the sample area. The different values of logm-logca obtained in Hg-air porosimetry show that the main flow regime of the invading fluids is the apillary fingering. The experimental values of logm are onstant.935 while the experimental values of logca range from to Capillary Pressure ( -5 Pa) A Sampling urve P =.7 t (R) V(t) B Sampling urve V = t -.34 t o P (t) Low injetion High injetion Time Figure. Temporal evolution of apillary pressure urves P (t) and injeted merury volume V(t). Definition of different parameters of pore network omplexity. P (t) and V (t) are sampling urves of pressure and volume versus time; t o is the time of hange from rapid rate to slow rate; t f is the time of total ore saturation; R is apillary pressure flutuations. DYNAMICS OF HG-AIR CAPILLARY FLOW The simplest equation to alulate the dynamis of Hg-air apillary flow at the pore-sale is attributed to Washburn. By ombining with the Hagen-Poiseuille equation, the apillary veloity (u) is given by the following equation: u dh dt P = R 8µ h γ osθ = 8µ h R t f C. ρgh R Merury volume (m 3 ) (3)

4 SCA4-44 4/5 where h is the length of fluid penetration ; P = P-ρgh is the pressure drop between the menisus and the bulk liquid ; R is the tube radius ; ρ is the density ; µ is the fluid visosity ; θ is the ontat angle and γ is the interfaial tension. Sorbie et al. [4] have reexamined the basis of the Washburn equation and have extended his equation. Aording to these authors, ertain additional inertial terms may be of importane when onsidering the range of pore sizes and the aspet ratios ommonly enountered within porous media. For steady-state flow, Sorbie et al. [4] give a slightly different form of equation (3) : 4 3 dh P ( R ) u + 4εR = dt 8µ h where ε is a fator in the Washburn equation relating to the wall slip ondition (not analysed here). For a single apillary and only under visous fores the pore filling time t f, is found by integrating the equation (4) (ε=) : R (4) tf 4H µ = or R P H = R tf P µ (5) where H is the total length of fluid penetration (or total tube length).when the flow is entirely apillary dominated, Sorbie et al. give the pore filling time t f by the following formula : H µ tf = or R γ osθ H = t f R γ osθ µ (6) The Washburn equation predits that wider tubes will fill up more quikly than narrow ones. So, for visous dominated systems, the final time t f is proportional to /R while for apillary dominated systems the final time t f is proportional to /R. We alulated the length of Hg-air front displaement h and the apillary veloity flow dh/dt from relationship (6) for different arbonate textures. Results show that in all ases the apillary veloity dh/dt dereases as the apillary flow time inreases (Figures 3, 4). It is due to the fat that merury injetion investigates pores the pore-throat size of whih dereases. The samples with two-three modes strutures, large well-onneted pores show a high apillary veloity flow (Figures 3, 4).

5 SCA4-44 5/5 4.8 umulative length of merury-air front displaement (m) apillary veloity flow dh/dt (m/se) 3 time of apillary flow (s) Figure 3. Length of merury-air front diplaement and apillary veloity flow versus time in texture II. Φ = 6.79 %, k = md. Cumulative length of merury-air front displaement (m) apillary veloity flow dh/dt (m/se) Time of apillary flow (s) Figure 4. Length of merury-air diplaement front and apillary veloity flow versus time in texture IV: Φ=38.7 % ; k=87.4 md. TRANSPORT PROPERTIES FROM HG-CAPILLARY FLOW Many attempts have been made to alulate permeability k from primary apillari parameters suh as diameters, lengths and positions of the pores and throats. Chatzis []