1. Introduction to Capillary Pressure Some slides in this section are modified from NExT PERF Short Course Notes, 1999. However, many of the slides appears to have been obtained from other primary sources that are not cited by NExT. Some slides have a notes section.

2. Determine fluid distribution in reservoir (initial conditions) Accumulation of HC is drainage process for water wet res. S w = function of height above OWC (oil water contact) Determine recoverable oil for water flooding applications Imbibition process for water wet reservoirs Pore Size Distribution Index, Absolute permeability (flow capacity of entire pore size distribution) Relative permeability (distribution of fluid phases within the pore size distribution) Reservoir Flow - Capillary Pressure included as a term of flow potential for multiphase flow Input data for reservoir simulation models Applications of Capillary Pressure Data

3. DRAINAGE AND IMBIBITION CAPILLARY PRESSURE CURVES Drainage Imbibition SiSi SmSm S wt PdPd PcPc 00.5 1.0 Modified from NExT, 1999, after … DRAINAGE Fluid flow process in which the saturation of the nonwetting phase increases Mobility of nonwetting fluid phase increases as nonwetting phase saturation increases IMBIBITION Fluid flow process in which the saturation of the wetting phase increases Mobility of wetting phase increases as wetting phase saturation increases Four Primary Parameters S i = irreducible wetting phase saturation S m = 1 - residual non-wetting phase saturation P d = displacement pressure, the pressure required to force non-wetting fluid into largest pores = pore size distribution index; determines shape

4. DRAINAGE PROCESS Fluid flow process in which the saturation of the nonwetting phase increases Examples: Hydrocarbon (oil or gas) filling the pore space and displacing the original water of deposition in water-wet rock Waterflooding an oil reservoir in which the reservoir is oil wet Gas injection in an oil or water wet oil reservoir Pressure maintenance or gas cycling by gas injection in a retrograde condensate reservoir Evolution of a secondary gas cap as reservoir pressure decreases

5. IMBIBITION PROCESS IMBIBITION Fluid flow process in which the saturation of the wetting phase increases Mobility of wetting phase increases as wetting phase saturation increases Examples: Accumulation of oil in an oil wet reservoir Waterflooding an oil reservoir in which the reservoir is water wet Accumulation of condensate as pressure decreases in a dew point reservoir

6. Flow Units Gamma Ray Log Petrophysical Data Pore Types LithofaciesCore 1 2 3 4 5 Plugs Capillary Pressure  vs k P c vs. S w Function Reflects Reservoir Quality High Quality Low Quality Function moves up and right, and becomes less “L” shaped as reservoir quality decreases

7. Effect of Permeability on Shape Decreasing Permeability, Decreasing A B C 20 16 12 8 4 0 0 0.20.40.6 0.8 1.0 Water Saturation Capillary Pressure Modified from NExT 1999, after xx)

8. Effect of Grain Size Distribution on Shape Well-sorted Poorly sorted Capillary pressure, psia Water saturation, % Modfied from NExT, 1999; after …) Decreasing

9. The pressure difference existing across the interface separating two immiscible fluids in capillaries (e.g. porous media). Calculated as: P c = p nwt - p wt CAPILLARY PRESSURE - DEFINITION - Where: P c = capillary pressure P nwt = pressure in nonwetting phase p wt = pressure in wetting phase One fluid wets the surfaces of the formation rock (wetting phase) in preference to the other (non-wetting phase). Gas is always the non-wetting phase in both oil-gas and water-gas systems. Oil is often the non-wetting phase in water-oil systems.

10. Capillary Tube - Conceptual Model Air-Water System Water Air  hh Considering the porous media as a collection of capillary tubes provides useful insights into how fluids behave in the reservoir pore spaces. Water rises in a capillary tube placed in a beaker of water, similar to water (the wetting phase) filling small pores leaving larger pores to non-wetting phases of reservoir rock.

11. The height of water in a capillary tube is a function of: –Adhesion tension between the air and water –Radius of the tube –Density difference between fluids CAPILLARY TUBE MODEL AIR / WATER SYSTEM This relation can be derived from balancing the upward force due to adhesion tension and downward forces due to the weight of the fluid (see ABW pg 135). The wetting phase (water) rise will be larger in small capillaries.  h=Height of water rise in capillary tube, cm  aw =Interfacial tension between air and water, dynes/cm  =Air/water contact angle, degrees r=Radius of capillary tube, cm g=Acceleration due to gravity, 980 cm/sec 2  aw =Density difference between water and air, gm/cm 3 Contact angle, , is measured through the more dense phase (water in this case).

12. Rise of Wetting Phase Varies with Capillary Radius WATER AIR 1 234 Ayers, 2001

13. CAPILLARY TUBE MODEL AIR/WATER SYSTEM Air Water p a2 hh p a1 p w1 p w2 Water rise in capillary tube depends on the density difference of fluids. P a2 = p w2 = p 2 p a1 = p 2 -  a g  h p w1 = p 2 -  w g  h P c = p a1 - p w1 =  w g  h -  a g  h =  g  h

14. Combining the two relations results in the following expression for capillary tubes: CAPILLARY PRESSURE – AIR / WATER SYSTEM

15. CAPILLARY PRESSURE – OIL / WATER SYSTEM From a similar derivation, the equation for capillary pressure for an oil/water system is P c = Capillary pressure between oil and water  ow = Interfacial tension between oil and water, dyne/cm  = Oil/water contact angle, degrees r = Radius of capillary tube, cm