Effective and Relative Permeability PDF

EFFECTIVE PERMEABILITY, RELATIVE PERMEABILITY AND LABORATORY MEASUREMENT Prof. T. Kumar Dept. of Petroleum Engg. IIT(ISM) Dhanbad-826004 Effective and Relative Permeability 1. Effective permeability: The permeability o...

EFFECTIVE PERMEABILITY, RELATIVE PERMEABILITY AND LABORATORY MEASUREMENT Prof. T. Kumar Dept. of Petroleum Engg. IIT(ISM) Dhanbad-826004 Effective and Relative Permeability 1. Effective permeability: The permeability of a rock to a particular fluid at saturations less than 100%, i.e., when other fluid(s) is present. This is measured in darcys or millidarcies and is therefore the dimensional equivalent of absolute permeability, hence: kg = effective permeability to oil, darcys or md kw = effective permeability to water, darcys or md kg = effective permeability to gas, darcys or md Individual values of ko, kw and kg may vary from zero up to the absolute value, k: 1 2. Relative permeability: This is merely a convenient, dimensionless quantity defined by: Since effective permeability may range from zero to k, the relative permeability may have any value between zero and one: Effective permeability to non-wetting phase at irreducible wetting phase saturation [e.g. ko(Sw=Swi)] because definition of base permeability varies, the definition used must always be: confirmed before applying relative permeability data noted along with tables and figures presenting relative permeability data Example: Calculating permeability (Data from Lab) The following laboratory data are given from relative permeability tests. Cross – sectional area of the core = 5 cm2, Core length =3 cm, Pressure at out let face of the core = 1 atm, Pressure at inlet face of the core = 2 atm, Viscosity of the water = 1.0 cp, Viscosity of oil = 1.25 cp. Saturation and rate data are as follows: 2  Relative permeability curves are essential in understanding how different fluids flow through porous media, such as reservoir rocks. These curves represent the permeability of each fluid phase (e.g., water, oil, gas) relative to the total permeability of the rock. Here are some key points about relative permeability curves: Wetting and Non-Wetting Phases: In a water-oil system, water is typically the wetting phase, and oil is the non-wetting phase. The relative permeability of the wetting phase (water) usually decreases rapidly as its saturation decreases, while the non-wetting phase (oil) shows a more gradual change12. Curve Shapes: The wetting phase relative permeability 3 curve is often concave upwards, while the non-wetting phase curve has an “S” shape3. This difference is due to the way each phase occupies the pore spaces within the rock.  Irreducible Saturation: The point at which the wetting phase (e.g., water) ceases to flow is known as the irreducible water saturation. At this point, the wetting phase occupies the smallest pore spaces, where capillary forces are strongest14. Residual Saturation: For the non-wetting phase (e.g., oil), there is a residual saturation level below which the phase will not flow. This is because the non-wetting phase occupies the larger pore spaces, which are more critical for flow1. Relative permeability curve: Applications: These curves are crucial for predicting the behavior of multiphase flow in reservoirs, which helps in designing efficient extraction methods and enhancing oil recovery2. Consider the two-phase flow behaviour depicted in figure below. The entire pore space is filled with water and oil so that Sw + So =100% at all times. To visualize what is happening, assume that the rock is originally 100% saturated with oil. Further, assume that we introduce water into every pore simultaneously and that a water-wet equilibrium is instantaneously established. This, of course, we cannot do, except mentally to visualize the mechanism involved. When water is first introduced, it is adsorbed by the rock and held immobile both on the rock surfaces and in the small corners around the junctions of the individual grains. The immobility is indicated by krw =0 in region A. Note, however, that kro is essentially constant at 1.0 over the same saturation range. As this process continues, the water saturation reaches some critical value Swc at which water becomes mobile, (krw >0). 4 At this time, both oil and water flow; as water saturation is increased (and oil saturation is decreased), however, kro decreases and krw increases, as shown in region B. Continued increase of Sw causes the oil saturation to reach a residual value Sor at which oil becomes mobile (kro =0) and only water flows. This the minimum saturation to which oil may be reduced by injecting water. If it were possible to remove the oil by some other means, krw would continue to increase and finally reach the value of one as shown. This process could have been visualized in reverse just as well. It should be noted that this example portrays oil as non-wetting phase and water as wetting. The distribution of the wetting and non-wetting phases is commonly classified as pendular, finicular, or insular, depending on their saturations. In region A, the aqueous phase exists mainly as pendular rings around the grain junctions which may only contact each other via and extremely thin adsorbed layer on the rock surface (Fig.). In region B, both phases exist in continuous flow paths through their own pore networks, and both are said to be in finicular saturation. As water saturation continues to increase, the oil saturation is finally reduced to point where the connecting threads break and oil becomes discontinuous at the value Sw. Thus, in region C the oil exists in small, isolated groups of pores (islands) or in a state of insular saturation. Again, this discussion has considered water as the wetting phase and oil as non-wetting; however, the general concepts apply to any system of wetting and non-wetting fluids. Therefore, in summary: Region Wetting phase Non-wetting phase saturation saturation A Pendular, immobile Finicular, mobile B Finicular, mobile Finicular, mobile C Finicular, mobile Insular, immobile 5 Relative permeability measurements: (a) Steady state method: A common method for measuring two-phase relative permeability utilizes the apparatus shown in Fig.3. This is a slight modification of the Penn-State method developed by Morse et al. The test sample is confined at the ends between samples having similar properties. Intimate contact is maintained between the three cores to eliminate any capillary effects at the ends (particularly the down-stream end) of the test sample. This ensures that the saturation distribution of each fluid will be uniform during a steady state flow test. The up-steam plug also serves as a mixing head for the injected fluid. The cores are first saturated with the fluids to be displaced, (which is commonly oil), and the weight of the test section is recorded. A constant oil flow rate is then established such that the desired pressure drop occurs. The oil flow rate is then reduced slightly and the 6 displacing fluid (oil or water) is simultaneously injected at a rate sufficient to maintain the originally established pressure drop. Equilibrium is established when the respective input and outflow volumes are equal. (b) Unsteady state method: It is a commonly used method and it consumes less time. In this method, core is saturated with one phase which is displaced by other phase by injection at constant rate. The volume of fluids being produced is monitored at the outlet. Close readings of pressure drop across the core and fluid volumes produced are taken after breakthrough. The relative permeabilities are computed corresponding to outlet-end saturation. Saturations are determined either gravimetrically by removing and weighing the test section, or electrically by measuring resistivity. The oil rate is then decreased further and the gas or water flow rate increased proportionately. End Effect in measurement: End effect arise from the saturation discontinuity existing at the outflow face of a porous medium when mounted for a flow test. The fluids flowing through the core are discharged into a region void of the porous medium. This results into a saturation gradient at the outflow face. Precaution should be taken to prevent it by putting a dummy piece of the porous disc. Drainage and imbibition processes; and Hysteresis Effect: As was discussed for capillary-pressure data, there is also a saturation history effect for relative permeability. The effect of saturation history on relative permeability is illustrated in Figure. If the rock sample is initially saturated with the wetting phase (e.g., water) and relative- permeability data are obtained by decreasing the wetting-phase 7 saturation while flowing non-wetting fluid (e.g., oil) in the core, the process is classified as drainage or desaturation. If the data are obtained by increasing the saturation of the wetting phase, the process is termed imbibition or re-saturation. The nomenclature is consistent with that used in connection with capillary pressure. This difference in permeability when changing the saturation history is called hysteresis. Since relative permeability measurements are subject to hysteresis, it is important to duplicate, in the laboratory, the saturation history of the reservoir. Drainage Process It is generally agreed that the pore spaces of reservoir rocks were originally filled with water, after which oil moved into the reservoir, displacing some of the water, and reducing the water to some residual saturation. When discovered, the reservoir pore spaces are filled with a connate water saturation and an oil saturation. If gas is the displacing agent, then gas moves into the reservoir, displacing the oil. This same history must be duplicated in the laboratory to eliminate the effects of hysteresis. The laboratory procedure is to first saturate the core with water, then displace the water to a residual, or connate, water saturation with oil after which the oil in the core is displaced by gas. This flow process is called the gas drive, or drainage, depletion process. In the gas drive depletion process, the non-wetting phase fluid is continuously increased, and the wetting phase fluid is continuously decreased. Imbibition Process The imbibition process is performed in the laboratory by first saturating the core with the water (wetting phase), then displacing the water to its irreducible (connate) saturation by injection oil. This “drainage” 8 procedure is designed to establish the original fluid saturations that are found when the reservoir is discovered. The wetting phase (water) is reintroduced into the core and the water (wetting phase) is continuously increased. This is the imbibition process and is intended to produce the relative permeability data needed for water drive or water flooding calculations. Reference: 1. Amyx, J. W., Bass, Jnr. D. M., Whiting, R. L.: Petroleum Reservoir Engineering, McGraw-Hill, 1960 2. Gatlin, C.: Petroleum Engineering – Drilling and Well completions, Prentice-Hall Inc., N.J., 1960 3. Ahmed, T.: Reservoir Engineering handbook, Gulf publications, 2005. 9