Vietnam National University - Ho Chi Minh City University of Technology Faculty of Geology & Petroleum Engineering Department of Drilling - Production Engineering Course Reservoir Engineering Trần Nguyễn Thiện Tâm Email: trantam2512@hcmut.vn 12/11/2017 Reservoir Engineering 1 References Holditch Resevoir Engineering (Schlumberger) 12/11/2017 Reservoir Engineering 2 Chapter 2 Reservoir rock properties 12/11/2017 Reservoir Engineering 3 Contents Reservoir Porosity Permeability Saturation 12/11/2017 Reservoir Engineering 4 Reservoir A subsurface body of rock having sufficient porosity and permeability to store and transmit fluids. 12/11/2017 Reservoir Engineering 5 Porosity The fraction of total volume that is available for the storage of fluids. VpVb Vma Porosity Vb Vb 12/11/2017 Reservoir Engineering 6 Porosity Rock matrix Pore space 12/11/2017 Reservoir Engineering 7 Pore-Space Classification Total porosity, ϕt Total Pore Space t Bulk Volume Effective porosity, ϕe Interconnected Pore Space e Bulk Volume 12/11/2017 Reservoir Engineering 8 Comparison of Total and Effective Porosities Very clean sandstones: ϕt = ϕe Poorly to moderately well -cemented intergranular materials: ϕt ≈ ϕe Highly cemented materials and most carbonates: ϕe < ϕt 12/11/2017 Reservoir Engineering 9 Permeability Permeability is a property of the porous medium and is a measure of the capacity of the medium to transmit fluids. 12/11/2017 Reservoir Engineering 10 Absolute Permeability When the medium is completely saturated with one fluid, then the permeability measurement is often referred to as specific or absolute permeability.
12/11/2017 Reservoir Engineering 11 Effective Permeability When the rock pore spaces contain more than one fluid, then the permeability to a particular fluid is called the effective permeability. Effective permeability is a measure of the fluid conductance capacity of a porous medium to a particular fluid when the medium is saturated with more than one fluid. 12/11/2017 Reservoir Engineering 12 Relative Permeability Relative permeability is defined as the ratio of the effective permeability to a fluid at a given saturation to the effective permeability to that fluid at 100% saturation. Oil: keo kro k Water: kew krw k Gas: keg krg k 12/11/2017 Reservoir Engineering 13 In-Situ Saturation Rock matrix Water Oil and/or gas 12/11/2017 Reservoir Engineering 14 Fluid Saturation Saturation is defined as that fraction, or percent, of the pore volume occupied by a particular fluid (oil, gas, or water).
total volume of the fluid fluid saturation pore volume Applying the above mathematical concept of saturation to each reservoir fluid gives volume of oil volume of gas So Sg pore volume pore volume volume of water Sw pore volume 12/11/2017 Reservoir Engineering 15 Fluid Saturation The saturation of each individual phase ranges between zero to 100%. By definition, the sum of the saturations is 100%, therefore Sg + So + Sw = 1.0 12/11/2017 Reservoir Engineering 16 Example A core, 2.75 cm long and 2.75 cm in diameter has a porosity of 25%. It is saturated with oil and water, where the oil content is 1. a) What is the pore volume of the core? b) What are the oil and water saturations of the core? 12/11/2017 Reservoir Engineering 17 Average porosity Arithmetic average ϕ = Σϕi/n Thickness-weighted average ϕ = Σϕihi/Σhi Areal-weighted average ϕ = ΣϕiAi/ΣAi Volumetric-weighted average ϕ = ΣϕiAihi/ΣAihi where n = total number of core samples hi = thickness of core sample i or reservoir area i ϕi = porosity of core sample i or reservoir area i Ai = reservoir area i 12/11/2017 Reservoir Engineering 18 Example Calculate the arithmetic average and thickness-weighted average from the following measurements: Sample Thickness, ft Porosity, % 1 1.1 10 12/11/2017 Reservoir Engineering 19 Average permeability Average Permeability (Parallel Flow): n k h i i kavg i 1n h i 1 i Average Permeability (Series Flow): n L i kavg in1 Li i 1 ki 12/11/2017 Reservoir Engineering 20 Example Production well Flow direction k3 = 10 mD k1 = 25 mD h1 = 15 ft k2 = 400 mD h2 = 50 ft L3 = 10 ft L12 = 140 ft 12/11/2017 Reservoir Engineering 21 Original hydrocarbon volume in place One important application of the effective porosity is its use in determining the original hydrocarbon volume in place.
Consider a reservoir with an areal extent of A acres and an average thickness of h feet. The total bulk volume of the reservoir can be determined from the following expressions: Bulk volume = 43,560Ah, ft3 or Bulk volume = 7,758Ah, bbl where A = areal extent, acres h = average thickness 12/11/2017 Reservoir Engineering 22 Original hydrocarbon volume in place The reservoir pore volume in cubic feet gives: PV = 43,560Ahϕ, ft3 Expressing the reservoir pore volume in barrels gives: PV = 7,758Ahϕ, bbl Volume of Gas In Place in cubic feet gives: GIP = 43,560Ahϕ(1 – Sw), ft3 Volume of Oil In Place in barrels gives: OIP = 7,758Ahϕ(1 – Sw), bbl 12/11/2017 Reservoir Engineering 23 Darcy’s Equation kA dp q dL 12/11/2017 Reservoir Engineering 24 Darcy’s Equation TABLE 2.1 – UNIT SYSTEMS USED FOR DARCY’S LAW SI British cgs Darcy Oilfield k m2 ft2 cm2 darcy md p Pa lbd/ft2 dyne/cm2 atm psia q m3/s ft3/sec cm3/s cm3/s RB/D μ Pa. s lbf-sec/ft2 cp cp cp A m2 ft2 cm2 cm2 ft2 12/11/2017 Reservoir Engineering 25 Example Calculation of Permeability of Porous Media. A fluid of viscosity of 1.2 cp flows through a cylindrical core at a rate of 0.25 cm3/s with a pressure drop of 2.
Core dimensions are a length of 12 cm and a 5 cm2 flow area (i., the area perpendicular to the direction of flow). Determine the core permeability. 12/11/2017 Reservoir Engineering 26 Example A sand body is 2000 feet long, 200 feet wide and 12 feet thick. It has a uniform permeability of 345 md to oil at 17 per cent connate water saturation.
The porosity is 32 percent. The oil has a reservoir viscosity of 3. Answer the following: i. If flow takes place parallel to 2000 ft length above saturation pressure, what pressure drop will cause 100 barrels per day (BPD) to flow through the sand body, assuming the fluid behaves essentially as an incompressible fluid? ii.
What is the apparent velocity of the oil in feet per day at the 100 BPD flow rate? iii. What is the interstitial average velocity in feet per day? iv. Calculate initial oil in place in barrel. 12/11/2017 Reservoir Engineering 27 Example Note: Darcy equation in field units is Qo = 0.L, here flow rate is in BPD, ΔP is in psi, viscosity is in cp, permeability is in mD, length is in ft, and area is in sq ft, 1 Barrel = 5.61 cubic feet 12/11/2017 Reservoir Engineering 28 Example Relative Permeability Calculations From Steady-State Tests.2 shows a set of steady-state oil/water relative permeability experiments measured at several water saturations.
Assuming the core size and conditions are the same as in Example 2.1, determine: (1) the oil and water relative permeabilities and (2) the oil- and water-phase permeabilities. Oil viscosity is 5 cp, and water viscosity is 1. 12/11/2017 Reservoir Engineering 29 Example 12/11/2017 Reservoir Engineering 30 Special types of fluid saturations Connate (interstitial) water saturation, Swc Critical oil saturation, Soc Residual oil saturation, Sor Movable oil saturation, Som Critical gas saturation, Sgc Critical water saturation, Swc 12/11/2017 Reservoir Engineering 31 Connate (interstitial) water saturation, Swc The terms irreducible water saturation, connate water saturation, and critical water saturation, generally denoted by Swi (or Siw), are extensively used interchangeably to define the water saturation at which the water phase remains immobile. 12/11/2017 Reservoir Engineering 32 Critical oil saturation, Soc For the oil phase to flow, the saturation of the oil must exceed a certain value, which is termed critical oil saturation.
At this particular saturation, the oil remains in the pores and, for all practical purposes, will not flow. 12/11/2017 Reservoir Engineering 33 Residual oil saturation, Sor During the displacing process of the crude oil system from the porous media by water or gas injection, there will be some remaining oil left that is quantitatively characterized by a saturation value that is larger than the critical oil saturation. This saturation value is called the residual oil saturation, Sor. The term residual saturation is usually associated with the nonwetting phase when it is being displaced by a wetting phase.
12/11/2017 Reservoir Engineering 34 Movable oil saturation, Som Movable oil saturation Som is another saturation of interest and is defined as the fraction of pore volume occupied by movable oil as expressed by the following equation: Som = 1 − Swc − Soc 12/11/2017 Reservoir Engineering 35 Critical gas saturation, Sgc As the reservoir pressure declines below the bubble-point pressure, gas evolves from the oil phase and consequently the saturation of the gas increases as the reservoir pressure declines. The gas phase remains immobile until its saturation exceeds a certain saturation, called critical gas saturation, above which gas begins to move. 12/11/2017 Reservoir Engineering 36 Critical water saturation, Swc The critical water saturation, connate water saturation, and irreducible water saturation are extensively used interchangeably to define the maximum water saturation at which the water phase will remain immobile. 12/11/2017 Reservoir Engineering 37 Rock Wettability Rock wettability is the tendency of either the water phase or the oil phase to preferentially maintain contact with the rock surface in a multiphase fluid system.
The most common method of determining rock wettability is by measurement of the contact angle, θ between the rock surface and the fluid system. The rock surface is considered to be water-wet when θ < 90o and oil-wet when θ > 90o 12/11/2017 Reservoir Engineering 38 Surface and interfacial tension In dealing with multiphase systems, it is necessary to consider the effect of the forces at the interface when two immiscible fluids are in contact. When these two fluids are liquid and gas, the term surface tension is used to describe the forces acting on the interface. When the interface is between two liquids, the acting forces are called interfacial tension.
12/11/2017 Reservoir Engineering 39 Surface and interfacial tension Surface tension rh w g gw 2 cos Interfacial tension rhg w o ow 2 cos 12/11/2017 Reservoir Engineering 40 Capillary Pressure Capillary pressure, pc is commonly defined as the difference in the pressure of the non-wetting phase and the pressure of the wetting phase. This is represented as: pc = pnw – pw pnw = pressure in the non-wetting phase; pw = pressure in the wetting phase. 12/11/2017 Reservoir Engineering 41 Capillary Pressure For a water-wet rock in an oil/water system, the capillary pressure derived from Eq. is: pc = po - pw Similarly, for an oil-wet rock in an oil/water system, the capillary pressure is: pc = pw - po By convention, the capillary pressure in a water-wet rock is designated as positive.
Hence, capillary pressure in an oil-wet rock is designated as negative. 12/11/2017 Reservoir Engineering 42 Capillary Pressure Gas-liquid system 2 gw cos 2 gw cos pc h r rg w g where σgw = gas-water surface tension, dynes/cm Oil-water system 2 ow cos 2 ow cos pc h r rg w o where σow is the water-oil interfacial tension, dynes/cm. g = acceleration due to gravity, cm/sec2 (980.7) ρw = water density, gm/cm3 r = capillary radius, cm h = capillary rise, cm pc = capillary pressure, dynes/cm2 12/11/2017 Reservoir Engineering 43 Example Calculate capillary pressure and capillary rise in an oil-water system from the following data: θ = 30° ρw = 1.75 gm/cm3 r = 10−4 cm σow = 25 dynes/cm g = 980.7 cm/sec2 12/11/2017 Reservoir Engineering 44 Capillary Pressure The phenomenon of capillarity in reservoirs can be discussed in terms of capillary pressure as measured in capillary tubes.
