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Ref.1: Brill & Beggs, Two Phase Flow in Pipes, 6th Edition, 1991. Chapter 2. Ref.2: Guo, Lyon & Ghalambor, Petroleum Production Engineering, Elsevier Science & Technology, 2007, Chapter 1&2. Introduction A complete oil or gas production system consists of a reservoir, well, flowline, separators, pumps, and transportation pipelines. Introduction A ‘‘reservoir’’ is a porous and permeable underground formation containing an individual bank of hydrocarbons confined by impermeable rock or water barriers and is characterized by a single natural pressure system. Hydrocarbon accumulations are classified as oil, gas condensate, and gas reservoirs. Gas wells: GOR >100,000 scf/stbo Compositional model Gas condensate wells: 5,000<GOR< 100,000 scf/stbo Oil wells: GOR< 5,000 scf/stbo Black oil model Black Oil Model Gas Oil Ratio ‘‘Solution GOR’’ is defined as the amount of gas (in standard condition) that will dissolve in unit volume of oil when both are taken down to the reservoir at the prevailing pressure and temperature; that is, Rs Gas volume Oil volume in standard conditions in stock tank conditions standard condition is 14.7 psia and 60 oF ( scf ) ( stbo ) Rs remains constant at pressures above bubble-point pressure. It drops as pressure decreases in the pressure range below the bubble-point pressure. Black Oil Model Gas Oil Ratio Lasater correlation (recommended for oAPI>15): 1. Calculate P ( psia ) g gd o T( R) ggd is sp. gr. of dissolved gas at sc. 2. Obtain yg from Figure 2.2. 3. Obtain Mo from Figure 2.1. 4. Calculate ( 379 . 3 )( 350 ) g o Rs Mo yg 1 yg C C is the tuning parameter (default value of C is 1.0). Black Oil Model Gas Oil Ratio Standing correlation (recommended for oAPI<15): Calculate P ( psia ) 10 o 0 . 00091 T ( F ) 10 18 0 . 0125 R s g gd o API 1 . 2048 C C is the tuning parameter (default value of C is 1.0). Black Oil Model Oil Formation Volume Factor ‘‘Oil formation volume factor’’ is defined as: Bo Oil volume Oil volume in reservoir conditions ( bbl ) in stock tank conditions ( stbo ) Bo is always greater than unity. At a given reservoir temperature, Bo remains nearly constant at pressures above bubble-point pressure. It drops as pressure decreases in the pressure range below the bubble point pressure. Black Oil Model Oil Formation Volume Factor Standing correlation: g gd B o 0 . 972 0 . 000147 R s g o 0 .5 o 1 . 25 T ( F ) C is the tuning parameter (default value of C is 0.0). 1 . 175 C Black Oil Model Oil Density Res. Cond.: P, T Free gas: mgf (lbm) Oil: Fo (bbl) Density: o (lbm/ft3) Free gas: mgf (lbm) Dissolved gas: Vgd (scf) Dissolved gas density: gd (lbm/scf) = ggd (0.0764) S.C. P =14.73 psia T = 60 oF Oil: Lo (stbo) Oil density: Lo (lbm/scf) = go (62.4) Mass Balance: o V gd m gf 5 . 614 Fo o m gf V gd gd 5 . 614 L o Lo L o gd 5 . 614 Lo 5 . 614 Fo L o Fig. 2.18 o 0 . 0136 R s g gd 62 . 4 g o Bo Black Oil Model Specific Gravity of Free Gas Gas Mass Balance: Total produced gas at s.c. = Dissolved gas + Free gas R p L o 0 . 0764 g gt R s L o 0 . 0764 g gd R p R s L o 0 . 0764 g gf g gf R p g gt R s g gd R p Rs 0 . 56 g gf g gt , 0 . 56 g gd and g gt g gd Where Rp is the produced Gas Oil Ratio (Rp ≥ Rs). Black Oil Model Oil Viscosity 1- Viscosity of saturated oil (Beggs and Robinson): A- Dead oil viscosity (P =1.0 atm) OD 10 X 1, X 10 ( 3 . 0324 0 . 02023 T o API ) , 1 . 163 T F o B- Live oil viscosity o ( cp ) A B OD , A 10 . 715 R s 100 0 . 515 , B 5 . 44 R s 150 0 . 338 Black Oil Model Oil Viscosity 2- Viscosity of undersaturated oil (Vazquez): m P o ob , Pb 2 .6 P m 10 3 .9 10 1 . 187 5 P 5 .0 Procedure for calculating Pb: -Assume Pb=P and calculate Rs (from Standing or Lasater) - If Rs>Rp the oil is undersaturated, otherwise the oil is saturated -For undersaturated oil, assume Rs=Rp -Calculate Pb from Standing or Lasater correlation. Black Oil Model Oil Viscosity Standing Correlation: A- Dead oil viscosity (P =1.0 atm) 1 . 8 10 0 . 32 o 4 . 53 API 7 OD A 360 T ( o F) 200 , A 10 8 . 33 0 . 43 o API B- Saturated oil viscosity o ( cp ) 10 OD , a b 0 . 68 b 10 8 . 62 10 5 Rs a R s 2 . 2 10 0 . 25 10 1 . 10 10 3 Rs 7 R s 7 . 4 10 4 0 . 062 10 3 . 74 10 3 Rs C- Undersaturated oil viscosity o ob 0 . 001 ( P Pb ) 0 . 024 ob 0 . 38 ob 1 .6 0 . 56 Black Oil Model Gas-Oil Surface Tension Baker and Swerdloff correlation: 1- Dead oil surface tension (sOD): An estimate of oil surface tension at atmospheric pressure, can be obtained from Figure 2.37. Note: Extrapolation beyond the temperature rang of [68 oF 100 oF] is not recommended. 2- Live oil surface tension (sO): The surface tension of crude oil containing dissolved gas expressed as a percent of sOD can be obtained from Figure 2.38. Black Oil Model Free Gas Density 1- Engineering Equation of state: P V z n R T gf M gf PM M air g gf gf gf gf z RT P g gf 29 10 . 72 z T lbm 2 . 70 g gf P ( psia ) 3 o ft z T ( R) Black Oil Model Free Gas Density 2- Gas formation volume factor (Bg): zn RT Bg o V V sc P z sc n R T sc 0 . 0283 z T ( R ) P ( psia ) Psc gf gf gf sc Bg air g gf sc Bg lbm 0 .0764 γ gf 3 Bg ft Black Oil Model Free Gas Compressibility Factor 1- Standing and Katz correlation: T pr 2- Brill and Beggs correlation: A 1 . 39 (T pr 0 . 92 ) 0 .5 D 10 10 T T pc , P pr z A (1 A ) e B P , Figure 2.21 P pc C P pr D 0 . 36 T pr 0 . 1 B ( 0 . 62 0 . 23 T pr ) Ppr C 0 . 132 0 . 32 log 0 . 066 0 . 037 T 0 . 86 pr (T pr ) 2 ( 0 . 3106 0 . 49 T p r 0 . 1824 T p r ) 6 2 0 . 32 Ppr P pr 10 9 ( T p r 1 ) Black Oil Model Free Gas Pseudocritical Properties 1- Brown et al. correlation: Figure 2.20 Valid for H2S < 3%, N2 < 5%, and total content of inorganic compounds less than 7%. Ppc ( psia ) 709 . 604 58 . 718 g gf T pc ( R ) 170 . 491 307 . 344 g gf o 2- Ahmed correlation: Ppc ( psia ) 678 50 ( g gf 0 . 5 ) 206 . 7 y N 2 440 y CO 2 606 . 7 y H 2 S T pc ( R ) 326 315 . 7 ( g gf 0 . 5 ) 240 y N 2 83 . 3 y CO 2 133 . 3 y H 2 S o Black Oil Model Free Gas Viscosity 1- Carr et al. correlation: A- Gas viscosity at atmospheric pressure (1): Figure 2.35 Valid for 40 < T(oF) < 400 B- Viscosity ratio (/1): Figure 2.36 Valid for 1.0 < Ppr < 20.0 C- Free gas viscosity: gf 1 ( cp ) 1 Black Oil Model Free Gas Viscosity 2- Lee et al. correlation: gf ( cp) 1 10 K 4 ( 9 . 4 0 . 02 M 209 19 M X 3 .5 986 T Where gf gf )T 1 .5 T 0 . 01 M gf T R and gf o ( 2 .4 0 .2 X ) K exp X gf gr 0 . 0433 g gf P ( psia ) 3 o zT( R) cm Black Oil Model Water (Brine) Density A- Water formation volume factor (Bw): Figure 2-13 Figure 2-14 Bw B y Bw ' w Figure 2-11 B- Water density (w): w w Figure 2-19 sc Bw Black Oil Model Water Viscosity A- Viscosity of pure water (Van Wingen correlation): w’ : Figure 2.32 B- Viscosity of brine (Frick correation): w (cp) = w’ Ratio , Ratio: Figure 2.33 Compositional Model The critical properties of components that are usually found in gas and gas condensate wells are shown in this Table. The components that are heavier than n-Hexane are usually shown as a pesudocomponent (C7+). For calculating the properties of gas and gas condensate wells, the compositional model is recommended. Many gas or gas condensate wells exhibit retrograde condensation, phenomena in which condensation occurs during pressure reduction (shaded region within the two-phase envelope of Figure). Compositional Model Flash Calculation Free gas flowrate: V Composition: yi Res. Cond.: P, T Composition: Zi for i = 1, … , n Mole flowrate: F Equilibrium Flash Ki = yi / xi Condensate flowrate: L Composition: xi At equilibriu By definition Therefore : m : fi fi v : l fi yi Pi , v Ki v yi xi i f i xi P i l l l v i SRK or PR Compositional Model Gas and Liquid Density Once the compressibilities of each phase is determined, the gas and liquid densities can be determined from: V L P MV n , ZV R T PM MV yi M i i 1 n L ZLRT , M L xM i i i 1 Other properties can be calculated based on the composition of liquid and gas phases (GPSA, Engineering Data Book, 11th edition, 1998, Chapter 23). Compositional Model Pesudocomponents If you like to use compositional model for oil wells, the oil must defined as some pesudocomponents based on distillation curve. There are several methods of measuring and reporting distillation curves of crude oil and petroleum fractions: 1- ASTM D 86 2- True Boiling Point (TBP) 3- Simulated Distillation by GC (ASTM D 2887) 4- Equilibrium Flash Vaporization (EFV) 5- Distillation at Reduced Pressures (ASTM D 1160)