Page 5 - Petroleum Production Engineering, A Computer-Assisted Approach

Guo, Boyun / Petroleum Production Engineering, A Computer-Assisted Approach Guo-prelims Final Proof page xiii 29.12.2006 10:39am

LIST OF SYMBOLS xiii

q wh flow rate at wellhead, stb/day V 0 pump displacement, ft 3
R producing gas-liquid ratio, Mcf/bbl, or V P initial pore volume, ft 3
dimensionless nozzle area, or area ratio V r plunger rising velocity, ft/min
A p =A b , or the radius of fracture, ft, or gas V res oil volume in reservoir condition, rb
3
constant, 10:73 ft -psia=lbmol-R V s required settling volume in separator, gal
r distance between the mass center of V slug slug volume, bbl
counterweights and the crank shaft, ft or V st oil volume in stock tank condition, stb
cylinder compression ratio V t A t (D V slug L), gas volume in tubing, Mcf
r a radius of acid treatment, ft V Vsc specific volume of vapor phase under
R c radius of hole curvature, in. standard condition, scf/mol-lb
r e drainage radius, ft V 1 inlet velocity of fluid to be compressed, ft/sec
r eH radius of drainage area, ft V 2 outlet velocity of compressed fluid, ft/sec
3
R p pressure ratio n 1 specific volume at inlet, ft =lb
3
R s solution gas oil ratio, scf/stb n 2 specific volume at outlet, ft =lb
r w radius of wellbore, ft w fracture width, ft, or theoretical shaft work
r wh desired radius of wormhole penetration, m required to compress the gas, ft-lb f =lb m
R 2 A o =A i W air weight of tubing in air, lb/ft
r Ri vertical pressure gradient in the curvic section W c total weight of counterweights, lbs
of lateral i, psi/ft W f weight of fluid, lbs
1
S skin factor, or choke size, ⁄ 64 in. W fi weight of fluid inside tubing, lb/ft
S A axial stress at any point in the tubing string, W fo weight of fluid displaced by tubing, lb/ft
psi WOR producing water-oil ratio, bbl/stb
specific gravity of fluid in tubing, water ¼ 1,
S f W p plunger weight, lb f
or safety factor W s mechanical shaft work into the system, ft-lbs
specific gravity of gas, air ¼ 1 per lb of fluid
S g
specific gravity of produced oil, fresh water ¼ 1 fracture width at wellbore, in.
S o w w
specific gravity of produced solid, fresh w w average width, in.
S s
water ¼ 1 X volumetric dissolving power of acid solution,
3
3
S t equivalent pressure caused by spring tension, ft mineral/ ft solution
psig x f fracture half-length, ft
S w specific gravity of produced water, fresh x i mole fraction of compound i in the liquid
water ¼ 1 phase
T temperature, 8R x 1 free gas quality at upstream, mass fraction
t temperature, 8F, or time, hour, or retention y a actual pressure ratio
time, min y c critical pressure ratio
T av average temperature, 8R y i mole fraction of compound i in the vapor
T avg average temperature in tubing, 8F phase
T b base temperature, 8R, or boiling point, 8R y L liquid hold up, fraction
T c critical temperature, 8R Z gas compressibility factor in average tubing
T ci critical temperature of component i, 8R condition
T d temperature at valve depth, 8R z gas compressibility factor
TF 1 maximum upstroke torque factor z b gas deviation factor at T b and p b
TF 2 maximum downstroke torque factor z d gas deviation factor at discharge of cylinder,
T m mechanical resistant torque, lb f -ft or gas compressibility factor at valve depth
t r retention time 5:0 min condition
T sc standard temperature, 520 8R z s gas deviation factor at suction of the cylinder
T up upstream temperature, 8R z 1 compressibility factor at suction conditions
T v viscosity resistant torque, lb f -ft z z the average gas compressibility factor
T 1 suction temperature of the gas, 8R DZ elevation increase, ft
T T average temperature, 8R
u fluid velocity, ft/s
mixture velocity, ft/s Greek Symbols
u m
superficial velocity of liquid phase, ft/s a Biot’s poroelastic constant, approximately 0.7
u SL
superficial velocity of gas phase, ft/s b gravimetric dissolving power of acid solution,
u SG
V volume of the pipe segment, ft 3 lb m mineral=lb m solution
v superficial gas velocity based on total cross- « 0 pipe wall roughness, in.
sectional area A, ft/s f porosity, fraction
V a the required minimum acid volume, ft 3 h pump efficiency
V fg plunger falling velocity in gas, ft/min g 1.78 ¼ Euler’s constant
V fl plunger falling velocity in liquid, ft/min g a acid specific gravity, water ¼ 1.0
V g required gas per cycle, Mscf g g gas-specific gravity, air ¼ 1
V gas gas volume in standard condition, scf g L specific gravity of production fluid, water ¼ 1
3
V G1 gas specific volume at upstream, ft =lbm g m mineral specific gravity, water ¼ 1.0
3
V G2 gas specific volume at downstream, ft =lbm g o oil specific gravity, water ¼ 1
V h required acid volume per unit thickness of g oST specific gravity of stock-tank oil, water ¼ 1
3
3
formation, m =m g S specific weight of steel (490 lb=ft )
3
V L specific volume of liquid phase, ft =mol lb, or g s specific gravity of produced solid, water ¼ 1
volume of liquid phase in the pipe segment, g w specific gravity of produced water, fresh
3
ft , or liquid settling volume, bbl, or liquid water ¼ 1
3
specific volume at upstream, ft =lbm m viscosity
V m volume of mixture associated with 1 stb of oil, m a viscosity of acid solution, cp
3
ft , or volume of minerals to be removed, ft 3 m od viscosity of dead oil, cp