Reservoir Fundamentals KNW1

porosity

ratio of pore volume to bulk volume
phi = V_p/V_b => 0<phi<1

pore throat factors & responsibilities

determines permeability

their number, size & distribution controls:

• resistivity

• flow

• capillary force

porosity factors

• size

• shape

• distribution (sorting)

• arrangement (packing)

permeability

capacity of a porous material for transmitting a fluid controlled by the size of the pore throats & capillaries [mD]
1mD = 10e-15 m2

Darcy law

description of single-phase flow in porous media
q_darcy = phi*velocity = -k//µ (pressure gradient-rho*g)

permeability tests

• core flooding in lab

• pressure transient test for field

reservoir velocities

• volumetric flux: discharge of a volume per time Q=dV/dt [m3/s]

• darcy velocity: the velocity of porous medium would be an open volume q=Q/A [m/s]

• interstitial velocity: the actual velocity of a fluid element as the fluid moves through the pore space in the porous medium v=q/phi [m/s]

permeability upscaling

changing from the micro to continuum scale via porosity REV
- flow parallel to the layers → arithmetic avg: k_avg = ∑kihi/∑hi
- flow perpendicular to the layers → harmonic avg: k_avg = ∑Li/∑(Li/ki)

wiener bounds

The effective property of a heterogeneous media is bounded between harmonic and arithmetic averages.

fluid pressure

the weight of the fluid column above the reservoir depth
p_fl = p0+rho*g*z p0+G*z

density order of a reservoir fluids

water>oil>gas

fluid contact tests

• fluid pressure regimes

• fluid densities from formation samples

• capillary pressure data from core samples

• seismic survey

total pressure of reservoir

weight of the formation rock & fluids

transition zone factors

• rock structure

• heterogeneity

total pore volume

volume of fluid filled pores
Vp=Vw+Vo+Vg

fluid saturation

the proportion of each fluid within the total pore volume
Si = Vi/Vp => Sw+So+Sg=1

fluid saturation of heterogeneous formation

saturation varies through the layers thus we go with the avg saturation
So,avg = ∑phi*hi*Soi/∑phi*hi

capillary rise

a competition between the capillary force & gravity
p_c = p_g
(2*sigma(F1F2)*cosø)/r = rho*g*h

PVT experiment

1. recombine crude oil & gas in the right proportions

2. control pressure by Hg-pump pressure gauge at const. temp →injected Hg acts as piston controlling the volume in the pressure cell

main parameters of reservoir volume

• solution gas oil ratio Rs=V_gs/V_os [scf/stb]

• oil formation volume factor Bo=V_or/V_os [rb/stb]

• gas formation volume factor Bg=V_gr/V_fg [rb/scf]

  V_gs=V_sg+V_fg

  Vsg = volume of solution gas

  Vfg = volume of free gas

  Vos = volume of oil surface cond.

  Vor = volume of oil res. cond.

fluid types

• incompressible → liquids under pressure maintenance conditions c = 0

• slightly compressible → liquids under pressure depletion conditions c = const

• compressible → gases & supercritical fluids under pressure variation c(p)

compressibility by volume & density

fractional changes in volume due to unit change in pressure [psi^-1]:

cv = - 1/V * ∂V/∂p

cp= 1/rho * ∂rho/dp

surface (stock tank) pT-condition

• p = 14.696 psi

• T = 60°F =15,556 °C 16°C

ideal gas EOS

• low pressure pV = nRT

• high pressure pV = ZnRT

compressibility z factor parameters

• gas composition

• temp

• pressure

sensible heat

changes the temp of a substance w/o changing its state

latent heat

changes the state of a substance w/o changing its temp

water recharge

a doublet system w/ a hot producer and a cold re-injector:

• injection into a single-phase liquid water region: increase or maintain pressure

• injection of cold water into two-phase (steam-water) reservoir: decrease pressure & temp until condensation

• injection of cold water into a superheated steam zone: increase pressure as long as no two phase zone develops

solubility

the ability of a substance to be dissolved in the solvent

• increases w/ pressure

• decrease w/ increasing temp & salinity

miscibility

the ability of one substance to dissolve in another substance forming a homogenous solution (usually liquid)

critical locus

the max pressure at which two phases can exist

cumulative gas volume formula

F = ∑V_g

expansion factor formula

E = V_g/V_m,g

compressibility z-factor formula

Z = p/p_sc T_sc/T 1/E = 35.37 p/ET

shrinkage factor formula

c_bs = V_o in the separator/V_o at BP

GOR

the ratio of gas to oil produced at stock-tank cond.

GOR = V_g/V_o in the separator

Derivation of Field Relevant Parameters

• flash (FE): liberation process in reservoir

• differential (DLE): liberation process around well → same as flash experiment starts at bp pressure and after each step, gas is removed from the cell by const pressure Hg-injection

oil formation volume factor

Bo = V_o/c_bf [rb/stb]

solution gas oil ratio

the solubility of natural gas in crude oil depending on temp, pressure & composition of o&g

R_si - R_s = 5.615F/c_bf [scf/stb]

gas formation volume factor

Bg = 1/ 5.615E [rb/scf]

Apparent molecular weight formula

M_a = ∑yiMi

Volume at standard conditions formula

RT_sc/p_sc

gas density formula

rho = m/V = pMa/ZRT

specific volume formula

v = V/m = ZRT/pMa = 1/gas density

gas expansion factor formula

Eg = 1/Bg

gas formation volume factor

Bg = V_res/V_sc = 0.02827 ZT/p [ft3/scf] = 0.005035 ZT/p [rb/scf] = 351.64 ZT/p [m3/sm3]

gas specific gravity formula

gamma g = rho_gas,sc/ rho_air,sc = M_a/M_air = Ma/28.96

critical pT formula

p_c = ∑yipci

T_c = ∑yiTci

reduced pT formula

p_r = p/p_c

T_r = T/T_c

quality lines

determines the percentage of liquid & gas at the given PVT conditions

black oil reservoir

• includes large, heavy, nonvolatile molecules

• covers a wide temp range

• aka low shrinkage crude oil or ordinary oil

• brown to dark green color

volatile oil reservoir

• more intermediate molecules (ethane to hexane)

• smaller temp range

• Tc closer to the Tres

• release large amount of gas in the reservoir

• lower amount of oil in the separator

• aka high shrinkage crude oil or near critical oil

• Tc >Tres

• greenish to orange color

retrograde gas reservoir

• Tc<Tres<Tct

• fewer heavy HC

• smaller temp range

• reservoir is initially in gas phase & as the pressure decreases below the dew point, liquid condenses

• translucent or slightly coloured

• aka gas condensate

wet gas reservoir

• The hydrocarbon mixture exists as a gas in the reservoir and two-phase in the surface

• Tres>Tc

• translucent

• smaller HC molecules

• entire envelope is below Tres

dry gas reservoir

• The hydrocarbon mixture exists as a gas both in the reservoir and in the surface since it doesn’t have enough heavier molecules to form liquid in the separator or field

• Tres>Tc

• primarily methane w/ some intermediates

separator flash expansion

stimulates the surf separation conditions of reservoir fluid

1. PVT cell is connected to a separator system

2. the separator maintains a fixed pT-condition that mimics surface facility conditions

3. the bp oil is then flashed through the separator system to stock tank conditions

FCM process

injecting a primarily slug that is miscible w/ the crude oil

material balance

Keep track of mass and be able to convert form reservoir to surface conditions to predict recovery & determine the principle res drive mechanism

oil volume

Vo = V*N_G*phi*Soi

total oil volume at sc

N = V*N_G*phi*Soi/Boi

connate water

water naturally trapped in rock pores due to capillary force → lowest in-situ water saturation

water expansion formula

cw = -1/Swc ∂Swc/∂p due to pressure & effective pore pressure decrease

pot aquifer model

assumes the gas field is in contact with an aquifer, which responds instantly to any decline in reservoir pressure (maintaining pressure) used for

• rel. slow production

• small aquifers

• well connected & high permeable aquifers

reservoir tank model

describes the effective volumetric properties

Oil production formula

N - Np = V*N_G*phi*So/Bo

Rf = Np/N = 1 - (Boi*So)/(Bo*Soi)

gas production formula

G - Gp = V*N_G*phi*Sgi/Bg

Rf = Gp/G = 1 - (Bgi/Bg) = 1- (pZi/piZ)

Water drive gas res formula

G - Gp = (V*N_G*phi*Sgi/Bg)-(We/Bg)

Gp = G(1-(Bgi/Bg)) + We/Bg

Rf = Gp/G = (1 - (Bgi/Bg))+ Bgi(1-Swc-Sgr)/Bg(1-Swc) = 1 - (Bgi*Sgr)/Bg(1-Swc)

Water influx formula

We = Wc∆p = W(Cø+Cw)∆p = Vinv*phi(1-Swc-Sgr)

material balance formula

F = N(E0 + mEg + (1+m)Er) + We = N(Bo-Boi+Bg(Rsi-Rs)) + mNBoi((Bg/Bgi)-1) + (1+m)NBoi(cø+SwcCw/1-Swc)∆p + Wc∆P

m = Vgc/Voc

main drive mechanism

• gas cap drive

• water drive

• solution gas drive

• combined drive = gas cap + water

Solution gas drive MBE conditions

• energy source: evolved solution gas expansion

• RF = 5-30%

  • m = 0

  • Cg »Cw => Cw & Cø =0

  • W = 0

F = NE0
Np(Bo+Bg(Rp-Rs)) = N(Bo-Boi+Bg(Rsi-Rs))

gas solution drive well placement

• artificial lift at early stages

• steep dip: wells in down dip but not too close to WOC to form a secondary gas cap

• shallow dip: well as low as possible to keep was from secondary gas cap

Gas cap drive MBE conditions

• Energy source: gas cap & evolved solution gas expansion

• RF = 20-50%

  • Cg »Cw => Cw & Cø =0

  • W = 0

F= N(E0+mEg)

Np(Bo+Bg(Rp-Rs)) = N(Bo-Boi+Bg(Rsi-Rs))+mNBoi(Bg/Bgi -1)

gas cap well placement

higher recover w/ gas driving oil downwards => to avoids the problem of extensive gas production:

• Well completions near the bottom of the oil column

• horizontal wells low in the oil column

wells should be placed far away from gas cap w/ long life time

types of aquifer

• confined/ excxpansion: The aquifer is bounded by impermeable rock so that the reservoir and aquifer together form a volumetrically closed unit. parameters:

  • compressibility of aquifer water & matrix

  • relative size of aquifer to HC accumulation

• unconfined/ artesian: The reservoir rock outcropped at one or more places where it may be refilled by surface water.

water drive type

• bottom water drive → linear geometry

• edge water drive→ radial geometry

water drive MBE conditions

• Energy source: aquifer expansion

• RF = 30-70%

• Cg »Cw => Cw & Cø =0

• m = 0

• SwcCw=0

F= NE0 + Wc∆p

Np(Bo+Bg(Rp-Rs)) = N(Bo-Boi+Bg(Rsi-Rs))+Wc∆p

water drive well placement

there is an early water breakthrough due to water coning & viscous fingering => well should be perforated high in the oil zone to maximise distance to WOC

combined drive

• m = 0

• Rp-Rs = 0

• W = 0

• Rs = 0

• SwcCw =0

  F =N(E0+Er)

  NpBo = N(Bo-Boi)+NBoi(Cø/1-Swc)∆p

Z-factor

describes the deviation of a gas from ideal gas law

Z = V_actual/V_ideal

solution drive

oil reservoirs that don’t initially contain free gas but develop free gas on pressure depletion. applies when the pressure drops below the BP

water cut

the ratio of water produced compared to the volume of total liquids produced from an oil well

natural drive mechanism

pressure différence between the reservoir & the surf

secondary gas cap

formed by migration of librated gas to the top by buoyancy → weak drive mechanism

depends on:

• permeability

• permeability aniostrophy

• dipping angle

gravity drainage

a type of reservoir drive mechanism caused by the difference in densities of oil & gas & gas segregation → weak and slow mechanism

depends on steepness of the reservoir