Definition of Terms:

Porosity of a rock is a measure of storage capacity that is capable of

holding fluids (pore volume) or quantitatively porosity is the ratio of pore

volume to the total volume (bulk volume).

∅= Pore volumeBulk volume

- Absolute porosity is ratio of the total pore space in a rock to the bulk

volume.

- Effective Porosity is the ratio of interconnected pore spaces to the bulk

volume.

Saturation is defined as fraction or percent of pore volume occupied by a

particular fluid (oil, gas, water).

S=Total volumeof the fluidPore volume

- Critical Oil Saturation Soc is the saturation of oil at which oil remains in

the pores and for all practical purposes will not flow.

- Residual Oil SaturationS¿ is the saturation value of the oil that remains

after a displacing process of crude oil system by water or gas injection.

- Critical water Saturation Swc (Irreducible Water SaturationSwirr ) is the

maximum water saturation at which water phase will remain immobile. It

also called connate water saturation.

- Movable Oil Saturation Som is fraction of pore volume occupied by

movable oil Som=1−Swirr−Soc

- Critical Gas Saturation Sgc is the saturation under which gas will remain

immobile.

Wettability is the tendency of a fluid to spread or adhere to a solid surface

in the presence of other immiscible fluids.

- Distribution of fluids in porous media is a function of wettability.

-The wetting phase fluids tend to occupy the smaller pores of the rock

while the non-wetting phase fluids occupy the more open channels.

- Force at the interface when two immiscible fluids are in contact is called

– Surface tension when the two fluids are liquid and gas.

– Interfacial tension when the two fluids are two different liquids. Surface

or interfacial tension has the unit of force per unit length (dynes/cm)

Capillary forces in a petroleum reservoir are the result of the combined

effect of the surface and interfacial tension of the rock and fluids, pore

size, pore geometry and the wetting characteristics of the system.

Capillary Pressure Pc exists when two immiscible fluids are in contact

where a discontinuity in pressure exists between the fluids and this

depends upon the curvature of the interface separating the fluids.

Capillary pressure is excess pressure in the non-wetting phase and hence a

function of saturation. Pc=Pnw−Pw

- Leveret J function relates lab capillary measurements to field

measurements.

Permeability K is a property of a porous medium that measures the

capacity and ability of the formation to transmit fluids.

– Absolute Permeability K is the measurement of the permeability

conducted when a single fluid or phase is present in the medium.

– Effective permeability K e is the ability to flow or to transmit a particular

fluid when other immiscible fluids are present in the reservoir.

– When a wetting and non-wetting phase flow together in a reservoir rock

each phase follows separate and distinct path.

– Relative Permeability K ℜ is the ratio of effective permeability of a

particular fluid at given saturation to the absolute permeability of that

fluid at 100% saturation. Kℜ=K e

K ( where e can be oil gas or water) –

Keep in mind that K ro + K rw + K rg ≤1.0 –

Relative Permeability curves shows 4 important observations:

1- The wetting phase relative permeability shows that small saturation of

the non-wetting phase will drastically reduce the relative permeability

of the wetting phase because non-wetting phase occupies the larger

pore spaces where flow occurs with the least difficulty.

2- The non-wetting phase relative permeability curve shows that the non-

wetting phase begins flowing at relatively low saturation of the non-

wetting phase. This point is the critical oil saturation Soc .

3- The wetting phase relative permeability curve shows that the wetting

phase will cease to flow at a relatively high saturation; this because

wetting phase fluid occupies the smaller pore spaces where capillary

forces are at high, the saturation of water at this point is called

irreducible water saturation Swirr.

4- The non-wetting phase relative permeability curve shows that, at the

lower saturation of wetting phase, changes in the wetting phase

saturation have only a small effect on the magnitude of the non-

wetting phase relative permeability curve. That’s because at low

saturation the wetting phase fluid occupies the small pore spaces that

do not contribute materially to flow.

– Critical saturation is measured in the direction of increasing saturation,

while irreducible saturation is measured in the direction of reducing

saturation.

– Drainage process is the displacement of wetting phase fluid (water) by

non-wetting phase fluid (oil)

– Imbibition process is the opposite of drainage, that is displacement of

non-wetting phase fluid by wetting phase fluid.

– The Methods used for calculating relative permeabilities and

relationships are:

1- Wyllie and Gardner Correlation

2- Pirson’s Correlation

3- Corey’s Method

– The level and distribution of permeability are the most difficult reservoir

property to determine and are more variable than porosity.

– Because smaller scale heterogeneity always exists even in the most

homogeneous reservoirs, core permeability must be averaged to

represent the flow characteristics of the entire reservoir or individual

reservoir layers (units).

– There are three simple permeability-averaging techniques:

a- Weighted Average Permeability

b- Harmonic Average Permeability

c- Geometric Average Permeability

– Permeability is measured by passing a fluid of a known viscosity µ

through a core plug of measured dimensions. Then by measuring flow

rate and pressure drop permeability can be obtained by solving Darcy’s

Equation: K= q μ LA∆ p where q is flow rate through core, µ

is viscosity of the fluid, L is length of the core, A is the cross sectional

area of the plug and ∆ p is the pressure difference across the core plug.

– Dry gas is usually used (air, N 2 or He) in permeability determination

because of its convenience, availability and to minimize fluid-rock

reaction.

– Klinkenberg Effect: Permeability measurements made with gas as the

flowing fluid is greater than those with liquid as flowing fluid.

Klinkenberg attributed that to the fact that liquids have zero velocity at

the sand grain surface, while gases exhibit slippage at the sand grain

surface. This slippage results in higher flow rate for gases at given

pressure differential. He also found that for a given porous medium as

the mean pressure increased the calculated permeability decreased.

j k g=kL+c [ 1pm ]

where k g is measured gas permeability

b k L is equivalent liquid permeability i.e. absolute permeability, k

I c is the slope of the line and pm is the mean pressure

– In an actual porous system Swirr is expected to increase as permeability

decrease. The idea behind that is that lower permeabilities result from

increasing non-uniformity of pore structure by gradation of particles and

hence irreducible water content is a function of permeability to an

extent as permeability is dependent upon the variation of pore structure.

– Timur Equation provides rough approximation of permeability from

water saturation and porosity. k=8.58102 ϕ4.4

Swirr2 –

Reservoir Heterogeneity is classified into vertical and areal

heterogeneity. A formation is said to have a uniformity coefficient of

zero in specified property when that property is constant throughout the

formation thickness while a completely heterogeneous formation has a

uniformity coefficient of unity. It is important to recognize that there are

no homogeneous reservoirs, only varying degrees of heterogeneity.

– Dykstra-Parsons permeability variation (V) is widely used descriptor of

the vertical heterogeneity of a formation. V=K50−K 84.1

K50 –

Permeability interpolating and/or extrapolating methods:

- (Areal heterogeneity)

a- The Polygon Method

b- The Inverse Distance Method

c- The Inverse Distance Squared Method

Overburden Pressure is caused by the weight of overlaying layers; it varies

from one area to another depending on depth, nature of structure,

consolidation of formation and geological & and history of rocks.

– Pressure in the rock pore space does not normally approach the

overburden pressure.

– Typical Value of over burden pressure is 1 psi per foot of depth.

– Typical Value of pore pressure is 0.5 psi per foot of depth.

– Effective Overburden is the pressure difference between overburden

pressure and internal pore pressure.

– Compressibility is a measure of the relative volume change of fluid or

solid with a unit change in pressure. It decreases with increasing porosity

and effective overburden pressure.

Pay Zone is the commercially productive portion of the well.

- Net pay thickness discounts for unproductive portion of the reservoir.

- Intervals of low porosity, which implies low permeability and probably

high Swirr will be cut off productive zone height such as shale streaks.

- A reservoir is confined to certain geological boundaries such as gas oil

contact GOC, water oil contact WOC and gas water contact GWC.

- Net pay is defined by imposing the following criteria:

a- Lower limit of porosity

b- Lower limit of permeability

c- Upper limit of water saturation.

- The choice of the previous criteria depend on total reservoir volume,

the range of permeability values, the range of porosity values and the

distribution of porosity and permeability values.

Types of Reservoir Fluids:

1- Incompressible Fluids: fluids whose volume or density does not

change with pressure.

2- Slightly Compressible Fluids: exhibit small change in volume or

density with change sin pressure.

3- Compressible Fluids: fluids that experience large changes in volume

as a function of pressure.

Flow Regimes:

1- Steady-State Flow: When pressure at every location in the reservoir

remains constant i.e. does not change with time.

2- Unsteady-State Flow: also called transient flow is fluid flowing

condition where rate of change of pressure with respect to time at

any location of the reservoir is not zero or constant.

3- Pseudosteady-State Flow: When pressure at different locations in

the reservoir is declining linearly as a function of time i.e. at a

constant declining rate.

Flow Geometries:

1- Radial flow

2- Linear flow

3- Spherical and hemispherical flow

Electrical Properties of Formation:

- The rock matrix (grain crystals) of the rock are insulators, oil and gas are

insulators too. Water is conductive because of the salt content

(electrolytes). Therefore water content in formation Sw can be

measured by flowing electrical current through zones or intervals of

interest. Water saturation Sw is related to resistivity of formation and

porosity by Archery’s equation.

- Resistance is the property of an entire component or section of a

circuit, which is a function of material and geometry.

- Resistivity is the material property, a function of only material and

temperature.

Useful Information, terms and Relations:

Porosity and permeability are directly proportional to grain size sorting, while

Irreducible water saturation is inversely related to good sorting.

Grain size does not affect porosity but is directly proportional to permeability.

Grain shape affects both porosity and permeability.

Low porosity implies low permeability and probably high Irreducible water

saturation.

A very porous system would not exceed 44% porosity, granite stone is known for

its zero porosity.

Low irreducible water saturation would fall between 15% to 17 %

Relative permeability in a ternary is expected to be low because 3 fluids are

competing to flow.

Tortuosity is the ratio of path length to overall length.

Important formation rock densities

Sand stone 2.65 g/cc

Lime stone 2.71 g/cc

Dolomite 2.87 g/cc

Bubble point pressure is pressure below which gas bubbles come out of solution.

Boi is the formation volume factor, it accounts for the fact that some of the

reservoir fluid is gas not oil

GOR: gas to oil ratio

Rock matrix, oil and gas are all insulator, only water is conductive because of the

presence of salt (electrolytes) in it.

Fr is formation resistivity factor used for the detection of hydrocarbon zones.

Over balance drilling is the drilling with pressure in the well bore exerted by the

drilling fluid, higher than pressure of formation being drilled.

SP is self-potential or spontaneous-potential is a result electrical imbalance

caused by difference in salinity between drilling mud and connate water.

Log data give porosity, height of the zone, resistivity of formation water and total

resistivity and lithology.

Core tests give data such as absolute and relative permeabilities and residual oil

saturation.

From visual inspection of core samples the flowing are given

-Rock type

- Grain size which g permeability, Swirr and capillary pressure.

- Grain size distribution permeability,Swirr and porosity.

- Consolidation.

- Staining give idea about residual oil saturation

- Lamination or layering how clay affect permeability

Equations:-

Porosity

Porosity∅=Pore volumeBulk volume

Arithmetic Average Porosity = ∑ ϕin where n is number of samples

Thickness-Weighted Average Porosity = ∑ϕi hi

∑ hi where h is thickness of sample

ρb=ρf (ϕ )+ρma(1−ϕ ) where b is bulk, f is fluid and ma is matrix

Saturation

Fluid Saturation ¿ total volumeof fluidpore volume

Average saturation s=∑ ϕihi s

∑ ϕih i

so+sg+sw = 1

Capillary Pressure

Pc=Pnw−Pw where Pwis pressure of the wetting phase

Pnw is pressure of the non-wetting phase

Pc=( h144 )∆ ρ where h is height and ∆ ρ is density difference in pcf

Leverett J-Function: J (Sw )=0.21645Pcσ √ kϕ

Pc rse=Pc labσ resσ lab

Timur Equation: k=8.58102 ϕ4.4

Swc

• Darcy’s Equations:

Linear Incompressible Fluid Q=k A(P2−P1)

µ L

Compressible Fluid Q=k A(P1

2−P22)

2µ LPB

Radial Incompressible Fluid Q=0.00708 k h(Pe−Pw)

Boµ ln( ℜrw

)

ℜ=√ 43560 Aπ

Where k: permeability in Darcy

A: cross sectional area across the flow in cm2

µ: viscosity of flowing fluid in cp

L: length in cm for lab application and ft. for field application

PB: base pressure

h: height in ft.

Pe : drainage pressure in psi

Pw :well bore pressure in psi

re: drainage radius in ft.

rw: well bore radius in ft.

• Quantitative Equations:

Original Oil In Place OOIP=(7758 )(h)(ϕ )(A )(1−sw )

Bo=bbl

Original Gas In Place OOIP=(43560 )(h)(ϕ)(A)(1−sw)

Bg=cuft

• Archie’s Equation:

Swn = 1ϕmRw

Rt n usually = m ≈ 2 therefore sw=1

ϕ √ RwRt

Ohm’s law V = IR

• Unit Conversion:

2.54 cm/in

7758 bbl. / acre ft.

43560 sq. ft. / acre

5280 ft. / mile

640 acre / aq. Mile

5.164 cu ft. / bbl.

760 mm Hg / atm.

14.7 psi / atm.