_saturation and capillary pressure in reservoir rocks

8/10/2019 _Saturation and Capillary Pressure in Reservoir Rocks

1/30

Jiyu Wang

akkalaurea Thesis

Saturation and Capillary Pressure inReservoir Rocks

Supervised by: Prof. Ruthammer, Gerhard

Approval date: 15thFeb. !!"

#ate$ !%&11&!1'


2/30

Table of Contents

Abstract................................................................................................................................ 4

1 Introduction: Reservoir Rocks........................................................................................5

1.1 (mportant properties of reservoir rocks......................................................................................5

1. )he types of Reservoir Rocks................................................................................................... *1..1 S+#S)- RSR/-(R R-C0S...................................................................................................*1.. C+R-+) RSR/-(R R-C0S...................................................................................................21..3 Shale..................................................................................................................................................%

2 luids Saturation in Reservoir Rock.........................................................................1!

.1 4ethods of #eterminin Fluid Saturation................................................................................1!.1.1 #etermination of Fluid Saturations from Rock Samples..........................................................................1!.1. #etermination of Fluid Saturations by 6traction 7ith a Solvent................................................................13.1.3 #etermination of Fluid Saturations 7ith lectric 8 ell 9os :(ndirect;........................................................1'

. )he


3/30

List of Figures

Fiure 1$ Pores in reservoir rocks............................................................................................ 5

Fiure $ Permeability in Reservoir Rocks...............................................................................*

Fiure 3$ Sandstone dienesis :@onation from Scott -ilfield, orth Sea,


4/30

Saturation and Capillary Pressure in Reservoir Rocks

Abstract

)he aim of this baccalaureate thesis 7as to ive an overvie7 of reservoir rocks and searchin

for determination of fluids saturation and capillary pressure in reservoir rock, in order to find outthe relationship bet7een fluid saturations and capillary pressure.

)he focal point in this baccalaureate thesis 7as ho7 to determine the value of fluids saturation

and capillary pressure in reservoir rocks, 7hat can be concluded to t7o methods, AdirectA and

BindirectA method. y the euipment, 7e can read the value of fluids saturation and capillary

pressure directly. ut 7e also can calculate them throuh the other properties in reservoir

rocks, e.. porosity, resistivity from los, 7hen the condition can not supply the euipment,

7hich 7e need. )his is indirect method. o matter 7hich method is used in the determination,

7e need a result to kno7 about the relation bet7een capillary pressure and fluids saturation in

the end. So that 7e 7ill kno7, ho7 7ill the capillary pressure effect on the fluids saturation.

Further, 7e 7ill et more information.

+uthor$ Diyu 8an Pae$ 4


5/30


1 Introduction: Reservoir Rocks

+ reservoir rock is capable of storin a fluid and producin it into boreholes. +lthouh the term

Breservoir rockA suests the function of storae only, the ability to produce fluids into 7ells iseually important. For e6ample, a 7ater=saturated shale or clay may contain as much 7ater

per unit volume as an auifer capable of producin lare volumes of 7ater per day. )he fluids

produced form reservoir rocks are oil, as, and 7ater, and in eneral a reservoir rock capable

of producin one of these fluids is capable of producin the others. Some 7riters limit the term

Breservoir rockA to rocks 7hich produce oil or as, but there seems to be no valid reason for

restrictin the term to rocks 7hich contain a particular fluid. (n the interest of clearness and

consistency, it seems advisable to define a reservoir rock by its litholoic characteristics, and

not by the type of fluid it contains.

Imortant roerties of reservoir rocks

+ fundamental property of a reservoir rock is its porosity. Eo7ever, for it to be an effective

reservoir rock, the fundamental property is permeability. oth porosity and permeability are

eometric properties of a rock and both are the result of its litholoic :composition; character.

)hey determine the rate of production of fluids, the amount that can be stored in the reservoir,

the ultimate production, and the type of secondary methods 7hich should be applied. /ariations

in pore si@e, that are closely related to permeability, determine to a lare deree the relative

amounts of hydrocarbons and 7ater in each stratum of the reservoir rocks

Figure 1: Pores in reservoir rocks

+ rock 7ith pores is referred to as porous. )his means it has tiny holes throuh 7hich oil may

flo7. Reservoir rocks must be porous, because hydrocarbons can occur only in pores. )he

definition of porosity is$

T

P

V

V=

Eere

is porosity, PV

is volume of porous in the rock, TV

is total volume of rock. )he

porosity depends on the location of the rock :heteroeneity;, the compressibility of rock and the

pressure.

+uthor$ Diyu 8an Pae$ !


6/30


Figure 2: Permeability in Reservoir Rocks

+ reservoir rock is also permeable. )hat means its pores are connected. (f hydrocarbons are in

the pores of a rock, they must be able to move out of them.


7/30


Figure 3: Sandstone digenesis (zonation from Scott Oilfield !ort" Sea #$%

)he uality of the initial sandstone reservoir is a function of the source area for the materials,

the depositional process, and the environment in 7hich the deposition took place. Sandstone

reservoirs are enerally 5 meters thick, are lenticular and linear spatially, and less than 5!

kmin area. )hey rane in ae from the oldest bein Cambrian :in +leria; to the younest

bein Pliocene :Caspian reion in


8/30


CARB&$AT' R'#'R(&IR R&C)#

Carbonates are predominantly composed of calcite and dolomite, 7ith clay and uart@ as

common secondary minerals. Carbonates can be both framental and precipitated rock. (f themain mineral is calcite, carbonate rock is referred to as limestone. #olomite rock is the term for

carbonates 7ith dolomite as their main constituent. #olomite rock is almost al7ays a secondary

rock formed from limestone by replacement of part of the calcium in calcite by manesium, a

process called dolomiti@ation. Carbonate rocks enerally form in 7arm sea 7ater at shallo7

depths, ankle deep to about ! ft. )he hard, usually calcareous parts of the oranisms pile up

on the seafloor over time, formin beds of lime particles. +lae, simple plants, are one of the

reatest contributors of lime particles, but any shelled animal may contribute 7hole or

framented shells to the pile. Reefs, banks of lime mud, and lime sand bars are commonly

found preserved in rocks.

Figure &: ' t"insection )"otomicrogra)" of a limestone

)his particular sample comes from an interval that is not a ood reservoir rock. Circular rains

composed of calcite :finely crystalline, reddish=stained areas in a rain; and dolomite :clear,

coarse crystals; are completely cemented by medium crystalline calcite. o porosity is visible

)he most interestin and perhaps impressive aspects of carbonate reservoir rocks are theirfossil content. Fossils rane from the very small sinle cell to the larer shelled animals. Prior

to the 1%!Js, carbonate reservoir rocks 7ere relatively rare and prior to 1%5! they 7ere all

rearded as essentially oranic rocks. ut this chaned 7hen te6tural studies of carbonates in

(ra and the ahamas sho7ed that carbonates are also the result of inoranic processes. 4ost

carbonate rocks are deposited at or in very close pro6imity to the site of creation.

)ransportation of material is less common and sortin is essentially non=e6istent. )he Kbest=

sortedK carbonate rocks are -olites in 7hich the KrainsK are the same si@e and shape. ut

-olites are not KsortedK at all, but 7ere formed 7ith the si@es and shapes that they have in the

carbonate rock and 7ere cemented in place. H1I

+uthor$ Diyu 8an Pae$ ,


9/30


10/30


1 Fluids #aturation in Reservoir Rock

+s a result of the oriins of the oil and its formation and miration conditions, the reservoir rocks

contain the follo7in fluids$

:a; 9iuid hydrocarbons$ oil from the liht fraction to asphalts,

:b; Gaseous hydrocarbons.

:c; 8ater :salt 7ater;.

)hese fluids 7hich are distributed in a certain manner in the porous medium under reservoir

temperature and pressure conditions are, in eneral, found to have uite different distributions in the

cores brouht to the surface.

)hese modifications are due to the follo7in factors$

:a; Firstly, to causes 7hich are difficult to avoid$

:1;. (nvasion of drillin mud or filtrate.

:;. Gas e6pansion due to the fall in pressure durin the raisin of the core.

:b; Secondly, there are often handlin errors such as the 7ashin of the cores in 7ater, or

dryin at hih temperatures or the lack of preservation.

)he uantity of fluid contained in the pores, e6pressed as a percentae of / pis called fluid

saturation.

.ethods of %etermining Fluid #aturation

)here are t7o approaches to the problem of determinin the oriinal fluid saturations 7ithin a

reservoir rock. )he direct approach is the selectin of rock samples and measurin the

saturations of these samples as they are recovered from the parent formations. )he indirect

approach is to determine the fluid saturation by measurin some other physical property of

direct approach, such as usin electric los or capillary=pressure measurements.

%etermination of Fluid #aturations from Rock #amles

(n determinin fluid saturations directly from a sample removed from a reservoir, it is necessary

to understand first ho7 these values are measure second, 7hat these measured values

represent and third, kno7in 7hat they represent, ho7 they can be applied.

(n order to measure values of oriinal rock saturations there have been essentially three

methods devised. )hese methods involve either the evaporation of the fluids in the rock or theleachin out of the fluids in the rock by e6traction 7ith a solvent.

+uthor$ Diyu 8an Pae$ 1/


11/30


Figure ,- Retort distillation a))aratus-

-ne of the most popular means of measurin the initial saturations is the retort method. )his

method takes a small rock sample. y heatin the sample and measurin the volumes of 7ater

and oil driven off, it measures the fluid saturations in the sample. )he sample is crushed and

7eihed before bein placed in the apparatus. (t is then heated in staes or directly to 1!!NF

durin 7hich the fluids are vapori@ed, collected, condensed and separated. Plateaus in the rise

of the cumulative 7ater volume 7ith temperature are sometimes analysed to indicate 7hen

free 7ater, surface clay=bound 7ater and interlayer clay=bound 7ater have been driven off. +nelectric retort is sho7n in Fiure *.

)he retort method has several disadvantaes. (n order to remove all the oil, it is necessary to

approach temperatures on the order of 1!!! to 1!!NF. +t temperatures of this manitude the

7ater of crystalli@ation 7ithin the rock is driven off, causin the 7ater=recovery values to be

reater than ?ust the interstitial 7ater.

Figure .- +y)ical retort calibration curve for /ater

+n e6ample of such a system is illustrated in Fiure ". Eere the 7ater removed in the first 3!

min 7as appro6imately the interstitial 7ater. +s the application of heat 7as continued, the 7ater

of crystalli@ation 7as removed, amountin to appro6imately cc of 7ater out of a total

recovery of 2 cc. )hus, it is seen that an error of 33 per cent is possible if the 7ater of

crystalli@ation is not accounted for.



12/30


Figure 0- +y)ical retort calibration curve for oil

)he second error 7hich occurs from retortin samples is that the oil itself 7hen heated to hih

temperatures has a tendency to crack and coke. )his chane of a hydrocarbon molecule tends

to decrease the liuid volume and also in some cases coats the internal 7alls of the rock

sample itself. )he effect of crackin and cokin in a retort is sho7n in Fiure *, 7herein !.' ccof oil actually in the sample yields about !.5 cc in the receivin vessel. )hus a fluid correction

must be made on all sample data obtained 7ith a retort. efore retorts can be used calibration

curves must be prepared on various ravity fluids to correct for the losses from crackin and

cokin 7ith the various applied temperatures. +nother correction curve can also be obtained

7hich correlates recovered.

)he retort is a rapid method for the determination of fluid saturations, and utili@in the

corrections yields satisfactory results. (t ives both 7ater and oil volumes, so that the oil and

7ater saturations can be calculated from the follo7in formulas$

ccvolumepore

ccwaterSw

,

,=

ccvolumepore

ccoilSo

,

,=

ow SSS =1

(n order to obtain realistic values of fluid saturation it is necessary to choose the proper drillin

fluid or resort to correlations similar to that reported by 0ennedy et al. Fiure % sho7 the

correlations that correlate hydrocarbon saturations before and after corin. (t is noted that for

cores of 5= and 1!=millidarcy permeability, the initial and final hydrocarbon saturation yields and

final hydrocarbon saturation yields an appro6imate straiht line for initial saturations reater

than 15 per cent. #ata for cores of from 1"= to 3!'!=millidarcy permeability 7ere correlated in

the same manner as the data for the lo7=permeability samples. )hese also resulted in astraiht=line correlation for initial hydrocarbon saturations reater than 15 per cent.



13/30


Figure - aboratory determination of fluid saturation-

Correlations such as presented in Fiure % can be used to correct saturations measured from

cores to oriinal conditions. +dditional data are reuired before universal correlations can be

established.

+ttempts have been made to use tracers in the drillin fluid to determine the amount of 7ater inthe core 7hich is due to mud filtrate invasion. )he theory 7as that mud filtrate displaced only

oil. )hus, 7hen the core is recovered to the surface, the salt concentration of the core 7ater

can be determined. 0no7in the salt concentration in the reservoir 7ater and the tracer

concentration in the drillin fluid, it 7as thouht possible to calculate the volume of filtrate and

reservoir 7ater in the core. + lare fraction of the initial reservoir 7ater may have been

displaced by the invadin filtrate, so the tracer method 7ould ive lo7 values of reservoir 7ater

saturation.

%etermination of Fluid #aturations b" '1traction 2ith a#olvent

Figure 1- 4odified 'S+4 e5traction a))aratus

6traction can be accomplished by a modified +S)4 method or a centrifue method. (n the

standard distillation test the core is placed so that a vapor of toluene, asoline, or naphtha rises

throuh the core and is condensed to reflu6 back over the core. )his process leaches out the oil

and 7ater in the core. )he 7ater and e6tractin fluid are condensed and are collected in a

raduated receivin tube. )he 7ater settles to the bottom of the receivin tube because of its

reater density, and the e6tractin fluid reflu6es back into the main heatin vessel. )he process

is continued until no more 7ater is collected in the receivin tube. )he distillation apparatus issho7n in Fiure 1!. )he 7ater saturation can be determined directly.

ccvolumepore

ccwaterSw

,

,=

)he oil saturation is an indirect determination. (t is necessary to note the 7eiht of the core

sample prior to e6traction. )hen, after the core has been cleaned and dried, the sample is

aain 7eihed. )he oil saturation as a fraction of pore volume is iven by

)/,)(,(

gm)water,ofwt-gmcore,dryof,(

ccgmildensityofoccporevolume

wtgmcorewetofwtSo

=

)he core can be completely cleaned in the +S)4 e6traction apparatus, or once all 7ater is

removed, the remainder of the cleanin can be done in a so6hlet e6tractor :Fiure 11;. )hemechanics of the so6hlet e6tractor are essentially the same as the +S)4 e6traction apparatus



14/30


e6cept that no receivin vessel is supplied for trappin 7ater. )he cleanin solution is

continually vapori@ed and condensed on the core. )his action leaches out the oil and 7ater

from the core. )he +S)4 e6traction method does less damae to a core sample and results in

perhaps the cleanest core of any of the saturation determinations. )he core sample is ready for

porosity or permeability determinations after this e6traction process.

efore permeability and porosity can be measured, it is necessary to clean the core sample ina device similar to the so6hlet e6tractor or one 7hich uses centrifual force. )hus, usin the

core sample in a device is similar to the so6hlet e6tractor or one 7hich uses centrifual force.

)hus, usin the +S)4 distillation only one additional step is reuired to obtain information from

7hich to calculate fluid saturations in the core.

Figure 11- So5"let e5tractor

%etermination of Fluid #aturations 2ith 'lectric 4ell Logs

5Indirect6

8ell los are techniue used in the oil and as industry for recordin rock and fluid properties

to find hydrocarbon @ones in the eoloical formations. +t first, the symbols 7hich appear in

this section 7ill be shortly described$

1. S'O 7ater saturation$ the percentae of the pore space filled 7ith 7ater :as opposed to

hydrocarbons or air;.

. RO resistivity$ the resistance to electrical current flo7 presented by a unit volume of rock.

3. R'O 7ater resistivity$ the electrical resistance of the 7ater fillin the pore space in the

rock. )his value varies 7ith 7ater salinity and temperature.

'. O porosity$ the void space bet7een rains that is enerally filled 7ith liuids or ases.

5. $ Formation Factor. )he ratio bet7een R!of 1!! saturated rock and R7, and depends

upon the litholoical characteristics of the rock and the effective porosity.

)he matri6 of a rock 7hich does not contain clay is an insulator. )he electrical conductivity of

this rock is due solely to the conductin net7ork formed by the interstitial 7ater contained in the

pores. For a iven rock sample, there is a constant ratio bet7een the resistivity R !of rock

1!! saturated 7ith conductin brine and the resistivity R 7of this brine. )his constant 7hich

7as first introduced is called Formation Factor. 8e have the euation of FF$



15/30


w

o

R

RFF=

:Ro resistivity of sample 1!! saturated 7ith brine 7hose o7n resistivity is R7;

8e have the Formation Factor is linked to porosity by an euation of the form$

m

aFF

=

8here a and m are constants characteri@in the rock :m varyin from 1.3 to . and more,

dependin upon the state of cementation of the reservoir;.

Since oil is an electrical insulator, it can be seen the fact, that a certain uantity of 7ater is

replaced by oil in the rock means an increase in resistivity.

+rchie has sho7n e6perimentally that bet7een the true resistivity :Rt; of the rock partially

saturated 7ith oil, the value S of the 7ater saturation correspondin to this resistivity and the

resistivity Roof the rock 1!! saturated 7ith oil there is the follo7in euation$

RRRRS

t

on == :Resistivity Ratio;

)his can be 7ritten$

t

wn

R

RFFS

)(=

n , if the rock is 7ater 7et,

QnQ', if the rock is oil 7et.

)his euation makes it possible to obtain the in situ rock interstitial 7ater saturation on the

basis of resistivity measurements.

(f the formation is homoeneous and is visibly oil=bearin at the top and 7ater=bearin at the

base electrical los make it possible to determine Roand Rtimmediately

+uthor$ Diyu 8an Pae$ 1!


16/30


070 The 8se of Core9%etermined Fluid #aturations

)he saturation values obtained directly from rock samples are usually not reliable for

determinin the uantity of each fluid in the rock. -ther uses e6ist for fluid=saturationdeterminations from core samples. 8ater saturations obtained from core samples cut 7ith oil=

base mud are essentially reliable. )he saturations of cores cut 7ith 7ater=base mud are used to

determine the oriinal oil=as contact, oriinal oil=7ater contact, and 7hether a sand is

productive of oil or as.

)he t7o tables belo7 sho7 these invasions in the cases of t7o different types of mud$

'ater base *udand oil base *ud.

a; /ariation in fluid saturation for a core bet7een the reservoir and the surface in the case of

7ater base mud$

Saturation -il Gas 8ater +t surface 1 '! '2

shrink e6pand e6pulse

(n core barrel 15 ! 25

flush invade

(n reservoir "! ! 3!

b; /ariation in fluid saturation of a core bet7een reservoir and surface in the case of oil base

mud$

Saturation -il Gas 8ater

+t surface '! 3! 3!shrink and e6pulse

(n core barrel "! ! 3!

invade

(n reservoir "! ! 3!

)he determination of contacts is made by carefully studyin the residual oil saturations of the

cores as a function of depth. (n the oil=saturated reions the samples 7ill have essentially a

constant value for residual oil saturations, probably 15 per cent or reater. (n the as reion the

oil saturation is small or vanishes. )hus the depth of the as=oil contact is defined by a sharpincrease in oil saturation. (n the 7ater @one, the oil saturation radually disappears 7ith depth.

y observin these chanes in oil saturation, it is possible to choose the depth of the 7ater=oil

contact.

(t is possible to establish a correlation of the 7ater content of cores and permeability from

7hich it can be determined 7hether a formation 7ill be productive of hydrocarbons. Such a

correlation is sho7n in Fiure 1, 7herein it can be noted that lo7=permeability formations 7ith

core 7ater saturations as hih as 55 percent may be considered productive. For hiher

permeability formations the upper limits of 7ater saturations may be slihtly less than 5! per

cent. )hus, from the investiation of saturation values of cores one can ather that a formation

7ould be productive if the 7ater saturation in the surface samples 7ere less than 5! per cent.

+uthor$ Diyu 8an Pae$ 1*


17/30


Figure 12- imiting values of total core /ater for oil and gas )roduction

+nother reason for measurin fluid saturations of surface samples is to obtain other

correlations such than direct or in direct measurements of other physical properties may also

ive indications of initial fluid distributions. )he measurement of electrical resistivity of the core

samples, prior to cleanin, permits correlations of electrical resistivities 7ith other physical

properties to aid in electrical lo interpretation.

)hus, in summary it is seen that althouh fluid=saturation determinations made on core

samples at the surface may not ive a direct indication of the saturations 7ithin the reservoir,they are of value and do yield very useful and necessary information.

+uthor$ Diyu 8an Pae$ 1+


18/30


19/30


(t is therefore easy to e6tend the definition of pressures 1p and 2p to the 7hole space

:althouh only a part of the space is occupied by each of the fluids;. (n the case of a porous

medium in euilibrium, it is permissible, for the pressures, to consider the medium as

continuous.

Capillary pressure 7ill then be defined at every point in the porous medium by

12 PPPc = :'.3;

From '.1 and '., the capillary pressurec

P is a 7ell=defined function of the uantity @$

dzgzpzp

z

z

cc)()()(

0

120 += :'.';

Caillar" Forces ; ettabilit"

)he fluid distribution in porous media is affected by the forces at fluid&fluid interfaces, and also

by forces at fluid&solid interfaces. 8ettability is the tendency of one fluid to adhere to a solid

surface in the presence of another fluid. 8hen t7o immiscible fluids are in contact 7ith a solid

surface, one fluid is usually attracted more stronly than the other fluid. )he more stronly

attracted phase is called the 'etting p&ase.

8ettability can be determined 7hen checkin for the contact anle$

Figure 13- 6ettability of fluids

)he solid is considered 7ater=7et, if the contact anle is smaller than %!N. +t contact anles

larer than %!N, the fluid is referred to as oil=7et. (ntermediate 7ettability occurs, 7hen the

contact anle is close to %!N :Fiure 13;. y convention, contact anles are measured

throuh the 7ater phase. 8ater=7et is that the entire rock surface of both lare and small pores

is coated 7ith 7ater. -il=7et is that the oil completely coats the rock surface. (ntermediate

7ettability tends for both oil and 7ater to 7et the rock surface.

(n case of 7ettin fluid, the contact anle is smaller than %!N. +t contact anles larer than %!N ,

the fluid is referred to as non=7ettin. (n oil&7ater phase, 7ater is 7ettin fluid, and oil is non=7ettin fluid.

%rainage and Imbibition

8hen 7e talk about capillary pressure, BdrainaeA and BimbibitionA 7ill not avoid to be talked.

#ependin on the 7ettin properties of the fluids there are essentially t7o different types of

displacement in t7o=phase flo7 in porous media. B#rainaeA is the displacement of the 7ettin

fluid by a non=7ettin fluid. (n the contrary, B(mbibitionA is the displacement of non=7ettin fluid

by a 7ettin fluid. .. in 7ater=oil displacement processes, mostly 7ater 7ill be the 7ettin

fluid.

+uthor$ Diyu 8an Pae$ 1-


20/30


Figure 1&- 7rainage and imbibition

Fiure 1' sho7s a typical capillary pressure curve for a 7ater=oil system in a porous rock. )he

capillary pressure curve consists of t7o branches$ a main drainae, a main imbibition.

+t S7O1, the start of the drainae, an KentranceK pressure needs to be e6ceeded before oil can

enter the sample. )hen a plateau is reached. +t decreasin 7ater saturations, the capillary

pressure rises to very hih values. )his means that 7hen oil is in?ected into this system, an

ever hiher in?ection pressure is reuired to force the ne6t bit of 7ater out. )he capillary

pressure oes to infinity at the connate 7ater saturation S7r.

8hen the oil pressure is slo7ly decreased, 7ater 7ill spontaneously imbibe and the saturation

7ill increase. )he capillary pressure decreases, and is in eneral smaller than the drainae

capillary pressure for the same saturation, an effect called capillary hysteresis. 8hen the oil

pressure is eual to the 7ater pressure :p cO!;, the saturation reaches the spontaneous 7ater

imbibition saturation Sor. (ncreasin the saturation from this point can only be accomplished by

forcin the 7ater in. +n ever hiher 7ater pressure is reuired to force the ne6t bit of oil out,

until the residual oil saturation Sorhas been reached. ote that pcoes to minus infinity at 7ater

saturations near S7O1=Sor.

.ethods of measuring caillar" ressure

)hese measurements are difficult because the proress to 7ard euilibrium, at 7hich capillary

pressure is to be determined, is enerally very slo7. )herefore, measurements take a very lon

time, and 7e can never be uite sure that euilibrium has been effectively established.

%esortion .ethod

)he sample under study rests on a semi=permeable diaphram :Fiure 1!; 7hich allo7s the

7ettin phase to flo7 throuh, but not the non7ettin phase. )he 7ettin phase of the sample

communicates throuh this diaphram 7ith the atmosphere. )he non7ettin phase bathin the

sample is maintained at constant pressure. uilibrium is reached 7hen the flo7 of the 7ettin

phase throuh the semi=permeable diaphram stops. )he pressure is then chaned on the

non7ettin phase in order to determine the follo7in euilibrium.

+uthor$ Diyu 8an Pae$ 0/


21/30


Figure 1*- Semi)ermeable dia)"ragm

Restored state method

(f 7e suppose a rock sample from a field located at heiht habove the @ero capillary level, the

pair of fluids present in the field is characteri@ed by$

=0 Specific ravity of oil

=w Specific ravity of 7ater

T = (nterfacial tension of pair of fluids.

8e have the capillary pressure$

.)( 0 ConstghP wC +=

+ meniscus radiusr corresponds to this capillary pressure and this pair of fluids such that$

)(cos2

wc Sgr

T

r

TP ==

Group :) cos ) characteri@es the pair of fluids :); and the solid :;. (n order to make the

non7ettin fluid penetrate into pores 7ith radius r 7ith system :), ;, a pressure Pc is

necessary, 7hile 7ith system :T , ; a pressure cP is necessary. Pressures Pcand cPare linked by the euation$

)his makes it possible to choose one pair of fluids or another in order to study pore morpholoy

or saturation states correspondin to various values for capillary pressure.

)he relation bet7eenr and water saturation Swis not riorously constant if 7e o from one pair

to another, but it 7ill be supposed that there is an invariable relation bet7een Swandr. Eence

the relation 7hich is e6perimentally obtained in the laboratory bet7een cP and Sw can

therefore be validly transformed for the real pair by the euation$

.)(

cos

cos0 ConstghP

T

TP wcc +=

=


=

coscos

'

T

P

T

P cc


22/30


(f cP , T , are kno7n for one pair, T , for the other pair and also w , 0 , thefollo7in curves can be plotted$

:a; Capillary pressure in terms of 7ater saturation :Fiure 1*;

:b; -r 7ater saturation in terms of the distance habove the @ero capillary level

)he heiht his iven by the euation$

g

zPPh

ow

occ

)(

)(

=

Figure 1,- 8a)illary )ressure curve-(restored states met"od%-

:a; (f h is counted from the @ero capillary level 0)( == oc zP

:b; +nd if h is counted from the 7ater&oil interface :B7ater levelA; previously defined as

0)( oc zP

.ercur" in


23/30


Figure 1.- 4ercury in9ection met"od

(n the case of the 7ater&air pair 7here the 7ettin phase is displaced, there is al7ays a path

throuh 7hich circulation is possible leadin to the creation of irreducible saturation in the pores

7hich do not participate in this circulation.

(n the case of the mercury&air pair, this condition does not e6ist and the curves. -btained do

not sho7 the characteristic asymptote for irreducible saturation. )he latter can perhaps bedefined by the saturation correspondin to the beinnin of the rectilinear part of the curve :if

this point is marked; or, if not, to the saturation correspondin to a pressure of, for e6ample, 1!

to 15 or ! bars dependin upon the samples.

)he shape of the curves obtained by plottin the euation for capillary pressure as a function of

mercury saturation e6pressed as a percentae of pore volume is very variable from one

sample to another :pore volume is carefully determined by an appropriate method such as

immersion in a solvent;.

Fiure 12 concerns a homoeneous matri6 medium. )he beinnin of the curve corresponds

to a surface effect, i.e. the mercury has not yet definitely entered the pores. y means of a

Bsurface correctionA it is clearly possible to eliminate this part. )he part represented by a broken

line is then obtained.

Figure 10- 8a)illary )ressure by mercury in9ection: "omogeneous matri5 medium

(n certain cases 7here the pore radii are small, the PS1 threshold can be hih$ up to 3! bars

abs., and even more.

Fiure 1% makes it possible to distinuish$



24/30


Figure 1- 8a)illary )ressure mercury in9ection: medium v macro)ores and matri5

:a; )he macropores, the part - > a 7hich are invaded under very lo7 pressures.

:b; )he pores constitutin the matri6 :as above; 7hich are relatively reularly distributed. )he

part ab corresponds to channels 7hich can be used for circulation 7hile the part bd

corresponds to the 7indins of the channels.

Fiure ! corresponds to the case of t7o homoeneous matri6 media separated by an

intermediate medium, for e6ample calcite, coatin the pores. )he tanential departures of the

curve from the abscissa should also be noted. )his shape can be interpreted by observin that

the macropores have later been filled by another medium

Figure 2- 8a)illary )ressure by mercury in9ection in t"e case of 2 matri5-

)he speed and accuracy of this method account for the fact that it is very 7idely used. (t is

ho7ever not suested for very clayey samples since for a iven pressure the saturation is too

hih because the pores are invaded by clay.



25/30


26/30


3 Relationshi bet2een caillar" ressure

and fluids saturation

9et us e6amine the microscopic sinificance of capillary pressure. +t euilibrium, a difference

in pressure proportional to the curvature c of the interface e6ists bet7een the t7o sides of the

interface separatin t7o immiscible fluids, the stroner pressure bein on the concave side$

cTPP = 12 :'.5;

) is the interfacial tension. (t is characteristic of the pair of fluids under consideration. uation'.5 is a special case for a fluid velocity every7here @ero.)he capillary pressure therefore depends on the curvature of the interface separatin the t7ofluids and on the interfacial tension. From hydrostatic euilibrium condition ".', the curvature ofthe interface is a function of the uantity @.(n a block of porous medium sufficiently small, the influence of ravity may, on that scale, benelected, and the interface, in all the pores, has a constant curvature related to the value ofthe capillary pressure by uation '.5.

)his interface should, accordin to capillary la7s, ?oin the solid surface of the porous medium

under a definite anle , the 7ettin anle. (f the capillary pressure is iven, the interfacebet7een the t7o fluids is sub?ect to certain conditions. (ts curvature is iven by uation '.5,

and the contact anle at the points 7here it ?oins the solid surface is also iven.

Figure 21- 5am)le for t"e )osition of t"e interface

(n some simple cases, this is sufficient to establish completely the position of the interface.

Consider, for e6ample, the case of a conic capillary tube 7ith an anle of at the ape6:Fiure 1;. )he interface in this tube 7ill be spherical. (f its curvature c and its anle of contact

are prescribed, its position follo7s immediately. )he proportion of, for instance, fluid 1

contained in this pore 7ill thus be directly related to the capillary pressure. )his type of

reasonin has led to the belief that for a iven porous medium there is a relationship bet7een

capillary pressure and saturation$

)( 1Spp cc =

6amination of this simple model also sho7s that the pressure must be hiher in the

non7ettin fluid.

+uthor$ Diyu 8an Pae$ 0*


27/30


28/30


#ummar"

-n the basis of this bakk. )hesis, )he follo7in conclusion is offered$

1. 9aboratory techniue has been developed to measure the capillary pressure and

fluid saturation from rock sample or rock los under different euipment. ut it is

a little difference bet7een the value on the stand condition and the reservoir

condition. So the correction factor is searched and iven to convert the

laboratory condition to field condition.

. #rainae and imbibition curve sho7 that the direct relation bet7een 7ettin fluid

saturation and capillary pressure$ 7ith the increasin of capillary pressure, the

fluid saturation decreases that follo7in drainae curve. (n the country, 7ith the

decreasin of capillary pressure, the fluid saturation increases that follo7in

imbibition curve.

3. )he results of microscopic sinificance indicate that the interfacial area bet7een

fluid phases per volume of porous medium becomes a 7ell=defined macroscopicproperty at an averain volume similar to that of saturation. Simulated

immiscible displacement e6periments 7ere performed to e6plore ho7 the

interfacial area bet7een fluid phases chanes durin imbibition and drainae in

t7o=fluid system.

+uthor$ Diyu 8an Pae$ 0,


29/30


References

H1I........ reference fromhttp$&&leeric.isu.edu&bbb&'&rocus.html

3 . iesner u. F. 8eber$A Geophysikalishe ohrlochmessunen:#eutsch;A,-E

9eoben,1%%"

' Robert P. 4onicard$ BProperties of reservoir rocks$ Core analysisA, 1%2! ditions

)echnip, Paris

5 Charles 4. 4arle$ B4ultiphase flo7 in porous mediaA, 1%21 editions )echnip, Paris

* Dames 8. +my6$ BPetroleum reservoir enineerin = Physical PropertiesA, 4cGra7=

Eill,1%*!

" Dohn C. Calhoun,DR$ BFundamentals of reservoir enineerinA, Revised edition

copyriht 1%53

2 8illiam #. 4cCain$ B)he properties of Petroleum fluids > second editionA, Penn7altbooks, -klahoma,1%%!

+uthor$ Diyu 8an Pae$ 0-
http://leeric.isu.edu/bgbb/4/rocus.htmlhttp://leeric.isu.edu/bgbb/4/rocus.htmlhttp://leeric.isu.edu/bgbb/4/rocus.htmlhttp://leeric.isu.edu/bgbb/4/rocus.html


30/30


$omenclature

.....Porosity

PV ...)otal volume of rock HmTI

TV ...Porous volume of rock HmTI

wS ...8ater saturation

oS ...-il saturation

wrS ..Residual 7ater saturation

R .....Resistivity

wR ....8ater resistivity

FF ...Formation Factor

cP ......Capillary pressure HpsiI

0 .....#ensity of oil Hk&mTI

w .....#ensity of 7ater Hk&mTI

T.......(nterfacial tension of pair of fluids

c ........Constant for curvature

_saturation and capillary pressure in reservoir rocks

Documents