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ENPE 523 Introduction to Reservoir Engineering

Mingzhe Dong

Chapter 4 Oil Reservoirs – Recovery Mechanisms and Material Balance Equations There are two objectives of this chapter: 1) to discuss the various primary recovery mechanisms and their effects on the overall performance of oil reservoirs; 2) to learn the material balance equations and use them to predict the volumetric performance of different oil reservoirs.

4.1 Reservoir Recovery Processes 4.1.1 Primary production In primary production oil is displaced to the production well by natural reservoir energy. There are basically six driving mechanisms that provide the natural reservoir energy for oil recovery: x Fluid and rock expansion x Solution gas drive x Gas cap drive x Water drive x Gravity drainage drive x Combination drive 4.1.2 Secondary Recovery (Waterflooding) In second recovery or waterflood, water is injected into the reservoir formation to maintain the reservoir pressure and to displace oil. The water from injection wells physically sweeps the displaced oil to adjacent production wells as shown in Figure 4.1. Water flooding is the least expensive and the most widely used secondary recovery method. However, waterflooding can only recovery a small portion of the oil in place which is dependent on properties of the oil and the reservoir. Potential problems associated with waterflood techniques include: x

x x

Inefficient recovery. Recovery of primary production and waterflooding in different reservoirs are: Heavy oil ~ 5-10% IOIP or OOIP (Initial or original oil in place) Medium oil ~ 15% Light oil ~ 25 –35% Early water breakthrough and high water cut Low oil production rate

Main reasons for low oil recovery by waterflood include: x x

Oil viscosity too high Heterogeneity of the porous formation (low sweeping efficiency) 1

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x

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Trapping of oil by capillary forces

Figure 4.1 Schematic diagram of waterflood

4.1.3 Tertiary Oil Recovery (Enhanced Oil Recovery) Enhanced oil recovery (EOR) is a generic term of techniques for increasing the recovery of crude oil after waterflood. Using EOR, 30-60 %, or more, of the reservoir's original oil in place can be recovered compared with 20-40% using primary and secondary recovery. Enhanced oil recovery methods can be classified into: Immiscible gas injection (Natural gas, flue gas, nitrogen, CO2) Mechanisms: x Vaporizing the light components x Gas drive x Viscosity reduction x Enhanced gravity drainage in dipping reservoirs x WAG injection (water-alternating –gas) As an example, Figure 4.2 shows the process of miscible CO2 injection. Miscible gas injection (CO2, hydrocarbons /solvents, flue gas) Mechanisms: x Generate miscibility x Swell the oil 2 Winter 2016

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Reduce oil viscosity Enhance gravity drainage

Figure 4.2 Schematic diagram of CO2 injection for EOR Chemical Floodings Polymer flooding Surfactant flooding Alkaline flooding

Increasing water viscosity Reducing capillary pressure NaOH (or Na2CO3) reacting with natural organic acids to produce in-situ surfactant Surfactant – polymer flooding Alkaline – polymer flooding Alkaline-surfactant-polymer flooding (ASP) Mechanisms: x Lowering oil-water interfacial tension x Solubilization of oil in some micellar systems x Emulsification of oil and water x Wettability alternation x Mobility enhancement

Figure 4.3 Surfactant flooding

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Thermal recovery Steam drive Cyclic steam injection (steam huff ‘n’ puff or CSS) Steam assisted gravity drainage (SAGD) Mechanisms: x Viscosity reduction x Supplying pressure to drive oil to the producing wells or gravity drainage In-situ combustion (air injection) Mechanisms: x Lowering viscosity x Steam distillation x Upgrading

4.2 Drive Mechanisms (Primary production) Water drive Energy available from free water in the reservoir to move the hydrocarbon out of the reservoir. Water drive reservoirs can have bottom-water drive (Figure 4.4) or edgewater drive (Figure 4.5).

Figure 4.4 Bottom-water drive reservoir

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Figure 4.5 Edgewater drive reservoir

Gas drive There are two types of gas drives: x Solution gas drive (dissolved gas drive) Light hydrocarbon components in the oil become gaseous when the reservoir pressure is decreased. Gas evolution and expansion will take more pore space and push oil out of the formation through production well (Figure 4.6). x Gas cap drive In some reservoirs, there is a gas cap on the top of the oil layer in equilibrium with the oil layer. When the reservoir pressure is reduced, the pressure of the compressed gas in the gas cap expands and pushes the oil downward to production well (Figure 4.7).

Figure 4.6 Solution gas drive reservoir

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Figure 4.7 Gas-cap dive reservoir

Combination drive More than one drive can work in a reservoir at the same time, such as: x Gas cap and bottom water x Solution gas and bottom water Gravity drainage ʊ*UDYLW\GUDLQDJHPD\EHDSULPDU\SURGXFLQJPHFKDQLVPLQWKLFN reservoirs that have a good vertical communication in steep dipping reservoirs. However, it is a slow process (Figure 4.8).

Figure 4.8 Gravity drive reservoir

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4.3 General Material Balance Equation General material balance equation can be applied to all reservoir types. General material balance equation can provide insight for different reservoir drives. The purpose of material balance is to predict how these fluids behave in the reservoir as reservoir pressure declines. Major volume changes in fluids includes: x Oil, gas, and water production x Remaining oil and gas expansion x Water influx Other volume changes include water and formation compressibilities: x Water and formation compressibilities are less significant in o gas reservoirs o gas cap reservoirs o undersaturated oil reservoirs below Pb (there is appreciable gas saturation) x Water and formation compressibilities are generally neglected in above reservoirs, except in undersaturated reservoirs producing above the bubble point. In the derivation of the general material balance equation, the changes in the oil, gas, water, and rock volumes that occur between the start of production and any time t are considered. The change in the rock volume is expressed as a change in the pore volume, which is simply the negative of the change of the rock volume. In the development of the general material balance equation, the following symbols are used: N Initial reservoir oil, STB Np Cumulative produced oil, STB Boi Initial oil formation volume factor, bbl/STB Bo Oil formation volume factor, bbl/STB Bt Total oil formation volume factor, bbl/STB Bgi Initial gas formation volume factor, bbl/SCF Bg Gas formation volume factor, bbl/SCF Bw Water formation volume factor, bbl/STB G Initial reservoir gas, SCF Gf Amount of free gas in the reservoir, SCF Rsoi Initial solution gas-oil ratio, SCF/STB Rso Solution gas-oil ratio, SCF/STB Rp Cumulative produced gas-oil ratio at time t, SCF/STB W Initial reservoir water, bbl Wp Cumulative produced water, STB We Water influx into reservoir, bbl cw Water isothermal compressibility, psi-1 cf Formation isothermal compressibility, psi -1 'p Change in average reservoir pressure, psi Swi Initial water saturation Vf Initial void space, bbl 7 Winter 2016

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The development of the general material balance for oil reservoirs can be best understood by defining the following terms first: Oil NBoi (N-Np)Bo NBoi - (N-Np)Bo

Original (initial) oil volume in place (expressed at reservoir conditions) Oil volume in reservoir at time t (expressed at reservoir conditions) Change (decrease) in oil volume in reservoir at time t (expressed at reservoir conditions)

Gas GBgi

m

Original (initial) free gas volume in place (expressed at reservoir conditions)

GBgi

Ratio of initial free gas (in gas cap) to the original

NBoi

(initial) oil in place (expressed at reservoir conditions) Therefore mNBoi ª mNB º oi » « B ¬« gi ¼»

= GBgi = Original (initial) free gas volume in place (expressed at reservoir conditions) Original (initial) free gas in place (expressed at standard conditions)

NRsoi

Original solution gas volume (expressed at standard conditions)

ª mNBoi º  NRsoi » « «¬ B gi »¼

Gp

N p Rp

N  N R p

so

Original gas (both free and solution) volume in reservoir (expressed at standard conditions) Cumulative volume of produced gas at time t (expressed at standard conditions) Volume of solution gas remaining in oil at time t (expressed at standard conditions)

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Change in Oil Volume:

Change in

Initial reservoir

=

oil volume

Oil volume change

-

oil volume

= NBoi í (NíNp)Bo

Oil volume at p

(reservoir volume)

(4.1)

Change in Free Gas Volume: Define:

m

Initial reservoir free gas volume Initial reservoir oil volume

GBgi

(4.2)

NBoi

Initial free gas volume = GBgi = mNBoi Free gas in the reservoir at t =

Initial gas Free + dissolved Free gas at time t

í

Gas produced

í

Gas remaining in solution

º ª mNB oi  NRsoi »  N p R p  N  N p Rso « ¼» ¬« B gi

(in SCF)

(in SCF)

º ª mNB oi  NRsoi  N p Rp  N  N p Rso » Bg « »¼ «¬ Bgi º ª mNBoi  NRsoi  N p Rp   N  N p Rso » Bg Change in free gas volume mNBoi  « ¼» ¬« B gi (reservoir volume)

Re servoir free gas volume at time t

(4.3)

Change in Water Volume: Change in water volume =

Water influx

í

Water produced

+

Water expansion 9

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Change in water volume We  Wp Bw  Wcw 'p

(in bbls)

(4.4)

Change in the Void Space Volume:

V f c f 'p

Change in pore space

(4.5)

Initial void space can be expressed as:

NBoi  mNBoi 1  Swi

Vf

(4.6)

Initial water reservoir volume:

W

Vf Swi

NBoi  mNBoi S wi 1  S wi

(4.7)

Combination of the changes in water and rock volumes:

Change in water volume

=

=

We  Wp Bw 

+

Change in pore volume

NB oi  mNB oi NBoi  mNBoi S wic w 'p  c f 'p 1  Swi 1  Swi

ª cw S wi  c f We  Wp Bw  (1  m) NBoi « ¬ 1  S wi

º »' p ¼

(4.8)

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Equating the changes in the oil and free gas volumes to the negative of the changes in the water and rock volumes:

Change in oil volume

+

Change in free gas volume

Change in water volume

=

+

Change in pore space volume

ªmNB oiB g º NBoi  NBo  N p Bo  mNBoi  « »  NRsoi Bg  N p R p Bg  NBg Rso  N p Bg Rso «¬ Bgi »¼ ªc S  c f º ˙ W e W p B w  (1 m )NBoi « w wi (4.9) »'p ¬ 1  S wi ¼ By inserting the definition of Bt

Bt

Bo  ( Rsoi  Rso ) Bg

Equation (4.9) can be simplified to

§ B · N ( Boi  Bt )  N p Bt  ( R p  Rsoi ) Bg  mNBti ¨1  g ¸ ¨ Bgi ¸¹ © ªc S  cf º ˙W e W pB w  (1 m )NB oi « w wi »'p ¬ 1  S wi ¼

>

@

(4.10)

Rearranging Equation 4.10 gives:

N ( Bt  Boi ) 

ª c S  cf mNBoi ( B g  B gi )  (1 m) NBoi « w wi Bgi ¬ 1  S wi

N p [Bt  (R p  Rsoi ) Bg ]  W p Bw

º » 'p W e ¼

(4.11)

In Equation 4.11, there is the following relation: [Bt  (R p  Rsoi )Bg ] [Bo  (R p  Rso )Bg ]

Therefore, either term can be used in the calculation depending on the convenience of the calculation and the availability of the corresponding data.

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Discussion of Eq. (4.11): The left-hand side of the equation x x x

The first two terms account for the expansion of any oil and/or gas zones. The third term accounts for the change in pore volume, which includes pore space decrease and expansion of the connate water. The fourth term is the amount of water influx that has occurred into the reservoir.

The right-hand side of the equation x x

The first term represents the production of oil and gas. The second term represents the water production.

The material can only be used when there is pressure and production data as well as PVT data of the reservoir fluids. Also needed are reservoir rock properties. To aid the analysis, the type of drive mechanism that motivates the petroleum fluids to be produced should be known. One key assumption of the material balance method is that the pressure throughout the reservoir is constant. That is, the pressure and fluid properties are averaged throughout the entire reservoir.

4.4 Material balance equations for undersaturated oil reservoirs For undersaturated oil reservoirs: x Initial reservoir pressure is higher than the bubble point pressure of the oil (no gas cap or m = 0). x Free gas develops after p < pb. x There may be water influx. The general material balance equation (Equation 4.11) for undersaturated oil reservoirs can be simplified as:

ª cw Swi  c f º N ( Bt  Boi )  NBoi « » ' p  We ¬ 1  Swi ¼

N p[ Bt  ( R p  Rsoi ) Bg ]  Wp Bw

(4.12)

In equation 4.12 the effect of water and formation commpressibilities are accounted for. Rearranging Equation 4.12 gives the equation of calculating N (initial oil in place):

N

N p[ Bt  ( R p  Rsoi )Bg ]  We  Wp Bw ª c S  cf º Bt  Boi  Boi« w wi » 'p ¬ 1  S wi ¼

(4.13)

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Equations 4.12 and 4.13 are general material balance equation for undersaturated oil reservoirs. 4.4.1 Solution gas drive reservoir In a solution gas drive reservoir, the major drive mechanism is the expansion of the solution gas that was originally dissolved in the oil. As shown in Figure 4.9, there are two stages of a solution gas drive reservoir. In the first stage, the oil is undersaturated (p < pb) and there is no gas phase in the reservoir. As fluids (oil and water) is produced from the reservoir, the pressure falls until it reaches and decreases below the bubble point pressure of the reservoir and some of the dissolved gas comes out of solution to form gas bubbles (gas phase). In this stage, free gas exists in the reservoir.

Figure 4.9 Two production stages of solution gas reservoir A schematic of the typical production history of a solution gas drive reservoir is shown in Figure 4.10. The reason for the slight dip in the produced GOR is because after free gas forms, the gas saturation has to rise above the critical gas saturation to become mobile in the reservoir. Later in the process, the produced GOR drops because most of the gas has been produced from the reservoir.

Figure 4.10 Pressure and produced gas-oil ratio history in a solution gas drive reservoir 13 Winter 2016

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Material Balance @ p > pb In this case, x Assume that water influx is zero, We = 0 x All the gas produced at the surface originates from dissolved gas in the oil. there is: Rso = Rsoi = Rp. Also, @ p > pb, Bt = Bo and Boi = Bti The generalized material balance simplifies to:

ª c wS wi  c f º N (Bo  Boi )  NBoi « »'p ¬ 1  S wi ¼

N pB o  B wW p

(4.14)

Solve for N: N

N pB o  BwW p

(4.15)

ªc S c º Bo  Boi  Boi « w wi f » ' p ¬ 1 S wi ¼

Oil compressibility, co, is often used with the following definition:

co

vo  voi v oi ( p i  p )

Bo  B oi Boi 'p

(4.16)

Therefore,

Bo  Boi

Boi c o 'p

(4.17)

Expansion of oil is

N ( Bo  Boi )

NB oic o 'p V f S oco 'p

NBoi So co 'p 1 S wi

(4.18)

Substituting (4.18) into (4.14) and rearranging gives:

ª co S o  c w S wi  c f NB oi « 1 S wi ¬

º » 'p ¼

N p Bo  BwW p

(4.19)

Effective fluid compressibility, ce, is defined as:

ce

co So  cw Swi  c f 1  Swi

(4.20)

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Eq. (4.19) can be written as

NBoi ce 'p

N p Bo  BwWp

(4.21)

And N is calculated as

N

N pB o B wW p

(4.22)

Boi ce 'p

If the water production Wp is negligible: N

N p Bo ce 'p B oi

(4.23)

The recovery factor is calculated as B oic e ' p (4.24) N Bo In an undersaturated oil reservoir at pressures above bubble point pressure both oil expansion and water and formation compressibilities contribute to the oil production. Neglecting the water and formation compressibilities can introduce an error as high as 70% in the estimation of original oil in place from the production data. FR

Np

Material balance @ p < pb In this case, there is no initial gas cap (m = 0), and we will assume that water influx is zero (We = 0). The gas compressibility is usually a couple orders of magnitude higher than that of the water and rock. Once appreciable gas saturation has developed in the reservoir, the water and formation compressibilities are negligible. The generalized material balance simplifies to

N

N p [ Bt  ( Rp  Rsoi ) Bg ]  Wp Bw Bt  Bti

,

which can be written as

N

N p[ Bo  ( R p  Rso ) Bg ]  Wp Bw B o  B oi  (R soi  R so ) B g

(4.25)

or

N[( Bo  Boi)  ( Rsoi  Rso ) Bg ] N p[ Bo  ( Rp  Rso ) Bg ]  Wp Bw

(4.26)

The left hand side of this equation...