2 Reservoir Fluid Flow & Natural Drive Mechanisms

8/10/2019 2 Reservoir Fluid Flow & Natural Drive Mechanisms

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Gas Reservoirs

Gas reservoirsare hydrocarbon reservoirs that contain dry gas (i.e., the methane

mole fraction is greater than 95%). Behavior of these reservoirs is governed by thegas equation of state and the material balance equation. Three quantitiespressure,volume, and temperaturedefine the state of a gas. As we mentioned, in most

hydrocarbon reservoirs the temperature is considered to be constant.

Gas Equations of State

Ideal Gas Equation:

TheIdeal Gas Equationof state is derived from Boyles law, Charles or Gay Lussacslaw, and Avogadros law:

pV = nRT = (18)

where: p = pressure, psia

V = volume, ft3

n = number of pound-moles

R = gas constant = 10.732

T = temperature, R = 460 + F

W = weight, lb

M = molecular weight, lb/lb-mole

Equation 18 is used to calculate the number of moles of gas when the pressure and volume areknown. This allows the determination of the moles of gas left in the reservoir as the Pres suredeclines, and thus recovery in moles. However, each mole of any ideal gas occupies a volume of

379.4 ft3(10.74 m3) at 60F (289K), and 14.7 psi (101 kPa). Therefore, recovery in standardvolumes is:

379.4 x (number of moles recovered)= standard ft3or

0.74 x (number of moles recovered)= standard ft3

Real Gas Equation:

While Equation 18 is used in many calcula tions not pertaining to hydrocarbonsystems, it was found that the behavior of hydrocarbon systems deviates from the

ideal or Perfect gas law. The deviation from ideal behavior increases with pressure

and decreases with temperature. This deviation is attributable to the fact that theperfect gas law assumes that the kinetic motion of gas molecules (i.e., theirtendency to fly apart) is much stronger than the electrical attractive forces. This

assumption is not valid at high pressure and relatively low temperature. Under most


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reservoir engineering pressure conditions, the molecules are brought close to each

other, and the attractive forces become important. To correct for the deviation from

ideal gas behavior, a gas deviation fac tor, or compressibility factor, is introducedinto Equation 18. It becomes

pV = znRT (19)

where z is the dimensionless deviation, or gas compressibility, factor.

z-Factor Correlations:

The z factor may be obtained from correlations given in Katz 1959 and Standing andKatz 1942. The correlations give z as a function of pseudoreduced temperature and

pressure

These quantities are defined by

Pr= , and Tr= where Pcand Tcare the pseudocritical pressure and temperature for the hydrocarbon system.(The critical temperatureis the temperature at which the meniscus that separates the liquid andvapor phases of a fluid disappears. The vapor pressure at this critical temperature is called thecritical pressure. Above the critical temperature, there is no reason to draw any distinctionbetween liquid and vapor, since there is a complete continuity of states.)

The preferred way to obtain Pcand Tcis by calculating them from a gas

compositional analysis, i.e.,

Pc= (20)

Tc=

(21)

where:ni= mole fraction of component i

Pci = critical pressure of component i

Tci = critical temperature of component i

The sum is taken over all the components. Pci and Tci are listed in Katz et al. (1959) andStanding (1952) and are given in Table 1.
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Table 1

Equations 20 and 21 require knowledge of the gas composition. If this is not

available one may use correlations given in Katz 1959. These give Pcand Tc values asfunctions of gas gravity.

Application of the Real Gas Equation of State

Volumetric Calculations

Equation 19 may be used simply to calculate the number of moles, and thus thestandard cubic feet of gas in a gas reservoir. The value of z can be less than, equal

to, or greater than 1.0. It very seldom exceeds a value of 1.10. However, it can be

as low as 0.3.

p/z versus Cumulative Production

We mentioned that the equation of state together with the material balance equation

defines the behavior of a gas reservoir. The MBE for a gas reservoir with no waterinflux and neglecting compressibilities of rock and its associated water is

GpBg= G( Bg- Bgi) (22)


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where:Gp= cumulative gas produced, SCF (m

3)

Bg= gas formation-volume factor, RB/SCF (m3/standard m3)

G = original gas in place, SCF, (m3)

Bgi= taken at the original pressure pi

Bg is calculated by

(23)

where Tr is the reservoir temperature in R , and standard conditions are taken at 14.7 psi (101kPa) and 60F (289 K). Substituting for Bgin Equation 22 and simplifying gives

(24)This equation shows that a plot of Gpversus p/z on rectangular coordinate paper should result ina straight line. The extrapolation of the straight line to any p/z value gives total recovery at that

pressure value, and its extrapolation to p/z = 0 gives the initial gas in place (Figure 1 ).


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Figure 1

The p/z plot is used in the petroleum industry to predict gas recovery versus pressure, and initialgas in place. It is evident that some pressure and production data are required to establish astraight line. The more data that becomes available, the better the definition of the straight line,and the more accurate the prediction. One must always remember that we are usually dealingwith field data where inaccuracies are present, and where scatter occurs. Therefore, any p/z plotshould be routinely updated as pressure and production data allow.

Effect of Water Influx Ifwater influx is present, Equation 22 becomes

BgGp= C(Bg- Bgi) + We (25)where Weis the water influx. Equation 24 becomes

(26)Since Weis a function of pressure and time (i.e., it is not constant), and Bgis a function ofpressure, a plot of Gpversus p/z will not give a straight line. However, at early time We isnormally small, and, because of this, the plotted points may appear to fall on a straight line. Sucha straight line will have a relatively flat slope, and its extrapolation to p/z = 0 will give anerroneously high value for G. Later tine production data will not continue on a straight line trend.


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Rather, they will curve with a slope as shown in Figure 2.

Figure 2

Recovery Factors

Gas recovery by pressure depletion usually is the most efficient means of producing

gas reservoirs and results in a maximum recovery. Recovery can easily be calculated

by Equation 24, and requires an estimate of the level of abandonment pressure. Thisrecovery can also be approximated by

Recovery in percent = 1 - 100When water influx is present, recovery is adversely affected because of the tendency for theencroaching water to trap portions of the gas in the reservoir, perhaps 15 to 50% or more. Thistrapped gas is unrecoverable. In addition, heterogeneities and stratification may cause theencroaching water to bypass a por tion of the reservoir and prematurely "water out" the producingwells. Generally speaking, when water influx is present, reservoir and production engineers maytry to "outrun" the water by producing the gas at a high rate. This tends to maxi mize the effect ofthe expansion part of the recovery mechanism, before the water can move into the gas-saturatedportion of the reservoir. The success of such a technique depends to a large extent on thepermeability characteristics and geometry of the reservoir rock, the reservoir aquifer sys tem, and


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the location of the producing wells. Other strategies for handling water influx, as outlined by theGas Research Institute in its publication Managing Water-Drive Gas Reservoirs(1993) include

continuing to produce watered-out wells in order to lower reservoir pressure and thusremobilize trapped gas

selectively recompleting wells with multiple horizons

drilling additional wells to avoid bypassing reserves

increasing off-season takes to maximize the net present value of reserves

Abnormal-Pressure Gas Reservoirs

Abnormally pressured gas reservoirs are those reservoirs whose average fluid

pressure gradient is substantially higher than 0.433 psi/ft (9.796 kPa/m), which isthe average for normally pressured reservoirs. Abnormal pressures can result from a

number of conditions, some of which include undercompaction of sediments,

chemical diagenesis, tectonic activity (e.g., faulting), fluid density differences andfluid migration. For such reservoirs, the effective rock compressibility could beseveral orders of magnitude higher than that of normal reservoirs.

p/z Behavior

In applying the MBE to gas reservoirs with no water influx, it is normally assumed

that the rock and its associated water expansion is insignificant compared to that of

the gas expansion and is normally ignored. This assumption underlies the linear p/zversus cumulative production plot. In the case of abnormally pressured gasreservoirs, the compressibility of the rock cannot be ignored. It acts to maintain the

pressure at a relatively high value. Thus a plot of p/z versus cumulative gas

production for these reservoirs will show two distinct slopes (Perez and Robinson1976). The early slope exists during the period of abnormally high pressure (becauseof gas expansion, as well as pressure maintenance resulting from formation

compaction, crystal expansion and water expansion), and the later one characterizes

the reservoir when the pressure reaches the normal value (Figure 3).
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Figure 3

Extrapolation of the early slope to obtain initial gas in place will result in anoptimistic value. In this sense it is similar to the p/z plot when water influx is

present, as discussed earlier. If the second straight line is adequately defined it may

be extrapolated to obtain an estimate of the initial gas in place. If only the first slopeis defined the engineer is advised against using the p/z technique for determininggas in place: instead, the MBE with compressibility terms should be used.

Material Balance Equation with Compressibility Terms

The MBE for a gas reservoir with no water influx is

GpBg= G(Bg- Bgi) + (Swcw+ cr) (pi- pR)

The first term on the right-hand side is the gas expansion and the second term is the

expansion of the rock and associated water. The left-hand side term is the gas

production. All are expressed in reservoir volumes. The initial gas in place G is then


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(27)Equation 27 should be used to calculate the initial gas in place, in place of the normal p/z versus

Gpplot for abnormally pressured reservoirs.


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Gas Condensate Reservoirs

Gas condensate reservoirshave been defined as those hydrocarbon reservoirs thatyield gas condensate liquid in the surface separator(s).

A retrogradegas condensate reservoir is one whose temperature is below the

cricondentherm (the maximum temperature at which liquid and vapor phases cancoexist in equilibrium for a constant-composition multicomponent system). Aspressure decreases below the dewpoint due to production, a liquid phase developswithin the reservoir, which process is called retro grade condensation. Performance

prediction for a gas retrograde condensate reservoir becomes a complex matter. One

way of predicting performance is to simulate the reservoir depletion by a laboratorystudy using a high-pressure cell. Modern models are also available to reservoirengineers as compositional reservoir simulators with which an equation of state is

used to calculate phase behavior.

Condensate Fluids

Development of reservoirs that contain condensate hydrocarbon fluids requiresengineering methods that are significantly different from crude oil or dry gas

reservoirs. An understanding of the properties of these fluids is necessary for properanalysis and planning of a recovery scheme.

Condensate fluids production is predominantly gas from which liquid or distillate is

condensed. Typically, distillate API gravity is higher than 45 API, while the gas-oilratio can range from 5000 to 100,000 SCF/bbl (890 to 18,000 m3/m3). The liquid

content ranges from 10 bbl/MMSCF (56 m3/Mm3) for very lean condensate systemsto 200 or more bbl/MMSCF (1100 m3/Mm3) for rich ones (Eilert et al. 1957; Standing1952).

The composition of a gas condensate lies between that of a volatile oil and a dry gas.Thus, the methane mole fraction is normally between 0.75 and 0.90, in contrast to

0.95 for dry gas and less than 0.70 for volatile oil. Further, the mole fraction of theheavy components (C7+) is several times larger than that for a dry gas.

The pressure and temperature of gas condensate reservoirs play a strong role in

their physical behavior. We will briefly review the effects of pressure andtemperature on condensate systems here.

Figure 1shows a pressure-temperature phase diagram.


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Figure 1

The figure shows that if the reservoir pressure and temperature are such as to place

the reservoir in the single-phase gas region (Point E), the reservoir fluids will remain

single-phase as the reservoir is depleted isothermally. This is so because theisothermal line will never cross the two-phase region. If we consider a reservoir at

point A, the reservoir fluid is single-phase. However, as the pressure declines, a

point B is reached at which the first drop of liquid appears. Liquid saturationincreases as the pressure declines, until it reaches a maximum of over 10%. Uponfurther decline in pressure this process is reversed, and if point D is achieved all the

liquid disappears. This reversal of typical behavior, condensation of fluids as thepressure declines, gives rise to the term retrograde condensation.

Retrograde condensation may result in a considerable loss of valuable hydrocarbons.For all practical purposes, the condensed liquid phase is lost to production. Itsvolume is very seldom large enough to form a saturation above the critical value

required for liquid flow. Thus, as the pressure falls below the dewpoint value, the gas

produced is progressively deficient in recoverable liquid content. Because of this,care should always be exercised to maintain the pressure of such reservoirs abovethe dewpoint value.


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The compressibility factor, z, can be determined from pseudore duced pressure and

temperature correlations. This requires the availability of proper correlations

representing relatively large portions of high molecular weight components in themixture. Eilert et al. (1957) provides correlations of the pseu docritical values andmolecular weight of C7+ fractions. For lean condensates, formation-volume factors

used for natural gases may be used to obtain good approximations. For rich

condensate systems, such approximations are not adequate. Formation-volumefactors should be obtained from laboratory measurements.

A highly important property of a condensate system in any enhanced processemployed to recover such fluids is miscibility. (Miscibility exists when two fluids are

able to mix in all proportion without any interface forming between them.) In

general, a condensate reservoir gas is miscible with any dry hydrocarbon gas. Forsystems near the dewpoint, miscibility should be determined by laboratorymeasurements made with a high degree of accuracy in order to define the phase

behavior in the region of interest. (Miscibility will be covered in the module dealingwith miscible EOR processes.)

Calculations of Initial Gas and Condensate in Place

Calculations of initial gas and condensate in place require the use of the real gasequation of state, with some modifications. First we calculate volumetrically thevolume of gas condensate per volume of reservoir:

(28)

where:

379.4= volume of one mole, SCF/moleG = gas condensate volume, SCF/acre-ft

= reservoir pressure, psia

V = gas volume per reservoir volume, ft3/acre-ftz = the gas deviation factor

R = the gas constant (10.73)TR= reservoir temperature, (R)

From the produced surface gas-oil ratio, Rs(scf of dry gas per bbl of condensate), wecalculate the number of moles of gas and condensate by

and

(29)


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where:

ng= mole of produced gas per bbl of produced liquidn0= moles of condensate in one bbl

= density of condensate, lb/ft3M0= molecular weight of condensate, lb-mole

The fraction of gas in the condensate under reservoir conditions is

(30)

The volume of the gas in place per acre-ft is

V = G fg(31)

and the initial distillate in place = G (l - fg) (32)

The molecular weight of the tank oil (M0), if not known, may be estimated by usingthe following formula developed by Cragoe (1929):

(33)

where ois the oil-specific gravity.

The above calculations are illustrated in Example 1.

Example 1

Given:

Reservoir pressure = 2700 psiaReservoir temperature = 200F

Porosity = 0.20 Interstitial water saturation = 0.15Oil gravity at 60F - 45 API

Daily stock tank oil = 200 bblDaily separator gas = 3000 MSCFDaily stock tank gas = 100 MSCF

The gas deviation factor at reservoir conditions z = 0.8

calculate the initial gas and distillate in place per acre-ft


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Hydrocarbon pore volume/acre ft, V = 43560 0.2 (1-0.15) = 7405 ft3

G = = 1339 MSCF/acre ft.(from Equation 28)

= 155.6 (from Equation 33)

= 0.8 62.4 = 50

(from Equation 30)

Volume of gas/acre ft = 96 1339 = 1285.4 MSCF(36.4 103m3)

Volume of condensate/acre ft = 1339-1285.4 = 53.6 MSCF (1.5 103m3)

In other words, each acre foot of reservoir contains 1339 MSCF of gas, of which 96%

will be produced as gas at the surface, and the remainder of which will be liquidcondensate at the surface.

As long as the gas condensate fluid remains as single-phase gas in the reservoir, its

performance may be calculated as described previously. However, when reservoir

temperature and pressure conditions are such as to place the gas in the two-phaseregion, a liquid phase will develop when the pressure falls below the dewpoint value(retrograde condensation). Prediction of performance then becomes complex.

Retrograde Gas Condensate Reservoirs

Performance One way of predicting the performance is to simulate the reservoir

depletion by a laboratory study. A representative fluid sample is placed in a highpressure cell at reservoir pressure and temperature. The pressure is then decreasedby "producing" the cell, simulating reservoir depletion. The volume of the cell is keptconstant, simulating the constant pore volume of the reservoir. The pressure

decrease is achieved by removing incremental amounts of gas. The condensate

phase is not removed because it normally forms an immobile phase in the reservoir.Measured liquid recovery from an analysis of the removed gas volumes gives theexpected liquids recovery under depletion.


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Another way of calculating performance is by use of equilibrium ratios. An

equilibrium ratio, K, is the ratio of the mole fraction of any hydrocarbon component

in the gas phase to the mole fraction of the same component in the liquid phase.Equilibrium ratios are functions of pressure and composition, and therefore they arenot easy to define for complex multicomponent retrograde systems. When K values

are available from a laboratory analysis, the engineer can calculate the distribution of

any component in the gas and liquid phases as a function of pressure andtemperature.

Modern methods of reservoir engineering rely on compositional reservoir simulatorsto predict performance. These models use an equation of state to calculate phasebehavior.


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Retrograde Gas Condensate Reservoirs

Pressure Maintenance by Gas Cycling

Retrograde condensation may cause a significant fraction of the liquid content of thegas condensate to be left in the reservoir. Distillates are a very valuable part of the

accumulation. Because of this,pres sure maintenance above the dewpoint during theexploitation of the reservoir is commonly practiced.

One way of maintaining pressure is by injecting the dry gas component of the

produced wet gas. This is what is left of the produced wet gas after the liquid hasbeen removed at the surface. This operation is called gas cycling. The injected drygas partially maintains reservoir pressure and at the same time becomes miscible

with oil and drives the wet gas toward the producing wells. However, in some cases,the volume of the dry gas component will represent only a fraction of the producedgas volume. In such a case, if the injection volume is not supplemented with

additional gas, a gradual decline of the reservoir pressure may take place, and liquid

loss may result. The degree of gas volume augmentation will depend on the pres

sure level of the reservoir relative to the dewpoint value.

Recovery from cycling operations depends on the cycling efficiency of the operation.This value is the product of three efficiencies: the areal sweep, EA; the vertical

sweep, EI; and the microscopic displacement, ED. The areal sweep efficiency is a

function of the location of the wells and their rate of production and injection, andthe heterogeneity of the reservoir. It is the area swept by the injected gas divided bythe total area of the reservoir. The invasion or vertical ef ficiency, EI, is a strong

function of stratification and the permeability variation among the reservoir layers.

EI is the portion of a vertical section of the reservoir contacted by the injected fluid,divided by the hydrocarbon area in all layers behind the injected fluid front. If a

highly permeable layer (a "thief" zone) exists, dry gas will channel through it to theproducing well, resulting in a low EI value.

Use of Material Balances

Laboratory-obtained data from the constant-volume cell described previously may beused to predict gas condensate reservoir performance. The data give in crements of

gross gas produced as a function of pressure as well as the liquid in each increment

of gas. Thus, total gross gas and liquid production in percent of initial gas in place asa function ofpressure may be calculated. Also total liquid recovery can be obtained.

If a volumetric estimate for the initial gas condensate in place is available, thelaboratory data may be used to give incremental recovery of gas and liquid as a

function of pressure. On the other hand, if cumulative gas production for a knownaverage reservoir pressure is given, then the laboratory data may be used to

calculate the initial gas in place and subsequent recovery. For example, assume thatat an average reservoir pressure of 3000 psia, Gp MMscf of gas had been produced.From laboratory depletion data at 3000 psi, the total incremental gas recovery is

some percent (say, X) of the initial gas in place. Thus, initial gas in place in thereservoir may be calculated by


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MMSCF (34)

Knowing G, and the percent gas recovery and liquid condensation with pressure fromlaboratory data, reservoir performance calculation is straightforward.

Pressure Maintenance by Water Drive

Some gas condensate reservoirs are under active water drive. The water influx maybe sufficient to maintain the reservoir pressure above its dew-point value in somecases. If not, it may have to be augmented by water injection. Ultimate recovery is

still controlled by the three recovery efficiencies described earlier. However, in thecase of water displacing gas, ED is considerably smaller. Water tends to trap gas,resulting in a poor displacement ef ficiency. Assuming E1and EA are the same,

recovery by water drive is normally lower than that by gas cycling by about 20%. It

should also be noted that E1 may not be the same as that for gas cycling because ofthe difference in density between water and dry gas. Water tends to segregate to the

bottom of the perforated interval while gas will override the top. Permeabilitydistribution in the various layers determines whether EVS for a water drive is lessthan, equal to, or greater than EVS for gas cycling. Again, reservoir simulators arethe best available tools to accurately predict performance in complicated reservoirsituations.


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Solution Gas Drive Reservoirs

Production Mechanism

A solution gas drive reservoiris one in which the principal drive mechanism is theexpansion of the oil, the expansion of the gas dissolved in the oil, and the expansion

of the rock with its associated water. Two phases of production may occur in suchreservoirs. The first phase is that in which the pressure is above the bubble-pointvalue. During this period, no free gas phase exists and the reservoir oil isundersaturated. The second phase occurs when the pres sure falls below bubble-

point and a free gas phase exists.

Undersaturated Reservoirs (Expansion Drive)

For these reservoirs there is no initial gas cap; that is, m = 0 in the material balance

equation (MBE). Furthermore, Rs = Rsi = Rp, since all the gas produced at the

surface has been dissolved in the oil. In addition, Bt = B0, and it is assumed that thewater influx (if present) is negligible. The MBE reduces to

Np B0 =N (B0 - Boi) + N Boi

or

Np Bo = N Boi (38)

However,

So= 1 - Swi, and the oil compressibility, co=

Substituting in the above equation gives

NpBo= N Boi

or

NpBo= N Boice p (39)

where ce is the effective compressibility of the reservoir and is given by


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With the MBE, the reservoir is viewed as a homogeneous tank where the productionis due to the expansion of the systems. Percent recovery (from Equation 39) as thepressure declines is given as

(40)

Example 2 illustrates the calculation of the fractional recovery in an undersaturated

reservoir when the pressure drops from 4500 psia to the bubble-point value of 4000psia.

Example 2

The values for co, cw, and cr are, respectively, (12, 4, and 8) l0-6 per psi, and Boi,

and Bo are 1.24 and 1.25 reservoir bbl per STB.

The initial water saturation = 0.2.

We simply substitute into Equation 40 to find

500 = 1.14 l0-2 = 1.14%

Example 2 illustrates two important points. The first is that recovery by expansion

above the bubble-point is typically very small. Thus, expansion drive above the

bubble-point makes the smallest contribution to the overall production mechanism.The second point is that the magnitude of the combined water and rock expansion ince is comparable to that of the oil and must be accounted for in the calculations.

Saturated Reservoirs

Below the bubble-point, gas will be liberated from the oil and will exist as a free gas

phase. A good approximate value for the value of the gas compressibility is cg =

, which is obtained from the definition of compressibility for an ideal gas. Thus,the gas compressibility is generally several orders of magnitude larger than the rockand oil com pressibility. At 4000 psia for example, Cg = 1/4000 = 250 l0-6 per psi.

To illustrate the relationship between recovery and pressure decline, we return onceagain to the MBE. For simplicity, assume that at discovery the reservoir had no gas


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cap. Assume also that the rock and associated water expansion may be ignored,

since the gas compressibility is considerably larger. Ifwe also assume negligiblewater influx, the MBE becomes

Np [Bt + (Rp - Rsi) Bg] = N (Bt - Bti) (41)

The fractional recovery is

at abandonment conditions. (42)

Equation 42 shows that percent recovery is a function of two parameters: the PVT

properties of the oil and gas, and cumulative gas production as indicated by Rp For a

given oil reservoir, recovery is basically inversely proportional to Rp or the total gasproduced at abandonment pressure. This means that in the case of solution gas drive

reservoirs, the engineer must strive to minimize gas production to obtain more

efficient recovery. The more gas that remains in the reservoir, the larger the amountof energy available for the production of oil. A schematic diagram of the GORequation, as shown in Figure 1, clearly indicates the adverse effect of gas productionon recovery.


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Figure 1

_


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Typical Producing Performance

Pressure, GOR, Water Production Profiles

Once free gas develops and the saturation exceeds a critical value, the gas will startto be produced in dispropor tionate quantities. Figure 1illustrates a typical GOR

history.

Figure 1

Above the bubble-point the GOR is constant, since all the gas production comessolely from the dissolved gas. As the pressure declines below the bubble-point a free

gas phase develops and the gas in solution declines slightly. The pro duced gascontinues to be supplied solely from the dissolved gas until the gas saturation

exceeds the critical value. During this period the GOR declines. Subsequently, the

free gas begins to flow and constitutes part of the produced GOR. Its contributionincreases as the gas saturation increases and far exceeds the decline in the amountofgas in solution. This is why the GOR rises sharply. The subsequent decline in GOR

sets in when the reservoir pressure declines significantly and much of the original

dissolved gas has been produced. At that point, the contribution of the gas insolution to GOR becomes negligible, and the GOR may be approximated by


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Since Bg is proportional to its value increases rapidly as the pressure declines (

Figure 2). On the other hand, the change in the values of the other parameters is

relatively small. This explains the rapid decline of the GOR shown in Figure 1.

Figure 2

Initially, the water production may be zero or close to it, especially if no aquifer

exists. This is so because the water saturation in the absence of an aquifer is usually

equal to or very close to the critical saturation required for flow. As the pressuredeclines, the rock and water expand. Thus the relative water saturation increasesslightly and water produc tion may also increase slightly as shown in Figure 1.

Pressure Maintenance

In many solution gas drive reservoirs, pressure maintenance by water injection is

employed to enhance ultimate recovery. There are several advantages of initiating
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water injection at or near the bubble-point pressure and prior to the development of

a significant gas phase. One advantage is linked to the nature of relative

permeabilities. The oil and water relative permeabilities are higher when a gas phaseis not present than when an appreciable gas saturation is established. Thus, for thesame pressure drawdown at the wells, the oil production rate is higher. Another

important advantage is that the rate of water injection required to maintain a certain

level of production is lower. To maintain pressure, the injection rate must be equal tothe total fluid withdrawal in reservoir volumes. The total fluid withdrawal associatedwith one surface volume is

Bt+ (Rp- Rsi)Bg

where:

Bt= two phase formation-volume factor, RB/STBRp= cumulative produced GOR, SCF/STB

Rsi= initial gas in solution, SCF/STBBg= gas formation-volume factor, RB/scf

At or close to the bubble-point, Rp= Rsiand the withdrawal is approximately Bti= Boi,

Conversely, if pressure maintenance is started at a pressure level significantly belowthe bubble-point pressure, the value of (Rp- Rsi) Bgcan be significant and the total

withdrawal associated with one surface volume is considerably larger than Boi. Thus

more water injection is required to maintain the same level of oil production. Froman economic point of view it is advisable to initiate pressure maintenance at or closeto the bubble-point pressure.


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Material Balance Equation Applications

The material balance equation for a solution gas reservoir may be used for two

purposes. Ifproduction data are available the MBE may be used to calculate theinitial oil in place. When combined with Darcy's law it may also be used to predictrecovery versus pressure.

Quantifying Reservoir Performance, Calculation of Initial Oil In Place We will examine

first the use of the MBE to calculate N, or initial oil in place. Once again, the MBE(ignoring rock and water compressibility) is

Np[Bt+ (Rp- Rsi) Bg] + WpBw= N (Bt- Bti)In order to simplify the paperwork, let us indicate the left hand side, which represents the totalproduction in reservoir volumes, by the term F. We can also simplify the equation further, by

substituting Eofor (Bt- Bti), which represents the expansion of the oil and its associated gas. TheMBE then becomes

F = N EoEquation 43 is the equation of a straight line. A plot of F versus E oshould give a straight line

passing through the origin with a slope equal to N ( Figure 1). This solution method is known asthe MBE as an equation of a straight line and is discussed in detail by Havlena and Odeh (1963,

1964).

Figure 1


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Usually production data is tabulated on a monthly or quarterly basis. Average

reservoir pressure for the same time periods is also tabulated. Using the PVT data

available from a laboratory analysis or from correlations, F and Eoare calculated for

the necessary time periods and plotted on rectangular coordinate paper. If there isno active aquifer the points should show a straight line trend. A straight line that

results in the minimum standard deviation and that passes through the origin isdrawn. The slope is N, the initial oil in place.

The mathematical requirement that the line should pass through the origin is very

important. Whenever one deals with field data, there will be scatter ofthe datapoints. Without the above requirement it is conceivable that a straight line thatminimizes the standard deviation without passing through the origin may be fitted to

the plotted points. The MBE as an equation of a straight line dictates that the origin

must be a point, and thus imposes a very important condition which must besatisfied for an acceptable solution.

Performance Prediction Techniques The MBE, together with the GOR equation derivedfrom Darcy's law (Equation 12), may be used to predict performance. Three methods

are normally used, those developed by Tarner, Tracy, and Muskat (Craft andHawkins 1959; Muskat 1949; Tracy 1955), as outlined below.

Tarner MethodIn the Tamer method, one guesses at, or assumes, an incremental recovery of

oil,Npresulting from an incremental decline in pressure. The incremental decline inpressure should not be taken as greater than 200 psia (1400 kpa). The incremental

gas produced, Gpdue to Npis then calculated by two methods: the MBE, and the

GOR equation (Equation 12). If the assumed Npis too large, Gpcalculated by theMBE will be too small, while that calculated by the GOR equation will be too large.

Thus, the error in Npresults in two opposing errors in the Gpvalues. The twoGpvalues agree only when the assumed Npis correct. Specifically, thecalculations proceed as follows:

1. Assume AN to be produced when the average reservoir pressure declines from pjto

pj+l(i.e., by pj).

2. Use the MBE equation to calculate NpRp= Gpby

(44)

Note in Equation 44, = sum of all the increments that have been produced. Thus

=


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Gpj+lis the total gas produced. The calculations are made for one surface volume of oil, i.e., N =1.

3. Calculate the incremental gas produced Gpjdue to pj by

= -

where is the total gas produced corresponding to the average reservoir pressure pjand

corresponds to the pj+lpressure.4. Calculate Soby

5. Calculate Sg, if needed, Sg= 1 - So- Swi

6. Determine krg/krocorresponding to Sgor So

7. Calculate R (i.e., GOR) by the GOR equation

8. Calculate Gpby

Compare calculated in Step 3 with that calculated in Step 8. If they agree within a

reasonable tolerance, accept the assumed Npjand continue the calculations by assuming a

new Npcorresponding to a new incremental pressure drop. The calculations are continued until

an abandonment pressure is reached. If Gpjof Step 3 does not agree with that of Step 8,assume a new value for Npjand repeat the calculations. Be guided by the observation that if

Gpjof Step 3 is smaller than GpjofStep 8, one needs to guess a smaller Npj. value. Theopposite is also true.

To illustrate the above method of calculation let us consider the following example.

We want to calculate the incremental oil recovery by solution gas drive when thepressure declines from an original bubble-point pressure of 2500 psia to a pressureof 2300 psia.

Example 3

Given the following data:


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p Bo Rs Bg

103 o g Bt

psia RB/STB Scf/STB RB/Scf cp cp RB/STB

2500 1.498 721 1.048 .488 .0170 1.498

2300 1.463 669 1.155 .539 .0166 1.523

Also given:

Sg krg/kro

0 0

.06 0

.07 0.001

.09 0.009

Swi= 0.2, and pb= 2500 psiaThe solution is as follows:

1. Assume an incremental oil recovery Np= .018 to occur when the pressure declines to2300 psia. Since the pressure at the beginning of the calculation step is the bubble-point

value, then Npin this case represents the total recovery, i.e.,

Np= Np= .018

2. Solve for Gpby MBE:

Gp= [(Bt- Bti) - NpBt]) + NpRsi

= 10.89 Scf(0.308 m3)

=.767


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Sg= 1.02 - 0.767 = 0.033

3. Calculate P by the GOP equation:

For Sg= .033, krg/kro= 0, thus,

P2300 = 0 + Rs= 669 (119.41 m2/m3at 17237.5 kPa)

R2500 = 0 + Rsi = 721 (128.41 at 15858.5 kPa)

4. Calculate Gp by the GOP equation:

= 12.51 Mscf (.3542 m3)

5. Gpcalculated in Step 2 is not close enough to that of Step 4. Because the value ofStep 2 is smaller than that of Step 4, our next guess will be to decrease p. Let p=.016. For this value Gpby MBE will be 12.8 (.342 m

3), while that by the GOR will be

11.12 (.3149 m3). To arrive at the next guess one plots the assumed pvalues versus

the difference between the calculated Gpvalues. The intersections of the lineconnecting the plotted points with the line of A(Gp) = 0 gives the next estimate of p. Inthis example the intersection gives an estimate of p= .01675.

For p= .01675, Gpby the MBE = 11.635 (0.3295 m3), while that of the GOR equation =11.640 (0.3296 m

3). This is a good check and the value is accepted.

The next step is to lower the pressure by another increment and to repeat the

calculations. This is continued until an abandonment pressure is reached. The gives

the oil recovery as a fraction.

Tracy Method

In Tracy's method one guesses at R in place of pThe calculations proceed asfollows:

1. Guess at a value of Rj+1as the pressure declines from pjto pj+1

2. Estimate the average R for the increment between pjand pj+1by

3. Calculate Npj resulting from the drop in pressure to pj+lby


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where Npjand Gpjare respectively the cumulative oil and gas produced at the average reservoirpressure pj

4. Calculate by

5. Determine krg/kro= corresponding to

6. Calculate R by

Compare R of Step 6 with R of Step 1. If the comparison is favorable, accept and proceed to thenext calculation increment; otherwise repeat the calculations starting with Step 1.

The advantage of Tracy's method is that the calculation converges faster than in

Tamer's. This is so because a small error in the guessed value of R results in asmaller error in the calculated p(i.e., the error is dampened out). In Tarner's

method, the opposite is true a small error in presults in a larger error in Gp

Muskat Method

Muskat's method is different from Tamer's and Tracy's in that it does not require a

trial and error procedure. However, it requires that one take the derivatives of

various parameters. These are represented by differences. Thus, the pressure mustbe taken in small intervals for the Muskat representation to be acceptable. Becauseof this, the Muskat method is best suited for computers.

Basically, the Muskat method calculates the produced gas-oil ratio by two methods,which are

where qgand qoare respectively the rates of gas and oil production in surface volumes. However,qgand qoindicate the rates of change with respect to time of the gas and oil in the reservoir. Inequation form,

and


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The two terms on the right-hand side of the qgequation represent the gas in solution and the gassaturation. Since

we can write

Expanding and solving for gives

where R is

Thus, the incremental change in the oil saturation Sodue to an incremental pressure decline pis calculated. The calculations proceed incrementally until an abandonment pressure is reached.

Total oil recovery Npis

where:Vp= the pore volume in barrelsSoi= initial oil saturation

So= oil saturation at abandonment pressure = Soi- SoRecovery Factor

Recovery by solution gas drive, as indicated previously, depends on the PVT

properties and the efficiency of gas utilization in the reservoir to provide the driving

energy. Recovery under the best conditions seldom exceeds 30%. When conditionsare not favorable, such as for relatively viscous oil, or highly heterogeneousreservoirs, or both, recovery could be below 10%. As a rule of thumb one thinks ofrecovery around 15% for solution gas reservoirs.

A Case History of a Solution Gas Drive Reservoir

A good example of a solution gas drive reservoir is the Gloyd-Mitchell zone of the

Rodessa field, located in Louisiana. (This resume is based on Craft and Hawkins


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Figure 2

The behavior of the gas-oil ratio, reservoir pressure, and oil production are therepresentatives of a typical gas drive mechanism.


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Gas Cap Drive Reservoirs


The same theoretical methods for computing recovery from solution gas drive

reservoirs may be applied to gas cap drive reservoirs. The assumptions are (1) that

no gravity segregation of the gas liberated from the oil occurs, and (2) that the gascap gas diffuses through the oil to supply additional expansion energy, while thelocation of the gas-oil contact remains at its original position.

In reality, the gas-oil contact moves downward, although en gineers attempt tomaintain the gas cap movement at a uniform level for optimum recovery. If the gas

cap shows definite ex pansion as indicated by a high level of reservoir pressure, andthe producing wells remain at low gas-oil ratio, gravity is maintaining a uniform

movement of the gas cap. The low produced gas-oil ratio continues until the gas cap

reaches the wells, at which point a sizeable increase in the produced gas-oil ratiooccurs. Recovery in such cases is greatly dependent on the completion intervals andwell locations.


Pressure, GOR, Water Production Profiles

Muskat (1949) published a theoretical study of the effect of gas cap size on reservoir

pressure and recovery. His results show that the presence of an active gas capcauses additional recovery over that obtained from solution gas drive, and causeshigher pressure throughout the reservoir life. The produced gas-oil ratio is lower in

the early production life and much higher in the late production life (Figure 1).Fluctuations in the GOR will result from successive high GOR production rates from

wells higher on the structure.


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Figure 1

The presence of a gas cap has no significant effect on water production, and it isassumed that no aquifer exists. Water production due to connate water saturation, ifit occurs, will be insignificant, or will be similar in nature to that for a solution gasdrive reservoir.

Selective GOR Control

As we stated earlier, if the gas cap expands uniformly because of gravity

segregation, the gas-oil ratio will increase dramatically when the gas cap reaches the

perforated intervals in a producing well. It is advisable in this case to close or

recomplete the wells at a lower interval. Continued production without recompletionwill not result in any appreciable additional oil from the wells, but will result in

considerable loss of gas that should be kept in the reservoir to maintain the

pressure. In some reservoirs, the gas may cusp into a producing well through apermeable zone. This also results in less recovery. Selective recompletion, or theshutting in of wells, should be considered to prevent unnecessary depletion of the

reservoir energy.

Recovery Factor


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Gas cap gas drive generally results in a higher recovery when compared to solution

gas drive. As a rule of thumb, the additional recovery can range from as low as 1%

to as high as 10%. Recovery is affected by the size of the gas cap, and the degree ofthe heterogeneity of the reservoir. The larger the gas cap, and the less the degree ofheterogeneity, the higher the additional recovery. Furthermore, the location of the

wells can appreciably affect recovery. For gas cap drive reservoirs, the wells should

be ideally located down dip. Ifthe gas cap advances uniformly, and gravity segregation maintains the uniform advance, overall recovery can be very high and may beover 50%. This value for recovery is normally associated with gravity drainage.

A Case History of a Gas Cap Drive Reservoir

In this case history, based on Muskat (1949) and Craft and Hawkins (1959), we seea good example of a gas cap expansion associated with a substantial gravity

drainage, as shown by the performance of the Parinas Sandstone reservoir of theMile Six Pool in Peru. The formation has an average angle of dip of 17 30 and anaverage cross-sectional area of 1,237,000 sq ft (114917 m2). The oil had a specific

gravity of 0.78, a viscosity of 1.32 cp, an average specific permeability of 0.3 darcy,

and an initial solution gas of 400 scf/STB (71.2 m

3

/m

3

) at 850 psia (5.86 MPa)original reservoir pressure. Gas of the original overlain gas cap had a viscosity of0.0134 cp.

This field had been subjected to a complete pressure-maintenance operation

throughout its history (since 1933) by returning produced gas to the gas cap. Thus,

the reservoir pressure had been maintained within 200 psi (1.38 MPa) of its originalvalue (850 psi) (5.86 MPa). The gas-oil contact moved over a vertical distance ofmore than 400 ft (131 m) as the result of gas cap expansion during the first five

years of oil production. This expansion undoubtedly had been facilitated by theeffective gas injection and the pressure maintenance opera tion that had beeninitiated at the beginning. The limited rise in gas-oil ratio shown during the producinglife indicates that in the downstructure oil saturation had been maintained at a high

level as a result of oil gravity drainage. The reser voir pressure remained almostconstant up to 1946. This indi cates that the injected gas had remained in the gascap and was not being dissolved in the oil zone to supplement the solution gas drive

mechanism. A combination of a high structural relief, good formation permeability,and low viscosity of oil had formed a most favorable condition for the development ofa significant gravity drainage in this field. With gas injection, at an average rate,exceeding the gas withdrawals, the pressure was kept almost constant. The GOR

increased very little, caus ing a continuous expansion of the gas cap and a loweringof the gas-oil contact. As a result of these favorable conditions, in conjunction withgood oilfield practice, oil recovery reached above 85% of the initial oil in place.

Figure 2shows the performance characteristics of this oil field.


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Figure 2


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Gas Cap Drive Reservoirs

Material Balance Applications

The material balance equation for a gas cap drive reservoir is obtained by assuming

that natural water influx is zero (We= 0), and that the effect of rock and water

compressibilities in oil zone as well as in gas cap compared to the gas compressibilityis negligible. With these assumptions, the MBE becomes

Np[Bt+ (Rp - Rsi) Bg] = N [(Bt- Bti) + (Bg- Bgi)] (45)This equation is rather cumbersome. A better understanding of the mechanism may be gained bywriting the equation in the form suggested by Havlena and Odeh (1963), which is

F = N (Eo+ Eg) (46)where

F = cumulative production in reservoir volumes

N = initial oil in place in surface volumes

Eo= Bt- Bti

Eg= Bg- Bgi

Equation 46 is used with production data to determine N and the effective size of the gas cap, m.

The way to use the equation is to plot F versus Eo+ (m Bti/Bgi)Egfor an assumed value of m (

Figure 1 ).


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Figure 1

If the selected value of m is too small, the plot will curve upward, and if it is too large it will curvedownward. A correct value of m will give a straight line that passes through the origin. Theimportance of the origin as a required point cannot be overemphasized. It is the only known fixedpoint that guides the plot. The slope of the straight line is N, the initial oil in place.


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When speaking of a water drive reservoir, we mean natural water drive as opposed

to artificial water injection. Water moves into the reservoir from the aquifer inresponse to a pressure drop that causes the water and the rock in the aquifer toexpand. Ifthe aquifer is small, one may assume that the pressure drop is

instantaneously trans mitted throughout the reservoir. Cumulative water influx willthen be given by

We= Vwct p (47)where :

We= total water influx in reservoir volumes

Vw= volume of water in the aquifer in reservoir volumes

ct= total compressibility = cw+ cr, 1/psi

cw= water compressibility, l/psi

cr= rock compressibility, l/psi

p = pi- p, psi

pi= initial pressure

p = pressure at time t that We is calculated.

The rock and water compressibilities are in the order of 5 l0-6per psia. For an aquifer of 109RB,

and assuming a pressure drop, p, of 1000 psi,We= 10910 l0-6 1001

107RB (1.59 106m3)

Thus, the total water influx amounts to about one-hundredth of the original oil volume if thereservoir is equal in size to the aquifer. Unless the aquifer is very large compared to the oilvolume, the effect of water influx on recovery is not significant.

When the aquifer is large, the assumption that the pressure drop is instantaneously

transmitted throughout the reservoir is not valid. There is a time lag between thepressure change at the oil-water boundary and when it is felt throughout the aquifer.

This means that Weis a function of time and p, and Equation 47

We= Vwctpis not adequate for calculating We. Chatas (1953) gives a good illustration of the calculationprocedure.

Gravity Segregation Effects


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Since the density of water is higher than that of oil or gas, the force of gravity tends

to segregate water at the bottom part of the reservoir. This segregation, especially in

the case oflayered dipping reservoirs, can be advantageous. It tends to keep thewater front uniform as it moves updip and minimizes water channeling in highpermeability layers. The locations of producing wells and the depths of their

completed intervals strongly affect the performance of water drive reservoirs.

Reservoir simulators are the best tools for studying the combined effects of theabove variables.


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Water Drive Reservoirs


Pressure, GOR, Water Cut

Whether water influx materially influences the behavior of the reservoir depends onits magnitude. For reservoirs predomi nantly producing under water drive (i.e., the

water influx ap proximately balances the total withdrawal), the reservoir pressure is

maintained (Figure 1).

Figure 1

The GOR stays approximately constant at the solution gas level because there willnot be any free gas flowing. Water cut, which is defined as percent water in the totalfluid produced, will increase in stepwise fashion. Until water breaks through into awell, the water cut will probably be negligible. However, as soon as water breaks

through, a jump in water cut occurs due to the sudden rise in water production. It

continues at about the same level until water breaks through in another well. Howquickly an individual well "waters out" after water breaks through depends on the

ratio of the viscosity of the oil to water, the relative permeability characteristics, and

the degree of reservoir heterogeneity. When the mobility ratio of water to oil is


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favorable, that is, when it is less than or equal to 1.0, the well will normally water

out shortly after water breakthrough, although the time to breakthrough will belonger. The mobility ratio is defined by

(48)where krwand kroare measured at the residual oil and water saturations, respectively.

For reservoirs that are not under strong water drive, the performance may be onlypartially influenced by water influx.

Selective Water Cut Control

When water breaks through into a well, it usually occurs in the most permeable

zone. If the reservoir is fairly homogeneous in permeability, water breaks through atthe bottom part of the completed interval because of gravity and the densitydifferences between oil and water. If production is continued without any remedial

measures, handling the produced water volumes may soon become a problem. In

some instances the presence of a water column in the wellbore can exert highenough backpressure to kill the well. In these cases, water Production is controlled

by squeeze cementing of the watered-out interval and recompletion in differentzones. In relatively homogeneous reservoirs, it is advisable to locate the completion

interval at the top of the formation to take advantage of gravity segregation andallow longer production of water-free oil. This method of completion is also used toprevent water coning when a bottom water drive exists.

A Case History of a Natural Water Drive Reservoir

This resume of the history of the Coldwater field in Isabella County, Michigan (Criss

and McCormick 1962, McCormick 1975), is a good example of a reservoir under an

effective natural water drive. This field was discovered in 1944 and its developmentcompleted in 1946, with 81 producing wells. Oil production was from a vugulardolomite, had a 48.6 API gravity, and had been regulated since the discovery ofthe

field, ranging from 4600 B/D (731 m3/D) to 6700 B/D (1065 m3/D). By the end of1952, oil declined slowly to 3600 B/D (572 m3/D) and water production increasedfrom 1800 B/D to 21,000 B/D (3340 m3/D). The cumulative oil and water production

was 12.763 million barrels (2.03 million m3) and 25.8 million barrels (4.1 million m3)

respectively. The bottomhole pressure from its original value of 1453 psi (10.0 MPa)dropped to 1378 psi (9.5 MPa) by the end of 1952, but it still was above the bubble-

point (1190 psi; 9.5 MPa). This pressure drop of 75 psi (0.52 MPa) over severalyears of production indicates a strong water drive. By the end of the same year 7.1

million barrels, or 56% of the field recovery, was recovered by flowing wells andthere were only 13 water-free flowing wells remaining. All other wells flowed until awater cut of 5% to 10% was reached.

By 1961, the Coldwater field had reached an advanced rate of depletion with all wells

producing with a water cut in excess of 80%. The field production continued underproration at 85 B/D (13.5 m3/D) per well until the end of 1961 when allowable


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restrictions were removed. By this time, a cumulative recovery of 20 million barrels

(3.2 million m3) of oil had been reached. Eventually, all wells were equipped to pump

and fluid volumes lifted reached 600 (95.4 m3/D) to 800 B/D (127 m3/D) per well. By1973, the oil production further declined to about 150 B/D (24.m3/D) from 20 activewells. Up to 1974 cumulative recovery reached 21.94 million barrels (3.5 million m3)

and water continued to encroach into all wells, even those located at the crest of the

structure. Fluid levels indicated that the reservoir was under active water drive. Byreturning the produced water into the aquifer, the reservoir pressure was kept at or

near the initial saturation pressure and GOR remained constant until the end of theproducing life of the field.


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Material Balance Applications

We refer to Havlena and Odeh (1963)1. The entire MBE equation is

Np[(Bt+ (Rp- Rsi) Bg] + BwWp= N [(Bt - Bti) + (Swcw+ cr) p

+ (Bg- Bgi)] + We

For saturated reservoirs, or when We is appreciable, or both, we can ignore compressibility of therock and its associated water. The MBE becomes

F = N Eo+ N Eg+ We (49)where:

F = total fluid withdrawals in reservoir volumes

Eo= oil expansion = Bt- Bti, and

Eg= gas cap gas expansion = Bg- Bgi

Equation 49 has three possible unknowns: N, m, and W e.

When the pressure is above the bubble-point, m = 0, and Equation 49 becomes

F = N Eo+ We

(50)Water influx is a function of time, pressure drop, and the physical properties of the aquifer, suchas permeability, size, compressibility, porosity, and viscosity. We write

We= C f(tD, p) (51)where:

C= constant

tD= dimensionless time that includes actual time and the physical properties

of the aquifer

(tD= 6.323 l0-3 [ ] where , , , ceand Aoare aquifer properties)

p = pressure drop at the oil water interface.

Equation 50 indicates that if We(which is the parameter with the greatest uncertainty) iscalculated correctly as a function of time, and a plot of F/Eoversus We/Eois made on rectangularcoordinate paper, a straight line should occur. The value of F/Eowhen We/Eo= 0 gives N, theinitial oil in place. The calculations (Havlena and Odeh 1963, 1964) proceed as follows:

1. From the available data estimate the properties of the aquifer and calculate tDas afunction of a time interval, for example, at three, six, or nine months.


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2. From production data calculate F/Eo, and p at the selected time intervals.

3. Calculate f (tD, p) of Equation 51 for the selected time intervals.

4. Plot F/Eo versus [f(tD, p)/Eo] on rectangular coordinate paper.

If the selected properties of the aquifer are correct (i.e., if Equation 51 is accurate) the plot will be

a straight line (Figure 1 ).

Figure 1

The slope of the straight line is C, the water influx constant in Equation 51. The extrapolation ofthe straight line to

gives the value of N. If the plotted points curve upward, the assumed water influx is too low; onthe other hand, if they curve downward, the assumed water influx is too high. New values for theaquifer parameters must be assumed, and the calculations repeated until a straight line occurs.An example of this procedure is beyond the scope of this introductory module, but may be foundin Havlena and Odeh (1963, 1964)

2.

1Havlena, D. and A.S. Odeh (1963): "The MBE as an Equation of a Straight Line."

Trans. AIME 228.


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2Havlena, D. and A.S. Odeh (1963): "Field Cases in the MBE as an Equation of aStraight Line. Part II" Trans. AIME 231.


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Gravity Drainage Mechanism

Conditions Needed for Segregation

Gravity drainage is one of the most efficient recovery mechanisms when conditions

are favorable. Under the influence of gravity, water, oil, and gas separate according

to their densities. Gravity drainage is a slow process. The rate of recovery from areservoir influ enced solely by this mechanism is time-dependent, similar to the caseof the water drive mechanism.

Gravity drainage is most effective in thick reservoirs with high vertical fluidcommunication and continuity. It is also effective in thin reservoirs with an

appreciable angle of dip (at least 10 to 15) and a favorable permeability to flow inthe vertical direction. Reservoirs with shale stringers or laminations are not goodcandidates for gravity drainage.

Conditions and parameters needed for effective gravity drainage are indicated byconsidering the following equation. The rate of segregation of gas in an oil reservoir

is

(52)where:

qs= rate of gravity segregation in RB/D

A = cross-sectional area of the linear bed in ft2

= oil-specific gravity minus gas-specific gravity

= angle of dip in degrees

= gas viscosity in cp

kg= gas, effective vertical permeability evaluated at So= 1 - Swc- Sgr, in md

o= oil viscosity in cp

ko= oil, effective vertical permeability evaluated at So= 1 - Swc- Sgr, in md

Equation 52 shows that the factors favorable to gravity segregation are

, the difference in specific gravity between the oil and the gas. The higher it is, thefaster the segregation.

high vertical koand kg


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low o

a high dip angle

a large cross-sectional area available to segregation.

Recovery Factor

As we stated, gravity drainage is the most efficient drive mechanism. When completesegregation (i.e, full gravity drainage) occurs, recovery may approach

If the initial oil saturation is 80% and Sor= 25%, recovery is 68% of the initial oil in place. In manyreef reservoirs where vertical communication is good and the oil viscosity is low it is notuncommon to obtain recovery by gravity segregation in the range of 60%. The main disadvantageof gravity drainage is that it is a slow process. Therefore, one hardly ever takes full advantage of

gravity drainage because the oil production rate is normally much higher than the segregationrate.


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Combination Drive Reservoirs

Typical Performance

When a reservoir is producing under the influence of more than one drivemechanism, as is often the case, we say that it is producing under a combination

drive. The relative contribution to recovery of the various drive mechanisms maychange with time. At any time one can obtain their relative effect from the materialbalance equation.

(53)

The terms on the right hand side are, respectively, the oil expansion, the gas cap gasexpansion, the expansion of the rock and its associated water, and the water influx.Dividing both sides by F, the total production gives

(54)

Each term on the right-hand side indicates the relative contribution of the drivemechanism to recovery (oil, gas, and water), and is called the drive index. Equation54 does not include a gravity segregation effect.

Equation 54 is used when water production occurs and no active aquifer is present.

However, when an active aquifer is present, it is customary to show the contributionof each drive mechanism to the recovery of total hydrocarbon rather than totalfluids. Thus, Equation 53 is written as

where: FHis the total hydrocarbon recovered in reservoir bbl and is equal to Np(Bt+(Rp- Rsi)Bg) = F - WpBw

Dividing both sides by FHgives:

The terms of the right-hand side of Equation 54a are, respectively, the contribution

to the total hydrocarbon recovery of the expansion of the hydrocarbon in the oilzone, of the gas cap gas, of the rock and its associated water in the oil zone, and of

the net water influx. The MBE cannot be used to deter mine how much of theproduced gas originates from the gas cap gas and thus is cycled through. Where gas

cap gas is known to be produced, Equation 54a gives too high a drive index for thegas cap gas.


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If one drive index dominates the performance, the reservoir behavior will be close to

that of the particular drive mechanism. On the other hand, if several drive

mechanisms are effective, the overall reservoir performance will be highly influencedby the location of wells and the rate of withdrawal

from the individual wells. For example, if the reservoir is producing under a

combination of gas cap expansion and water influx, one expects the reservoirperformance to be significantly different when the wells are located downdip than

when they are located updip or strategically placed between the gas-oil contact andthe oil-water contact.

Precise prediction of reservoir performance under combination drive requires the useof reservoir simulators. This is by far the best method to study the effects of variousdrive mechanisms and the interplay between them, the effects of well locations and

completion intervals, and the effects of the rate of production.

Material Balance Equation Application

Equation 54 gives the MBE under oil expansion, gas cap gas expansion, and waterinflux. The equation shows that under these drive mechanisms three unknowns, N,

m, We, exist. The solutions of the MBE equation using production data do not permitthe simultaneous determination of three unknowns. Because of this, one of the three

must be obtained or estimated prior to the application of the MBE. It is customary to

estimate m volumetrically from isopach maps and to then solve for Weand N. Forthis purpose the MBE is written as

(55)

A Case History of a Combination Drive Mechanism

The Leduc D-3 pool, one of Canadas major oil fields, was discovered in 1947. Our

resume of its performance is based on Hors-field (1962) and Wellings (1975). Thereservoir is composed of carbonate rock extended to an area of 21,640 acres (87.57

million m2). The average oil pay zone was 35.2 ft (10.73 m) and underlain by a largewater-bearing reef 900 ft (274 m) thick and overlain by a large gas cap with a

thickness of 158 ft (48.16 m). The original gas cap was calculated to occupy a

volume of 431,800,000 Mscf (12,228.5 million m3). The initial oil in place wascalculated to be 307,408,000 STB (56.4 million m3). The development wascompleted by the end of 1954, with 535 oil wells drilled. The reservoir was saturated

at the original pressure of 1,894 psig (13.1 MPa) at reservoir temperature of 150F(65.5C). The original gas-oil ratio was 550 scf/bbl (97.9 m3/m3). The gravity of oilproduced was 39 API.

The production rate remained relatively constant during the three years following the

blowout in Well No. 3 (which occurred in March 1948 and was killed in September1948). The reservoir pressure declined accordingly at a uniform rate of about 1 psi

(6.895 kPa) per month. Increasing the rates of production in 1952 and 1953accelerated the rate of pressure decline. Therefore, the allowable pressure was


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reduced to prevent excessive shrinkage losses in the reservoir. (The differential

liberation curves indicated that the reservoir oil would shrink to 71.6% of its originalvolume if the reservoir pressure was allowed to decline to atmospheric.)

A volumetric balance calculation confirmed the existence of a combination drive

mechanism. The contribution of each component drive to the replacement of oil

withdrawals is shown in Figure 1.

Figure 1

To 1954, the water drive had contributed 50%, the gas cap had contributed 40%,and solution gas drive had contributed 10% to the replacement of reservoir oil.

New discoveries (other adjacent fields) during 1952-53, which were proven to have a

common aquifer with D-3 pool, had caused an interference. During this period,

pressure decline in Leduc D-3 amounted to 100 psi (68.95 kPa). In order to preventthis undesirable pressure decline and to avoid shrinkage losses in the Leduc D-3reservoir, water-injection operations started in 1955. A volume of 18.5 million

barrels (2.94 million m3) of fresh water was injected up to 1957, which arrested the

pressure decline and increasing GOR. It was estimated that up to 1957 waterinjection could prevent the loss of one million barrels of oil which would have


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occurred by shrinkage of the reservoir oil under natural depletion. As a result of the

water injection, the descent of the gas-oil contact was de creased and the ascent of

water-oil contact was increased. By the end of 1957, with a cumulative oil productionof 90 million barrels (14.3 million m3), the effective thickness of pay zone wasreduced to approximately 23 ft (7.015 m) which is an indication of the excellent

production that was characteristic of the Leduc D-3 pool. This was due to the very

high permeability of the reservoir and the large ratio of the horizontal to verticalpermeability. Pool performance is shown in Figure 2and Figure 3.

Figure 2


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Figure 3

Detailed studies were made on natural depletion, continued water injection, and

pressure maintenance by both water and gas injection. It was concluded that for

maximum recovery, the water and gas injection operation together should beconsidered. For implementation of this new injection scheme, a unitization of 456

wells in the main pool was accomplished in 1960 and was followed by gas injection in1961. By 1974, a production recovery of 70% or more of the initial oil in place was

accomplished. The gas-oil contact showed again the steady rise of water-oil contactand lowering of gas-oil contact. The bottomhole pressure never dropped below 1350

psi (9.3 MPa). The aim was to keep the gas-oil contact at 2992 ft (912 m) sub-sea,allowing the water-oil contact to move upward to replace oil voidage. By the end of

1974, when only 8 ft (2.44 m) of pay zone was left (Figure 4), the average GORwas 2000 scf/ STB (356 m3/m3) and water-oil ratio was 0.5.


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Figure 4

The absence of oil and water coning throughout most of the pools history confirmsthat a high ratio of horizontal to vertical permeability existed throughout the oil zone.

This characteristic allows the pool to be maintained for a very thin oil zone and is

perhaps the most significant factor contributing to the outstanding performance of

this pool under combination drive. The reservoir performance of Leduc D-3 till 1975is shown in Figure 5.


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Figure 5

Documents

2 Reservoir Fluid Flow & Natural Drive Mechanisms