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# Gas in place and recoverable volumes

This page discusses various aspects of gas reservoir performance, primarily to determine initial gas in place and how much is recoverable. The equations developed can used to form the basis of forecasting future production rates by capturing the relationship between cumulative fluid production and average reservoir pressure.

## Gas in place

### Volumetric determination

Original gas in place (OGIP) can be estimated volumetrically with geological and petrophysical data:

....................(1)

In oilfield units with gas measured in Bscf and Bgi in ft3/Mscf,

....................(2)

In SI units with gas measured in std m3 and A in m2,

....................(3)

### Material-balance determination of OGIP

Material-balance equations provide a relationship between original fluids in place, cumulative fluid production, and average reservoir pressure. For many gas reservoirs, a simple material-balance equation can be derived on the basis of the following assumptions:

• Gas-filled pore volume is constant
• Gas dissolved in water or liberated from the rock is negligible
• Reservoir temperature is uniform and constant

With these assumptions, the real-gas law can be used to derive

....................(4)

This equation can be rearranged to get the usual volumetric gas material-balance equation,

....................(5)

This equation is the basis for the p/z-vs.-Gp graph used to analyze gas reservoirs.

## Determining average reservoir pressure

Reservoir engineers have often used pressure contour maps or some approximate methods to determine field average reservoir pressure for p/z analysis. Usually, however, individual well pressures are based on extrapolation of pressure buildup tests or from long shut-in periods. In either case, the average pressure measured does not represent a point value, but rather is the average value within the well’s effective drainage volume (see Estimating drainage shapes).

By combining the assumptions used to assign drainage shapes and considerations of the gas law, the following procedure could be used for developing an average reservoir pressure at any point in time.

1. Be certain to determine average reservoir pressure accurately. Sometimes, shut-in times are inadequate to achieve complete buildup. When this occurs, one way to approximate reservoir pressure from a long shut-in is to use the Matthew-Brons-Hazebroek method[1] estimating the semilog straight-line slope from reservoir properties rather than a buildup test. Of course, buildup tests are the preferable way to determine average reservoir pressure when economically feasible. An alternative way to ramp up an incomplete buildup is to run a buildup test early in the life of a well, noting the time to complete buildup and the percentage buildup at shorter times. Then, these percentages can be used in subsequent shut-in tests of shorter times than those required for full buildup.
2. For each well, make a graph of p/z vs. Gp. In general, these graphs will not necessarily yield a straight line. If the well’s drainage volume is changing with time, these will be curves. Either way, pass a smooth curve (not necessarily straight) through the data points.
3. To estimate the average p/z for a given well’s drainage volume at a given point in time, first determine the cumulative gas produced for that well at the desired time, then use the value of Gp to get a value of well p/z from the graphs created in Step 2.
4. Estimate the average production rate for each well at the desired time. This should be some reasonable average "eye-balled" from production curves, and not necessarily a specific daily rate.
5. Determine the reservoir average p/z as the average of the individual-well values (Step 2), weighted by their production rate:

....................(6)

where nw is the number of active producing wells. This procedure works reasonably well and is straightforward.

Accurate determination of average reservoir pressure is particularly difficult in tight gas sands. Shut-in pressures may not be near average reservoir pressure for several months or years, obviously too long to be of any value. In addition, low-permeability reservoirs can have significant pressure differences across the field because certain areas can be drained more effectively than others.

Poston and Berg[2] discuss methods for adjusting p/z plots for the lack of sufficient buildup time in determining average reservoir pressures. Although these methods have some validity, they also are prone to large errors because of data uncertainties. A recommended practice is, where feasible, to perform advanced pressure-transient-analysis methods on pressure-buildup tests to provide the means to extrapolate to expected values of average reservoir pressure. Such methods rely on the extrapolation of buildup pressures followed by a correction that incorporates drainage shape and volume. The problem with these techniques is that the correction for drainage shape and volume can be very significant (because of low reservoir permeabilities), and these techniques are highly uncertain, given the extent of heterogeneities and compartmentalization in typical tight gas reservoirs. Calibration of pressure-buildup analyses against actual well responses and reservoir simulation history-match studies can be helpful.

Another problem in tight reservoirs is the variation in average reservoir pressure across the field, both because of reservoir compartmentalization and because of low permeabilities. In higher-permeability gas reservoirs, this problem is generally not so severe, meaning that the average reservoir pressure needs to be measured only in a few wells to generate accurate p/z analyses. When variations in average reservoir pressure are large, however, methods need to be used to account for differences across the field.

Although reservoir simulation is one possibility to deal with this problem, it is also possible to use a "compartmentalized-reservoir model"[3] to incorporate these effects. This model treats the reservoir as a set of communicating "tanks." The technique is basically a history-matching process that uses compartment volumes and compartment-to-compartment transmissibilities as tuning parameters. This method is important and has technical value, although it does not address the problem of required long shut-in times. The method has been applied to several reservoirs with very good results; hence, its use is recommended.

## Volumetric reservoirs

In volumetric dry- and wet-gas reservoirs, p/z vs. cumulative gas production will be a straight line intercepting the gas-production axis at the OGIP. An example is given in Fig. 1. The intercept (Gp = 0) on the p/z axis is pi/zi, and the intercept on the Gp axis (p/z = 0) is G. This graph provides a convenient method of using average-reservoir-pressure data to estimate OGIP and recoverable reserves once an abandonment p/z is established. When these plots are applicable, results for OGIP are generally considered very accurate after approximately 10% of gas reserves have been produced (sometimes a bit earlier).

When only a small amount of early data is available, the OGIP can be determined from any point (Gp, p/z) by

....................(7)

When placing the straight line through p/z data, it is usually prudent to consider the first point (i.e., at field discovery pressure) as more accurate than others. Because there has been little field depletion and there has been sufficient time for pressures to return to stabilized conditions, discovery-pressure measurements are generally reliable. Regression approaches to placing the p/z-s.-Gp line should take this into consideration.

Volumetric estimates based on cores, well logs, fluid analyses, and geological estimates of reservoir size provide a "rock-based" estimate of gas in place, while material-balance relationships provide a "fluids-based" or "pressure-based" estimate. These two types of estimates are essentially independent (except for the use of consistent values of Bgi). Thus, when the two estimates are combrble, there is greater certainty in the OGIP estimate. It is now a common practice to develop geologic and simulation models of a reservoir to determine reserves and depletion strategies and to evaluate alternative development scenarios. Acquisition of p/z data can provide another measure of the volume being drained by a well or set of wells in what is thought to be a common reservoir. Differences between models and p/z data can be a valuable tool in managing a reservoir and detecting opportunities for additional development or deferral of expenditures that become unnecessary because of a change in the size of a resource.

Well-deliverability forecasts can be used to predict the economic limit of production for a field (income= costs) and the resulting pa/za. Recoverable reserves then become

....................(8)

## Highly compressive reservoirs

For some high-pressure gas reservoirs (e.g., geopressured or abnormally pressured reservoirs), the combined rock and water compressibility can result in a nonlinear p/z plot (Fig. 2). Ignoring this effect can lead to large overestimates of the OGIP. Local knowledge is the best source of information about whether these effects should be considered. Such performances usually should be suspected for geopressured reservoirs.

If the pore volume and water can be considered to have constant compressibility, then the change of gas-filled pore volume with pressure is

....................(9)

Using the first two terms in a Taylor series expansion for the exponential function,

....................(10)

where ....................(11)

The material-balance equation for a compressive reservoir then becomes

....................(12)

Eq. 12 suggests that if the effective reservoir compressibility, ce, can be estimated, then the p/z plot for such reservoirs can be linearized by multiplying the p/z values by 1 - ceΔp. However, there is typically very little knowledge of the effective system compressibility, meaning that this relationship is of limited practical use for reservoir engineering purposes. In addition, the effective system compressibility may even change with time, typically becoming smaller as reservoir pressure declines and the reservoir rocks compact.

There is sometimes a change in the slope of the p/z plot when an abnormally pressured gas reservoir reaches normal pressure, as shown in Fig. 2. Approaches suggested for analyzing geopressured gas reservoirs include methods to account for some unusually high apparent values of the effective pore-volume compressibility. Soft-sediment compaction, shale dewatering, and limited aquifer influx are among the physical effects proposed by various authors. For further information on this topic, the reader is referred to papers by Hammerlindl,[4] Roach,[5] Prasad and Rogers,[6] Bernard,[7] Fetkovich et al.,[8] Ambastha,[9] Yale et al.,[10] El Sharkawy,[11] and Gan and Blasingame.[12] Poston and Berg[2] also provide an evaluation of different methods of accounting for pressure support experienced in geopressured reservoirs.

Many overpressured reservoirs, however, do not demonstrate the change in slope, as illustrated by Fig. 3. These data are from four wells in a common reservoir with an initial pressure gradient > 0.65 psi/ft. As indicated, there was no change in slope when the reservoir pressure reached a normal gradient. The reservoir consists of a competent sandstone that may have a low effective compressibility.

Considering the previous discussions, using early p/z has many uncertainties. Best practices would suggest that early-time analyses use ranges for effective pore-volume compressibility based (where possible) on analogous or similar regionally located reservoirs to reduce the high uncertainty in early data and its potential dramatic effect on estimates of OGIP.

Abandonment conditions for highly compressive reservoirs are determined in the same manner as those for volumetric reservoirs.

## Waterdrive reservoirs

Fig. 4 shows a typical p/z plot for a gas reservoir with an active waterdrive. Note that for a given value of cumulative gas production, pressures are higher than for a volumetric reservoir.

The material-balance equation for a waterdrive reservoir is

....................(13)

If it can be assumed that volumetric estimates of G are accurate, then Eq. 13 can be rearranged to calculate a water-influx history for comparison against contact mapping.

....................(14)

This can be used with different aquifer models to determine how to predict future water influx. This will be discussed further in the next section.

Using Eq. 13 to estimate G requires information about the cumulative water influx. Estimates may be obtained by mapping water movement using watered-out wells, logging surveys, or data from infill wells.

By writing Eq. 13 in terms of a volumetric sweep efficiency, Ev, and the residual gas saturation to water displacement, Sgr, the material-balance calculation can then be written as

....................(15)

If Ev is taken to be the estimated volumetric sweep efficiency at abandonment, then this equation represents all possible abandonment conditions regardless of the rate of water influx. An abandonment line can then be drawn on the p/z plot, the bottom point of which is at p/z = 0, Gp = G, and the top point of which is at p/z = pi/zi. A straight line connecting these two points is the locus of all possible abandonment points. The intersection of this abandonment line and the actual p/z-vs.-Gp line, as illustrated in Fig. 5, gives an estimate of ultimate recovery.

Many factors affect gas-recovery potential when a waterdrive is active. The main considerations are how much of the reservoir will be invaded by water, what the pressure decline will be, and what the trapped-gas saturation will be behind the waterfront. Simple 3D simulations can be used to study the strength of an aquifer based on its size relevant to the gas volume and the variation in rock quality. A good reservoir description is the key to a successful prediction. How the reservoir is affected is also a function of withdrawal rates. Strong aquifers can sustain reservoir pressure and result in low recoveries. Gas saturations trapped behind the invading water are typically about one-third of the initial hydrocarbon saturation. If volumetric sweep is high and there is little pressure depletion (BgaBgi), then a reservoir with Swi equal to 25% of pore volume would experience a recovery of

....................(16)

Recoveries as low as 50% of OGIP can occur in adverse circumstances, but more often recoveries exceed 70% of OGIP owing to partial pressure depletion. There are documented cases[13][14] in which a significant increase in offtake rate has resulted in pressure depletion of a waterdrive reservoir when withdrawal rates were sufficient to outrun invading water. Recovery from reservoirs that exceed 1 Tcf OGIP with permeabilities greater than 250 md will normally be unaffected by an aquifer of any size if field depletion occurs over a 20-year period or less. Again, a simple simulation model will confirm how potentially effective an aquifer may be.

The effect of a weak to moderate waterdrive is often difficult to detect with a simple p/z plot. Often, a straight-line plot will occur (Fig. 4) and will lead to incorrect estimates. Cole[15] has suggested an improved method. If the expansibility of water is small compared to gas expansibility, then the material balance can be arranged as

....................(17)

Cole’s methodology is to plot the left side of the equation against Gp. The shape of the resulting plot will vary depending on the existence and strength of a waterdrive, as illustrated by Fig. 6.

Data from a volumetric reservoir will plot as a horizontal line. A weak waterdrive yields an early increase in ordinate values followed by a negative slope. The initial increase may not be detected because many pressure measurements are needed very early in the producing life of the reservoir. Moderate to strong waterdrives give overstated OGIP values. This plot is very sensitive to the effects of water influx and is a good qualitative tool. Back extrapolating the plot to OGIP has been suggested. In practice, the slope usually changes with each pressure measurement, and extrapolation is difficult to impossible.

Pletcher[16] has suggested a further modification to the Cole plot to account for rock and water compressibility. In doing so, Eq. 17 becomes

....................(18)

where F = G(Eg + Efw) + We,

....................(19)

The shapes of the resulting plots are the same as those in Fig. 6, but they do avoid the negative slope of a Cole plot that results from an abnormally pressured reservoir with no water influx.

Depletion behavior of retrograde-condensate reservoirs can be handled through the p/z analyses discussed previously, with the caveat that the z factor must be the two-phase z factor (see Natural gas properties). Two-phase z factors either may be obtained from laboratory tests or predicted from composition with an EOS. In wet-gas and retrograde-condensate reservoirs, cumulative gas produced must include both gas and liquid (as equivalent gas) production. This is particularly important for high-liquid-yield gases.

In the calculation of future reserves for planning purposes, it is usually necessary to break out gas and liquid reserves separately, perhaps even by individual gas component. For wet-gas reservoirs, liquid yields from a particular gas can be expected to remain constant with time, so long as the gas is processed in the same manner. Changes in separator conditions and/or gas-processing facilities could result in changing liquid yields, however.

Retrograde-condensate reservoirs, on the other hand, will produce at a variable yield as the reservoir pressure declines. Determination of the expected yields can be based on laboratory tests and/or EOS calculations. The PVT test presented in Natural gas properties shows how yields of the various gas components can vary over time.

## Pressure maintenance and cycling operations

Pressure maintenance of a retrograde-condensate gas reservoir can exist by virtue of an active waterdrive, water-injection operations, gas-injection operations, or combinations of all of these. Certain reservoirs may contain fluids near their critical points and are thereby candidates for special recovery methods, such as the injection of specially tailored gas compositions to provide miscibility and phase-change processes that could improve recovery efficiency. These usually are not regarded as gas/condensate cases. All these improved-recovery methods are best studied with simple-to-complex computer models. Simple models can be used initially to screen prospects, and then more-detailed studies including compositional considerations can be conducted.

### Waterdrive and water-injection pressure maintenance

Recovery from retrograde-condensate gas reservoirs with a waterdrive or water injection is subject to the same considerations as for water injection into oil reservoirs. To make a recovery assessment, the first requirement is a good description of the rock and fluid characteristics of the reservoir and the aquifer. Variations in the permeability of various strata, mobility ratios, and gravity-stable advance of the water front will affect the volumetric sweep. Sgr should be approximately the same as described earlier for dry- and wet-gas displacements by water. The favorable mobility ratio can result in a high volumetric sweep. There is strong evidence, however, that displacement efficiency by water is not high. While Buckley et al.[17] indicated that the displacement efficiency of water displacement of gas can be as high as 80 to 85%, experiments and field observations by Geffen et al.[18] indicate that it may be as low as 50%. All things considered, the recovery of gas condensate in the vapor phase by water injection is likely to be appreciably lower than by cycling, and any consideration of water injection for gas/condensate recovery should be accompanied by detailed experimental work on cores from the specific reservoir involved. This will help to determine whether water can, in fact, accomplish a high-enough displacement efficiency to justify its use.

Premature water breakthrough can, and often does, result in "load up" and loss of the ability of a well to flow. It is difficult to obtain economical flow rates by artificial lift. This loss of productivity may result in premature abandonment of the project. The problems would be particularly serious for deeper reservoirs in which the cost of removing water would be a significant factor. Yuster[19] discusses possible remedial methods for drowned gas wells. Bennett and Auvenshine[20] discuss dewatering gas wells. Dunning and Eakin[21] describe an inexpensive method to remove water from drowned gas wells with foaming agents.

Generally, the use of water injection for maintaining pressure in a gas/condensate reservoir will be unattractive where a wide range of permeabilities exists in a layered reservoir and selective breakthrough of large volumes occurs early in the life of the reservoir.

### Dry-gas injection

Comparative economics determine whether a gas/condensate reservoir should be produced by pressure depletion or by pressure maintenance (i.e., does the additional condensate recovery justify the cost of compressing, injecting, and processing the injected gas?). Delayed gas sales also may be a factor. The objective of using dry-gas injection is to maintain the reservoir pressure usually above or near the dewpoint to minimize the amount of retrograde condensation. Dry field gases are miscible with nearly all reservoir gas/condensate systems; methane normally is the primary constituent of dry field gas. Dry-gas cycling of gas/condensate reservoirs is a special case of miscible-phase displacement of hydrocarbon fluids for improving recovery. Experimentation has shown that the displacement of one miscible fluid by another that is miscible is highly efficient on a microscopic scale; usually, the efficiency is considered 100% or very nearly so. Cycling does result in liquid recoveries at economical rates while avoiding waste of the produced gas when a market for that gas is not available.

#### Inert-gas injection

The use of inert gas to replace voidage during cycling of gas/condensate reservoirs can be an economical alternative to dry natural gas. One of the first successful inert-gas-injection projects was in 1949 at Elk Basin, Wyoming,[22] where stack gas from steam boilers was used for injection. In 1959, the first successful use of internal-combustion-engine exhaust was seen in a Louisiana oil field.[23] The first use of pure cryogenically produced N2 to prevent the retrograde loss of liquids was in the Wilcox 5 sand in the Fordoche field located in Pointe Coupee Parish, Louisiana.[24] In the Fordoche field, the N2 amounted to approximately 30% of the natural-gas/N2 mixture injected.

Studies by Moses and Wilson[25] confirmed that the mixing of N2 with a gas/condensate fluid elevated the dewpoint pressure. Moses and Wilson also presented data to show that the mixing of a lean gas with a rich-gas condensate would result in a fluid with a higher dewpoint pressure. The increase in dewpoint pressure was greater with N2 than with the lean gas. In the same study, results are presented from slimtube displacement tests of the same gas/condensate fluid both by pure nitrogen and by a lean gas. In both displacements, more than 98% recovery of reservoir liquid was achieved. These results also were observed by Peterson[26] using gas-cap gas material from the Painter field located in southwest Wyoming. The authors concluded that the observed results were obtained because of multiple-contact miscibility.

Cryogenic-produced N2 possesses many desirable physical properties.[27] Those that make nitrogen most useful for a cycling fluid are that it is totally inert (noncorrosive) and that it has a higher compressibility factor than lean gas (requires less volume). The latter advantage is partially offset by increased compression requirements when compared with lean gas.

The use of inert gas as a cycling fluid offers both advantages and disadvantages. The major advantages are early sale of residue gas and liquids and a higher recovery of total hydrocarbons because the reservoir contains large volumes of inert gas rather than hydrocarbons at abandonment. Disadvantages are production problems and increased operating costs caused by corrosion if combustion or flue gas is used, possible additional capital investments and operating costs to remove inert gas from the sales gas (a condition aggravated by early breakthrough of inerts), and potential costs to pretreat before compression and/or to fund reinjection facilities.

## Nomenclature

 a = empirical constant A = drainage area, reservoir area, L2 AOF = absolute open flow potential, std L3/t b = empirical constant B = formation volume factor, L3/std L3 Bgi = initial gas formation volume factor, L3/std L3 c = compressibility, Lt2/m cf = pore-volume compressibility, Lt2/m cw = water compressibility, Lt2/m C = constant in gas-deliverability equation CA = Dietz shape factor, dimensionless D = non-Darcy-flow coefficient, t/std L3 Efw = cumulative formation and water expansion, L3 Eg = cumulative gas expansion, L3 ER = recovery efficiency, fraction Et = total cumulative expansion, L3 Ev = volumetric sweep efficiency, fraction F = cumulative reservoir voidage, L3 G = original gas in place, std L3 GE = gas equivalent, std L3/std L3 Gpc = cumulative gas production during a period of constant rate, std L3 h = average reservoir thickness, L kg = measured gas permeability, L2 kl = effective liquid permeability, L2 K = parameter in Lee et al.2 viscosity correlation n = number of moles of gas or exponent in gas-deliverability equation nc = total number of components in gas mixture nw = number of wells Np = cumulative condensate production, std L3 p = pressure, m/Lt2 = average pressure, m/Lt2 = variable of integration in real-gas potential equation, m/Lt2 PI = productivity index, std L3/t/m/Lt2 q = production rate, std L3/t R = universal gas constant, mL2/nt2T S = mechanical skin, dimensionless Sgi = initial average gas saturation, fraction Swi = initial water saturation, fraction t = time, t tc = time of constant-rate production, t T = temperature, T u = volumetric flux ( q/A ), L3/t/L2 V = volume, L3 Vm = molar volume, L3/n We = cumulative water influx, L3 Wp = cumulative water produced, std L3 xj = mole fraction of component j in liquid phase X = parameter in Lee et al.2 viscosity correlation yj = mole fraction of component j in gaseous phase Y = produced condensate yield, std L3/std L3 z = gas deviation factor, dimensionless zj = mole fraction of component j in mixture ρ = density, m/L3 ϕ = porosity, fraction

## References

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4. Hammerlindl, D.J. 1971. Predicting Gas Reserves in Abnormally Pressured Reservoirs. Presented at the Fall Meeting of the Society of Petroleum Engineers of AIME, New Orleans, Louisiana, 3-6 October 1971. SPE-3479-MS. http://dx.doi.org/10.2118/3479-MS.
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