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Gas cap drive reservoirs

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In some instances, oil reservoirs are discovered with a segregated gas zone overlying an oil column. The overlying gas zone is referred to as a primary gas cap. In addition to free gas, gas caps usually contain connate water and residual oil. The underlying oil column is sometimes referred to as an oil leg. In other instances, as reservoir pressure declines with production, gas evolves in the reservoir (see Solution gas drive reservoirs) and migrates to the top of the structure to add to an existing primary gas cap or to form a gas cap. If properly harnessed, gas caps can enhance oil recovery considerably. The degree with which they improve recovery depends mainly on their size and on the vertical permeability and/or formation dip. Producing wells usually are completed only in the oil leg to minimize gas production.

Properties

Broadly, gas caps are classified as segregating or nonsegregating. Table 1 summarizes the distinguishing characteristics of each.

Segregating gas caps are gas caps that grow and form an enlarged gas cap zone. Fig. 1 shows a schematic of a segregation drive reservoir. Two different segregation mechanisms are possible:

  1. Expansion of and frontal displacement by pre-existing gas cap gas
  2. Upward migration of oil-column gas as solution gas is liberated and a free-gas phase forms

The second mechanism involves the simultaneous downward movement of oil to balance the upward flow of gas. This diametric flow pattern is referred to as counterflow. [1] Pirson[2] refers to the first mechanism as passive segregation and the latter mechanism as active segregation. Hall[1] refers to the first mechanism as segregation drive without counterflow and the second mechanism as segregation drive with counterflow. Both mechanisms are time-dependent, and their displacement efficiency depends on the gas/oil density difference, the producing rate, and the vertical permeability.

Both segregation mechanisms yield a progressively descending gas-oil contact (GOC). The segregation-drive mechanisms can be augmented by crestal gas injection.

If neither of these segregation mechanisms is present, the gas cap is called a nonsegregating gas cap. Nonsegregating gas caps do not form an enlarged gas-cap zone, and their GOC appears stationary. The gas-cap gas expands but the displacement efficiency is so poor that the expanding gas appears to merely diffuse into the oil column. Fig.2 illustrates the distribution of water, oil, and gas in a nonsegregation-drive gas-cap reservoir.

Broadly, gas caps act to mitigate the pressure decline, extend the life of the reservoir, and ultimately improve the oil recovery. The degree of oil-recovery improvement depends on the following:

  • Size of the gas cap
  • Whether it is a segregation drive or nonsegregation drive gas cap

To understand the mechanics of gas cap reservoirs, numerical simulation results of segregating and nonsegregating gas caps are presented. Each example uses the fluid-property data in Table 2. Each example also uses the reservoir data summarized in Table 3, except that the initial pressure is 1,640 psia instead of 2,000 psia and the gas-cap thickness is 10 ft. The gas, oil, and water saturations in the gas cap are 60, 20, and 20%, respectively. The gas cap initially contains 270,000 STB of oil and 816 MMscf of gas; the oil leg initially contains 210 million STB of oil and 1.718 Bscf of gas. The total original oil in place (OOIP) = 2.37 million stock tank barrels (STB), and original gas in plae (OGIP) = 2.534 Bscf, and m = 0.33. For reference, the segregating- and nonsegregating gas cap cases are compared with an identical reservoir without a gas cap (base case).

Performance

Non-segregation drive gas caps

Fig. 3 plots pressure as a function of cumulative oil recovery for a nonsegregation drive gas cap reservoir. For comparison, this figure includes the results of the no gas cap (base) case. This figure also includes the results of other cases, which are discussed later in this page. All recoveries are reported as a fraction of the original oil-leg OOIP to make direct comparisons valid. The nonsegregation drive gas cap case consistently yields higher oil recoveries at a given pressure than the no gas cap case, which illustrates the superior recovery performance of gas caps. Viewed another way, the nonsegregation drive gas cap case consistently yields a higher pressure at a given oil recovery than the no gas cap case, which illustrates the superior pressure maintenance ability of gas caps.

Fig. 4 is a composite figure and shows the performance as a function of time. This figure includes the:

  • Gas/oil ratio (GOR)
  • Gas saturation
  • Oil rate
  • Oil-recovery histories

The GOR history shows that nonsegregating gas caps eventually yield higher producing GORs than the no gas cap reservoir. The higher GOR is caused by higher gas saturation in the oil leg. The higher gas saturation is caused by the gas cap gas migrating from the gas cap into the oil leg as the pressure declines.

Fig. 4 also shows the effect of a nonsegregating gas cap on the oil-rate history. The nonsegregating gas cap consistently yields higher oil rates than without the gas cap. If an economic limit corresponding to a minimum oil rate of 20 STB/D is arbitrarily assumed, then the no-gas-cap case is terminated after 13.8 years while the nonsegregation-drive gas-cap case is terminated after 15.2 years. This comparison shows that the presence of a gas cap extends the primary-recovery life of the reservoir. The curve endpoints denote the time of termination. The no-gas-cap case is slightly different from the black oil case discussed earlier due to the assumed lower original pressure.

Fig. 4 includes the fractional oil recovery history; Fig. 5 shows the gas recovery history. The curve endpoints denote the time of the economic limit. Table 4 summarizes the conditions at the economic limit. The no gas cap and nonsegregation drive gas cap cases recover 23.7% and 26.8% of the oil leg OOIP, respectively. Thus, the nonsegregating gas cap recovers more oil than without the gas cap. The nonsegregating gas cap also is terminated at a higher pressure, producing GOR, gas saturation, and gas rate than without the gas cap. The nonsegregating gas cap recovers 74.9% of the oil-leg OGIP while the no gas cap case recovers 52.3% of the oil-leg OGIP. The nonsegregating gas cap recovers more gas because some of the gas-cap gas infiltrates the oil leg and is produced. In conclusion, the presence of a nonsegregating gas cap:

  • Yields higher ultimate oil and gas recoveries
  • Accelerates recovery
  • Extends the primary recovery life of a reservoir

The effect of a gas cap on oil recovery is related directly to its size relative to the size of the oil leg. The size of the gas cap is described effectively in terms of the dimensionless variable m, which is defined as the ratio of the initial free-gas and free-oil phase volumes (see Eq. 5). If all the free gas is located in the gas cap, all the free oil is located in the oil leg, and the oil leg and gas-cap porosities and connate water saturations are the same, then m represents the ratio of the gas cap and oil leg pore volume (PV). Fig. 6 shows the effect of m on the final fractional oil recovery for an nonexpanding gas cap reservoir. The results in Fig. 6 use the same reservoir data as in the previous simulations except different gas-cap sizes are considered. Other reservoir conditions may yield slightly different results. The most noticeable improvement in oil recovery comes as m increases from 0 to 2.0.

The gas cap size also affects the peak GOR. As the gas cap increases, the peak GOR increases. Fig. 6 shows the peak GOR as a function of m for the west Texas reservoir properties. The peak GOR increases with the gas cap size because more gas cap gas migrates into the oil column as the gas cap increases. In summary, nonsegregation drive gas cap reservoirs tend to yield final fractional oil recoveries in the range of 15 to 40% of the OOIP. Segregation drive gas cap reservoirs tend to yield even higher final oil recoveries.

Segregation drive gas caps

Segregating gas caps are characterized by progressively descending gas/oil contacts (GOCs). The movement of the GOC is caused by active or passive gravity segregation. Active gravity segregation is the simultaneous migration of gas upward and drainage of oil downward. Passive segregation is the natural expansion of the gas-cap gas. Both of these processes involve frontal displacement of oil at the GOC. Frontal displacement helps drive oil to the producing wells. Frontal displacement does not dominate in nonsegregation drive gas cap reservoirs. The extent to which gravity segregation occurs depends on the vertical permeability and the rate at which fluids are withdrawn from the reservoir. The greater the vertical permeability and slower the fluid withdrawal, the more pronounced the effects of gravity segregation.

Figs. 3 through 5 include simulation results of a segregation drive gas cap reservoir. These simulations assume properties identical to those of the nonsegregation drive gas cap simulations except gravity segregation is included. The simulations assume no free gas production from the gas cap.

Fig. 3 shows the pressure as a function of cumulative oil recovery. This figure shows that oil recovery in a segregation-drive gas-cap reservoir at a given pressure is consistently greater than that in a nonsegregation-drive gas-cap or nongas-cap reservoir, especially at low pressures when the effects of gas expansion become pronounced. The oil recovery performance is discussed below.

Fig. 4 shows the effect of a segregating gas cap on the GOR history. Only a marginal increase in the GOR is noted; after 15 years, the GOR actually decreases slightly. This type of GOR behavior is characteristic of segregation drive gas cap reservoirs. [3][4][5] The segregating gas cap effectively drives and concentrates oil into the shrinking oil leg. The oil leg shrinks as the GOC descends; thus, the segregating gas cap minimizes the gas saturation in the oil leg. The GOR reversal coincides with a reversal in the gas saturation. Fig. 4 includes the gas saturation history. The gas saturation steadily increases until it peaks at approximately 0.25 PV; then it decreases. The GOR and gas saturation reversals occur at a moderate to low pressure when the expansion of the gas cap gas becomes pronounced. The change in the position of the GOC yields a measure of the oil leg shrinkage. At termination, the GOC has descended approximately 9.3 ft into the original 20-ft oil column.

Fig. 4 includes the oil-rate history. The oil rate for the segregating gas cap is consistently higher than for the nonsegregating gas cap or without the gas cap. The oil rate eventually flattens out to between 20 and 50 STB/D and stays within this range for 15 to 31 years. This moderate but steady oil rate explains the superior performance and long life of segregation drive gas cap reservoirs. Table 4 summarizes and compares the primary-recovery lifetimes of the various cases:

  • Segregating gas cap has a life of 31.3 years
  • Nonsegregating gas cap has a life of 15.2 years
  • Solution gas drive (base case) has a life of 13.8 years

Fig. 4 includes the cumulative oil recovery history. The segregating gas cap reservoir recovers 38.7% of the oil-leg OOIP while the nonsegregating gas cap and solution gas drive reservoirs recover 26.8 and 23.7% of the OOIP, respectively. Such a high recovery level for a segregation-drive reservoir is not uncommon. It is not uncommon for gravity drainage reservoirs to realize recoveries as high as 60 to 70% of the OOIP; however, they generally require a long time to do so. The curve endpoints in Fig. 4 denote the time of the economic limit. The segregating-gas-cap reservoir terminates at a pressure of 508 psia.

Fig. 5 shows the gas recovery history. The segregating gas cap reservoir recovers 91.1% of the oil-leg OGIP. This recovery level is considerably greater than the nonsegregating gas cap or solution gas drive reservoirs (74.9 and 52.3%, respectively). One reason segregating gas cap reservoirs tend to yield such high gas recoveries is that they often recover some of the original gas cap gas, which migrates into the oil leg. In addition, they generally realize lower termination pressures.

The final fractional oil recovery in a segregating-gas-cap reservoir is a strong function of the vertical communication within the reservoir. Vertical communication dictates the extent of segregation. If vertical communication is good, then most of the gas cap gas will be available for segregation. It will also be available to help drive oil through frontal displacement to the producing wells. If vertical communication is poor, then very little, if any, of the gas cap gas will segregate. In summary, segregation is controlled principally by three variables:

  • Vertical reservoir permeability
  • Producing rate
  • Well spacing

As well spacing and vertical permeability increase and as the producing rate decreases, the effect of gravity segregation increases. For the effects of gravity segregation to be important, however, the well spacing may need to be prohibitively large or the producing rate may need to be prohibitively low. In such reservoirs, the vertical permeability is not high enough to permit much gravity segregation.

The likely role of gravity segregation can be measured in terms of a gravity number, Ng. Ng is defined as the ratio of the time it takes a fluid to move from the drainage radius to the wellbore to the time it takes a fluid to move from the bottom of the reservoir to the top. In oilfield units, the gravity number is

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

where:

  • kv = vertical permeability, md
  • Δρ = density difference, lbm/ft3
  • re = drainage radius, ft
  • q = producing rate at reservoir conditions, RB/D
  • μo = oil viscosity, cp

Gravity segregation is likely pronounced if Ng > 10; gravity segregation is likely unimportant if Ng < 0.10.For example, if kv = 10 md, Δρ = 50 lbm/ft3, re = 930 ft, q = 500 RB/D, and μo = 1 cp, then Ng = 21.3 and the effects of gravity segregation are likely important. If the vertical permeability is kv = 0.10 md instead of 10.0 md, then Ng = 0.21 and the effects of gravity segregation are relatively unimportant.

Gas reinjection

One method for improving oil recovery is to reinject a portion of the produced gas. The reinjected gas helps maintain reservoir pressure. One obvious drawback of gas reinjection is that gas sales revenues are reduced or delayed. The overall intention of gas reinjection is to increase the net profit despite lower gas sales. When there is no sales outlet for produced gas, reinjection can improve oil recovery until a sales outlet is established. Regulations may require reinjection until sales are possible. Inert gases such as nitrogen or carbon dioxide also could be used to supplement or replace natural gas reinjection.

Figs. 3 through 5 present simulation results of a gas reinjection scenario. In this scenario, 70% of the produced wellhead gas is reinjected into the gas cap, and the gas cap is nonsegregating. This means that only 30% of the produced wellhead gas is available for sales. The non-reinjected gas is referred to as sales gas. This term is sometimes a misnomer because not all of the non-reinjected gas is necessarily sold. In practice, some of the sales gas is used routinely as fuel for power or utility requirements.

Fig. 3 shows the effect of gas reinjection on pressure as a function of oil recovery. Oil recovery at a given pressure is consistently higher for the gas-reinjection case than for the other cases in Fig. 3, except at very low pressures at which the segregating gas cap case yields superior performance. Gas reinjection leads to higher oil recoveries because the compressed reinjected gas effectively adds extra energy to the reservoir.

Fig. 4 shows the effect of gas reinjection on the GOR history. Gas reinjection leads to very high producing GORs, significantly higher than the other cases. The GOR is higher because the gas saturation is higher. The gas saturation is higher because reinjected gas and initial gas cap gas migrate into the oil leg during pressure depletion. This occurs because the gas cap is nonsegregating. High producing GORs are a characteristic feature of reservoirs subject to gas reinjection if there is little or no active gravity drainage. High producing GORs mean that large volumes of produced gas will have to be handled and processed at the surface.

Fig. 4 includes the effect of gas reinjection on the oil rate history. This figure shows that the oil rate is higher for the first 8 1/2 years for the gas reinjection case than for any of the other cases. After 8 1/2 years, the oil rate for the segregating-gas-cap case is slightly greater than the oil rate for the gas reinjection case. These results demonstrate that gas reinjection is an effective means to arrest the normal oil-rate decline dramatically.

Fig. 4 also shows the effect of gas reinjection on the fractional oil-recovery history and that the gas-reinjection case is superior to the other cases. The gas-reinjection case recovers 36.7% of the original oil leg OOIP at its economic limit of 18 1/2 years. Only the segregating gas cap reservoir recovers more oil (38.7%); however, the segregating-gas-cap reservoir requires more time to recover the additional oil.

Fig. 5 shows the effect of gas reinjection on the fractional gas-recovery history. The fractional gas recovery is the cumulative produced wellhead gas normalized by the original oil leg OGIP. The gas reinjection case recovers 177% of the oil leg OGIP (see Table 4). More than 100% of the oil leg OGIP is produced because some of the reinjected gas is produced. Because 30% of the produced gas is not reinjected, 0.30 × 177 or 53.1% of the oil leg OGIP is available for gas sales. This sales gas recovery is comparable to the case without gas reinjection (52% OGIP).

Reservoirs subject to gravity drainage are especially attractive for gas reinjection. Crestal gas injection into the developing gas cap is the preferred strategy because gravity drainage helps control the movement of the injected gas. Excellent sweep and displacement efficiencies and high oil recoveries can be realized. The Tensleep pool in the Elk Basin field in Wyoming is a good example. [6][7][8] This pool was projected to recover approximately 64% of the OOIP. See the immiscible gas injection in oil reservoirs page for more information on gravity drainage.

Material-balance analysis

The purpose of a material-balance analysis includes confirming the producing mechanism and estimating the following:

  • Original oil-in-place (OOIP)
  • Original gas-in-place (OGIP)
  • Size of the gas cap

The applicable material-balance equation for initially saturated oil reservoirs is[9][10][11]

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

This equation is applicable to all initially saturated reservoirs regardless of the distribution of the initial free gas. For example, this equation is applicable to reservoirs whether the initial free gas is segregated into a gas cap or uniformly dispersed throughout the reservoir. Eq. 2 also applies to waterdrives; however, if the following methods are applied to water drives, the water-influx history must be reliably known. If the water influx history is unknown, then the methods in material balance in water drive reservoirs must be applied.

The quantities Gfgi and Nfoi are related to N (OOIP) and G (OGIP) by the following equations:

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

and RTENOTITLE....................(4)

where m is the ratio of the free gas phase and free oil phase volumes and is defined by:

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

The dimensionless variable m is sometimes called the dimensionless gas cap volume.

Because Gfgi and Nfoi are independent, they must be determined simultaneously. At least two sets of the independent variables (F, We, Egwf, Eowf) must be known at two or more pressures (other than the initial pressure) to determine the set (Gfgi, Nfoi). If three or more sets (F, We, Egwf, Eowf) are known, then multiple sets (Gfgi, Nfoi) can be determined. The optimal set is determined by one of two least-squares solution techniques: iterative or direct methods.

In the iterative method, Eq. 2 is expressed as

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

where Et is the total expansivity expressed per unit volume of stock-tank oil and is defined by

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

The solution procedure to estimate the OOIP and OGIP involves the following steps:

  1. Compute F, Egwf, and Eowf for each data point (i.e., average reservoir-pressure measurement).
  2. Guess m.
  3. Compute Et(m) with Eq. 7.
  4. Estimate Nfoi with a least-squares analysis using Eq. 8.
    RTENOTITLE....................(8)
    where j denotes the data point index and n is the total number of data points.
  5. Compute the residual R for each data point with
    RTENOTITLE....................(9)
  6. Compute sum of the squares of residual, Rss, as
    RTENOTITLE....................(10)
  7. Return to Step 2 and repeat until Rss is minimized.
  8. Compute G, N, and Gfgi from Eqs. 3 through 5.

Minimization algorithms speed solution. This procedure is ideally suited for spreadsheet calculation, especially spreadsheet programs that contain minimization algorithms.

The use of Eq. 8 in Step 4 to determine Nfoi is equivalent to the slope of a (FWe)-vs.-Et(m) plot. This graphical solution method can be substituted for Eq. 8 in Step 4 if desired. Overall, Steps 2 through 7 are equivalent to the graphical procedure of varying m until the straightest possible (FWe)-vs.-Et(m) plot is realized. [12] Fig. 7 shows the qualitative effect of m on the shape of the (FWe)-vs.-Et plot.

  • If m is too small, the plot curves upward slightly
  • If m is too large, the plot curves downward slightly

Once m is determined, the final (FWe)-vs.-Et plot is used to confirm the producing mechanism. The linearity of the plot is a measure of material balance and the applicability of the presumed producing mechanism. If the plot exhibits considerable curvature, then either:

  • The presumed mechanism is incorrect

or

  • Additional producing mechanisms are active

If curvature exists, the shape of the curvature provides insight into the true producing mechanism. For instance, if the plot curves upward, this indicates that net withdrawal exceeds net expansion and that water influx, for example, has been ignored or is possibly underestimated.

As an alternative to the iterative method, Walsh[11][13] presented a direct method. This method is based on least-squares multivariate regression. The least-squares equations are simple but lengthy. The technique is ideally suited for spreadsheet calculation. Walsh’s method is especially attractive because it avoids iteration and the complications of attaining and judging convergence.

Havlena and Odeh[12] proposed another solution method in which (FWe)/Eowf is plotted vs. (Egwf /Eowf); the slope of the plot is equal to Gfgi and the y-intercept is equal to Nfoi. This method is popular and attractive because it yields a direct solution. In theory, this method is perfectly acceptable. In practice, however, it has shown to be unreliable because it suffers from hypersensitivity to pressure uncertainty. [13][14] The method has been shown to yield highly erroneous Gfgi and Nfoi estimates in the presence of only small amounts of uncertainty. For instance, Walsh[13] shows that only a 5-psi pressure uncertainty yielded an error of more than 150% in Nfoi and an error of more than 250% in Gfgi. The hypersensitivity is caused by the fact that the divisor (Eowf) approaches zero as the pressure approaches the initial pressure. Small errors in Eowf, in turn, produce large errors in the quotients: (FWe)/Eowf (Egwf /Eowf)

Tehrani[15] calls this problem a "loss in resolving power." Because of this hypersensitivity, this method should be used cautiously.

Walsh[13] tested the direct and iterative methods for their tolerance to uncertainty. He observed sensitivity, but the degree of sensitivity was less than the method of plotting (FWe)/Eowf vs. (Egwf /Eowf). He concluded that material-balance methods for gas-cap reservoirs should be used cautiously.

Nomenclature

Bg = gas FVF, RB/scf
F = total fluid withdrawal, L3, RB
G = total original gas in place, L3, scf
Gfgi = initial free gas in place, L3, scf
Egwf = composite gas/water/rock FVF, RB/scf
Eowf = composite oil/water/rock FVF, RB/STB
Et = total expansivity, RB/STB
kv = vertical permeability, L2, md
N = total original oil in place, L3, STB
Nfoi = initial free oil in place, L3, STB
Ng = dimensionless gravity number
q = producing rate at reservoir conditions (RB/D) or surface conditions (STB/D),v L3/t
re = reservoir drainage radius
Rj = residual for point j, L3, RB
Rs = dissolved GOR, scf/STB
Rss = sum of squares of the residual, L6, RB2
Rv = volatilized-oil/gas ratio, STB/MMscf
Vfgi = initial volume of free gas, L3, RB
Vfoi = initial volume of free oil, L3, RB
We = cumulative water influx, L3, RB
Δρ = density difference, m/L3, lbm/ft3 and g/cm3
μo = oil viscosity, m/Lt, cp

Subscripts

i = initial condition
j = index

References

  1. 1.0 1.1 Hall, H.N. 1961. Analysis of Gravity Drainage. J Pet Technol 13 (9): 927-936. SPE-1517-G. http://dx.doi.org/10.2118/1517-G
  2. Pirson, S.J. 1958. Oil Reservoir Engineering. New York City: McGraw-Hill Book Co. Inc.
  3. Muskat, M. 1949. Physical Principles of Oil Production. New York City: McGraw-Hill Book Co. Inc.
  4. Katz, D.L. 1942. Possibilities of Secondary Recovery for the Oklahoma City Wilcox Sand. Trans., AIME 146: 28.
  5. Hill, H.B. and Guthrie, R.K. 1943. Engineering Study of the Rodessa Oil Field in Louisiana, Texas, and Arkansas. Report Investigation 3715, US Bureau of Mines, Washington, DC, 87.
  6. Garthwaite, D.L. and Krebill, F.K. 1962. Supplement 1962: Pressure Maintenance by Inert Gas Injection in the High Relief Elk Basin Field. In Field Case Histories, Oil Reservoirs, Vol. 4. Richardson, Texas: Reprint Series, SPE.
  7. Garthwaite, D.L. 1975. Supplement, 1975: Pressure Maintenance by Inert Gas Injection in the High Relief Elk Basin Field. Field Case Histories, Oil and Gas Reservoirs, Vol. 4a. Richardson, Texas: Reprint Series, SPE.
  8. Stewart, F.M., Garthwaite, D.L., and Krebill, F.K. 1955. Pressure Maintenance by Inert Gas Injection in the High Relief Elk Basin Field. Trans., AIME 204: 49.
  9. Walsh, M.P. 1995. A Generalized Approach to Reservoir Material Balance Calculations. J Can Pet Technol 34 (1). PETSOC-95-01-07. http://dx.doi.org/10.2118/95-01-07
  10. Walsh, M.P., Ansah, J., and Raghavan, R. 1994. The New, Generalized Material Balance as an Equation of a Straight Line: Part 2 - Applications to Saturated and Non-Volumetric Reservoirs. Presented at the Permian Basin Oil and Gas Recovery Conference, Midland, Texas, 16-18 March 1994. SPE-27728-MS. http://dx.doi.org/10.2118/27728-MS
  11. 11.0 11.1 Walsh, M.P. and Lake, L.W. 2003. A Generalized Approach to Primary Hydrocarbon Recovery. Amsterdam: Elsevier.
  12. 12.0 12.1 Havlena, D. and Odeh, A.S. 1963. The Material Balance as an Equation of a Straight Line. J Pet Technol 15 (8): 896–900. SPE-559-PA. http://dx.doi.org/10.2118/559-PA
  13. 13.0 13.1 13.2 13.3 Walsh, M.P. 1999. Effect of Pressure Uncertainty on Material-Balance Plots. Presented at the SPE Annual Technical Conference and Exhibition, Houston, Texas, 3-6 October 1999. SPE-56691-MS. http://dx.doi.org/10.2118/56691-MS
  14. Wang, B. and Hwan, R.R. 1997. Influence of Reservoir Drive Mechanism on Uncertainties of Material Balance Calculations. Presented at the SPE Annual Technical Conference and Exhibition, San Antonio, Texas, 5-8 October 1997. SPE-38918-MS. http://dx.doi.org/10.2118/38918-MS
  15. Tehrani, D.H. 1985. An Analysis of a Volumetric Balance Equation for Calculation of Oil in Place and Water Influx. J Pet Technol 37 (9): 1664-1670. SPE-12894-PA. http://dx.doi.org/10.2118/12894-PA

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See also

Primary drive mechanisms

Solution gas drive reservoirs

Waterdrive reservoirs

Oil fluid characteristics

PEH:Oil_Reservoir_Primary_Drive_Mechanisms