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Water and gas coning
Coning is a production problem in which gas cap gas or bottomwater infiltrates the perforation zone in the near-wellbore area and reduces oil production. Gas coning is distinctly different from, and should not be confused with, free-gas production caused by a naturally expanding gas cap. Likewise, water coning should not be confused with water production caused by a rising water/oil contact (WOC) from water influx. Coning is a rate-sensitive phenomenon generally associated with high producing rates. Strictly a near-wellbore phenomenon, it only develops once the pressure forces drawing fluids toward the wellbore overcome the natural buoyancy forces that segregate gas and water from oil.
Contents
- 1 Basis of terminology
- 2 Impact of coning
- 3 Predicting coning
- 4 Example: Determining the critical production rate for both horizontal and vertical well alternatives
- 5 Coning strategies
- 6 Schols’ correlation
- 7 Chierici et al. correlation
- 8 Partially penetrating wells
- 9 Variables affecting coning
- 10 Additional measures to control coning
- 11 Example 1: Computing critical rate to prevent coning
- 12 Example 2: Computing optimum perforation length to prevent coning
- 13 Example 3: Optimum perforation length to prevent coning in a bottom water gas cap reservoir
- 14 Nomenclature
- 15 References
- 16 Noteworthy papers in OnePetro
- 17 External links
- 18 See also
Basis of terminology
The term coning is used because, in a vertical well, the shape of the interface when a well is producing the second fluid resembles an upright or inverted cone (Fig. 1). Important examples of coning include:
- Production of water in an oil well with bottomwater drive
- Production of gas in an oil well overlain by a gas cap
- Production of bottom water in a gas well
In a horizontal well, the cone becomes more of a crest (Fig. 2), but the phenomenon is still customarily called coning. In a given reservoir, the amount of undesired second fluid a horizontal well produces is usually less than for a vertical well under comparable conditions. This is a major motivation for drilling horizontal wells, for example, in thin oil columns underlain by water.
Impact of coning
Coning is a problem because the second phase must be handled at the surface in addition to the desired hydrocarbon phase, and the production rate of the hydrocarbon flow is usually dramatically reduced after the cone breaks through into the producing well. Produced water must also be disposed of. Gas produced from coning in an oil well may have a market, but also may not. In any event, production of gas in an oil well after the cone breaks through can rapidly deplete reservoir pressure and, for that reason, may force shut in of the oil well.
Several strategies may apply to wells with a potential to cone. One is to try to predict the rate at which a well will cone and produce at a lower rate as long as possible. Or, optimal economics may result by producing at a much higher rate, causing the well to cone, but increasing the cumulative hydrocarbon volume produced (and present value) at any future date. A horizontal well may be preferred to a vertical well.
Predicting coning
Most prediction methods for coning predict a "critical rate" at which a stable cone can exist from the fluid contact to the nearest perforations. The theory is that, at rates below the critical rate, the cone will not reach the perforations and the well will produce the desired single phase. At rates equal to or greater than the critical rate, the second fluid will eventually be produced and will increase in amount with time. However, these theories based on critical rates do not predict when breakthrough will occur nor do they predict water/oil ratio or gas/oil ratio (GOR) after breakthrough. Other theories predict these time behaviors, but their accuracy is limited because of simplifying assumptions.
The calculated critical rate is valid only for a certain fixed distance between the fluid contact and the perforations. With time, that distance usually decreases (for example, bottom water will usually tend to rise toward the perforations). Thus, the critical rate will tend to decrease with time, and the economics of a well with a tendency to cone will continue to deteriorate with time.
Whether a cone will move toward perforations depends on the relative significance of viscous and gravitational forces near a well. The pressure drawdown at the perforations tends to cause the undesired fluid to move toward the perforations. Gravitational forces tend to cause the undesired fluid to stay away from the perforations. Coning occurs when viscous forces dominate.
The variables that could affect coning are:
- Density differences between water and oil, gas and oil, or gas and water (gravitational forces)
- Fluid viscosities and relative permeabilities
- Vertical and horizontal permeabilities
- Distances from contacts to perforations.
Coning tendency turns out to be quite dependent on some of these variables and insensitive to others.
A number of prediction methods have been published. There is no guarantee of great accuracy when using any of these methods because they all contain significant simplifying assumptions. In particular, areal and vertical variations in vertical permeability (because of flow barriers of varying extent) can cause the prediction methods to differ significantly from what actually happens in the field. Accordingly, the prediction methods are best used for quick approximations, screening, and comparison of alternatives. Reservoir simulations, based on accurate reservoir characterization, will ultimately be required.
The coning prediction method proposed by Chaperon^{[1]} is of particular interest because of the variables it includes and because variations of the method are applicable to gas and water coning in both vertical and horizontal wells. For vertical wells, the Chaperon method calculates the critical rate for coning from the expression
....................(1) Chaperon paper uses "h", not "hc"
where
and h_{c} = distance from perforations to fluid contact, ft. For horizontal wells, the critical rate is given by
where
and
Example: Determining the critical production rate for both horizontal and vertical well alternatives
Consider a square, 160-acre drilling unit in an oil reservoir overlain by a gas cap. To determine the critical production rate (at or above which coning is likely to occur) for both horizontal and vertical well alternatives, assume the following well and formation properties: k_{h} = 80 md, a_{H} = 2,640 ft, μ_{o} = 0.5 md, ρ_{o} = 0.8 g/cm^{3}, ρ_{g} = 0.3 g/cm^{3} (~.0008 g/cm^3?? - a gas density cannot be .3 g/cm^3), L_{w} = 1,500 ft, h = 90 ft, B_{o} = 1.2 RB/STB, r_{w} = 0.33 ft, distance from top of perforations in vertical well to GOC = 80 ft, and distance from horizontal well to GOC = 80 ft. Consider two cases: Isotropic Reservoir A, where k_{v} = k_{h} = 80 md, and Anisotropic Reservoir B, where k_{v} = 8 md and k_{h} = 80 md.
Solutions. Isotropic Reservoir A (k_{v} = k_{h} = 80 md). For a horizontal well,
Here,
Then,
For a vertical well, note that = 1,489 ft.
and
Then,
Anisotropic Reservoir B (k_{v} = 8 md and k_{h} = 80 md). For a horizontal well,
For a vertical well,
Conclusions from example
The important conclusions and lessons from this example are:
- Vertical permeability has only a modest influence on critical coning rate, at least for this situation.
- The advantage of a horizontal well over a vertical well is substantial for both isotropic and anisotropic reservoirs in this situation.
- The same sorts of calculations could be made for an oil well coning water or a gas well coning water.
- These calculations give us no information on time at which the cone will break through to the producing well nor on GOR and oil production rate following breakthrough.
While these types of simple calculations can provide some insight on the potential for coning, a finely grided simulator model could be used to more effectively predict coning behavior including timing and the benefits of a horizontal well over a vertical one.
Coning strategies
Under ideal conditions in which no coning exists, flow is principally horizontal and mainly oil is produced. Fig. 3 illustrates a producing well with no coning. When coning exists, however, the overlying gas is drawn downward or bottomwater is drawn upward and into the oil column. Coning trades oil production for gas or water production. Fig. 4 illustrates a producing well subject to gas and water coning.
Two strategies commonly are used to minimize coning. One approach is partial perforation or penetration. In this approach, only a limited portion of the pay thickness is perforated. If gas coning is anticipated, the pay thickness near the GOC is not perforated. If water coning is anticipated, the pay thickness near the WOC is not perforated. In instances in which severe coning is expected, only a small portion of the pay thickness may be perforated. The variables in Fig. 5 define the length of the perforation interval, b, and its position within the pay thickness, h. The distance L_{g} is the distance between the top of the pay and the uppermost perforation, and the distance L_{w} is the distance between the bottom of the pay and the lowest perforation. The quotient b/h is the partial perforation fraction. Although this strategy will reduce and can eliminate coning problems, it suffers an obvious drawback; namely, it temporarily reduces oil production in the hope of eventually avoiding coning.
A second remedial strategy is based on the observation that there is a critical producing rate below which the cone stabilizes and will not reach the perforations. This critical rate is a function of the perforation length. As the perforation length increases, the critical producing rate decreases. Often, the critical producing rate is much less than the possible producing rate. This difference creates an operational decision:
- Produce at a rate greater than the critical and eventually risk coning
- Produce at a rate less than the critical and temporarily sacrifice oil production
If the critical rate is less than the minimum economic rate, then the operator has no choice but to produce above the critical rate or abandon the well.
To combat coning, a hybrid strategy is often used whereby a combination of partial perforation and a reduced producing rate is used. One especially unattractive consequence of gas coning is that it prematurely depletes the gas-cap gas and diminishes the gas-cap producing mechanism. Fortunately, gas coning is not as problematic as water coning because the density difference between oil and gas is greater than the difference between water and oil. This density difference through gravity segregation helps mitigate coning.
To develop an effective remedial strategy against coning, certain theoretical aspects regarding coning must be understood. Mathematically, coning is a challenging problem because of its complexity. To develop tractable analytical solutions, tenuous assumptions must be invoked. These assumptions limit the practical applicability of these solutions. The most reliable way to study coning is with a specially designed finite-difference simulator. ^{[2]}^{[3]}^{[4]} Nevertheless, certain analytical solutions and empirical correlations can be helpful and serve as a preliminary guide.
Muskat and Wyckoff ^{[5]} and Chaney et al.^{[6]} were among the first to contribute substantively to this problem. Since their efforts, several other authors have contributed to the body of literature. ^{[7]}^{[8]}^{[9]}^{[10]}^{[11]}^{[12]}^{[13]}^{[14]} Many of these works have led to similar correlations. Wheatley^{[13]} presented a comparison of some popular correlations. As a representative sample, the correlations of Schols^{[12]} and Chierici et al.^{[7]} are presented here. Both works apply to both water and gas coning. Both efforts also use the following equation to compute the critical producing rate:
where:
- Δρ = density difference (g/cm^{3})
- B_{o} = average oil formation volume factor (FVF)
- μ_{o} = average oil viscosity (cp)
- k_{o} = oil permeability (md)
- q_{Dc} = dimensionless critical producing rate
- h = pay thickness (ft)
- q_{c} is given in STB/D
The oil permeability, k_{o}, is the product of the horizontal permeability and the oil relative permeability. The dimensionless critical rate, q_{Dc}, is specified by correlation.
Schols’ correlation
Schols’ correlation^{[12]} is based on a numerical simulation study. The dimensionless critical producing rate is
where
- b is the length of the perforation interval
- r_{e} is the drainage radius.
This correlation applies to both water and gas coning; however, it directly applies only to cases in which water or gas coning exist separately. In other words, it does not directly apply to cases in which water and gas coning act simultaneously. The correlation can be used to predict the critical rate for a pre-existing completion or to predict the optimum perforation length for a future completion. In this latter application, the optimum perforation length is defined as the length at which the critical and theoretical producing rates are equal. The theoretical producing rate of a partially penetrating well is computed in this section. Example 1 illustrates the former application while Example 2 illustrates the latter application.
Chierici et al. correlation
The correlation by Chierici et al.^{[7]} was based on a potentiometric study. This was one of the most sophisticated correlations. It allows the vertical permeability to differ from the horizontal permeability. This can be an important factor because coning vanishes as the vertical permeability approaches zero. This correlation also treats the problem of simultaneous gas/water coning. This is important in situations in which a gas cap and bottomwater coexist.
The correlation of Chierici et al. was specified in terms of a series of charts. The charts used the following nomenclature. The dimensionless critical rate is denoted as ψ (previously defined as q_{Dc}) and the following dimensionless variables are defined as
and ....................(13) (original paper uses "h" not "b")
The dimensionless critical rate, ψ, is a function of r_{De}, ε, and δ. Figs. 6 through 12 show the charts. Each chart corresponds to a different value of r_{De}. Specific charts exist for r_{De} = 5, 10, 20, 30, 40, 60, and 80.
The chats are used differently depending on whether they are used to compute the critical rates or optimize the perforation length. The problem of optimizing the perforation length for simultaneous gas and water coning is more complicated than separate water or gas coning. The charts simplify the problem; however, the solution procedure depends on the application.
Calculating critical rates
For a pre-existing perforation length, b, the critical rates are computed with the following procedure:
- Compute δ_{g}, δ_{w}, ε, and r_{De} with Eqs. 10 through 13.
- Locate the correct chart or charts, depending on the value of r_{De}. Interpolation between two charts may be required.
- Compute ψ_{g} from the charts based on r_{De}, ε, and δ_{g}; then, compute ψ_{w} from the charts based on r_{De}, ε, and δ_{w}.
- Compute the critical rates to avoid water and gas coning with Eq. 8.
This procedure ignores the curves labeled Δρ_{og}/Δρ_{wo}. The calculation procedure is simplified if only bottomwater or a gas cap exists. If no bottomwater exists, then the calculation of ψ_{w} and δ_{w} can be ignored. Conversely, if no gas cap exists, then the calculation of ψ_{g} and δ_{g} can be ignored. Example 1 illustrates an application.
Calculating optimum perforation length
For a bottomwater, gas-cap reservoir, the procedure to calculate the optimum perforation (length and position) uses the curves labeled Δρ_{og}/Δρ_{wo} and is as follows:
- Compute r_{De} with Eq. 13. Also, compute Δρ_{og}/Δρ_{wo}.
- Assume a value of ε.
- Compute ψ and δ with the charts. These values correspond to ψ_{g} and δ_{g}.
- Compute L_{g} = hδ_{g} and L_{w} = h(1 – ε) – L_{g}.
- Compute the critical rate from Eq. 8. Only one critical rate is needed because the procedure assumes equal critical rates for gas and water coning.
- Return to Step 2. Assume a new value of ε, and repeat the calculation until an adequate range of ε is covered.
- Compute the theoretical producing rate of a partially penetrating well as a function of ε with Eq. 14. (See partially penetrating wells below).
- Plot the critical and theoretical producing rates as a function of ε . The value of ε at which the critical and producing rates intersect yields the optimal perforation interval.
This procedure is simplified if only a gas cap or bottomwater exists. The same procedure applies except Δρ_{og}/Δρ_{wo} is not calculated and δ_{g} = 1 – ε (if there is no bottomwater and only gas coning is a problem) or δ_{w} = 1 – ε (if there is no gas cap and only water coning is a problem). ψ is computed for a range of ε until an optimal value of ε is identified. Example 2 illustrates this procedure for a gas cap reservoir. Example 3 illustrates an application for a gas cap, bottomwater reservoir.
Partially penetrating wells
The theoretical producing rate of a partially penetrating well is needed to compute the optimum perforation length. Partially penetrating wells are wells that do not fully penetrate or are not fully perforated throughout the pay thickness. If vertical permeability exists, these wells will produce fluids from above and below the perforations. Fig. 13 illustrates fluid delivery into a partially penetrating producing well. Under these circumstances, fluid flow is obviously not strictly horizontal. The producing rate in partially penetrating wells with nonzero vertical permeability is greater than the rate with no vertical permeability.
Partially penetrating wells commonly are used to minimize coning. The critical rate gives a producing rate below which no coning will occur. Often, however, the critical flow rate is much less than maximum possible flow rate. To judge the difference, estimates for the flow rate of a partially penetrating well are needed. Several authors have offered analytical expressions to estimate the flow rate. ^{[15]}^{[16]}^{[17]} Most efforts yield estimates within a few percent of one another. The Kozeny expression, ^{[17]} for example, is
where
- k_{H} = horizontal permeability
- k_{v} = vertical permeability
- p_{e} = pressure at drainage radius
- p_{w} = wellbore pressure
- s = skin factor, q = oil producing rate, and the argument of the cosine assumes radians
This equation assumes units of md, ft, psi, cp, and STB/D. This equation also assumes steady-state flow in a circular drainage area, where r_{e} and r_{w} are the drainage and wellbore radii, respectively. Eq. 14 gives the Kozeny equation in SI units.
Variables affecting coning
The ratio of q_{c}/q is a measure of the tendency not to cone. As q c increases or q decreases, the likeliness to avoid increases. According to Eqs. 8 and 14, the ratio q_{c}/q is proportional to
This expression shows that the likeliness to control coning increases as the penetration interval b decreases. Eq. 15 also shows that the likeliness to control coning increases as the pay thickness increases, density difference increases, well spacing increases, and perforation length decreases. Horizontal permeability does not affect the likelihood of success. This expression also suggests that controlling coning in a thin reservoir may be difficult.
Additional measures to control coning
Other techniques have been applied to control coning. These include:
- Placing an artificial barrier above or below the pay to suppress vertical flow^{[18]}
- Injecting oil to control gas coning^{[19]}
- Use of horizontal wells
Barriers composed of cement and high-molecular-weight polymers have been tried. Another, although expensive, technique is to drill additional wells and produce them at the critical rate.
Example 1: Computing critical rate to prevent coning
Compute the critical rate (STB/D) for a well in a gas-cap reservoir with the following characteristics:
- k_{H} = 60 md
- k_{v} = 39 md
- h = 150 ft
- r_{e} = 933 ft (80-acre well spacing)
- r_{w} = 0.5 ft
- B_{o} = 1.25 RB/STB
- μ_{o} = 1.11 cp
- ρ_{o} = 0.714 g/cm^{3}
- ρ_{g} = 0.098 g/cm^{3}
The well is completed in only the lower 60 ft of the pay thickness.
Schols’ correlation
With Eq. 9, compute q_{Dc}. This yields
The critical rate is then computed with Eq. 8, which yields
Chierici et al. correlation
First, evaluate:
- L_{g} = 90 ft
- δ_{g} = 90/150 = 0.60
- ε = 60/150 = 0.40
- r_{De} = 5.01.
With the chart for r_{De} = 5, obtain ψ = 0.120. Evaluating Eq. 8 yields
Example 2: Computing optimum perforation length to prevent coning
For an uncompleted well in the gas-cap reservoir in Example 1, compute the optimum perforation length at a reservoir pressure of 1,800 psia. Assume a wellbore pressure of 1,500 psia and a skin factor of 10.
Schols’ correlation
Compute the dimensionless critical rate and critical rate as a function of b/h. Table 1 summarizes the results for b/h = 0 to 1.
Next, estimate the theoretical producing rate for a partially penetrating well. With Eq. 15 for b = 60 ft yields
Table 1 summarizes the results at other values of b. The rate varies from 0 to 808 STB/D, depending on the length of the perforation interval. The optimum perforation length corresponds to the value of b at which the critical and theoretical producing rates are equal. Fig. 14 shows a plot of q and q_{c} vs. b/h. The curves intersect at approximately b/h = 0.15. This corresponds to:
- b = 22.5 ft
- L_{g} = 127.5 ft
- q = 187 STB/D
In conclusion, only the lower 22.5 ft of the pay thickness should be perforated to avoid gas coning.
Chierici et al. correlation
First, compute δ_{g} = 1– b/h for a range of b/h. Next, compute r_{De}. From Example 1, r_{De} = 5. With the appropriate chart, compute ψ for the range of b/h. The charts use b/h as ε. Then compute the critical rate with Eq. 8. Table 2 summarizes the results. Fig. 14 plots q_{c} vs. b/h.
The optimal perforation length corresponds to the value of b/h at which the critical and producing rates are equal. This approximately occurs for b/h = 0.25. This corresponds to:
- b = 37.5 ft
- L_{g} = 112.5 ft
- q = 275 STB/D
In conclusion, only the lower 37.5 ft of the pay should be perforated. The method of Chierici et al. yields a wider perforation interval than the method of Schols (37.5 vs. 22.5 ft). The Chierici et al. method is consistently more liberal than Schols’ method.
Example 3: Optimum perforation length to prevent coning in a bottom water gas cap reservoir
Assume the gas cap reservoir in Examples 1 and 2 is underlain by water. The water density is 1.092 g/cm^{3}. Compute the optimum perforation length and position of the perforation interval with the Chierici et al. correlation.
Solution. First, compute Δρ_{og}/Δρ_{wo}. This yields (0.741 – 0.098)/(1.092 – 0.741) = 1.83. Next, determine δ_{g} and ψ from the charts for a range of ε. If ε = 0.40, for example, use the chart corresponding to r_{De} = 5 to determine that δ_{g} = 0.24 and ψ = 0.040. Table 3 summarizes the results for a range of ε values from 0.05 to 0.40. Next, compute the critical rate for each value of ψ with Eq. 8. Finally, compute the theoretical producing rate with Eq. 15.
An examination of Table 3 shows that the critical and producing rates are equal at ε = b/h = 0.075. This value of b/h corresponds to L_{g} = (0.385) (150) = 57.8 ft, b = (0.075) (150) = 11.3 ft, and L_{w} = 150 – 57.8 – 11.3 = 81 ft. In conclusion, the well should be perforated with an 11.3-ft interval located 57.8 ft below the GOC and 81 ft above the WOC.
Nomenclature
a_{H} | = | total width of reservoir perpendicular to the wellbore, ft |
B_{o} | = | oil formation volume factor, RB/Mscf |
h | = | net formation thickness, ft |
k_{h} | = | horizontal permeability, md |
L_{w} | = | completed length of horizontal well, ft |
r_{e} | = | external drainage radius, ft |
ρ | = | density, lbm/ft^{3} or g/cm^{3} |
μ_{o} | = | oil viscosity, cp |
μ_{w} | = | water viscosity, cp |
References
- ↑ Chaperon, I. 1986. Theoretical Study of Coning Toward Horizontal and Vertical Wells in Anisotropic Formations: Subcritical and Critical Rates. Presented at the SPE Annual Technical Conference and Exhibition, New Orleans, 5–8 October. SPE-15377-MS. http://dx.doi.org/10.2118/15377-MS
- ↑ Fetkovich, M.J., Reese, D.E., and Whitson, C.H. 1998. Application of a General Material Balance for High-Pressure Gas Reservoirs (includes associated paper 51360). SPE J. 3 (1): 3-13. SPE-22921-PA. http://dx.doi.org/10.2118/22921-PA
- ↑ Letkeman, J.P. and Ridings, R.L. 1970. A Numerical Coning Model. SPE J. 10 (4): 418-424. SPE-2812-PA. http://dx.doi.org/10.2118/2812-PA
- ↑ MacDonald, R.C. 1970. Methods for Numerical Simulation of Water and Gas Coning. SPE J. 10 (4): 425-436. SPE-2796-PA. http://dx.doi.org/10.2118/2796-PA
- ↑ Muskat, M. and Wyckoff, R.D. 1935. An Approximate Theory of Water-Coning in Oil Production. Trans., AIME 114: 144.
- ↑ Chaney, P.E. et al. 1956. How to Perforate Your Well to Prevent Oil and Gas Coning. Oil & Gas J. (7 May): 108.
- ↑ ^{7.00} ^{7.01} ^{7.02} ^{7.03} ^{7.04} ^{7.05} ^{7.06} ^{7.07} ^{7.08} ^{7.09} ^{7.10} Chierici, G.L., Ciucci, G.M., and Pizzi, G. 1964. A Systematic Study of Gas and Water Coning By Potentiometric Models. J Pet Technol 16 (8): 923–929. SPE-871-PA. http://dx.doi.org/10.2118/871-PA
- ↑ Bournazel, C. and Jeanson, B. 1971. Fast Water-Coning Evaluation Method. Presented at the Fall Meeting of the Society of Petroleum Engineers of AIME, New Orleans, 3-6 October. SPE 3628. http://dx.doi.org/10.2118/3628-MS
- ↑ Høyland, L.A., Papatzacos, P., and Skaeveland, S.M. 1989. Critical Rate for Water Coning: Correlation and Analytical Solution. SPE Res Eng 4 (4): 495–502. SPE-15855-PA. http://dx.doi.org/10.2118/15855-PA
- ↑ Kuo, M.C.T. 1983. A Simplified Method for Water Coning Predictions. Presented at the SPE Annual Technical Conference and Exhibition, San Francisco, California, 5–8 October. SPE-12067-MS. http://dx.doi.org/10.2118/12067-MS
- ↑ Meyer, H.I. and Garder, A.O. 1954. Mechanics of Two Immiscible Fluids in Porous Media. J. of Applied Physics 25 (11): 1400. http://dx.doi.org/+10.1063/1.1721576
- ↑ ^{12.0} ^{12.1} ^{12.2} Schols, R.S. 1972. An Empirical Formula for the Critical Oil Rate. Erdöl Erdgas, Zeitschrift (January): 6–11. Cite error: Invalid
<ref>
tag; name "r12" defined multiple times with different content Cite error: Invalid<ref>
tag; name "r12" defined multiple times with different content - ↑ ^{13.0} ^{13.1} Sobocinski, D.P. and Cornelius, A.J. 1965. A Correlation for Predicting Water Coning Time. J Pet Technol 17 (5): 594-600. SPE-894-PA. http://dx.doi.org/10.2118/894-PA
- ↑ Wheatley, M.J. 1985. An Approximate Theory of Oil/Water Coning. Presented at the SPE Annual Technical Conference and Exhibition, Las Vegas, Nevada, USA, 22-26 September. SPE 14210. http://dx.doi.org/10.2118/14210-MS
- ↑ Muskat, M. 1949. Physical Principles of Oil Production. New York City: McGraw-Hill Book Co. Inc.
- ↑ ^{16.0} ^{16.1} Saidikowski, R.M. 1979. Numerical Simulations of the Combined Effects of Wellbore Damage and Partial Penetration. Presented at the SPE Annual Technical Conference and Exhibition, Las Vegas, Nevada, 23–26 September. SPE-8204-MS. http://dx.doi.org/10.2118/8204-MS
- ↑ ^{17.0} ^{17.1} Chierici, G.L., Ciucci, G.M., and Pizzi, G. 1964. A Systematic Study of Gas and Water Coning By Potentiometric Models. J Pet Technol 16 (8): 923–929. SPE-871-PA. http://dx.doi.org/10.2118/871-PA
- ↑ Howard, G.C. and Fast, C.R. 1950. Squeeze Cementing Operations. Trans., AIME 189: 53.
- ↑ Richardson, J.G. and Blackwell, R.J. 1971. Use of Simple Mathematical Models for Predicting Reservoir Behavior. J Pet Technol 23 (9): 1145-1154. SPE-2928-PA. http://dx.doi.org/10.2118/2928-PA
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