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Oil well performance
When considering the performance of oil wells, it is often assumed that a well’s performance can be estimated by the productivity index. However, Evinger and Muskat pointed out that, for multiphase flow, a curved relationship existed between flow rate and pressure and that the straight-line productivity index did not apply to multiphase flow. The constant productivity index concept is only appropriate for oil wells producing under single-phase flow conditions, pressures above the reservoir fluid’s bubblepoint pressure. For reservoir pressures less than the bubblepoint pressure, the reservoir fluid exists as two phases, vapor and liquid, and techniques other than the productivity index must be applied to predict oilwell performance.
There have been numerous empirical relationships proposed to predict oilwell performance under two-phase flow conditions. Some of the key methods are described below.
Vogel's inflow performance relationship
Vogel was the first to present an easy-to-use method for predicting the performance of oil wells. His empirical inflow performance relationship (IPR) is based on computer simulation results and is given by
To use this relationship, the engineer needs to determine the oil production rate and flowing bottomhole pressure from a production test and obtain an estimate of the average reservoir pressure at the time of the test. With this information, the maximum oil production rate can be estimated and used to estimate the production rates for other flowing bottomhole pressures at the current average reservoir pressure.
Use of isochronal testing
Fetkovich proposed the isochronal testing of oil wells to estimate productivity. His deliverability equation is based on the empirical gas-well deliverability equation proposed by Rawlins and Schellhardt.
and requires a multiple rate test to obtain values of C and n. A log-log plot of the pressure-squared difference vs. flow rate is expected to plot as a straight line. The inverse of the slope yields an estimate of n, the flow exponent. The flow coefficient can be estimated by selecting a flow rate and pressure on the log-log plot and using the information in Eq. 2 to calculate C. An IPR can be developed by rearranging Fetkovich’s deliverability equation to obtain Eq. 3.
Multirate tests incorporating non-Darcy flow
Jones, Blount, and Glaze also proposed a multirate test method in which they attempted to incorporate non-Darcy flow effects. The basic equation to describe the flow of oil is
where a represents the laminar flow coefficient and b is the turbulence coefficient. To use the method, one must obtain multiple rate test information similar to Fetkovich’s method. A plot of the ratio of the pressure difference to flow rate vs. the flow rate on coordinate paper is expected to yield a straight line. The laminar flow coefficient a is the intercept of the plot, while the slope of the curve yields the turbulence coefficient b. Once a and b have been determined, the flow rate at any other flowing wellbore pressure can be obtained by solving
The maximum flow rate can be estimated from Eq. 5 by allowing the flowing bottomhole pressure to equal zero.
There are several other two-phase IPR methods available in the literature. Gallice and Wiggins provide details on the application of several of these methods and compare and discuss their use in estimating oilwell performance with advantages and disadvantages.
Single- and two-phase flow
In certain circumstances, both single-phase and two-phase flow may be occurring in the reservoir. This results when the average reservoir pressure is above the bubblepoint pressure of the reservoir oil while the flowing bottomhole pressure is less than the bubblepoint pressure. To handle this situation, Neely developed a composite IPR that Brown demonstrates. The composite IPR couples Vogel’s IPR for two-phase flow with the single-phase productivity index. The relationship that yields the maximum oil production rate is
The relationships to determine the oil production rate at various flowing bottomhole pressures are
when the flowing bottomhole pressure is greater than the bubblepoint pressure, and
when the flowing bottomhole pressure is less than the bubblepoint pressure. The flow rate at the bubblepoint pressure, qb, used in Eq. 8 is determined with Eq. 7 where pwf equals pb.
The appropriate J to use in Eqs. 6 and 7 depends on the flowing bottomhole pressure of the test point. If the flowing bottomhole pressure is greater than the bubblepoint pressure, then the well is experiencing single-phase flow conditions and J is determined by
When the flowing bottomhole pressure is less than the bubblepoint pressure, J is determined from
Once J is determined for the test conditions, it is used to calculate the complete inflow performance curve both above and below the bubblepoint pressure with Eqs. 7 and 8. The composite IPR is only applicable when the average reservoir pressure is greater than the bubblepoint pressure.
Wiggins presented an easy-to-use IPR for three-phase flow, which is similar in form to Vogel’s IPR. It was based on a series of simulation studies. It yields results similar to two other three-phase flow models and is easier to implement. Eqs. 11 and 12 give the generalized three-phase IPRs for oil and water, respectively.
Table 1 presents data for a multipoint test on a producing oil well used to demonstrate the two-phase IPR methods. The average reservoir pressure for this example is 1,734 psia.
To apply the IPR methods, obtain test information, which includes production rates, flowing bottomhole pressures, and an estimate of the average reservoir pressure. Vogel’s IPR is a single-rate relationship, and the highest test rate is used to demonstrate this IPR. The data obtained at the largest pressure drawdown can be used with Eq. 1 to solve for the maximum oil-production rate.
The estimated maximum oil production is 2,065 STB/D. This value is then used to estimate the production rate at other values of flowing bottomhole pressures to develop a complete inflow performance curve. Once again, Eq. 1 will be rearranged to calculate the production rate for a flowing bottomhole pressure of 800 psia.
Fetkovich’s IPR requires multiple test points to determine the deliverability exponent n. Table 2 shows the test data prepared for plotting. The data are plotted on a logarithmic graph, which is used to estimate the slope of the best-fit straight line through the data. The deliverability exponent n is the inverse of the slope. Once n is determined, Eq. 3 can be used to estimate the maximum oil production rate. Fig. 1 is the plot of the data that shows the best-fit straight line has a slope of 1.347 yielding an n value of 0.743. The estimated maximum oil production rate is 1,497 STB/D, as Eq. 15 shows.
Once the maximum rate is estimated, it is used with Eq. 3 to estimate production rates at other flowing bottomhole pressures to develop the inflow performance curve in a manner similar to that demonstrated with Vogel’s IPR. For Fetkovich’s method, the production rate is estimated to be 1,253 STB/D at a flowing bottomhole pressure of 800 psia.
To apply the method of Jones, Blount, and Glaze to this data set, Table 3 was prepared and the data plotted on a coordinate graph as shown in Fig. 2. The best-fit straight line yielded a slope of 0.0004 psia/(STB/D)2, which is the turbulence coefficient b. The intercept is the laminar flow coefficient and is determined to be 0.23 psia/STB/D. These values are used in Eq. 5 to determine the maximum oil production rate of 1,814 STB/D when the flowing bottomhole pressure is 0 psig.
This same relationship is used to estimate the production rate at other flowing bottomhole pressures to generate the inflow performance curve. For a flowing bottomhole pressure of 800 psia, the production rate is estimated to be 1,267 STB/D.
From this example, each of the three methods yielded different values for the maximum oil production rate as well as the production rate at a flowing bottomhole pressure of 800 psia. As a result, production estimates will be dependent on the IPR used in the analysis, and the petroleum engineer should be aware of this concern in any analysis undertaken.
The application of the composite IPR and Wiggins’ IPR is straight-forward and similar to applying Vogel’s IPR. In applying the composite IPR, the appropriate relationship must be used to estimate J because it depends on the flowing bottomhole pressure of the test point. With Wiggins’ IPR, estimates of both oil and water production rates are generated. The inflow performance curve will be developed by adding the estimated oil rates to the water rates to create a total liquid rate.
Future performance methods
Once the petroleum engineer has estimated the current productive capacity of a well, it is often desired to predict future performance for planning purposes. Standing was one of the first to address the prediction of future well performance from IPRs. He used Vogel’s IPR with a modified multiphase productivity index to relate current well performance to future performance. Unfortunately, his relationship requires knowledge of fluid properties and relative permeability behavior. This makes Standing’s method difficult to use because one must estimate saturations, relative permeabilities, and fluid properties at a future reservoir pressure.
Fetkovich suggested that Standing’s modified multiphase productivity index ratios could be approximated by the ratio of the pressures. He proposed that the future maximum oil production rate could be estimated from the current maximum production rate with
Fetkovich applied this idea to the use of his IPR. The exponent n in Eq. 17 is the deliverability exponent from his IPR; however, Fetkovich’s future performance method has been applied to other IPR methods by allowing the exponent to be one, which provides good results in many cases. This method requires no more information to apply than that obtained for applying the various IPRs. It is important to note that Fetkovich’s method assumes the deliverability exponent does not change between the present and future conditions. Uhri and Blount and Kelkar and Cox have also proposed future performance methods for two-phase flow that require rate and pressure data at two average reservoir pressures.
At the time Wiggins proposed his three-phase IPRs, he also presented future performance relationships for the oil and water phases. These relationships are presented in Eqs. 18 and 19.
In all cases, once the future maximum production rate is estimated from the current data, inflow performance curves at the future average reservoir pressure of interest can be developed with the IPR of one’s choosing.
- Evinger, H.H. and Muskat, M. 1942. Calculation of Theoretical Productivity Factor. Trans., AIME 146: 126.
- Vogel, J.V. 1968. Inflow Performance Relationships for Solution-Gas Drive Wells. J Pet Technol 20 (1): 83–92. SPE 1476-PA. http://dx.doi.org/10.2118/1476-PA.
- Fetkovich, M.J.: “The Isochronal Testing of Oil Wells,” paper SPE 4529 presented at the 1973 SPE Annual Meeting, Las Vegas, Nevada, 30 September–3 October.
- Rawlins, E.L. and Schellhardt, M.A. 1935. Backpressure Data on Natural Gas Wells and Their Application to Production Practices, Monograph Series No. 7, U.S. Bureau of Mines. Baltimore, Maryland: Lord Baltimore Press.
- Jones, L.G., Blount, E.M., and Glaze, O.H. 1976. Use of Short Term Multiple Rate Flow Tests To Predict Performance of Wells Having Turbulence. Presented at the SPE Annual Fall Technical Conference and Exhibition, New Orleans, Louisiana, 3-6 October 1976. SPE-6133-MS. http://dx.doi.org/10.2118/6133-MS.
- Gallice, F. and Wiggins, M.L. 2004. A Comparison of Two-Phase Inflow Performance Relationships. SPE Prod & Oper 19 (2): 100-104. SPE-88445-PA. http://dx.doi.org/10.2118/88445-PA.
- Neely, A.B. 1967. Use of IPR Curves. Houston, Texas: Shell Oil Co.
- Brown, K.E. 1984. The Technology of Artificial Lift Methods, 4. Tulsa, Oklahoma: PennWell Publishing Co.
- Wiggins, M.L. 1994. Generalized Inflow Performance Relationships for Three-Phase Flow. SPE Res Eng 9 (3): 181-182. SPE-25458-PA. http://dx.doi.org/10.2118/25458-PA.
- Sukarno, P. 1986. Inflow Performance Relationship Curves in Two-Phase and Three-Phase Flow Conditions. PhD dissertation, University of Tulsa, Tulsa (1986).
- Standing, M.B. 1971. Concerning the Calculation of Inflow Performance of Wells Producing from Solution Gas Drive Reservoirs. J Pet Technol 23 (9): 1141-1142. SPE-3332-PA. http://dx.doi.org/10.2118/3332-PA.
- Uhri, D.C. and Blount, E.M. 1982. Pivot Point Method Quickly Predicts Well Performance. World Oil (May): 153–164.
- Kelkar, B.G. and Cox, R. 1985. Unified Relationship To Predict Future IPR Curves for Solution Gas-Drive Reservoirs. Presented at the SPE Annual Technical Conference and Exhibition, Las Vegas, Nevada, 22-26 September 1985. SPE-14239-MS. http://dx.doi.org/10.2118/14239-MS.
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