Prediction of Capillary Fluid Interfaces During Gas or Water Coning in Vertical Wells
- Russell T. Johns (U. of Texas at Austin) | Larry W. Lake (U. of Texas at Austin) | Rafay Z. Ansari (U. of Texas at Austin) | Arnaud M. Delliste (U. of Texas at Austin)
- Document ID
- Society of Petroleum Engineers
- SPE Journal
- Publication Date
- December 2005
- Document Type
- Journal Paper
- 440 - 448
- 2005. Society of Petroleum Engineers
- 5.3.1 Flow in Porous Media, 5.6.4 Drillstem/Well Testing, 5.4.2 Gas Injection Methods, 4.1.2 Separation and Treating, 4.3.4 Scale, 5.6.9 Production Forecasting, 4.1.5 Processing Equipment, 2.2.2 Perforating, 5.1.1 Exploration, Development, Structural Geology, 5.3.2 Multiphase Flow
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Gas and water coning significantly reduce oil production, while increasingproduction costs. Simulation and experimental methods, coupled with simpleanalytical solutions or correlations, are typically used to identify the oilrate that minimizes coning and maximizes recovery. Current analyticalsolutions, however, are overly simplified in that they assume negligiblecapillary pressure, which leads to segregated flow. This paper presents newbenchmark analytical solutions that relax this assumption and also allow forsimultaneous two-phase flow.
The new coning solutions apply to vertical wells where in-situ fluids are invertical equilibrium. The development identifies the important dimensionlessgroups that control the effect of coning on oil recovery and illustrates howsimultaneous two-phase flow affects capillary fluid levels in the formation.Dimensionless two-phase production windows are constructed to identify criticalrates, the largest oil rate at which water (or gas) will not beproduced.From comparisons to simulation, we show that critical flow rateestimates are accurate for aspect ratios greater than approximately10.For aspect ratios less than 10, the critical rate estimates are alwaysconservative.
Water and gas coning are serious problems in oil production. A large oilrate may cause a second fluid to be produced through upward coning of water ordownward coning of gas into the well perforations. Once the second fluid isproduced, the oil rate is significantly reduced and the cost of water and gashandling is increased.
It is a common industry practice to reduce water coning in oil reservoirs byperforating vertical wells as far above the oil/water contact (OWC) as possibleand to produce the wells at or below the critical oil rate. Similarly, wellsare often perforated low in the oil column away from the gas/oil contact (GOC)in gas/oil reservoirs. The benefits of this practice are mixed in that limitedperforations may increase the pressure gradient (the drawdown) near the well,which can exacerbate coning.
There has also been success in reducing coning with polymers and gels.1 Amore recent and novel approach is to use downhole water-sink technology (DWS)where water is produced separately from the oil using dual packers.2 The waterproduction below the OWC may reduce upward water coning so that the oil ratecan be increased. The DWS technology, however, requires a good understanding ofhow fluid rates affect coning.
Dupuit3 published one of the first papers on the down coning of air intoaquifers. The Dupuit equation, which assumes vertical equilibrium, gives thesteady-state relationship between the water production rate and water tableelevation in the vicinity of a wellbore. The flowing water is segregated fromthe static air phase because capillary pressure is assumed to be negligible.The Dupuit equation is still used today to determine the elevation of the watertable when water is produced to a pumping well.4,5
Muskat and Wyckoff,6 who coined the term "water-coning," derived anapproximate steady-state solution for 2D water coning in an oil reservoir. Thewater is assumed to be stationary at steady-state oil flow so that waterproduction is not allowed. Pirson7 extended the Dupuit approach to single-phaseflow of oil in a gas/oil/water reservoir.All of the more recent methodshave assumed segregated flow or have used numerical simulation.8-12Relaxing the assumption of segregated flow in an analytical model is a goal ofthis work.
The research reported in this paper derives new solutions of "Dupuit form"that allow for both single- and simultaneous two-phase flow that include theeffect of capillary pressure and relative permeability on fluid interfaces. Thefirst section presents the mathematical model, the assumptions used, and thederivation of the general integral equation. The next sections presentsolutions of this equation for both single-phase flow and for simultaneoustwo-phase production of gas or water. We then discuss and illustrate theeffects of flow rates and scaling groups, such as the Bond number, on the fluidinterfaces. Last, we compare the analytical results to numerical simulation todetermine when the analytical solutions are most valid.The new exactsolutions are useful because they (a) provide benchmark solutions forvalidation of numerical simulation, (b) are significantly faster to estimatecritical flow rates than with numerical simulation, (c) identify importantscaling groups, and (d) aid in the development of DWS completiontechnology.1
|File Size||699 KB||Number of Pages||9|
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