Cone Breakthrough Time for Horizontal Wells
- Paul Papatzacos (Rogaland U.) | T.R. Herring (Fina Exploration Norway) | Rune Martinsen (Enterprise Oil Norge Ltd.) | S.M. Skjaeveland (Rogaland U.)
- Document ID
- Society of Petroleum Engineers
- SPE Reservoir Engineering
- Publication Date
- August 1991
- Document Type
- Journal Paper
- 311 - 318
- 1991. Society of Petroleum Engineers
- 5.6.4 Drillstem/Well Testing, 2 Well Completion, 4.1.5 Processing Equipment, 4.3.4 Scale, 5.2.1 Phase Behavior and PVT Measurements, 5.3.1 Flow in Porous Media
- 3 in the last 30 days
- 1,362 since 2007
- Show more detail
- View rights & permissions
|SPE Member Price:||USD 5.00|
|SPE Non-Member Price:||USD 35.00|
Recovery from an oil zone underlying a gas cap, overlying an aquifer, orsandwiched between gas and water can be improved by repressing the coningproblem through horizontal-well drainage. Literature methods to predict coningbehavior are limited to steady-state flow conditions and predict coningbehavior are limited to steady-state flow conditions and determination of thecritical rate, The results in this paper are based on new semianalyticalsolutions for time development of a gas or water cone and of simultaneous gasand water cones in an anisotropic infinite reservoir with a horizontal wellplaced in the oil column. The solutions are derived by a moving-boundary methodwith gravity equilibrium assumed in the cones. For the gas-cone case. thesemianalytical results are present ed as a single dimensionless curve (time tobreakthrough vs. rate) and as a simple analytical expression for dimensionlessrates >1/3 For the simultaneous gas- and water-cone case, the results aregiven in two dimensionless sets of curves: one for the optimum vertical wellplacement and one for the corresponding time to breakthrough, both as functionsof rate with the density contrast as a parameter. The validity of the resultshas been extensively tested by a general numerical simulation model. Samplecalculations with reservoir data from the Troll field and comparison with testdata from the Helder field demonstrate how the theory can be used to estimatethe time to cone breakthrough and its sensitivity to the uncertainties inreservoir parameters.
Ekrann 1 showed that the critical rate for coning toward a horizontal orvertical well approaches zero as the distance to the outer open boundaryapproaches infinity. The practical use of critical rates com-puted fromsteady-state flow situations is therefore questionable. Ekrann suggested thatthe time to cone break-through is a more relevant parameter. In a review of thereservoir engineering methods for predicting parameter. In a review of thereservoir engineering methods for predicting horizontal-well behavior. Joshibriefly discussed gas and water coning characteristics and stated that noinformation is available for calculation of breakthrough time for water and gascones. Giger and Karcher et al. present formulas to calculate critical ratesfor coning toward horizontal present formulas to calculate critical rates forconing toward horizontal wells during steady-state flow conditions, Chaperonsolved the same problems with the Muskat method by neglecting the cone-shapeinfluence on problems with the Muskat method by neglecting the cone-shapeinfluence on the flow pattern. To the best of our knowledge, Ref. 7 through 9describe the only methods available for analytic prediction of cone evolutiontoward horizontal wells. This paper summarizes the main assumptions andtheoretical results of these methods to verify the solutions by detailedsimulations and to demonstrate the applicability through examples relevant tothe Troll and Helder fields.
Physical Model Description. Fig. 1 is a sketch of the vertical crossPhysical Model Description. Fig. 1 is a sketch of the vertical cross section.The horizontal well is located at the origin of the Cartesian coordinate system(x.y), with the original gas/oil contact (GOC) at D and the original water/oilcontact (WOC) at D. The coordinates (x ,y ) and denote points on the movingboundaries between gas and oil and water and oil, respectively. Initially, thetwo interfaces are horizontal planes. After production begins, theirtime-dependent deflection toward the well, indicated in Fig. 1, is calculatedfrom the semianalytical solution.
Gravity equilibrium is assumed in both gas and water phases. This assumptionis valid at low rates and implies that only the diffusivity equation for oilhas to be solved. Water- and gas-phase mobilities therefore do not take part inthe semianalytical solution, but their densities are incorporated through themoving-boundary conditions. (Another solution, based on the assumption ofconstant pressure at the moving boundary is briefly discussed under Single-ConeSolution.)
The well is a horizontal, infinitely long line sink, and the reservoir hasno fixed boundaries. The solution is therefore valid in the infinite-actingperiod, and because there is no pressure support, no critical rate is expected.The flux is uniform and constant along the well axis, and the reservoir ishomogeneous and anisotropic. Other assumptions are incompressible fluids, zerocapillary pressure, sharp fluid interfaces, and complete displacement with noresidual oil left by either displacing phase.
|File Size||610 KB||Number of Pages||8|