The Application of Curvilinear Coordinate Systems To Predict the Behavior of Pattern Waterfloods in the Lekhwair Oil Field, Oman
Authors: Cottrell Charles W. 
Published: December 2007

Summary
Curvilinear coordinate systems in five-, seven-, and nine-spot symmetry element models have been used to achieve a more realistic representation of reservoir flow behavior. The grid pattern is chosen to approximate the streamtubes. and near each well this can be made the same as for history-matched single-well radial models. Consequently, the parameters obtained in a history match of a single well can be used directly in the curvilinear system, thereby obviating the need to adapt them for use in a cartesian one. In this way individual well behavior, including cusping and coning effects, can be realistically modeled.
Comparison runs have been made for a single-layer inverted nine-spot model with a favorable mobility ratio using two curvilinear and two cartesian grid patterns. Significant differences in the well performances are obtained, with the catiesian models yielding more optimistic results.
Satisfactory history matches of production performance were obtained for a typical drainage point in the Kharaib reservoir of the Lekhwair field using a multilayer single-well radial model. The parameters obtained were applied directly in curvilinear areal grid configurations of five-, seven-, and nine-spot symmetry elements to obtain predictions of waterflood behavior.
Since the mobility ratio (M= 0.7) of the system is favorable, high recoveries are obtained for all the pattern flood models-namely, + 56% of stock-tank oil initially in place (STOIIP) in the Kharaib. The equivalent result for natural depletion is 10%.

Introduction
The Lekhwair field in Oman comprises two chalky limestone reservoirs-the Lower Shuaiba and, below it, the Kharaib. They are separated by a 20- to 25- (6- to 8-m) layer of tight argillaceous limestone that appears to act as an effective seal. The structure consists of two adjacent, almost circular, anticliness both with a diameter of about 6 miles (10 km). The structures are of low relief, with only 275 ft (84 m) between the crest and the oil/water contact (OWC) in the main structure and 140 ft (43 m) in the subsidiary structure. Only the main structure, which contains about 750 million STB (120 × 10(6) stock-tank m3) OIIP, has been considered in this study. The subsidiary structure [300 MMbbl (50 × 10(6) m3)}] has similar, though somewhat poorer, reservoir characteristics and contains significant oil volumes only in the Lower Shuaiba reservoir.
The field was brought on stream in 1976, and after production of 3% of STOIIP, the producing GOR had increased from a solution value of 500 scf/bbl (90 std m3/m3) to more than 1,500 scf/bbl (270 std m3/m3), while reservoir pressure had declined 150 to 200 psi (1 to 1.4 MPa) below the initial value of 2,000 psia (14 MPa) at 3,750 ft (1143 m) subsea. Both Lower Shuaiba and Kharaib reservoirs are characterized by low permeability (less than 10 md): therefore, natural pressure support was not expected. PVT data originally indicated the oil to be undersaturated, with bubblepoints about 300 to 400 psi (2.1 to 2.8 MPa) below reservoir pressure: however, a recent sample taken under more stringent sampling conditions indicates a bubblepoint at current reservoir pressure. Therefore it is considered likely that the reservoirs contained oil with bubblepoints at, or close to, initial reservoir pressures.
Continued production by natural depletion is unlikely to yield high recoveries in these tight low-relief reservoirs. Pattern waterflooding as a means of secondary recovery, however, holds considerable promise.
JPT
P. 1385^