Abstract

This paper examines the effect of horizontal wellbore hydraulics and flow direction in the recovery from idealized heterogeneous reservoirs subject to bottom-water drive. It is shown that wellbore hydraulics significantly influence the inflow along the wellbore. However, the total rate of the well is not affected by wellbore hydraulics. It is also shown that the heterogeneities give rise to different wellbore pressure drops for different flow directions.

A novel multi-level technique where the coarse-grid. fine-grid and wellbore equations are solved separately was developed. Preliminary test runs with this technique show substantial reductions in CPU time when compared to the standard technique.

Introduction

The inclusion of wellbore hydraulics in reservoir simulation with horizontal wells has received much interest recently [1,2]. It was shown in [I] that wellbore hydraulics can have a significant effect on the inflow (flow into the well) along the wellbore. Although the prediction of the production from a horizontal well may be very similar with or without wellbore hydraulics. the inclusion of wellbore hydraulics yields a substantially different drainage pattern along the wellbore. To increase the resolution of the flow around the wellbore a hybrid grid system which consists of local elliptical refinement of the coarse Canesian grid was used. The studies in [I] were restricted to homogeneous reservoirs.

This paper examines the effect of wellbore hydraulics and wellbore flow directions in the prediction of recovery from heterogeneous reservoirs. The reservoirs under study contain zones with permeability contrasts and shale streaks.

This paper also describes a novel solution technique for converging the systems of coarse-grid equations, fine-grid equations and wellbore flow equations. In [I], all these equations were converged simultaneously using Newton's method. In this paper, a multi-level technique is described which allows the separate solution of the different systems of equations. Thus, the coarse grid equations, the fine grid equations and the wellbore equations were solved separately. Attempts have been made to solve separately the coarse and fine grid equations [3,4], but have not been very successful. The method described here is more comprehensive than those in [2] and [3] because the wellbore is also included in the calculations. The key to the success of this multi-level technique is the transfer of information between the different systems through judicious specifications of boundary conditions. The advantages of this technique are highlighted.

PROBLEM DESCRIPTION

The examples were derived from one of the cases in [11. Heterogeneities were represented by permeability contrasts and shale streaks. The reservoir is discretized into a 9x9x6 grid system shown in Figures 1 and Table I. Initial pressure and saturations are also given in Table 1. Data on fluid properties, relative permeabilities and capillary pressures are from the Seventh SPE Comparative Solution Project [2]. Fluids were produced at a constant liquid rate of 1431 std m3/day (9000 STB/day) from a horizontal well drilled in the top layer (Layer 1). The well passes through the gridblock centres and the entire length is open to flow.

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