Abstract
A two-dimensional (2D) analytical model is presented for gas/oil gravity drainage in a homogeneous, dipping reservoir. The sensitivity of gas/oil gravity drainage to key variables such as injection rate, oil relative permeability, and permeability anisotropy can be determined quickly with this model. Example calculations show that miscible-like recovery efficiencies are possible with immiscible gas injection into high-permeability dipping reservoirs with light oil. A procedure based on the analytical model has been developed to simulate immiscible gas injection into highly stratified reservoirs accurately. This simulation procedure allows a great deal of geological detail to be incorporated into reservoir models, because it permits relatively coarse grids. Application of the simulation procedure to a reservoir containing many discontinuous shales reveals that the presence of shales may favorably affect the recovery efficiency of an immiscible gas-injection process.
Introduction
Gas injection increasingly is being applied as a secondary or tertiary recovery process. High-permeability, light-oil reservoirs with a reasonable reservoir dip are particularly suitable candidates for gas injection. In these reservoirs, a gravity-stable injection scheme is often possible, leading to high sweep efficiencies. If the injection process is carried out at sufficiently high pressure, process is carried out at sufficiently high pressure, favorable phase behavior between reservoir fluid and injection gas can contribute significantly to the recovery of oil. Miscibility, however, is by no means always necessary to obtain high displacement efficiencies. Even in the case of an entirely immiscible displacement, a high displacement efficiency is possible if gravity drainage is the dominant production mechanism. Laboratory experiments have shown that, the residual oil saturation after gas invasion, is virtually zero in highly permeable sandstone cores containing connate water. The ultimate recovery of an immiscible process is then close to 100%. Whether oil saturations process is then close to 100%. Whether oil saturations in the gas-invaded zone will approach the residual value within the lifetime of a particular reservoir depends on the rate of gravity drainage for this reservoir. This problem, which is the main subject of this paper, has been studied by both analytical means and numerical simulation. In the following, first a 2D analytical model is introduced for gas/oil gravity drainage in a homogeneous, dipping reservoir. The model combines aspects from both one-dimensional (1D) vertical Buckley-Leverett drainage theory and Dietz' segregated flow theory for dipping reservoirs. Assumptions underlying the model have been verified by 2D cross-sectional simulations. Second, a procedure based on the analytical gravity-drainage procedure based on the analytical gravity-drainage model has been developed to simulate immiscible secondary gas injection into a highly stratified reservoir accurately. This is illustrated with an example of gas injection into a reservoir containing discontinuous shale layers.
Analytical Model for Gravity Drainage
Description of the Model. In this section, an approximate analytical model is formulated for immiscible, gravity-stable gas/oil displacement in a homogeneous, dipping layer. Fig. 1 shows a schematic cross section of the draining reservoir with some relevant flow characteristics. In this model, oil is assumed to be produced from downdip wells near the oil/water contact at a rate that ensures a gravity-stable displacement, while gas is injected in updip wells near the crest to fill the voidage. This causes the gas/oil contact (GOC) to move downward gradually. Behind the GOC some oil will be left, the amount of which depends on the oil relative permeability and on the tilt and rate of descent of the GOC. The gas-invaded region will continue to produce oil by after-drainage; this oil will collect at the bottom of the reservoir in a thin oil layer, which flows to the producers with the along-dip component of gravity as driving force. To make the essentially 2D model amenable to analytical calculation, the following assumptions are introduced.The model has infinite gas mobility.The model has negligible gas/oil capillary pressure. pressure.The GOC moves at a constant velocity, v GOC, x, and at a constant tilt angle, given by Dietz' theory for gravity-stable segregated flow in dipping reservoirs (evaluated for infinite gas mobility) as.............(1)with u max, x being the maximum along-dip gravity drainage ratei.e., in the direction of bulk fluid flow. This rate is defined as..............(2)
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Development of minimum tie line length method for determination of minimum miscible pressure in gas injection process
