Laboratory Models of Oil Reservoirs Produced By Natural Water Drive
Authors: Caudle B.H. , Silberberg I.H. 
Published: December 2007

Abstract
Reservoir depletion by natural water drive is typified by the movement of water from an aquifer into the adjacent oil-bearing formation. Prior studies of this type of water movement have generally neglected the resistance to flow in the aquifer and its effect on the movement of water into the oil bearing zone. A method for designing and operating scaled models of such reservoir systems is presented, Experimental data on a model of an edge-water-drive reservoir are shown and discussed.
Introduction
Most petroleum reservoirs derive at least a part of their productive capacity from water influx. This water may be injected from the surface or it may come from an aquifer adjacent to the oil zone. In either case, the reservoir engineer must be able to estimate the advance of the water as a function of either the elapsed time or the fluid produced. This paper describes a type of fluid flow model which includes the effect of viscous and gravitational forces in the reservoir and the surrounding aquifer. Natural water influx can be divided into three general (but widely overlapping) categories according to the direction of flow in the aquifer. These are shown schematically in Fig. 1. Fig. 1 (a) illustrates an edge-water-drive mechanism. In this case, water advances updip along the stratum but the movement of water is essentially horizontal and very little of the oil is actually underlain by water. The bottom-water drive (Fig. l (b)) is characterized by a thick aquifer underlying the oil zone. The water movement is generally vertical in the aquifer. The third category is illustrated in 1 (c). Referred to as the "thin oil column", this type of oil accumulation consists of oil over water in a relatively thin stratum. Fluid movement is horizontal in both the oil and water zones, except close to the producing well. One characteristic which all three of these types have in common is that part of the water flow takes place in the water invaded region of the oil reservoir while the remainder of the water flow occurs in the aquifer. The resistance to the flow of water usually will not be the same in these two regions. This occurs because the porous rock normally contains only water in the aquifer, while the water-invaded region always contains microscopic globules of bypassed oil (residual oil) which interfere with the flow of water through the rock. The production history of any type of a water-drive system is a function of two phenomena where the water goes, and how it displaces the oil in the area invaded by the water. It is usually impractical to study these two phenomena at the same time. In most cases one type of analysis is used to predict the gross movement of water in the reservoir, while a different type of analysis is employed to determine the amount of oil to be recovered from the gross volume contacted by the water. The portion of the oil reservoir which is invaded by water is mainly a function of the resistances to fluid flow in the several parts of the flow system. This gross water influx in the three types of natural water drive typically results in water cusping to the production wells either from the side or from below (water coning).In 1947, Muskat described a greatly simplified mathematical model for predicting the area invaded by water in a bottom-water-drive reservoir. This model used the Laplace equation and suitable boundary conditions to describe the isopotentials and streamlines in the flow system. The use of this model assumes that
the reservoir rock is homogeneous in nature, the oil and water mobilities are equal, there is no oil flowing in the water invaded region, and external forces - such as gravity - do not affect the flow.
This method has been used for both natural water drives and water injection projects. In this, as in most models, the method of images is used to reduce the size of the model necessary to describe the reservoir.
SPEJ
P. 25ˆ