The Choice Of Pattern Size And Shape For Regular Arrays Of Horizontal Wells
Authors: Suprunowicz R. , Butler R.M. 
Published: March 2010

Abstract
This paper is concerned with the choice of horizontal well patterns for draining oil reservoirs.
Horizontal wells, because they tend naturally to drain oval rather than circular areas, should be placed within elongated drainage patterns. Suitable shapes are rectangles (i.e. elongated squares) or elongated hexagons.
Quantitative means for defining the shape of the optimum pattern (e.g. the ratio of the length to the breadth of a rectangular pattern) are developed in this paper. The effect of varying the shape of the pattern is also discussed.
These methods allow the definition of a pattern (i.e. area and shape) of horizontal wells of a chosen length which will result in the same reservoir drainage, over-aIl, as would be obtained with conventional wells with a known spacing.
This paper also contains some examples of accurate diagrams which show the pressure distribution around horizontal wells for pseudo-steady-state flow within reservoir patterns of different aspect ratios and sizes.

Introduction
In recent years, the interest in using horizontal wells for oil production has increased steadily due to their successful field application, The relevant literature reports theoretical developments as well as practical information regarding drilling techniques, completion and testing of wells in particular oilfields. Some summarizing data can be found, for example, in References 1 to 4 and others.
For some purposes, a horizontal well can be treated as an infinite line sink. Examples of such an approach can be found in the literature(5,6).
In reality, however, each horizontal well has its finite length. From the point-of-view of drilling technique, there exist certain limitations of a well length(7). The maximum horizontal well length depends upon drag, torque, hole size, rate of build and pipe stresses, and all of these factors are interrelated.
Other authors have developed methods of predicting the productivity of finite horizontal wells, as, for example Joshi, and Karcher et al. Usually, the well is looked upon as a vertical fracture of a finite height equal to the well diameter(8). In some cases, uniform flow per well unit length has been assumed(10,11). It will be shown later in this paper that this assumption does not seem to be realistic.
In other sources(2,l0,12), the authors assume two distinctly different time periods in horizontal well operation: early time with a circular radial flow in a vertical plane perpendicular to the well, and a late time, with the horizontal pseudo-radial flow. However, as stared in Karcher et al. the first period is very short and may be considered negligible in comparison with the well life. Moreover, the assumption of a radial (or pseudo-radial) flow toward the line sink in the second period, may be an adequate approximation for an unconfined finite horizontal well. But, if the well drains a confined area, the equipressure lines can no longer be treated as ellipses or circles and their shape becomes more complex. This will be shown later in this paper.
In Babu et al., the authors develop the solution of a three dimensional problem described by the diffusivity equation.