Summary

The objective of this paper is to investigate the transient pressure behavior of dual lateral wells. An analytical solution to compute the pressure responses of dual lateral wells in Laplace domain is presented and the computational issues are addressed. The influences of the length, phase angle, and the vertical separation of the laterals on the characteristics of pressure responses are discussed. New flow regimes are identified and the conditions under which various flow regimes prevail are documented. Guidelines for the well test analysis of duallateral well responses are also presented.

Introduction

Productivity improvements expected from horizontal wells are usually proportional to the length of the well. As the well length increases, however, drilling and well control will become exceedingly difficult. In addition, transportation of a large volume of fluid along a long horizontal borehole results in considerable pressure losses in the wellbore that translates into productivity losses. Dual lateral wells are expected to provide an excellent alternative to drilling long single horizontal wells. Furthermore, duallaterals have better horizontal coverage than horizontal wells.

Prediction of production performance of multilateral wells has been discussed in the literature. Some case studies on the evaluation of multilateral well performance have also been presented. A detailed discussion of dual lateral well transient pressure responses, however, has not been presented.

Dual lateral wells exhibit complicated flow characteristics and these are reflected by the changes in their transient pressure responses. In many cases, responses of duallateral horizontal wells are analyzed by using an equivalent single horizontal well. This approach can be valid for certain phase angles and anisotropy ratios but may lead to significant errors in estimation of formation characteristics for many multilateral well configurations. In this study, we present a detailed analytical model to investigate the transient pressure responses of duallateral wells. This model considers:

  1. unequal lateral lengths,

  2. arbitrary phase angle,

  3. vertical separation,

  4. horizontal displacement,

  5. unequal skin effect, and

  6. three-dimensional anisotropy.

The formation is assumed to be infinite in the horizontal directions and bounded by impermeable layers at the top and bottom. The analytical solution to compute the pressure drop at any point in the reservoir is presented in the Laplace domain so that it can be easily used for variable rate problems. Computation of infinite-conductivity well responses is discussed. Asymptotic expressions to describe the early-, intermediate-, and late-time pressure behaviors are also provided.

Definitions and Analytical Solution

To derive analytical solutions for the transient pressure behavior of dual lateral wells, we first obtain a general expression for a single horizontal well that makes an arbitrary angle with the positive x-direction and then use the method of superposition in space to generate the solution for dual lateral wells. The details of the solutions for the pressure drop due to production from a single horizontal well and dual lateral wells are given in Appendix A. Here we define the coordinate system used in the solution, present the definitions of the dimensionless variables, and summarize the analytical solution.

Definitions. Consider a horizontal well with a length Lh in an anisotropic medium tilted by an arbitrary angle w measured counterclockwise from the positive x-direction as shown in Fig. 1. The origin of the coordinate system the intersection point of the axis of the vertical section of the well with the bottom boundary of the formation (see Fig. 2).

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