Summary
Most of the conventional horizontal-well transient-response models were developed during the 1980's. These models visualized horizontal wells as vertical wells rotated 90°. In the beginning of the 1990's, it was realized that horizontal wells deserve genuine models and concepts. Wellbore conductivity, nonuniform skin effect, selective completion, and multiple laterals are a few of the new concepts. Although well-established analysis procedures are yet to be developed, some contemporary horizontal-well models are now available. The contemporary models, however, are generally sophisticated. The basic objective of this paper is to answer two important questions:When should we use the contemporary models? andHow much error do we make by using the conventional models?
This objective is accomplished by considering examples and comparing the results of the contemporary and conventional approaches.
Introduction
Since the early 1980's, horizontal wells have been extremely popular in the oil industry and have gained an impeccable standing among the conventional well completions. The rapid increase in the applications of horizontal-well technology brought an impetuous development of the procedures to evaluate the performances of horizontal wells. These procedures, however, used the vertical-well concepts almost indiscriminately to analyze the horizontal-well transient-pressure responses.1–14 Among these concepts were 1) the assumptions of a line-source well and an infinite-conductivity wellbore, 2) a single lateral withdrawing fluids along its entire length, and 3) a skin region that is uniformly distributed along the well. It should be realized that for the lengths, production rates, and configurations of horizontal wells drilled in the 1980's, these concepts were usually justifiable. The increased lengths of horizontal wells, high production rates, sectional and multilateral completions, and the vast variety of other new applications toward the end of the 1980's made us question the validity of the horizontal-well models and the well-test concepts adopted from vertical wells. The interest in improved horizontal-well models also flourished on the grounds of high productivities of horizontal wells. It was realized that, in many cases, a few percent of the production rate of a reasonably long horizontal well could amount to the cumulative production rate of a few vertical wells. In addition, the productivity-reducing effects were additive; that is, a slight reduction in the productivity here and there could add up to a sizeable loss of the well's production capacity. Furthermore, the low oil prices also created an economic environment where the marginal gains and losses in the productivity may decisively affect the economics of many projects.
In the beginning of the 1990's, a new wave of developing horizontal-well solutions under more realistic conditions gained impetus.15–25 As a result, some contemporary models are available today for those who want to challenge the limitations of the conventional horizontal-well models. Unfortunately, the rigor is accomplished at the expense of complexity. Furthermore, even when a rigorous model is available, well-established analysis procedures are usually yet to be developed.
This paper presents a critique of the conventional and contemporary horizontal well-test-analysis procedures. The main objective of this assessment is to answer the two fundamental questions horizontal-well-test analysts are currently facing:When is the use of contemporary analysis methods essential? andIf the conventional analysis methods are used, what are the margins of error?
Background: The Conventional Methods
The standard models of horizontal-well-test analysis have been developed mostly during the 1980's.1-4,8,9 Despite the differences in the development of these models, the basic assumptions and the final solutions are similar. Fig. 1 is a sketch of the horizontal well-reservoir system considered in the pressure-transient-response models. A horizontal well of length Lh is assumed to be located in an infinite slab reservoir of thickness h. The elevation of the horizontal well from the bottom boundary of the formation (well eccentricity) is denoted by zw. The top and bottom reservoir boundaries are usually assumed to be impermeable, although some models consider constant-pressure boundaries.14,15
Before discussing the characteristic features of the conventional horizontal-well transient-pressure-response models, we must first define the dimensionless variables to be used in our discussion. We define the dimensionless pressure, time, and distance in the conventional manner except that we use the horizontal-well half-length, Lh/2, as the reference length in the system. These variables are defined, respectively, by the following expressions.Equation 1Equation 2Equation 3Equation 4
In Eqs. 1 through 3, k=the harmonic average of the principal permeabilities that are assumed to be in the directions of the coordinate axes (). We also define the dimensionless horizontal-well length, wellbore radius, and well eccentricity (distance from the bottom boundary of the formation) as follows.Equation 5Equation 6Equation 7
In Eq. 6, rw, eq=the equivalent radius of the horizontal well in an anisotropic reservoir.26
Mathematical description of a bounded oil reservoir with a horizontal well
