1. Introduction

Throughout their history, well test analyses for fractured wells have received many contributions. For practical purposes, let us name the most important ones for this chapter. A good place to start is by mentioning the work in [1], which described the pressure behavior for infinite-conductivity and uniform-flux fractured wells, so people started conducting interpretation tests on such wells by using type-curve matching. Later, [2] introduced the concept of finite-conductivity fractures and established the onset value of dimensionless conductivity as 300. Values lower than that are considered finite-conductivity values, and those above 300 are classified as infinite conductivity. In [2], a fine semi-analytical solution was introduced for describing the well-pressure behavior in hydraulically fractured wells. This solution was then applied in [3] to provide a well interpretation method using type-curve matching. Since then, other mathematical solutions have been presented for finite-conductivity fractures. Among them, the work in [4] using fractal theory is worth mentioning.

' The way of conducting well test interpretation was changed by the introduction of Tiab s direct synthesis (TDS) technique by [5]. This revolutionary and modern

technique focuses on the different flow regimes seen on the pressure derivative curve. Defined lines are drawn through each individual flow regime, and the intersection points found among them are read and used for reservoir characterization. Additionally, reading arbitrary points on the pressure and pressure derivative of each flow regime also serve for reservoir parameter determination. A great number of applications of the TDS technique are given in [6]. The second work [7], by the same author of [5], presented TDS technique for infinite-conductivity and uniformflux fractures in vertical wells. In [7], the elliptical or biradial flow regime was introduced and characterized. This elliptical flow is also seen in horizontal wells and was characterized in [8–10]. Because of the similarity between the mathematical models of hydraulic fractures and horizontal wells, this concept was applied by [11] to determine the average reservoir pressure in formations drained by horizontal wells using the TDS technique. The infinite-conductivity model in [7] also included the late-time pseudosteady-state period as well as some equations involved in the drainage area (conventional analysis for this case was included in [12]). This may be disadvantageous for inexperienced users of TDS technique when interpreting pressure tests without reaching reservoir boundaries because the equations involved the use of the unknown reservoir drainage area, although it can be still applied by using the intersection points. To overcome this drawback, [13] presented a new mathematical model excluding the late-time pseudosteady-state period.

TDS technique for finite-conductivity fractured wells is given in [14], with practical field applications to demonstrate the usefulness of the technique. The fracture parameters can be readily obtained by using an arbitrary point on the flow regimes. TDS technique plays an important role when analyzing short pressure tests because a user can "make up" nonexisting flow regimes since, for instance, the radial flow horizontal line can be obtained from the reservoir permeability even though radial flow regime is absent. [15, 16] extended the works of finite- and infinite-conductivity fractures in naturally fractured reservoirs. The equations provided by these works can also be applied to either homogeneous or naturally fractured formations since they involve a dummy variable that takes the value of one for the homogeneous case or the value of the dimensionless storativity coefficient for the case of a naturally fractured formation.

TDS technique has also been extended to several scenarios related to hydraulically fractured wells. For instance, when a finite-conductivity fracture intersects with a fault, the pressure trace changes; then, the equations developed in [17] apply for this case. There are cases where a threshold pressure is required to start the flow. The work in [18] includes this concept in uniform-fractured vertical wells, and the work in [19] includes the concept for horizontal wells. Also, when the fractured face is damaged, a pseudolinear flow regime develops along the fracture. [1] included TDS technique to characterize such systems. [16] presented TDS technique for fractured wells in gas composite reservoirs. TDS technique can also be usefully applied to transient-rate analysis, as seen in [20]. Application of TDS technique to horizontally isolated fractured wells was presented and characterized in [21] and in conventional analysis in [22]. The works in [23, 24] use TDS technique for shale reservoirs. Other applications of TDS technique to these systems are given by [25] under transient-rate analysis and [26] for pressure-transient analysis conditions. Other important applications of TDS Technique to fractured wells are given by [29, 30].

This chapter is devoted to the application of TDS technique to hydraulically fractured wells in either homogeneous or naturally fractured formations. Without given detailed derivations, the expressions for characterizing the hydraulic fracture parameters are presented along with the way they should be used. Important relationships and practical exercises are included.

Well Test Analysis for Hydraulically-Fractured Wells DOI: http://dx.doi.org/10.5772/intechopen.80996
