Summary Simplified analytical relations derived for homogeneous formations are usually applied to the determination of the productivity of horizontal wells, regardless of the presence of heterogeneities in the reservoir. Furthermore, complex well architectures and the wealth of completion options currently available cannot be taken into account properly because the well trajectory can only be schematized as a single horizontal wellbore. However, the use of numerical reservoir simulators to reliably forecast the productivity of horizontal wells draining heterogeneous reservoirs may be time-prohibitive or not feasible because of a lack of sufficiently detailed information, especially during the appraisal phase or the early stages of production. A new semianalytic technique is proposed in this paper to solve the inflow equations in an approximate yet reliable manner. A solution to 3D problems of single-phase flow into a horizontal well, taking into account friction in the wellbore, is provided for both single-layer reservoirs and reservoirs comprising two interfering layers. The method also has been extended to describe the fluid flow when the well intercepts one or more fractures. The presented technique allows very fast calculation of the well productivity in oil and gas reservoirs, offering great flexibility in the placement and architecture of the wells. The method has been applied to two field cases for which the well productivity under pseudosteady-state conditions was measured. One of these is a 200-m-long horizontal well draining an isotropic carbonatic reservoir and intersected by a natural low-conductivity fracture. The other is a similar well, intercepting a natural high-conductivity fault, but the oil-bearing formation is anisotropic. Good correspondence was found between the actual productivity and the predictions obtained by application of the proposed semianalytic technique. Introduction Horizontal wells are common practice in the present hydrocarbon industry, and smart wells (including multilateral completions and wells with selective access of different zones) are becoming increasingly commonplace. The modeling of such wells is, in many cases, not ideal. Areas in which improvements are welcome are well testing, well models in reservoir simulators, and fast models for quick assessment of many field-development options. Further, the handling of natural or hydraulic fractures is often suboptimal. In reservoir simulation, fine grids need to be selected to properly capture the flow behavior close to the well. Moreover, most reservoir simulators are not equipped with extensive well models, which are required when friction in the well becomes important or when two-phase flow develops in the well. This situation has prompted the development of a number of analytical and semianalytical tools, some of which are intended for implementation in a reservoir simulator. Most of the first models, as well as many of the more recent models, assume either constant influx density along the well or infinite well conductivity in a single homogeneous layer. Dikken introduced the effect of well conductivity for a single horizontal well in a homogeneous formation. He started with the assumption that the flow is mainly perpendicular to the wellbore, which allowed him to reduce the reservoir to a 2D flow domain, coupled to a friction model in the well. Others followed this approach, but 3Dmodels were developed as well. A second kind of extension are the multilayer models. Lee and Milliken and Kuchuk and Habashy used a method of reflection and transmission, while Basquet et al. used a "quadrupole" method relating the pressures between the various layers. The multilayer models are also, however, still limited to constant-influx or infinite-conductivity wells.

Summary Gas reservoirs are generally subject to non-Darcy effects, especially in the near-wellbore zone. In fact, the assumption of Darcy-flow regime is no longer valid because of inertial phenomena and/or turbulence. These could significantly reduce the peak performance of a gas well. Therefore, characterization and monitoring of the non-Darcy effects is key for defining an optimal reservoir-exploitation strategy. This is particularly true in the case of storage fields, where withdrawal- and injection-gas rates are typically very high (hundreds of thousands of m3/d) and determining and monitoring well performance is key to ensuring that deliverability meets demand and/or contract obligations. Pulse testing, which is dependent on a periodic variation of produced/injected rate, is an effective methodology to test a well during ongoing field operations without stopping production. Although pulse testing is very promising for monitoring well performance, it has never been exploited for this purpose. In this paper, the development of a method for pulse testing high-performing gas wells is presented and discussed. The pressure response to the imposed rates is analyzed in the frequency domain to evaluate reservoir and well properties. An analytical solution in the frequency domain taking into account wellbore-storage effects was derived. The method was applied to test a real gas well of a storage reservoir under two different pressure conditions to assess the effect of turbulence on deliverability. Although the pulse-testing technique might not replace traditional well testing for determining reservoir properties, it can be successfully applied to monitor well performance as a function of reservoir pressure.

Summary We present a semianalytic method for modeling the productivity testing of vertical, horizontal, slanted, or multilateral wells. The method is applicable to both oil and gas reservoirs and automatically accounts for well interference. The use of analytic expressions ensures that short-time transient behavior and long-time semisteady-state behavior are handled appropriately, whether close to the well or further into the reservoir. Calculation times are still very limited—on the order of a few minutes to a few seconds when all wells are vertical. This makes the tool suitable for evaluating well testing and determining well productivity. We based the approach on an earlier derived productivity prediction tool, in which the steady-state equations were solved. It has now been extended to solve the time-dependent diffusion equation. In our current method, the equations have first been transformed using the Laplace transformation. The expressions for the producing wells are combined with auxiliary sources outside the reservoir. The crux of the semianalytic method involves an adjustment of the positions and strengths of these sources in order to approximate the boundary conditions at the reservoir boundaries. The solution obtained is transformed back into the time domain by use of a Stehfest algorithm. The new approach has been validated with numeric tools, including both reservoir simulators and well-test interpretation software. Validations were performed with artificial cases and with field production data, using both single-well and multiple-well production tests. The results of these tests were excellent.

For decades, well tests have been widely used in the oil industry for evaluation of well productivity and reservoir properties, which provide key information for field development and facilities design. In conventional well tests equilibrium conditions are required in the reservoir before the test. Furthermore, a single well only can be produced at a time, inducing one or more pressure draw-down periods followed by a final pressure build-up which are the object of the interpretation. Harmonic testing has been developed as a form of well testing that can be applied during ongoing production or injection operations, as a pulsed signal is superimposed on the background pressure trend. Thus no interruption of well and reservoir production is needed before and during the test. If the pulsed pressure and rate signal analysis is performed in the frequency domain, a strong similarity exists between the derivative of the harmonic response function versus the harmonic period and the pressure derivative versus time, typical of conventional well testing. Thus the interpretation of harmonic well tests becomes very straightforward. In this paper, we present the derivation of type curves for the most commonly encountered well and reservoir scenarios and we validate the type-curves developed for horizontal wells against real data of a harmonic test performed on a gas storage well in Italy.

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