Summary Horizontal wells have emerged as a new means for well productivity enhancement. Simultaneously, they have brought forward the need to recognize and account for permeability anisotropies, including vertical-to-horizontal and horizontal-to-horizontal directions. In addition, there is the possibility of multiple horizontal drainholes emanating from the same vertical well. Performance relationships for the most interesting well configurations are presented including both early-time and late-time differences rather than only bounded flow regimes. Solutions for arbitrarily oriented single or multiple horizontal wells are introduced along with a discussion of well known existing relationships. Introduction It is a foregone conclusion that horizontal wells will capture an ever increasing share of all petroleum wells drilled. The performance of these wells depends greatly on appropriate reservoir selection, substantial predrilling formation evaluation and optimized completion and stimulation practices. There have been several attempts to describe and estimate horizontal well productivity and for injectivity indexes and several models have been employed for this purpose. Following the tradition of vertical well productivity models, analogous well and reservoir geometries have been considered. A widely used approximation for the well drainage is, conveniently, a parallelepiped model with no-flow or constant-pressure boundaries at the top or bottom and either no flow or infinite-acting boundaries at the sides. One of the earliest models was introduced first by Borisov (1964) assuming a constant pressure drainage ellipse whose dimensions depend on the well length. This configuration evolved into a widely used equation presented by Joshi (1988) accounting for vertical-to-horizontal permeability anisotropy and, adjusted by Economides et al. (1991) for a wellbore in elliptical coordinates. This model, while useful for first approximations and comparisons with vertical well productivity indexes, does not account for either early-time or late-time phenomena nor, more importantly, realistic well and reservoir configurations. Babu and Odeh (1989) used an expression for the pressure drop at any point by integrating appropriate point source (Green's) functions in space and time. Their solutions for various no-flow boundary positions include infinite-sum expressions, accounting for individual pseudosteady-state pressure drops. These forms are rather complicated and cumbersome to calculate. Using vertical well analogs, Babu and Odeh (1989) grouped their solutions into reservoir/well configuration shape factors and a (horizontal) partial penetration skin effect.

This paper presents conceptual and mathematical descriptions of the damage along and normal to a horizontal well. Expressions for the skin effect that take permeability anisotropy into account are developed. Stimulation methodology, respecting the shape of damage, is presented. Treatment effectiveness, partial stimulation, and corresponding volume and time requirements are quantified.

Summary This paper describes a model where wormholes, the primary feature of carbonate acidizing, are considered as fractals. The influences of acid volume, injection rate, fractal dimension, porosity, and the ratio of undamaged to damaged permeabilities on well performance are studied. Exact expressions of post-treatment skin effects are developed for vertical and horizontal wells. Introduction In the recent past, the industry viewed many studies describing the physics of matrix acidizing and its impact on treatment design and post-treatment well performance as simply interesting. The economics of matrix stimulation of common reservoir thicknesses (<100 ft) in vertical wells precluded wide application of these findings. However, the emergence of horizontal wells, penetrating formations with lengths up to 8,000 ft and more, and the need for massive volumes of stimulation fluids necessitated re-examination and extension of the understanding of the physics of these proc esses. This is especially true if treatment optimization is to be undertaken. Matrix stimulation and the stimulation method vary significantly among common reservoir lithologies. In matrix acidizing of sandstones, the stimulation fluids primarily attack the particles plugging the pore spaces; thus, the treatment may result in a stimulated "collar" around the well if insufficient acid is injected to remove all damage. In this paper, we deal with stimulation of carbonate formations, where treatment relies on reaction kinetics and where new flow paths, or wormholes, are created. The dendritic wormhole patterns have been identified to be fractals. Their shape and extent and the resulting post-treatment skin effect can be quantified with the model presented in this paper.

Summary This paper presents an optimization method for the matrix stimulation of horizontal wells that may include the deliberate blanking of well segments. The lengths of these segments are balanced against the stimulation fluid volumetric coverage of the perforated segments. The stimulation and completion design is optimized through the use of the net present value (NPV) as an economic criterion. Introduction Early in the development of horizontal well technology, discussion focused on the selection of appropriate reservoir candidates. With the evolution of a number of production prediction models, and after several field experiences, the issue of reservoir selection should be considered largely resolved. In general, horizontal wells are attractive in naturally fissured reservoirs, relatively thin formations with good vertical permeability, and reservoirs with drawdown-related problems, such as gas and water coning or sand production. In addition to such reasons as not drilling the well perpendicular to the maximum horizontal permeability in highly anisotropic formations, several authors reported that the skin effect, caused by formation damage, may have been responsible for horizontal well failures. This possibility can be shown by a simple calculation.

Drilling multiple-lateral wells and employing intelligent completion systems would very likely lead to considerably higher productivity and increased recovery at relatively low incremental costs. Completing such a well system is a challenge and today it is still considered an extravagant effort. An important reason is that the performance of wells with multiple-lateral completions has not yet been investigated fully. There are several potential configurations for multiple-lateral wells, including planar, multi-planar, branches etc. The reservoir geometry and especially the areal and vertical-to-horizontal permeability anisotropies are critical. Using a versatile simulation model, the calculation of the multiple-lateral well performance is presented. Based on example calculations, optimum spacing, length and number of sidetracks are identified for various reservoir conditions. Shape factors for a number of well configurations are presented. Introduction Multiple-lateral well systems have become a compelling recent topic in the petroleum industry. The reason is that these wells can provide several interesting, and previously inaccessible, opportunities to drain a reservoir efficiently. The idea of spanning a bundle of drainholes out of a single hole and connecting these drainholes with the surface is an appealing possibility. Similarly, drilling one or more horizontal sidetracks from an existing vertical wellbore is a means to enhance the production of the well. Although costly to drill and fraught with operational challenges, these wells may provide better economics than stimulating a specific horizontal well or drilling new wells. Obviously, any decision to drill (multi-) laterals should be based on careful evaluation of the expected well system performance, operational and economic risks, possible production scenarios and, very importantly, (selective) wellbore management and maintenance of the individual drainholes. The technology to drill lateral well branches (often short radius and often using coiled tubing) is available today. However, selection of the right candidates and production and completion technologies is critical. Thus, several new developments and improvements of existing concepts can be expected in this area. This paper highlights reservoir engineering and production aspects of multiple- lateral well systems. Uncomplicated methods for calculating inflow performance of various well configurations are presented and important production engineering concepts are discussed. Classification of Multiple-Lateral Well Systems Multiple-lateral systems are wells with more than one lateral leg branching into the formation(s). This general definition gives rise to several configurations listed below and pictured in Fig. 1:–Multi-branched wells (Fig. 1a)–Fork wells (Fig. 1b)–Several laterals branching into one horizontal "mother hole" (Fig. 1c)–Several laterals branching into one vertical mother hole (Fig. 1d)–Dual opposing laterals (Fig. 1e)–Stacked laterals (Fig. 1f) Selection of the most beneficial well system for a given reservoir is the challenge. The available systems can be and have been classified according to drilling (curvature, workover vs. coiled tubing rig, conventional vs. slimhole), completion (cased and perforated or slotted liner vs. open hole), production, and reservoir engineering aspects. This paper will be limited to the reservoir and production engineering aspects. P. 609