This paper presents screening criteria for vertical and horizontal wells with or without induced fractures. The parametric basis of such screening makes the decision on either type of well more objective. A simple procedure to calculate the optimum number of orthogonal transverse fractures in horizontal wells and their sizes is also presented. Two important comparisons have not appeared in the literature: (1) the performance of a fully completed horizontal well with that of a hydraulically fractured well and (2) the performance of a hydraulically fractured horizontal well with that of a hydraulically fractured vertical well. In addition, previous work does not take into account the effect of the plumbing system on well performance. This paper is intended to fill these gaps.
Keywords: sequestration carbon dioxide greenhouse gas management injectivity deep saline aquifers closed system injection The capture and subsequent geologic sequestration of CO 2 has been central to plans for managing CO 2 produced by the combustion of fossil fuels. The magnitude of the task is overwhelming in both physical needs and cost, and it entails several components including capture, gathering and injection. The rate of injection per well and the cumulative volume of injection in a particular geologic formation are critical elements of the process. Published reports on the potential for sequestration fail to address the necessity of storing CO 2 in a closed system. Our calculations suggest that the volume of liquid or supercritical CO 2 to be disposed cannot exceed more than about 1% of pore space. This will require from 5 to 20 times more underground reservoir volume than has been envisioned by many, and it renders geologic sequestration of CO 2 a profoundly non-feasible option for the management of CO 2 emissions. Material balance modeling shows that CO 2 injection in the liquid stage (larger mass) obeys an analog of the single phase, liquid material balance, long-established in the petroleum industry for forecasting undersaturated oil recovery. The total volume that can be stored is a function of the initial reservoir pressure, the fracturing pressure of the formation or an adjoining layer, and CO 2 and water compressibility and mobility values. Further, published injection rates, based on displacement mechanisms assuming open aquifer conditions are totally erroneous because they fail to reconcile the fundamental difference between steady state, where the injection rate is constant, and pseudo-steady state where the injection rate will undergo exponential decline if the injection pressure exceeds an allowable value. A limited aquifer indicates a far larger number of required injection wells for a given mass of CO 2 to be sequestered and/or a far larger reservoir volume than the former.
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.
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