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The value of horizontal multiple fractured wells can be maximized when the parameters with the greatest effect on productivity of such wells is understood. As a step towards achieving maximum value from horizontal multifractured wells, a computer model (MFHOW) has been developed that allows the user to quickly assess the impact of various well or reservoir properties on well performance. The model is generally three-dimensional and considers full time variability. It assumes single-phase oil flow and is based on semi-analytical techniques. The model may be used for modelling transverse or longitudinal fractures of varying type (uniform flux, infinite conductivity, finite conductivity). Flexibility to use various constraints and the option of multi-run sensitivity generation can be used for prognosis of multifractured horizontal well productivity and its diagnosis. The model solution that is developed can be used for general screening and optimization of a multifractured horizontal well because of the fast numerical algorithms implemented. For any given set of reservoir, fracture and well parameters the oil rate, cumulative production, well pressure, or productivity index can be determined. Various model features are presented through sensitivity results and comparison with actual data from a North Sea well. Introduction The application of horizontal wells and more specifically, that of multi-fractured horizontal wells for exploiting oil and gas reservoirs is firmly established within the industry. Various authors have made significant contributions in improving understanding of the flow behavior of such wells. The reference list at the end of this paper includes work by some of these authors [4–14]. Evaluation of multifractured horizontal well performance, or selection of the optimum perforation/stimulation design for such wells, may be approached through fine grid reservoir simulation. However, while reservoir simulation is the most advanced method of predicting well performance, it is often too time consuming to use for a parametric screening study. Often the data required is not available and the effort may not be warranted. As an alternative to simulation, the application of semi-analytical models can readily yield wellbore responses to various boundary conditions. Often this is sufficient to provide an understanding of factors of most influence on well performance. If simulation work is warranted, it can then proceed with the insight obtained from the analytical models. With the primary goal of providing a simple to use tool for generating well responses in hydraulically fractured horizontal wells, the MFHOW model was developed in concert with several North Sea operators. This paper provides a general overview of the model and solution methods employed. Some of the model features are presented through the use of actual well data. More MFHOW model features are detailed and reported in reference [1]. Model validation has been performed using a reservoir simulator [2]. For comparison purposes, simple homogenized model was considered with a multifractured-horizontal well. Fractures were transversal, fully penetrating of same half-length. In this approach we automatically generate a reservoir simulation grid that models a mutifractured horizontal well, oil inflow accurately. Model Description The MFHOW model is an extremely fast mini-simulator, permitting modelling of one-phase (slightly compressible) liquid flow into multifractured horizontal wells in a slab reservoir.

Summary Continuous improvements during well completion in addition to stimulation technology renew the need for multi-fractured horizontal well modeling. The present work investigates the productivity of a well with fractures by means of semi-analytical late-time approximations. These expressions are related to a vertical and a horizontal well with a single-fracture production. The flow in a fracture that is coupled to a horizontal well is of uniform flux (or of infinite conductivity flow) and the fractures can be positioned transversally or longitudinally. To successfully measure the production efficiency of a fractured-horizontal well, the effective wellbore radius and the equivalent single-fracture half-length were introduced. The effective wellbore radius was defined for a vertical well and could be extended for its horizontal counterpart. The equivalent fracture half-length was defined for a horizontal well with a single-transversal and a single-longitudinal fracture. The late-time approximations were developed for a fractured horizontal well positioned in the middle of an infinite oil reservoir. The developed expressions were employed for a multi-fractured horizontal well in order to define an effective wellbore radius and an equivalent fracture half-length (for both the transversal and the longitudinal fractures). A series of solutions corresponding to various conditions were given in a multiple-fractured-horizontal well model. It was possible to verify derived effective parameters of a fractured horizontal well by using a fast, robust and facile software program, a screening-tool product, that has been of considerable benefit to companies in the petroleum industry. Introduction Fractured wells are frequently considered in reservoir and production engineering. They constitute either hydraulically fractured wells to improve oil production or wells intersecting natural fractures. Hydraulically fractured horizontal wells represent a proven technology for producing oil and gas from tight formations. Hydraulic fractures reduce well drawdown, increase the productivity of horizontal wells by increasing the surface area in contact with formation, and provide high conductivity paths to the wellbore. Depending on the in-situ stress orientation, hydraulic fractures can be parallel (longitudinal) or perpendicular (transverse) to the horizontal well axis. Usually, two main fracture directions relative to the well direction appear. If a horizontal well is drilled perpendicularly to the axis of the least principal formation stress, a longitudinal fracture along the wellbore is generated by hydraulic fracturing. If, on the other hand, it is drilled parallel to the least principal stress direction, multiple transverse fractures can be generated. In general, horizontal wells with transverse fractures are favorable in low permeability reservoirs provided that a high conductive fracture conductivity can be obtained. Project economics in tight formations, however, depend strongly on well spacing and the number of hydraulic fractures required for the efficient draining of the reservoir. The present study aims at establishing an understanding of the influence of the (fracture-wellbore) system intersection angle on various predictions made through single-well modeling. This modeling was based on the developed mathematical models, able to reproduce the responses of acute systems to various forms of disturbances under a variety of conditions. The differential equation governing flow in conceptualized acute systems was derived from basic principles. Analytical solutions to this equation were reached for transient flowing conditions. The vertical well effective wellbore radius, rwv, which is greater than the actual wellbore radius, rw, constitutes a measure of the multi-fractured well efficiency. This efficiency can also be related to a single fracture with an equivalent half-length, Lfe, positioned transversally or longitudinally along a horizontal well.

A series of solutions corresponding to various conditions are given in a multiple-fractured-horizontal well model. We were able to develop a fast, robust and easy to use software program, a screening-tool product, we hope will be of significant benefit to companies in the petroleum industry. A practising engineer should be able to predict an optimum number of induced fractures in a horizontal well. Some existing analytical approaches are recognised to be inefficient and solutions should be compared to new solutions and new modelling techniques. Extension of the existing single phase oil flow SLAB model to a BOX model improves well production optimisation of a horizontal well with induced fractures; particularly prognosis and diagnosis features. The bringing together of rate-time and pressure-time analysis provides a total package to better characterise horizontal well with induced fractures behaviour. The tendency to over- or under-estimate the oil production needs to be corrected. Inclusion of a restart option is demonstrated in a real case study. This analytical screening-tool is useful for prognosis, diagnosis and improved modelling of oil production from horizontal or near-horizontal well with induced fractures. Introduction The use of horizontal wells for exploiting oil and gas reservoirs is firmly established within the industry. While reservoir simulation is the most advanced method of predicting well performance, it is too time consuming to use for a screening parametric study. Semi-analytical models can be used very efficiently to generate wellbore responses as a project screening tool. The models presented here are capable of forecasting oil production rates or wellbore pressures under single-phase flow conditions for various well configurations (vertical fractured well, horizontally perforated and multiple fractured horizontal well) for an adequate drainage area. Model Description The model is an extremely fast mini-simulator, modelling one-phase (slightly compressible) liquid flow into multifractured horizontal wells in a slab or box reservoir. Fractures are rectangular and vertical, and either transversal or longitudinal relative to well direction. They are also alternatively of finite conductivity, infinite conductivity or uniform flux type. Further, fractures are fully or partially penetrating, of equal or unequal length and spacing. There is no actual limitation on the number of fractures. The well is either open or perforated only at fractures; however, one special option is a partially perforated well with no fractures. Mathematical Model. The reservoir is modelled as an infinite slab of constant thickness (a finite box model being under construction) which is anisotropic but homogeneous (options for dual porosity etc. may be added). The combined use of Laplace transforms and Green's functions takes good care of the singular nature of fractures and all interference between them, the output being given for any given time interval. Concentrated use of mathematical analysis and numerical techniques developed specially for each option of the model yield many results in a fraction of a second, hence it is an efficient screening tool. Numerical Model. Corresponding mathematical model: Linear PDE of diffusion type is set up. The following solution methods are used: Various transforms and series expansions. Fast full time solutions can be given e.g. using Toeplitz matrix methods. Mathematical Model. The reservoir is modelled as an infinite slab of constant thickness (a finite box model being under construction) which is anisotropic but homogeneous (options for dual porosity etc. may be added). The combined use of Laplace transforms and Green's functions takes good care of the singular nature of fractures and all interference between them, the output being given for any given time interval. Concentrated use of mathematical analysis and numerical techniques developed specially for each option of the model yield many results in a fraction of a second, hence it is an efficient screening tool. Numerical Model. Corresponding mathematical model: Linear PDE of diffusion type is set up. The following solution methods are used: Various transforms and series expansions. Fast full time solutions can be given e.g. using Toeplitz matrix methods.

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