A Multiple Fractured-Horizontal Well Case Study

Abstract

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.

Three-Dimensional Study of Unsteady Flow in Fractured Horizontal Wells

“…They also examined the factors involved in determining the optimum number of transverse fractures for both finite and infinite reservoirs. The effect of hydraulic fracture on pressure behaviour has also been studied by Cvetkovic' et al [8]. All these authors have used an analytical model to solve flow for fractured horizontal wells, whereas we used, in this study, a numerical model to simulate the behaviour of fractured horizontal wells.…”