An Investigation of Fracture Asymmetry on the Pressure Response of Fractured Wells

Abstract

SPE Members Abstract This paper presents an investigation of the pressure response on hydraulically fractured wells flowing at constant flow rate through an asymmetric vertical fracture. The pressure behavior of wells intercepting asymmetric fractures of both infinite and finite conductivity was investigated by solving numerically and analytically the mathematical model. New solutions of the dimensionless wellbore pressure under production at constant flow rate are developed and are presented in terms of an asymmetry factor. New curves for these systems were generated and the deviation from the classical solution was readily detected. Some qualitative criteria to interpret the intensity of this effect are provided. Results of our investigation demonstrate that the relative position of the well in the fracture, i.e. the asymmetry condition, is an important consideration for the fracture characterization. Simulated pressure well tests indicated that at early times for fractures of moderate conductivity (CD < 5) the characteristic slope of one fourth is present, except for those cases of intense asymmetry (0.85 < xxlt; 1) where no evidence of straight line having one fourth slope was observed. However, it was also detected that at intermediate fracture conductivities (5 < CD < 50), even the case of complete asymmetry shows the characteristic slope of one fourth. It was also observed that as the asymmetry factor increases the end of the bilinear flow occurs earlier. The tabular solutions presented in this paper describe quantitatively the pressure behavior of fractured wells producing from asymmetric fractures for a wide range of asymmetry conditions. Our results are relevant in improving the fracture characterization of fractured wells as well as in the design of fracturing operations. Introduction Virtually all previous theoretical analyses of fractured wells have used the same restrictive assumptions used by Gringarten et. al, Cinco et. al, Wong et. al and Tiab postulating a symmetrycally homogeneous fracture frame. A few studies of the fracture asymmetry for fractured wells are available, while many others are available for the behavior of the symmetric fractures. The relevance of fracture asymmetry to pressure analysis was first discussed by Crawford and Landrum forty two years ago, but its significance in fracturing design applications has not yet been fully recognized. Demonstration of asymmetry effects in transient pressure analysis have also been made recently by Rodriguez et. al and Resureicao y Rodriguez. Among other evidences of this phenomenon, we would like to cite the fact that perforating scheme in wells, some heterogeneities along with the stress field gradients of developed reservoirs may be responsible of the presence of asymmetric fractures. This work is concerned with the analysis of fracture asymmetry effect on the pressure response of fracture wells. Solutions for this case are presented in tabular form for various asymmetry factors. The analysis is based on the numerical and analytical solutions to this problem, assuming constant conductivity and Darcy flow conditions.

Research for Unsteady Seepage Flow of Asymmetrical Fractured Vertical Wells in Coalbed

“…Xuejun Shan [7] explained the fracture geometry of the 21 CBM fracturing wells, the results show that there are three kinds of cracks in the form of expansion: single-wing cracks, asymmetric double-wing cracks, vertical and horizontal cracks symbiotic type, of which asymmetric two-wing cracks accounted for more than 90%. Many scholars at home and abroad have done a lot of research on this aspect [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24], the domestic aspects, Wei Chen [8] established the evaluation model of finite conductivity and symmetrical fractured vertical wells in coalbed methane reservoirs; Weiping Ouyang [9] uses the finite element method to establish the numerical well test model of vertical fractured well of coalbed methane infinite conductivity, and the double logarithmic well test theory chart is drawn; Haitao Cao [13] used the theory of point source function to deduce modern decreasing plate of CBM symmetrically fractured well production; Baojun Cao [14] established a model for asymmetric fracture productivity of volcanic rocks based on the principle of conformal transformation and equivalent filtrational resistance; Wenjuan Wu [15] took the Chang 6 oil reservoir in Ordos Basin as an example, using the logging data to carry out the geological modeling and studying the three-dimensional stress field established the numerical simulation model of the asymmetric fracturing in the ultra-low permeability oil and gas reservoirs; Jian Xiong [16] derived productivity prediction model of finite conductivity asymmetric vertical fractured wells in low permeability gas reservoirs based on the steady flow theory and conformal transformation. The foreign aspects, Benjamin, J. and Barker [17] studied the pressure dynamics of finite conductivity symmetrical fractured vertical well in coalbed methane with confined boundaries based on the assumption of two dimensional single-phase Darcy flow; K.H.Guppy [18] established a numerical and semi-analytical model to analyze the high velocity non-Darcy's flow behavior of the finite conductivity fractured wells in coalbed methane reservoirs; Fernando Rodriguez …”

“…The foreign aspects, Benjamin, J. and Barker [17] studied the pressure dynamics of finite conductivity symmetrical fractured vertical well in coalbed methane with confined boundaries based on the assumption of two dimensional single-phase Darcy flow; K.H.Guppy [18] established a numerical and semi-analytical model to analyze the high velocity non-Darcy's flow behavior of the finite conductivity fractured wells in coalbed methane reservoirs; Fernando Rodriguez [19] established a semi-analytical model of finite conductivity asymmetrical fractured well in oil reservoirs based on a new solution to the dynamic analysis of quasi-linear flow and bilinear flow pressure; B.D. Poe [20] gave a dynamic analysis model of pressure propagation in finite conductivity fractured wells with the change of spatial properties; Sergio Berumen [21] gave a pressure dynamic analysis of finite conductivity asymmetrically fractured well based on the numerical solution. Lei Wang [22][23][24] gave progressive decrease analysis of finite conductivity symmetrically fractured well of coalbed methane and a well test model of finite conductivity asymmetrically fractured well in oil reservoirs based on Laplace transform and Stehfest numerical inversion.…”