Modeling Boundary-Dominated Flow in Hydraulically-Fractured Wells

2021 ◽  
Author(s):  
Hafiz Mustafa Ud Din Sheikh ◽  
W. J. Lee ◽  
H. S. Jha
Keyword(s):  
Horizontal Wells ◽  
Drainage Area ◽  
Hydraulic Fractures ◽  
Simple Method ◽  
Shape Factors ◽  
Fracture Spacing ◽  
Aspect Ratios ◽  
Constant Rate ◽  
Spacing Ratio ◽  
Half Length

Abstract This paper presents a simple method to model boundary-dominated flow in hydraulically fractured wells, including horizontal wells with multiple fractures. While these wells are almost always producedat more nearly constant BHP rather than constant rate, use of material-balance time transforms variable-rate production profiles to constant-rate profiles, allowing us to use the pseudo-steady-state (PSS) flow equation for modeling. However, the PSS equation requires use of shape factors in applications, and shape factors available in the literature are available only for square-shaped bounded reservoirs with hydraulic fractures. In this work, we derived shape factors for wells centered in rectangular-shaped drainage areas with different length-to-width aspect ratios. The superposition principle can be used to transform transient radial flow and transient linear flow solutions into bounded reservoir solutions. At large times (when boundary-dominated flow is established), results from these solutions are similar to those obtained from the PSS equation. Therefore, for a pre-defined reservoir geometry, pressure drop values from superimposed transient flow equationscan be substituted back into the PSS equation to calculate shape factors for that reservoir geometry.We used shape factors previously presented by other authors for square drainage areas to validate themethod before applying it to calculate shape factors for more general drainage area configurations. We present shape factors for different fracture half-length to fracture-spacing ratios ranging from 0.2 to 10. Calculated shape factors, when plotted against the fracture half-length to fracture-spacing ratio, produced a smooth curve which can be used to interpolate shape factor values for other fracture configurations. We present applications of this methodology to example low-permeability wells. The use of the PSS equation for wells with vertical fracturescan be extended to multi-fractured horizontal wells (MFHWs) by incorporating the number of fractures in the equation; hence, shape factorsderived for wells with vertical fractures can also be used for MFHWs. Although our results are rigorously correct only for fluids with constant compressibility, use of pseudo-pressure and pseudo-time transformations extend application to compressible fluids, notably gases. Using the PSS equation in production data analysis allows us to calculate contributing reservoir volume and drainage area in a simple manner not requiring use of specialized software.

Characterizing Tight Oil Reservoirs With Dual- and Triple-Porosity Models

2016 ◽  
Vol 138 (3) ◽  
Author(s):  
Ezulike Daniel Obinna ◽  
Dehghanpour Hassan
Keyword(s):  
Aspect Ratio ◽  
Horizontal Wells ◽  
Production Data ◽  
Hydraulic Fractures ◽  
High Fracture ◽  
Type Curves ◽  
Fracture Spacing ◽  
Aspect Ratios ◽  
Fractured Horizontal Wells ◽  
Porosity Model

The response of existing transient triple-porosity models for fractured horizontal wells do not converge to that of linear dual-porosity model (DPM) in the absence of natural/microfractures (MFs). The main reason is the assumption of sequential-depletion from matrix to MF, and from MF to hydraulic-fractures (HFs). This can result in unreasonable estimates of MF and/or HF parameters. Hence, the authors proposed a quadrilinear flow model (QFM) in a previous paper which relaxes this sequential-depletion assumption to allow simultaneous matrix–MF and matrix–HF depletion. Also, it is proved that QFM simplifies to both DPM and linear sequential triple-porosity model (STPM). This work considers the implications of applying QFM, STPM, and DPM type-curves and analysis equations on production data of two fractured horizontal wells completed in the Bakken and Cardium Formations. A comparative study of the reservoir parameters estimated from the application of these models to the same production data reveals two key results. First, the application of DPM on the production data from reservoirs with active MF could result in overestimation of HF half-length. This happens to compensate for the extra fluid depletion pathways provided by MF. Second, the application of STPM on the production data from the reservoirs with active matrix–HF communication could result in overestimation of the MF intensity. Results from this study are significant when selecting the appropriate model for interpreting production data from fractured horizontal wells completed in formations with or without active MF. The DPM is appropriate if analog studies (e.g., outcrop, microseismic and image log analyses) reveal high fracture spacing aspect ratio (negligible MF) in the reservoir. Fracture spacing aspect ratio is MF spacing divided by the HF spacing. The STPM is appropriate if analog studies reveal low spacing aspect ratio (e.g., matrix–HF face damage or high MF intensity within a given HF spacing). QFM is appropriate for all fracture spacing aspect ratios.

Productivity and Drainage Area of Fractured Horizontal Wells in Tight Gas Reservoirs

2008 ◽  
Vol 11 (05) ◽  
pp. 902-911 ◽  
Author(s):  
Flavio Medeiros ◽  
Erdal Ozkan ◽  
Hossein Kazemi
Keyword(s):  
Horizontal Well ◽  
Oil And Gas ◽  
Horizontal Wells ◽  
Drainage Area ◽  
Dual Porosity ◽  
Hydraulic Fractures ◽  
Tight Gas ◽  
Natural Fractures ◽  
Tight Formations ◽  
Fractured Horizontal Wells

Summary This paper discusses the performance and productivity of fractured horizontal wells in heterogeneous, tight-gas formations. Production characteristics and flow regimes of unfractured and fractured horizontal wells are documented. The results show that if hydraulic fracturing affects stress distribution to create or rejuvenate natural fractures around the well, the productivity of the system is significantly increased. Unless there is significant contrast between the conductivities of the hydraulic and natural fractures, hydraulic fractures may not significantly contribute to the productivity. For extremely tight formations, the effective drainage area may be limited to the naturally fractured region around the well and the hydraulic fractures. It is also shown that very long transient flow periods govern the productivity and economics of fractured horizontal wells in tight formations. The results of this study are also applicable to oil production from fractured shale. Introduction Economic gas and oil production from low permeability reservoirs has been a challenge for the oil and gas industry. Because most of the high permeability reservoirs have been exploited and many low permeability reservoirs remain undeveloped, the latter have taken the industry attention recently. Particular attention has been given to tight-gas reservoirs with permeability in the range of micro-Darcies or below and to oil accumulation in fractured shale. Hydraulically fractured horizontal wells are the proven technology to produce oil and gas from tight formations. Hydraulic fractures reduce well drawndown, 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 in-situ stress orientation, hydraulic fractures can be parallel (longitudinal) or perpendicular (transverse) to horizontal well axis. Project economics in tight formations, however, depends strongly on well spacing and the number of hydraulic fractures required to drain the reservoir efficiently. Field evidence indicates that the drainage areas of fractured horizontal wells in tight formations may be limited to a rectangular region confining the horizontal well and the transverse hydraulic fractures. Also, there has been evidence that hydraulic fracturing in tight formations changes stresses in fracture drainage area, which could create or rejuvenate natural fractures in the near-vicinity of the horizontal well. This fracture network, which may be characterized as a dual-porosity system, may contribute significantly to improve productivity of the fractured horizontal well. Much work has been done (Soliman et al. 1990; Larsen and Hegre 1994; Temeng and Horne 1995; Raghavan et al. 1997; Wan and Aziz 1999; Al-Kobaisi et al. 2006) to investigate pressure-transient analysis and short- and long-term productivity of horizontal wells with single or multiple hydraulic fractures. The effect of a dual-porosity zone surrounding hydraulic fractures, however, has not been considered in the previous studies. The main objective of this study is to investigate the combined effects of a dual-porosity region and hydraulic fractures on the productivity of horizontal wells. The results presented in this work are based on a semianalytical model developed by Medeiros et al. (2006). The model was derived from the Green's function formulation of the solution for the diffusivity equation (Gringarten and Ramey, 1974, Ozkan and Raghavan, 1991a, 1991b) and has the capability to incorporate local heterogeneities. In this work, we use the semianalytical model to incorporate induced finite-conductivity fractures (transverse and longitudinal) along the horizontal well and naturally fractured zones around the hydraulically fractured horizontal well by using the dual-porosity idealization. We use the example data sets given in Tables 1 through 3 to consider different cases of horizontal wells with and without induced and natural fractures.

scholarly journals Numerical simulation on the simultaneous stress interference of parallel multiple hydraulic fractures

2021 ◽  
pp. 014459872110019
Author(s):  
Weiyong Lu ◽  
Changchun He
Keyword(s):  
Principal Stress ◽  
Hydraulic Fracture ◽  
Stress Ratio ◽  
Fracture Network ◽  
Hydraulic Fractures ◽  
Fracture Spacing ◽  
Induced Stress ◽  
Minimum Principal Stress ◽  
Fracturing Process ◽  
Stress Ratios

During horizontal well staged fracturing, there is stress interference between multiple transverse fractures in the same perforation cluster. Theoretical analysis and numerical calculation methods are applied in this study. We analysed the mechanism of induced stress interference in a single fracture under different fracture spacings and principal stress ratios. We also investigated the hydraulic fracture morphology and synchronous expansion process under different fracture spacings and principal stress ratios. The results show that the essence of induced stress is the stress increment in the area around the hydraulic fracture. Induced stress had a dual role in the fracturing process. It created favourable ground stress conditions for the diversion of hydraulic fractures and the formation of complex fracture network systems, inhibited fracture expansion in local areas, stopped hydraulic fractures, and prevented the formation of effective fractures. The curves of the maximum principal stress, minimum principal stress, and induced principal stress difference with distance under different fracture lengths, different fracture spacings, and different principal stress ratios were consistent overall. With a small fracture spacing and a small principal stress ratio, intermediate hydraulic fractures were difficult to initiate or arrest soon after initiation, fractures did not expand easily, and the expansion speed of lateral hydraulic fractures was fast. Moreover, with a smaller fracture spacing and a smaller principal stress ratio, hydraulic fractures were more prone to steering, and even new fractures were produced in the minimum principal stress direction, which was beneficial to the fracture network communication in the reservoir. When the local stress and fracture spacing were appropriate, the intermediate fracture could expand normally, which could effectively increase the reservoir permeability.

A convenient formulation of Sadowsky's model for elastic ribbons

2021 ◽  
Vol 477 (2255) ◽  
Author(s):  
Sébastien Neukirch ◽  
Basile Audoly
Keyword(s):  
Differential Equations ◽  
Constitutive Relation ◽  
Classical Problem ◽  
Constitutive Law ◽  
System Of Differential Equations ◽  
Dimensional Model ◽  
Simple Method ◽  
One Dimensional ◽  
Aspect Ratios ◽  
Nonlinear Constitutive Relation

Elastic ribbons are elastic structures whose length-to-width and width-to-thickness aspect ratios are both large. Sadowsky proposed a one-dimensional model for ribbons featuring a nonlinear constitutive relation for bending and twisting: it brings in both rich behaviours and numerical difficulties. By discarding non-physical solutions to this constitutive relation, we show that it can be inverted; this simplifies the system of differential equations governing the equilibrium of ribbons. Based on the inverted form, we propose a natural regularization of the constitutive law that eases the treatment of singularities often encountered in ribbons. We illustrate the approach with the classical problem of the equilibrium of a Möbius ribbon, and compare our findings with the predictions of the Wunderlich model. Overall, our approach provides a simple method for simulating the statics and the dynamics of elastic ribbons.

Revision of Pressure Transient Analysis in Mature Condensate-Rich Tight Gas Fields in Sultanate of Oman

2022 ◽  
Author(s):  
Ahmed Elsayed Hegazy ◽  
Mohammed Rashdi
Keyword(s):  
Transient Analysis ◽  
Horizontal Wells ◽  
Development Planning ◽  
Reservoir Modeling ◽  
Sultanate Of Oman ◽  
Pressure Transient Analysis ◽  
Pressure Transient ◽  
Full Field ◽  
Gas Fields ◽  
Half Length

Abstract Pressure transient analysis (PTA) has been used as one of the important reservoir surveillance tools for tight condensate-rich gas fields in Sultanate of Oman. The main objectives of PTA in those fields were to define the dynamic permeability of such tight formations, to define actual total Skin factors for such heavily fractured wells, and to assess impairment due to condensate banking around wellbores. After long production, more objectives became also necessary like assessing impairment due to poor clean-up of fractures placed in depleted layers, assessing newly proposed Massive fracturing strategy, assessing well-design and fracture strategies of newly drilled Horizontal wells, targeting the un-depleted tight layers, and impairment due to halite scaling. Therefore, the main objective of this paper is to address all the above complications to improve well and reservoir modeling for better development planning. In order to realize most of the above objectives, about 21 PTA acquisitions have been done in one of the mature gas fields in Oman, developed by more than 200 fractured wells, and on production for 25 years. In this study, an extensive PTA revision was done to address main issues of this field. Most of the actual fracture dynamic parameters (i.e. frac half-length, frac width, frac conductivity, etc.) have been estimated and compared with designed parameters. In addition, overall wells fracturing responses have been defined, categorized into strong and weak frac performances, proposing suitable interpretation and modeling workflow for each case. In this study, more reasonable permeability values have been estimated for individual layers, improving the dynamic modeling significantly. In addition, it is found that late hook-up of fractured wells leads to very poor fractures clean out in pressure-depleted layers, causing the weak frac performance. In addition, the actual frac parameters (i.e. frac-half-length) found to be much lower than designed/expected before implementation. This helped to improve well and fracturing design and implementation for next vertical and horizontal wells, improving their performances. All the observed PTA responses (fracturing, condensate-banking, Halite-scaling, wells interference) have been matched and proved using sophisticated single and sector numerical simulation models, which have been incorporated into full-field models, causing significant improvements in field production forecasts and field development planning (FDP).

High-resolution stratigraphic characterization of natural fracture attributes in the Woodford Shale, Arbuckle Wilderness and US-77D Outcrops, Murray County, Oklahoma

2018 ◽  
Vol 6 (1) ◽  
pp. SC29-SC41 ◽  
Author(s):  
Sayantan Ghosh ◽  
John N. Hooker ◽  
Caleb P. Bontempi ◽  
Roger M. Slatt
Keyword(s):  
Natural Fracture ◽  
Fracture Aperture ◽  
Aperture Size ◽  
Fracture Density ◽  
Area Formula ◽  
Woodford Shale ◽  
Fracture Spacing ◽  
Spacing Ratio ◽  
Fracture Intensity ◽  
Bed Thickness

Natural fracture aperture-size, spacing, and stratigraphic variation in fracture density are factors determining the fluid-flow capacity of low-permeability formations. In this study, several facies were identified in a Woodford Shale complete section. The section was divided into four broad stratigraphic zones based on interbedding of similar facies. Average thicknesses and percentages of brittle and ductile beds in each stratigraphic foot were recorded. Also, five fracture sets were identified. These sets were split into two groups based on their trace exposures. Fracture linear intensity (number of fractures normalized to the scanline length [[Formula: see text]]) values were quantified for brittle and ductile beds. Individual fracture intensity-bed thickness linear equations were derived. These equations, along with the average bed thickness and percentage of brittle and ductile lithologies in each stratigraphic foot, were used to construct a fracture areal density (number of fracture traces normalized to the trace exposure area [[Formula: see text]]) profile. Finally, the fracture opening-displacement size variations, clustering tendencies, and fracture saturation were quantified. Fracture intensity-bed thickness equations predict approximately 1.5–3 times more fractures in the brittle beds compared with ductile beds at any given bed thickness. Parts of zone 2 and almost entire zone 3, located in the upper and middle Woodford, respectively, have high fracture densities and are situated within relatively organic-rich (high-GR) intervals. These intervals may be suitable horizontal well landing targets. All observed fracture cement exhibit a lack of crack-seal texture. Characteristic aperture-size distributions exist, with most apertures in the 0.05–1 mm (0.00016–0.0032 ft) range. In the chert beds, fracture cement is primarily bitumen or silica or both. Fractures in dolomite beds primarily have calcite cement. The average fracture spacing indices (i.e., bed thickness-fracture spacing ratio) in brittle and ductile beds were determined to be 2 and 1.2, respectively. Uniform fracture spacing was observed along all scanlines in the studied beds.

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