Summary Horizontal wells with multiple hydraulic fractures have become a standard completion for the development of tight oil and gas reservoirs. Successful optimization of multiple-fracture design on horizontal wells began empirically in the Barnett Shale in the late 1990s (Steward 2013; Gertner 2013). More recently, research has focused on further improving fracturing performance by developing a model-derived optimum. Some researchers have focused on an economic optimum on the basis of multiple runs of an analytical or numerical model (Zhang et al. 2012; Saputelli et al. 2014). With such an approach, a new set of model runs is necessary to optimize the design each time the input parameters change significantly. Running multiple simulations for every optimization case might not always be practical. An alternative approach is to develop well-performance curves with dimensionless variables on the basis of the performance model. Such an approach was the basis for unified fracture design (UFD) for a single fracture in a vertical well (Economides et al. 2002). However, a similar systemized method to calculate the optimum for a horizontal well with multiple hydraulic fractures was missing. The objective of this study was to develop a rigorous and unified dimensionless optimization technique with type curves for the case of multiple transverse fractures in a horizontal well—an extension of UFD. The mathematical problem was solved in dimensionless variables. Multiple fractures include the proppant number (NP), penetration ratio (Ix), dimensionless conductivity (CfD), and aspect ratio (yeD) for each fracture, which is inversely proportional to the number of fractures. The direct boundary element (DBE) method was used to generate the dimensionless productivity index (JD) for a given range of these parameters (28,000 runs) for the pseudosteady-state case. Finally, total well JD was plotted as a function of the number of fractures for various NP. The effect of minimum fracture width was studied, and the optimization curves were adjusted for three cases of minimum fracture width. The provided dimensionless type curves can be used to identify the optimized number of fractures and their geometry for a given set of parameters, without running a more complicated numerical model multiple times. First, the proppant mass (and hence, NP) used for the fracture design can be selected on the basis of economic or other considerations. For this purpose, a relationship between total JD and NP, which accounts for the minimum fracture width requirement, was provided. Then, the optimal number of fractures can be calculated for a given NP using the generated type curves with minimum width constraints. The following observations were made during the study on the basis of the performed runs: For a given volume or proppant, NP, total JD for multiple fractures increases to an asymptote as the number of fractures increases. This asymptote represents a technical potential for multiple fractures and for high proppant numbers (NP≥100), with a technical potential of 3πNP. Below this asymptote, the more fractures that are created for a fixed NP, the larger the JD. In practice, minimum fracture width constrains the fracture geometry, and therefore maximum JD. For the case when 20/40 sand is used for multiple hydraulic fracturing of a 0.01-md formation with square total area, the optimal number of factures is approximately NP25. Application of horizontal drilling technology with multiple fractures assumes the availability of high proppant numbers. It was shown mathematically that the alternative low proppant numbers (NP≤20 for the previous case) are impractical for multiple fractures, because total JD cannot be significantly higher than JD for an optimized single fracture in the same area. This means that low formation permeability and/or high proppant volumes are needed for multiple fracture treatments.
Hydraulic fracturing is the overwhelming completion method in the international petroleum industry. It is estimated, that today it has become a $20 billion industry. It is also one of the most challenging enterprises, incorporating scientific information from geology, reservoir and production engineering, rock mechanics, complex fluid rheology and field economics. More than a decade ago we introduced the concept of Unified Fracture Design (UFD) as a means towards physical optimization. Since then UFD has been adopted by a great number of practitioners and hundreds of papers have been published. Not all approaches have been successful, nor have they been done appropriately. In this work we relook at the whole issue in a systematic way. We have identified and describe here a 9-step sequence to mitigate the gaps and help in the optimized field application of modern hydraulic fracturing. These include:Required minimum reservoir characterization: Typical log description.Estimate of k, h, interlayer stress contrast, distance from water.Optimization of fracture size using UFD. Maximum dimensionless PI at optimum conductivity. Optimization of drainage shape and stimulated reservoir volume (SRV).Unique monitoring execution, other than the traditional net pressure or injection variables. New benchmark indicators are used, cross-plotting descriptive variables such as: level of pressure vs. volume of fluid injected vs. operational characteristics, such as tip screen-out.4. Fracture injection tests, designed for fluid efficiency, closure pressure, leak-off coefficient and the newly developed capability for after-closure analysis for well and reservoir variables.For multifrac applications such as shale gas, horizontal wells in very low-permeability formations, zonal isolation and perforation strategies are essential issues.Design of injection schedule to accomplish the desired fracture geometry is the next concern. What happens if things go wrong? The strategy of contingencies must be in place before the execution starts.On-the-fly redesign responding to contingencies, such as net pressure constraints and formation barriers. Ability for alternative plans quickly.Once the job is completed the next step is whatever is necessary to close the fracture and flow the well back. What needs to be done in different geologic settings?Finally, to close the circle, performance evaluation is indicated, which involves comparison between actual performance and expectations and the definitive reconciliation of any discrepancies.
Numerous papers have been published in recent years on the subject of optimization of multiple transverse fractures in horizontal wells (for instance Saputelli et al., 2014). These studies usually focus on searching for an economical optimum based on multiple runs of 3D or 2D numerical simulator, each for certain fixed properties of hydraulic fractures. What we found missing is a systemized approach to calculate a solution to this problem. The objective of this study is to develop a systemized, rigorous mathematical and unified approach to the design of multiple transverse fractures in horizontal well – an extension of Unified Fracture Design (UFD). This paper provides a rigorous methodology to optimize the number of fractures (and consequently, fracture geometry) for a given amount of proppant. We follow the UFD concepts and solve our problem in dimensionless variables. For the case of multiple fractures these are: Proppant Number (NP), Penetration Ratio (Ix), Dimensionless Conductivity (CfD) and Aspect Ratio (yeD) for each fracture, which is inversely proportional to the number of fractures. We used the Direct Boundary Element method to generate the Dimensionless Productivity Index (JD) for a given range of these parameters (28,000 runs) for the Pseudo-Steady state case. Finally we plot total JD as a function of the number of fractures for various NP, which allows optimization. In addition, we generate minimum width curves for various proppants, which represent a practical constraint. Based on our study we found the following: For a given volume or proppant, NP, total JD for multiple fractures increases to an asymptote as the number of fractures increases. This asymptote represents a technical potential for multiple fractures and for high Proppant Numbers (NP ≥ 100) reaches a technical potential of 3πNP. Below this asymptote, the more fractures that are created for a fixed NP the larger the JD In practice however, there's a minimum fracture width (3 proppant grains), which constrains the fracture geometry and therefore maximum JD. It was shown, that for the case when 20/40 sand is used for multiple hydraulic fracturing of 0.01md formation with square total area, optimal number of factures reduces to approximately Np25. Application of horizontal drilling technology with multiple fractures assumes availability of high Proppant Numbers. We show mathematically that the alternative low Proppant Numbers (NP ≤ 20 for the case in p.3) are impractical for multiple fractures because total JD cannot be significantly higher than JD for optimized single fracture in the same area. In practice this means low formation permeability and/or high proppant volumes are necessary for multiple fracture treatments. Our work shows the methodology to determine optimum geometry and required volume to perform multifracture treatments. Total proppant mass (and hence, NP) used for the fracture design must be selected based on economic considerations. For this purpose we constructed a relationship between total JD and the NP, which accounts for the minimum fracture width requirement. Our paper presents a mathematically rigorous, systematic and comprehensive approach to the selection of optimal number of transverse hydraulic fractures in a horizontal well. Using the relationship between Proppant Number and maximum practical JD, the proppant mass should be selected for the treatment. Then, based on the formation and proppant permeability, the maximum number of fractures should be calculated for a given NP using the generated type curves and minimum width restriction.
For more than 50 years a vision of a hydraulic fracture that is vertical with two symmetrical wings has been accepted by two highly diverse sciences in petroleum production: fracture mechanics and production/reservoir engineering models. The fracture in both sciences has a height, a length tip-to-tip, and an average width. A fracture propagation model is usually employed to determine fracture dimensions. Linear elastic fracture mechanics points towards a relationship between fracture length (and, implicitly, height) and fracturing pressure. Therefore, pressure analysis during execution is supposed to 1) determine the generalized fracture geometry and 2) to quantify fracture dimensions such as length and width. Once the well is put on production, the fracture geometry can be determined either through a well test or through long-term production data analysis or both. The models employed for this exercise have been in wide use and have been credited with considerable success in hydraulic fracture treatment evaluation. Pressure patterns would lead to the determination of the apparent fracture half-length and fracture permeability-width product. Unfortunately, often there is a discrepancy to a severe discrepancy in the fracture dimensions obtained from the two methodologies. We present here several theories describing the discrepancy and we quantify the impact of reservoir and fracture parameters. These include reservoir areal permeability anisotropy, damage to the proppant pack, discontinuity in fracture conductivity and, of course, turbulence effects. We are applying this approach to 23 hydraulically fractured wells in a less-than 1 md oil and gas reservoirs in Western Siberia and achieve reasonable reconciliation between the results of the diverse methods of fracture geometry determination and the impact of reservoir and fracture variables. Fracture treatments, designed for other wells in the field take these conclusions into account.
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