Proppant Number Research Articles

Optimizing the Number of Fractures in a Horizontal Well

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.

A Unified Approach To Optimize Fracture Design of a Horizontal Well Intercepted by Primary- and Secondary-Fracture Networks

Summary The classical optimization design dependent on a single-fracture (SF) assumption is widely applied in performance optimization for hydraulically fractured wells. The objective of this paper is to extend the optimal design to a complex fracture network to achieve the maximum productivity index (PI). In this work, we established a pseudosteady-state (PSS) productivity model of a fractured horizontal well, which has the flexibility of accounting for the complexity of fracture-network dimensions. A semianalytical solution was then presented in the generalized matrix format through coupling reservoir- and fracture-flowing systems. Subsequently, several published studies on the PSS productivity calculation of a SF were used to verify this model, and a 3D transient numerical simulation of an orthogonal fracture network was used to perform further verification. We show that results from our solutions agree very well with those benchmarked results. On the basis of the model, we provide a detailed analysis on the productivity enhancement of the fracture-network/optimization work flow using unified fracture design (UFD). The results show the following: The PI is determined by fracture conductivity and complexity (network size, spacing, and configuration), and it is a function of fracture complexity and conductivity when the influence of proppant volume is not considered. Under the constraint of a given amount of proppant known as UFD, the maximum PI would be achieved when the best balance between network complexity and conductivity was obtained. It is more advantageous to minimize fracture complexity by creating relatively simple-geometry fractures with smaller network size and larger fracture spacing in the condition of small and intermediate proppant numbers. It should be the design goal to generate a complex network by creating relatively complex-geometry fractures with larger network size and smaller fracture spacing in the condition of a large proppant number. Increasing fracture complexity could reduce the optimal requirement of fracture conductivity. The proposed approach can provide guidance for a network-hydraulic-fracturing design for an optimal completion.

An Analytical Solution of the Pseudosteady State Productivity Index for the Fracture Geometry Optimization of Fractured Wells

The pseudosteady state productivity index is very important for evaluating the production from oil and gas wells. It is usually used as an objective function for the optimization of fractured wells. However, there is no analytical solution for it, especially when the proppant number of the fractured well is greater than 0.1. This paper extends the established fitting solution for proppant numbers less than 0.1 by introducing an explicit expression of the shape factor. It also proposes a new asymptotic solution based on the trilinear-flow model for proppant numbers greater than 0.1. The two solutions are combined to evaluate the pseudosteady state productivity index. The evaluation results are verified by the numerical method. The new solution can be directly used for fracture geometry optimization. The optimization results are consistent with those given by the unified fracture design (UFD) method. Using the analytical solution for the pseudosteady state productivity index, optimization results can be obtained for rectangular drainage areas with arbitrary aspect ratios without requiring any interpolation or extrapolation. Moreover, the new solution provides more rigorous optimization results than the UFD method, especially for fractured horizontal wells.

Determination of Performance of Multiple-Fracture Horizontal Well by Incorporating Fracture-Fluid Leakoff

Summary Multiple-fracture-horizontal-well (MFHW) technology plays a crucial role in production from less economically attractive reservoirs, through enhancing the well productivity. The formation around the fracture might be damaged considerably during fracturing processes because of the fracture-fluid leakoff into the reservoir. Different attempts have been made to achieve an optimal design for MFHWs; however, the effect of fracture-fluid leakoff has been neglected in most of these research investigations, leading to unrealistic and inaccurate results. This study aims to fill this knowledge gap. A new mathematical approach is introduced to evaluate the effect of the fracture-fluid-leakoff phenomenon on the fracture characteristics during hydraulic fracturing. The unified-fracture-design (UFD) concept is used in this research work to optimize the productivity of MFHWs where the direct boundary-element method (DBEM) is applied. The distributed-volumetric-sources (DVS) method, which offers a semianalytical response of a reservoir to closed outer boundaries with respect to a source, is also extended, and the results obtained from these two different techniques are compared. Then, the proposed methodology is applied to a synthetic case study to evaluate the influence of fracture-fluid leakoff on the productivity index (PI) and to obtain the fracture dimensions that result in the optimal productivity. It is concluded that leakoff leads to influx-pattern variation. Also, it is found that the optimal fracture for the leakoff case is shorter and wider at a constant proppant number, in contrast to the case without a leakoff event. This study proposes an accurate and reliable approach for productivity determination of MFHWs that can assist the petroleum industry to optimize hydraulic-fracturing operations.

Productivity analysis for a vertically fractured well under non-Darcy flow condition

In this paper, a semi-analytical solution of the pseudosteady-state (PSS) productivity index under non-Darcy flow condition is proposed. Based on the model, a new method of optimization of the fracture conductivity has been developed for non-Darcy flow in the fracture. Meanwhile, the effects of the Reynolds number, the proppant number and the fracture conductivity on the dimensionless productivity index have been discussed in detail.Results show that: (1) the classic UFD (Unified Fracture Design) curves of the Darcy-flow model underestimate the effect of the proppant number and are unsuitable for the non-Darcy-flow fracture optimization. Our discretized model provides a new tool to obtain the optimal fracture parameters for the case of non-Darcy flow condition. (2) for a given penetration ratio, the non-Darcy flow behavior exerts a strong influence on the productivity index with the dimensionless fracture conductivity CfD=0.1−1000 and a considerable productivity index drop can be observed. For the extremely low (CfD<0.1) or high (CfD>1000) dimensionless fracture conductivity, the effect of non-Darcy flow becomes negligible. (3) the effect of the non-Darcy flow on the productivity index becomes pronounced at large value of proppant number, Np. For a given proppant number, the optimal fracture conductivity is slowly increasing as the Reynolds number increases. However, the magnitude of the effect on the productivity index is gradually declining. At the Reynolds number less than 5, the non-Darcy flow has a relatively strong impact on the productivity index and an apparent fall of the maximum productivity index can be noticed, especially for a large proppant number. Beyond the value of 5, the declining trend of the maximum productivity index gradually slows down as the Reynolds number increases.

Productivity-Index Optimization for Hydraulically Fractured Vertical Wells in a Circular Reservoir: A Comparative Study With Analytical Solutions

Summary Productivity-index (PI) optimization by means of optimal fracture design for a vertical well in a circular reservoir is a canonical problem in performance optimization for hydraulically fractured wells. Recent availability of the exact analytical solution for the pseudosteady-state (PSS) flow of a vertically fractured well with finite fracture conductivity in an elliptical drainage area provides an opportunity to re-examine this fundamental problem in a more-rigorous manner. This paper first quantitatively estimates the shape-approximation-induced error in the PI when the exact solution for an elliptical drainage area is applied to a circular drainage area. It is shown that the shape-approximation-induced error in the PSS-flow PI is less than 1% for fracture penetration ratios up to 53%, and this error decreases significantly as the fracture conductivity is increased. PI optimization is then performed with the highly accurate analytical solution for this range of the penetration ratios. The results show that the optimal fracture conductivity increases linearly from 1.39 to 1.71 when the proppant number is increased from 0.0001 to 0.6. PI for the steady-state flow and a popular ad hoc PSS-flow PI are compared with the analytical PSS-flow PI. It is found that both the steady-state and the ad hoc PIs deviate significantly from the analytical PSS-flow PI. In particular, the optimal fracture conductivity for the steady-state flow and the ad hoc PIs decreases with the proppant number, opposite to the trend observed for the optimal fracture conductivity for the PSS flow. It is suggested that the ad hoc PI should be abandoned in favor of the more-rigorous analytical PSS-flow solution.

Non-Darcy effect on fracture parameters optimization in fractured CBM horizontal well

Coalbed methane (CBM) is an important part of energy in the world for its larger reserves, lower production cost. More and more countries and oil companies spent more and more money for CBM production in the past decades. Hydraulic fracturing is an important development method for the CMB production and the fracture parameters optimization is the key step for the hydraulic fracturing design.In this study, a fracture parameters optimization method is put forward which is based on the unified fracturing design (UFD) method. The maximum dimensionless productivity index and optimal dimensionless fracture flow conductivity of fractured wells for a certain proppant number are calculated, and then the optimal half-length and the width of the fracture, the dimensionless production index of fractured horizontal well are calculated correspondingly. All of the above is concluded under the condition that the non-Darcy effect in fracture is considered.Based on the result, the variation law of Reynolds number, the effective permeability, the optimal fracture half-length, the optimal fracture width and the optimum dimensionless production index to the free-gas saturation in CBM reservoir are obtained. We can conclude that the non-Darcy turbulent flow effect can decrease the proppant effective permeability in the fractures by mean of the generation of additional pressure drop, which will decrease the fracture diverting capacity and the production rate.

Finding Optimal Hydraulic-Fracture Angles in Productivity-Maximized Shale Well Design

This article, written by Special Publications Editor Adam Wilson, contains highlights of paper SPE 170965, “Optimal Hydraulic-Fracture Angle in Productivity-Maximized Shale Well Design,” by Nadav Sorek, SPE, Jose A. Moreno, Ryan Rice, Guofan Luo, and Christine Ehlig-Economides, SPE, Texas A&amp;M University, prepared for the 2014 SPE Annual Technical Conference and Exhibition, Amsterdam, 27–29 October. The paper has not been peer reviewed. In general, hydraulic fractures propagate perpendicular to the horizontal-well axis whenever drilling is parallel to the minimum principal-stress plane. However, operators frequently drill horizontal wells parallel to lease boundaries, resulting in slanted hydraulic-fracture planes at angles less than 90° from the well axis. This study provides a model for the inclined fracture case. It applies and further extends the unified-fracture-design approach for rectangular drainage areas, relating the dimensionless proppant number to the maximum productivity index in pseudosteady-state conditions. Introduction Industry experience suggests that horizontal shale-gas development is enhanced by drilling in the direction parallel to the local minimum principal horizontal stress. Because US mineral leases frequently are rectangular areas with north/south and east/west boundaries, operators often drill parallel to the lease boundaries, prioritizing well saturation over optimum fracture-length propagation. This practice leads to the creation of hydraulic-fracture planes that are slanted at an angle less than 90° with respect to the well axis. Extensive research has investigated the effects of angled fractures on well productivity. Theoretical and empirical data have been used to address the effect of wellbore azimuth on well performance in the Marcellus shale. Results showed that, for each degree a well was suboptimal to minimum horizontal stress, the estimated ultimate recovery decreased by 7.25 Mscf per foot of effective lateral length. Unified-fracture-design methodology indicates the hydraulic- fracturing treatment design that maximizes well productivity for any set of reservoir and proppant properties and a given injected-proppant mass. This methodology introduces the concept of proppant number, which describes the weighted ratio of propped-fracture volume to a square reservoir volume. This study applies and further extends the unified-fracture-design approach to show that, for any given set of reservoir and proppant properties along with a given proppant mass, as long as the created fractures define the same stimulated rock volume, there exists a well direction resulting in maximized well productivity that is not parallel to the minimum-stress direction. First, a correlation is established between the proppant number and the optimum drainage-area aspect ratio. Then, this correlation is used to express what the optimum fracture angle is for a specific proppant number.

Unified Fracturing Design for Water Injection Well under Steady State Flow Regime

Unified Fracture Design for fracturing optimization is a simple and reliable way to push the limit of the injection ability, reported frequently in recent years. However, most studies focus on fracture design under pseudo-steady state flow regime. The analysis of the different pressure systems between water injection well and oil production well tells us that the steady flow regime in the formation takes up most life span of water injection wells, associated with the field experience. To maximize injection capability for fractured vertical water wells under this regime, a physical optimization method is developed based on the concept of proppant number. Meanwhile, two new type curves without consideration of formation damage are obtained for quantifying the correlation between dimensionless injectivity and dimensionless conductivity. Then, calibrated design procedures accounting for gel damage and non-darcy effect, are also proposed. Finally, sensitivity studies are addressed to clarify the effect of several variables on the optimum fracture geometry.

Unified Fracture Design for very low permeability reservoirs

Unified Fracture Design (UFD) is a methodology for the design of optimal hydraulic fracturing treatments to maximize well performance. Many successful applications of UFD have been demonstrated for reservoirs with low to high permeability. However, UFD has not been systematically applied to reservoirs with very low (nanodarcy) permeability, such as shales. For such reservoirs, massive hydraulic fracturing combined with horizontal drilling has enabled the production of significant amounts of hydrocarbons in recent years. Yet a method for the design of optimal hydraulic fracture treatments for these reservoirs is currently lacking, with present practice relying mainly on rules of thumb and trial and error. This paper fills this gap by developing a design methodology through extension of UFD that addresses two important elements: (a) nanodarcy permeability reservoirs, and (b) fractures with highly elongated drainage areas, that are necessary because of the extremely small reservoir permeability. Simple explicit functions are developed that can be used for efficient computation of optimal fracture dimensions and the productivity index for large values of Proppant Number and highly elongated drainage area around each fracture. A case study is presented to demonstrate how the developed UFD extension can be used in practice and to illustrate the qualitative differences between standard UFD and the developed extension.

A new method to optimize the fracture geometry of a frac-packed well in unconsolidated sandstone heavy oil reservoirs

The worldwide proven recoverable reserves of conventional oil are less than the amount of the heavy oil. Owing to weakly consolidated formation, sand production is an important problem encountered during oil production in heavy oil reservoirs, for which frac-pack technique is one of the most common treatments. Hence, how to obtain the optimal fracture geometry is the key to increasing well production and preventing sand. Due to the faultiness that current optimization of the fracture geometry only depends on well productivity, fracture-flow fraction was used to describe the contribution of the fracture collecting and conducting fluids from the reservoir. The higher the fracture-flow fraction, the more likely bilinear flow pattern occurs, thus leading to smaller flow resistance and better results in oil productivity and sand prevention. A reservoir numerical simulation model was established to simulate the long-term production dynamic of a fractured well in rectangular drainage areas. In order to reach the aim of increasing productivity meanwhile preventing sand, a new method based on Unified Fracture Design was developed to optimize the fracture geometry. For a specific reservoir and a certain amount of proppant injected to the target layer, there exits an optimal dimensionless fracture conductivity which corresponds to the maximum fracture-flow fraction, accordingly we can get the optimal fracture geometry. The formulas of the optimal fracture geometry were presented on square drainage area conditions, which are very convenient to apply. Equivalent Proppant Number was used to eliminate the impact of aspect ratios of rectangular drainage area, then, the same method to optimize the fracture geometry as mentioned for square drainage areas could be adopted too.

Optimization of the Productivity Index and the Fracture Geometry of a Stimulated Well With Fracture Face and Choke Skins

Summary For a given reservoir of known permeability and dimensions, the proppant mass injected to the pay determines a unique proppant number. Unique to each proppant number, there exists an optimum dimensionless fracture conductivity that exclusively determines the optimum fracture dimensions.1 Impairments affecting flow perpendicular to the fracture surface are accounted for as fracture-face-skin effect. On the other hand, flow impairment caused by a reduction of the fracture conductivity near the wellbore is called choked fracture skin. Both effects have a large influence on the productivity of a fractured well. In this work, the performance of a fractured well is calculated with a direct boundary element method. This method provides the dimensionless productivity index, and the model allows for the presence of each of the two different skin effects. The fracture face skin was found to have a significant detrimental effect on the dimensionless productivity index, even changing the character of its dependence on the dimensionless fracture conductivity. The effect of the choke skin also was found to be potentially detrimental but less complex to account for because it can be represented as an apparent reduction in the proppant number.