The Experts below are selected from a list of 321 Experts worldwide ranked by ideXlab platform

Shijun Huang - One of the best experts on this subject based on the ideXlab platform.

  • A comprehensive model combining Laplace-transform finite-difference and boundary-element method for the flow behavior of a two-zone system with discrete Fracture network
    Journal of Hydrology, 2017
    Co-Authors: Linsong Cheng, Shijun Huang, Zhongyi Xu, Guanyang Ding
    Abstract:

    Abstract This paper provides a comprehensive model for the flow behavior of a two-zone system with discrete Fracture network. The discrete Fracture network within the inner zone is represented explicitly by Fracture segments. The Laplace-transform finite-difference method is used to numerically model discrete Fracture network flow, with sufficient flexibility to consider arbitrary Fracture geometries and Conductivity distributions. Boundary-element method and line-source functions in the Laplace domain are employed to derive a semi-analytical flow solution for the two-zone system. By imposing the continuity of flux and pressure on discrete Fracture surfaces, the semi-analytical two-zone system flow model and the numerical Fracture flow model are coupled dynamically. The main advantage of the approach occurring in the Laplace domain is that simulation can be done with nodes only for discrete Fractures and elements for boundaries and at predetermined, discrete times. Thus, stability and convergence problems caused by time discretization are avoided and the burden of gridding and computation is decreased without loss of important Fracture characteristics. The model is validated by comparison with the results from an analytical solution and a fully numerical solution. Flow regime analysis shows that a two-zone system with discrete Fracture network may develop six flow regimes: Fracture linear flow, bilinear flow, inner zone linear flow, inner zone pseudosteady-state flow, outer zone pseudoradial flow and outer zone boundary-dominated flow. Especially, local solutions for the inner-zone linear flow have the same form with that of a finite Conductivity planar Fracture and can be correlated with the total length of discrete Fractures and an intercept term. In the inner zone pseudosteady-state flow period, the discrete Fractures, along with the boundary of the inner zone, will act as virtual closed boundaries, due to the pressure interference caused by Fracture network and the mobility contrast of the two zones. The Dimensionless Fracture Conductivity of the Fracture network determines the characteristics of the bilinear flow and the inner zone linear flow. The mobility ratio, M, and storability ratio, Fs, primarily influence the flow behavior of the middle to later time. For a larger M, the ending time of the inner zone pseudosteady-state flow will be advanced and the beginning time of the outer-zone pseudoradial flow will be delayed. And the larger M also results in increasing of the values of the transient responses in these two periods. Duration of the outer-zone pseudoradial flow becomes longer, as Fs increases; the development of the outer-zone boundary-dominated flow is therefore postponed. Finally, idealization of dual-porosity model for the two zones will introduce two dips on the pressure derivatives on the log/log plot. Depending on the interporosity flow parameter, the time of the two dips varies. However, the dips are not very appreciable for the transient dual-porosity model, when the permeability of matrix system or Fracture density is relatively high.

  • a semi analytical model for the flow behavior of naturally Fractured formations with multi scale Fracture networks
    Journal of Hydrology, 2016
    Co-Authors: Linsong Cheng, Shijun Huang, Yonghui Wu
    Abstract:

    Summary This paper presents a semi-analytical model for the flow behavior of naturally Fractured formations with multi-scale Fracture networks. The model dynamically couples an analytical dual-porosity model with a numerical discrete Fracture model. The small-scale Fractures with the matrix are idealized as a dual-porosity continuum and an analytical flow solution is derived based on source functions in Laplace domain. The large-scale Fractures are represented explicitly as the major fluid conduits and the flow is numerically modeled, also in Laplace domain. This approach allows us to include finer details of the Fracture network characteristics while keeping the computational work manageable. For example, the large-scale Fracture network may have complex geometry and varying Conductivity, and the computations can be done at predetermined, discrete times, without any grids in the dual-porosity continuum. The validation of the semi-analytical model is demonstrated in comparison to the solution of ECLIPSE reservoir simulator. The simulation is fast, gridless and enables rapid model setup. On the basis of the model, we provide detailed analysis of the flow behavior of a horizontal production well in Fractured reservoir with multi-scale Fracture networks. The study has shown that the system may exhibit six flow regimes: large-scale Fracture network linear flow, bilinear flow, small-scale Fracture network linear flow, pseudosteady-state flow, interporosity flow and pseudoradial flow. During the first four flow periods, the large-scale Fracture network behaves as if it only drains in the small-scale Fracture network; that is, the effect of the matrix is negligibly small. The characteristics of the bilinear flow and the small-scale Fracture network linear flow are predominantly determined by the Dimensionless large-scale Fracture Conductivity. And low Dimensionless Fracture Conductivity will generate large pressure drops in the large-scale Fractures surrounding the wellbore. With the increasing of the interporosity flow parameter, flow exchange between the matrix and the small-scale Fracture network will be advanced and may mask the pseudosteady-state flow period. The duration of flow exchange increases and the dip caused by the interporosity flow gets deeper with the decreasing of the storability ratio. Finally, an appropriate choice of the pseudosteady or transient dual-porosity model to idealize the small-scale Fracture networks with the matrix depends entirely on a better understanding of the geological evidence supporting either model.

  • A semi-analytical model for the flow behavior of naturally Fractured formations with multi-scale Fracture networks
    Journal of Hydrology, 2016
    Co-Authors: Pin Jia, Linsong Cheng, Shijun Huang
    Abstract:

    Summary This paper presents a semi-analytical model for the flow behavior of naturally Fractured formations with multi-scale Fracture networks. The model dynamically couples an analytical dual-porosity model with a numerical discrete Fracture model. The small-scale Fractures with the matrix are idealized as a dual-porosity continuum and an analytical flow solution is derived based on source functions in Laplace domain. The large-scale Fractures are represented explicitly as the major fluid conduits and the flow is numerically modeled, also in Laplace domain. This approach allows us to include finer details of the Fracture network characteristics while keeping the computational work manageable. For example, the large-scale Fracture network may have complex geometry and varying Conductivity, and the computations can be done at predetermined, discrete times, without any grids in the dual-porosity continuum. The validation of the semi-analytical model is demonstrated in comparison to the solution of ECLIPSE reservoir simulator. The simulation is fast, gridless and enables rapid model setup. On the basis of the model, we provide detailed analysis of the flow behavior of a horizontal production well in Fractured reservoir with multi-scale Fracture networks. The study has shown that the system may exhibit six flow regimes: large-scale Fracture network linear flow, bilinear flow, small-scale Fracture network linear flow, pseudosteady-state flow, interporosity flow and pseudoradial flow. During the first four flow periods, the large-scale Fracture network behaves as if it only drains in the small-scale Fracture network; that is, the effect of the matrix is negligibly small. The characteristics of the bilinear flow and the small-scale Fracture network linear flow are predominantly determined by the Dimensionless large-scale Fracture Conductivity. And low Dimensionless Fracture Conductivity will generate large pressure drops in the large-scale Fractures surrounding the wellbore. With the increasing of the interporosity flow parameter, flow exchange between the matrix and the small-scale Fracture network will be advanced and may mask the pseudosteady-state flow period. The duration of flow exchange increases and the dip caused by the interporosity flow gets deeper with the decreasing of the storability ratio. Finally, an appropriate choice of the pseudosteady or transient dual-porosity model to idealize the small-scale Fracture networks with the matrix depends entirely on a better understanding of the geological evidence supporting either model.

Linsong Cheng - One of the best experts on this subject based on the ideXlab platform.

  • A comprehensive model combining Laplace-transform finite-difference and boundary-element method for the flow behavior of a two-zone system with discrete Fracture network
    Journal of Hydrology, 2017
    Co-Authors: Linsong Cheng, Shijun Huang, Zhongyi Xu, Guanyang Ding
    Abstract:

    Abstract This paper provides a comprehensive model for the flow behavior of a two-zone system with discrete Fracture network. The discrete Fracture network within the inner zone is represented explicitly by Fracture segments. The Laplace-transform finite-difference method is used to numerically model discrete Fracture network flow, with sufficient flexibility to consider arbitrary Fracture geometries and Conductivity distributions. Boundary-element method and line-source functions in the Laplace domain are employed to derive a semi-analytical flow solution for the two-zone system. By imposing the continuity of flux and pressure on discrete Fracture surfaces, the semi-analytical two-zone system flow model and the numerical Fracture flow model are coupled dynamically. The main advantage of the approach occurring in the Laplace domain is that simulation can be done with nodes only for discrete Fractures and elements for boundaries and at predetermined, discrete times. Thus, stability and convergence problems caused by time discretization are avoided and the burden of gridding and computation is decreased without loss of important Fracture characteristics. The model is validated by comparison with the results from an analytical solution and a fully numerical solution. Flow regime analysis shows that a two-zone system with discrete Fracture network may develop six flow regimes: Fracture linear flow, bilinear flow, inner zone linear flow, inner zone pseudosteady-state flow, outer zone pseudoradial flow and outer zone boundary-dominated flow. Especially, local solutions for the inner-zone linear flow have the same form with that of a finite Conductivity planar Fracture and can be correlated with the total length of discrete Fractures and an intercept term. In the inner zone pseudosteady-state flow period, the discrete Fractures, along with the boundary of the inner zone, will act as virtual closed boundaries, due to the pressure interference caused by Fracture network and the mobility contrast of the two zones. The Dimensionless Fracture Conductivity of the Fracture network determines the characteristics of the bilinear flow and the inner zone linear flow. The mobility ratio, M, and storability ratio, Fs, primarily influence the flow behavior of the middle to later time. For a larger M, the ending time of the inner zone pseudosteady-state flow will be advanced and the beginning time of the outer-zone pseudoradial flow will be delayed. And the larger M also results in increasing of the values of the transient responses in these two periods. Duration of the outer-zone pseudoradial flow becomes longer, as Fs increases; the development of the outer-zone boundary-dominated flow is therefore postponed. Finally, idealization of dual-porosity model for the two zones will introduce two dips on the pressure derivatives on the log/log plot. Depending on the interporosity flow parameter, the time of the two dips varies. However, the dips are not very appreciable for the transient dual-porosity model, when the permeability of matrix system or Fracture density is relatively high.

  • a semi analytical model for the flow behavior of naturally Fractured formations with multi scale Fracture networks
    Journal of Hydrology, 2016
    Co-Authors: Linsong Cheng, Shijun Huang, Yonghui Wu
    Abstract:

    Summary This paper presents a semi-analytical model for the flow behavior of naturally Fractured formations with multi-scale Fracture networks. The model dynamically couples an analytical dual-porosity model with a numerical discrete Fracture model. The small-scale Fractures with the matrix are idealized as a dual-porosity continuum and an analytical flow solution is derived based on source functions in Laplace domain. The large-scale Fractures are represented explicitly as the major fluid conduits and the flow is numerically modeled, also in Laplace domain. This approach allows us to include finer details of the Fracture network characteristics while keeping the computational work manageable. For example, the large-scale Fracture network may have complex geometry and varying Conductivity, and the computations can be done at predetermined, discrete times, without any grids in the dual-porosity continuum. The validation of the semi-analytical model is demonstrated in comparison to the solution of ECLIPSE reservoir simulator. The simulation is fast, gridless and enables rapid model setup. On the basis of the model, we provide detailed analysis of the flow behavior of a horizontal production well in Fractured reservoir with multi-scale Fracture networks. The study has shown that the system may exhibit six flow regimes: large-scale Fracture network linear flow, bilinear flow, small-scale Fracture network linear flow, pseudosteady-state flow, interporosity flow and pseudoradial flow. During the first four flow periods, the large-scale Fracture network behaves as if it only drains in the small-scale Fracture network; that is, the effect of the matrix is negligibly small. The characteristics of the bilinear flow and the small-scale Fracture network linear flow are predominantly determined by the Dimensionless large-scale Fracture Conductivity. And low Dimensionless Fracture Conductivity will generate large pressure drops in the large-scale Fractures surrounding the wellbore. With the increasing of the interporosity flow parameter, flow exchange between the matrix and the small-scale Fracture network will be advanced and may mask the pseudosteady-state flow period. The duration of flow exchange increases and the dip caused by the interporosity flow gets deeper with the decreasing of the storability ratio. Finally, an appropriate choice of the pseudosteady or transient dual-porosity model to idealize the small-scale Fracture networks with the matrix depends entirely on a better understanding of the geological evidence supporting either model.

  • A semi-analytical model for the flow behavior of naturally Fractured formations with multi-scale Fracture networks
    Journal of Hydrology, 2016
    Co-Authors: Pin Jia, Linsong Cheng, Shijun Huang
    Abstract:

    Summary This paper presents a semi-analytical model for the flow behavior of naturally Fractured formations with multi-scale Fracture networks. The model dynamically couples an analytical dual-porosity model with a numerical discrete Fracture model. The small-scale Fractures with the matrix are idealized as a dual-porosity continuum and an analytical flow solution is derived based on source functions in Laplace domain. The large-scale Fractures are represented explicitly as the major fluid conduits and the flow is numerically modeled, also in Laplace domain. This approach allows us to include finer details of the Fracture network characteristics while keeping the computational work manageable. For example, the large-scale Fracture network may have complex geometry and varying Conductivity, and the computations can be done at predetermined, discrete times, without any grids in the dual-porosity continuum. The validation of the semi-analytical model is demonstrated in comparison to the solution of ECLIPSE reservoir simulator. The simulation is fast, gridless and enables rapid model setup. On the basis of the model, we provide detailed analysis of the flow behavior of a horizontal production well in Fractured reservoir with multi-scale Fracture networks. The study has shown that the system may exhibit six flow regimes: large-scale Fracture network linear flow, bilinear flow, small-scale Fracture network linear flow, pseudosteady-state flow, interporosity flow and pseudoradial flow. During the first four flow periods, the large-scale Fracture network behaves as if it only drains in the small-scale Fracture network; that is, the effect of the matrix is negligibly small. The characteristics of the bilinear flow and the small-scale Fracture network linear flow are predominantly determined by the Dimensionless large-scale Fracture Conductivity. And low Dimensionless Fracture Conductivity will generate large pressure drops in the large-scale Fractures surrounding the wellbore. With the increasing of the interporosity flow parameter, flow exchange between the matrix and the small-scale Fracture network will be advanced and may mask the pseudosteady-state flow period. The duration of flow exchange increases and the dip caused by the interporosity flow gets deeper with the decreasing of the storability ratio. Finally, an appropriate choice of the pseudosteady or transient dual-porosity model to idealize the small-scale Fracture networks with the matrix depends entirely on a better understanding of the geological evidence supporting either model.

Yonghui Wu - One of the best experts on this subject based on the ideXlab platform.

  • a semi analytical model for the flow behavior of naturally Fractured formations with multi scale Fracture networks
    Journal of Hydrology, 2016
    Co-Authors: Linsong Cheng, Shijun Huang, Yonghui Wu
    Abstract:

    Summary This paper presents a semi-analytical model for the flow behavior of naturally Fractured formations with multi-scale Fracture networks. The model dynamically couples an analytical dual-porosity model with a numerical discrete Fracture model. The small-scale Fractures with the matrix are idealized as a dual-porosity continuum and an analytical flow solution is derived based on source functions in Laplace domain. The large-scale Fractures are represented explicitly as the major fluid conduits and the flow is numerically modeled, also in Laplace domain. This approach allows us to include finer details of the Fracture network characteristics while keeping the computational work manageable. For example, the large-scale Fracture network may have complex geometry and varying Conductivity, and the computations can be done at predetermined, discrete times, without any grids in the dual-porosity continuum. The validation of the semi-analytical model is demonstrated in comparison to the solution of ECLIPSE reservoir simulator. The simulation is fast, gridless and enables rapid model setup. On the basis of the model, we provide detailed analysis of the flow behavior of a horizontal production well in Fractured reservoir with multi-scale Fracture networks. The study has shown that the system may exhibit six flow regimes: large-scale Fracture network linear flow, bilinear flow, small-scale Fracture network linear flow, pseudosteady-state flow, interporosity flow and pseudoradial flow. During the first four flow periods, the large-scale Fracture network behaves as if it only drains in the small-scale Fracture network; that is, the effect of the matrix is negligibly small. The characteristics of the bilinear flow and the small-scale Fracture network linear flow are predominantly determined by the Dimensionless large-scale Fracture Conductivity. And low Dimensionless Fracture Conductivity will generate large pressure drops in the large-scale Fractures surrounding the wellbore. With the increasing of the interporosity flow parameter, flow exchange between the matrix and the small-scale Fracture network will be advanced and may mask the pseudosteady-state flow period. The duration of flow exchange increases and the dip caused by the interporosity flow gets deeper with the decreasing of the storability ratio. Finally, an appropriate choice of the pseudosteady or transient dual-porosity model to idealize the small-scale Fracture networks with the matrix depends entirely on a better understanding of the geological evidence supporting either model.

Pin Jia - One of the best experts on this subject based on the ideXlab platform.

  • A semi-analytical model for the flow behavior of naturally Fractured formations with multi-scale Fracture networks
    Journal of Hydrology, 2016
    Co-Authors: Pin Jia, Linsong Cheng, Shijun Huang
    Abstract:

    Summary This paper presents a semi-analytical model for the flow behavior of naturally Fractured formations with multi-scale Fracture networks. The model dynamically couples an analytical dual-porosity model with a numerical discrete Fracture model. The small-scale Fractures with the matrix are idealized as a dual-porosity continuum and an analytical flow solution is derived based on source functions in Laplace domain. The large-scale Fractures are represented explicitly as the major fluid conduits and the flow is numerically modeled, also in Laplace domain. This approach allows us to include finer details of the Fracture network characteristics while keeping the computational work manageable. For example, the large-scale Fracture network may have complex geometry and varying Conductivity, and the computations can be done at predetermined, discrete times, without any grids in the dual-porosity continuum. The validation of the semi-analytical model is demonstrated in comparison to the solution of ECLIPSE reservoir simulator. The simulation is fast, gridless and enables rapid model setup. On the basis of the model, we provide detailed analysis of the flow behavior of a horizontal production well in Fractured reservoir with multi-scale Fracture networks. The study has shown that the system may exhibit six flow regimes: large-scale Fracture network linear flow, bilinear flow, small-scale Fracture network linear flow, pseudosteady-state flow, interporosity flow and pseudoradial flow. During the first four flow periods, the large-scale Fracture network behaves as if it only drains in the small-scale Fracture network; that is, the effect of the matrix is negligibly small. The characteristics of the bilinear flow and the small-scale Fracture network linear flow are predominantly determined by the Dimensionless large-scale Fracture Conductivity. And low Dimensionless Fracture Conductivity will generate large pressure drops in the large-scale Fractures surrounding the wellbore. With the increasing of the interporosity flow parameter, flow exchange between the matrix and the small-scale Fracture network will be advanced and may mask the pseudosteady-state flow period. The duration of flow exchange increases and the dip caused by the interporosity flow gets deeper with the decreasing of the storability ratio. Finally, an appropriate choice of the pseudosteady or transient dual-porosity model to idealize the small-scale Fracture networks with the matrix depends entirely on a better understanding of the geological evidence supporting either model.

Michael J. Economides - One of the best experts on this subject based on the ideXlab platform.

  • Horizontal Hydraulic Fracture Design for Optimal Well Productivity in Anisotropic Reservoirs with Different Aspect Ratios
    Unconventional Resources Technology Conference Denver Colorado 12-14 August 2013, 2013
    Co-Authors: Francisco D. Tovar, Michael J. Economides, Kyung Jae Lee, Sergio E. Gonzales, Yun Suk Hwang, Andres M. Del Busto, Aderonke Aderibigbe, Christine Ehlig-economides
    Abstract:

    Summary The economic feasibility of the exploitation of unconventional resources is highly dependent on the ability of the operator to maximize individual well productivity, making hydraulic Fracture design and implementation the defining factor for a successful field development in most cases. Some unconventional reservoirs, as shallow coal bed methane and over-pressured oil and gas shale formations, commonly present the minimum principal stress in the vertical direction, resulting in the occurrence of horizontal hydraulic Fractures. Models for the transient flow and pressure behavior of horizontal Fractures emanating from vertical wells exist and clearly show distinct performance from those for vertical Fractures. This suggests that the widely accepted unified Fracture design (UFD) approach to maximize well productivity for vertical and horizontal wells with vertical hydraulic Fractures cannot be used for horizontal Fractures. Thereafter, the necessity for guidelines to model and design horizontal Fractures becomes evident. This investigation begins by presenting a new set of equations for horizontal Fracture design based on the UFD approach, which allows the direct calculation of Fracture width, half-length and Conductivity for a given proppant number. Later, a reservoir numerical simulator is used to model well productivity behavior for horizontal Fractures in homogeneous formations, with or without vertical to horizontal permeability anisotropy and for different aspect ratios as a function of suitably-defined proppant number, Dimensionless Fracture Conductivity, and Fracture penetration index parameters. The findings of this work reveal a complex behavior for horizontal Fractures that prohibits the extrapolation of previous generalizations between proppant number, penetration index and Dimensionless Fracture Conductivity established for vertical Fractures. For a number of scenarios, new relationships among these variables are provided to guide horizontal Fracture design. Anisotropy and reservoir aspect ratio were also found to significantly impact Fracture performance. Additionally, a set of multi-variable functions that permit the estimation of maximum achievable productivity index for the horizontal Fracture has been fitted, based on commonly known reservoir parameters and the proppant number. This investigation provides a comprehensive framework to assist the design of optimal horizontal Fracture geometry that maximizes productivity for a given mass of proppant.

  • Hydraulic Fracture Production Optimization with a Pseudo-3D Model in Low-permeability, Multi-layered Lithology
    All Days, 2012
    Co-Authors: Mei Yang, Peter P. Valko, Michael J. Economides
    Abstract:

    Abstract Systematic design and optimization procedures for hydraulic fracturing are available using two-dimensional (2D) (with constant Fracture height) and pseudo-three-dimensional (p-3D) models to maximize well production by optimizing Fracture geometry, including Fracture height, half-length and width. A multi-layered p-3D approach to design is proposed integrating Unified Fracture Design (UFD), Fracture propagation models and Linear Elastic Fracture Mechanics (LEFM) relationship to generate optimized Fracture geometry, including Fracture height, width and half-length to achieve the maximized production. Containment layers are discretized to allow for plausible Fracture heights when seeking convergence of Fracture height and net pressure. UFD sizes the Fracture geometry to physically optimize the hydraulically Fractured well performance. The Proppant Number is a correlating parameter, which in turn provides the maximum Dimensionless productivity index (JD) corresponding to the optimum Dimensionless Fracture Conductivity, CfD. Once the latter is determined, the optimum Fracture dimensions, i.e., Fracture length and width, are set. However, UFD in its original form needs the ability to calculate the Proppant Number and that is possible only if Fracture height is an input parameter and hence fraction of proppant ending up in the pay can be determined before the optimization. PKN or KGD Fracture propagation models in design mode provide basic treatment parameters to achieve a known target length and also associated net pressure. Linear Elastic Fracture Mechanics (LEFM) relationship can be used to obtain Fracture height associated to a given vertical pressure distribution via vertical stress profile and Fracture toughness profile. This study considers the contributions of all layers to the stress intensity factor at the Fracture tips to find the potential equilibrium height defined by the condition where the stress intensity factor minus Fracture toughness difference changes sign (but not necessary becomes zero.) After an equilibrium height and the corresponding net pressure are found, an optimization is carried out to find target length and a 2D design model is used to calculate treatment parameters, first of all net pressure. The ultimate goal is to find a consistent pair of these two different sub-models; when the assumed pressure condition in the LEFM part coincides with the resulting pressure condition from the UFD/2D part. Parts of this work also allows for determining conditions to avoid propagating into unintended layers (i.e. gas cap and/or aquifer) or to assure coverage of intended layers (such as a non-perforated layer with recoverable hydrocarbon.)

  • Hydraulic Fracture Optimization with a p-3D Model
    All Days, 2011
    Co-Authors: Termpan Pitakbunkate, Peter P. Valko, Mei Yang, Michael J. Economides
    Abstract:

    Abstract In 2002 we introduced the concept of Unified Fracture Design (UFD) as a coherent way to size the Fracture geometry for the expressed purpose to physically optimize the well performance. We used the Proppant Number as a correlating parameter, which in turn provided the maximum Dimensionless productivity index (JD) which corresponds to the optimum Dimensionless Fracture Conductivity, CfD. Once the latter is determined, the Fracture dimensions, i.e., Fracture length and width, are set. If one assumes the Fracture height is known and constant then the calculation is simple and a 2D Fracture propagation model can be used. However, Fracture height is not constant throughout the Fracture and it cannot be considered constant during execution, depending greatly on the net pressure and vice versa. We are presenting here an iterative procedure where the Fracture height is related to the net pressure. In the procedure, for any assumed net pressure, the Fracture height, along with the mass of proppant and the permeabilities of the reservoir and the proppant, lead to the Proppant Number which in turn determines the desired length and width. A Fracture propagation model, such as the PKN geometry for lateral growth, coupled with a changing Fracture height, leads to the calculation of the net pressure which is compared with the one assumed. Convergence of the assumed and calculated net pressure is what is sought. The design procedure presented here is for both oil and gas wells. The design also includes the calculation of required treating pressure and finally it incorporates economics for production enhancement optimization beyond the physical optimization using UFD. Comparison of the 2D to the p-3D results points to the need and importance of the p-3D in a large array of reservoirs.

  • Application of Pressure-Transient and Production-Data Analysis for Hydraulic-Fracture-Treatment Evaluation
    All Days, 2007
    Co-Authors: Michael J. Economides, Christine Ehlig-economides, Slavko Tosic
    Abstract:

    Abstract The Unified Fracture Design (UFD) concept provides a mechanism to determine the optimal hydraulic Fracture design for a given amount of a selected proppant, while modern hydraulic Fracture treatment execution offers the potential to achieve the optimal design. The proppant number is a ratio of the proppant permeability and proppant volume product to the formation permeability and reservoir volume product. The cost of the hydraulic Fracture treatment is directly related to the quality and quantity of proppant injected and successful achievement of the optimal Fracture treatment easily offsets this cost when appropriate economics and physical and logistical constraints are considered in the job design. Pressure transient and production data analyses are described in terms of Fracture length and Conductivity and do not address parameters important to the UFD evaluation. A previous paper described the use of post-treatment analysis to evaluate the effectiveness of the treatment in terms of Dimensionless productivity index, Dimensionless Fracture Conductivity, and the proppant number. With more and more permanent gauge installations, opportunities for pressure buildup analysis may occur under normal operating conditions without a specific test design. In this case both pressure transient and production data analysis may be available. The analysis addresses both single-phase oil and gas primary production and oil production under pressure maintenance or waterflood. Also, non-ideal Fractures with height growth beyond the producing formation thickness and Fracture skin are considered. Field examples will include both hard rock and soft rock fracturing case studies. The importance of this analysis is paramount for operators trying to optimize high value hydraulic Fracture treatments. Introduction Evaluation of post-treatment well performance has intrinsic value on at least three different and important stages. Because of the complexity of the operation and the confluence of different engineering and technical disciplines for wells that are hydraulically Fractured the task becomes even more cumbersome, although no less compelling. The first and most obvious verdict is the apparent success of a treatment. How much better does the well perform compared to the pre-treatment state? Clearly, the job would not be deemed successful if the well produces less than before. Similarly, for the job execution, did it go according to plan and design? Was all the intended proppant injected? This stage may lead to improvements in areas such as quality control and competence of personnel. Second, is the comparison between the actual well performance and the one expected from the design? While invariably Fracture treatment proposals by service companies and in-house personnel promise a post-treatment performance, the two rarely match and even rarer are attempts to reconcile the differences. Ehlig-Economides et al. (2006) presented an approach to use pressure transient analysis (PTA) and/or production data analysis (PDA) for the calculation of important post-treatment variables that would aid in the evaluation. The objectives of both techniques are to determine reservoir permeability (if unknown before the treatment), the Fracture half-length and Conductivity and, by extension, the post-treatment Fracture equivalent skin effect. PTA generally involves a pressure buildup test, whereas PDA employs long-term production rate and flowing bottomhole pressure data.

  • Pushing the Limits of Hydraulic Fracturing in Russia
    All Days, 2004
    Co-Authors: Michael J. Economides, Andronikos S. Demarchos, J.m. Mach, J. Rueda, D.s. Wolcott
    Abstract:

    Abstract We have established the concept of Unified Fracture Design (UFD) to maximize the Dimensionless productivity index (JD) following a hydraulic Fracture treatment. For a given mass of proppant there is a specific Dimensionless Fracture Conductivity, which we called the optimum, at which the JD becomes maximum. The Proppant Number is a seminal quantity unifying the propped Fracture and the drainage volumes and the two permeabilities, those of the proppant pack and the reservoir. For each injected proppant mass there is a corresponding Proppant Number and, at the optimum Conductivity, the Dimensionless PI can be readily determined. Increasing the proppant mass or the proppant-pack permeability would result in an increase in the JD, which has a maximum limit of approximately 1.9. In a recent publication we have shown how to push the limits in hydraulic fracturing by injecting very large volumes of proppant of very large retained permeability. There are physical constraints to our approach, one of which is an upper limit of the net pressure resulting from both the physical limitations of injection equipment and tubulars but also from the need to prevent undesirable Fracture height migration. However, the use of much larger proppant pack permeability leads to a correspondingly smaller width for the same Fracture Conductivity. The smaller width requirement allows the injection of far larger proppant masses before the net pressure constraints are met. This is a departure from current industry practices, which are aimed to "save" injection costs for a specific rate. Our approach, in medium to high permeability formations is to maximize the rate within the injection constraints. Rudimentary economics suggest that such treatments pay for themselves in just a few days of incremental production. We present here field case studies and results showing the application and success of our design approach. Introduction Valkó and Economides1,2 introduced a physical optimization technique to maximize the productivity index. They introduced the concept of the Dimensionless Proppant Number, Nprop, given by:Equation 1 where Ix is the penetration ratio and CfD is the dimesnionless Fracture Conductivity, Vr is the reservoir drainage volume, and Vp is the volume of the proppant in the pay. It is equal to the total volume injected times the ratio of the net height to the Fracture height. They also presented convenient algorithms to calculate JD and they found that for a given value of Nprop there is an optimal Dimensionless Fracture Conductivity at which the productivity index is maximized. At "low" proppant numbers, the optimal Conductivity, CfD=1.6. The absolute maximum for JD is 6/p=1.909 (this value is the productivity index for a perfect linear flow in a square reservoir). When the propped volume increases or the reservoir permeability decreases, the optimum Dimensionless Fracture Conductivity increases somewhat. Under the assumption of the pseudosteady-state flow regime Valkó and Economides1,2 presented correlations for the maximum achievable Dimensionless productivity index as a function of the proppant number.Equation 2 Similarly correlations have been presented for the optimal Dimensionless