Productivity Analysis of Volume Fractured Wells under Different Working Systems

The volume fracturing technique has been widely used to improve the productivity of ultralow-permeability reservoirs. This paper presents a new semianalytical model to simulate the pressure transient and production behaviour of finite conductivity vertical fractured wells with stimulated reservoir volume (SRV) in heterogeneous reservoirs. The model is based on the five-linear flow model, the Warren-Root model, and fracture conductivity influence function. The model is validated by comparing its results with a numerical model. One novelty of this model is its consideration of three different kinds of production prediction models. Constant rate, constant pressure, and compound working systems are taken into account. This paper illustrates the effects of the SRV size and shape, mobility ratio, initial flow rate, limiting wellbore pressure, and hydraulic fracture parameters under different working systems. Results show that the SRV and parameters of fractures have a significant influence on long-term well performance. Moreover, the initial rate can extend the constant rate period by 418%, and limiting wellbore pressure can effectively improve the cumulative recovery rate by 23%. Therefore, this model can predict long-term wells’ behaviour and provide practical guiding significance for hydraulic fracturing design.

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Optimization of Managed Drawdown for a Well With Stress-Sensitive Conductivity Fractures: Workflow and Case Study

Journal of Energy Resources Technology ◽

10.1115/1.4048980 ◽

2020 ◽

Vol 143 (8) ◽

Author(s):

Yunsheng Wei ◽

Junlei Wang ◽

Ailin Jia ◽

Cheng Liu ◽

Chao Luo ◽

...

Keyword(s):

Stress Sensitivity ◽

Gas Production ◽

Time Dependent ◽

Finite Conductivity ◽

Well Performance ◽

Fracture Conductivity ◽

Field Case ◽

Long Term Performance ◽

Term Performance

Abstract The effect of bottomhole-pressure (BHP) drawdown schedule on the well performance is generally attributed to the stress sensitivity in propped finite-conductivity fractures. The purpose of this work is to develop a detailed workflow of optimizing BHP drawdown schedule to improve long-term performance by finding a tradeoff between delaying conductivity degradation and maintaining drawdown. First, according to experimental data of propped fracture, an alternative relationship between conductivity and pressure drawdown is developed to mimic the change of fracture conductivity with effective stress. Second, based on the dimension-transformation technique, the coupled fracture-reservoir model is semi-analytically solved and seamlessly generates the time-dependent equation (i.e., transient inflow performance relationship (IPR)) which provides the production rate response to any BHP variation. Next, the value of BHP on the reversal behavior of rate is defined as the optimum BHP on the specified time-dependent IPR, and then the optimum profile of BHP drawdown over time is achieved. Finally, we corroborate the effectiveness of this workflow with a field case from Zhaotong shale in China. Field case substantiates that (1) the well with restricted drawdown has more advantage of improving the performance than that with unrestricted drawdown and (2) after inputting the optimum BHP drawdown into the history-unrestricted case, the long-term cumulative gas production could indeed be increased.

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Effect of Non-Darcy Flow on the Constant-Pressure Production of Fractured Wells

Society of Petroleum Engineers Journal ◽

10.2118/9344-pa ◽

1981 ◽

Vol 21 (03) ◽

pp. 390-400 ◽

Cited By ~ 24

Author(s):

K.H. Guppy ◽

Heber Cinco-Ley ◽

Henry J. Ramey

Keyword(s):

Constant Pressure ◽

Darcy Flow ◽

Flow In Porous Media ◽

Graphical Form ◽

Finite Conductivity ◽

Fracture Conductivity ◽

Type Curves ◽

Pressure Behavior ◽

Apparent Conductivity ◽

Constant Rate

Abstract In many low-permeability gas reservoirs, producing a well at constant rate is very difficult or, in many cases, impossible. Constant-pressure production is much easier to attain and more realistic in practice. This is seen when production occurs into a constant-pressure separator or during the reservoir depletion phase, when the rate-decline period occurs. Geothermal reservoirs, which produce fluids that drive backpressure turbines, and open-well production both incorporate the constant-pressure behavior. For finite-conductivity vertically fractured systems, solutions for the constant-pressure case have been presented in the literature. In many high-flow-rate wells, however, these solutions may not be useful since high velocities are attained in the fracture, which results in non-Darcy effects within the fracture. In this study, the effects of non-Darcy flow within the fracture are investigated. Unlike the constant-rate case, it was found that the fracture conductivity does not have a constant apparent conductivity but rather an apparent conductivity that varies with time. Semianalytical solutions as well as graphical solutions in the form of type curves are presented to illustrate this effect. An example is presented for analyzing rate data by using both solutions for Darcy and non-Darcy flow within the fracture. This example relies on good reservoir permeability from prefracture data to predict the non-Darcy effect accurately. Introduction To fully analyze the effects of constant-bottomhole-pressure production of hydraulically fractured wells, it is necessary that we understand the pressure behavior of finite-conductivity fracture systems producing at constant rate as well as the effects of non-Darcy flow on gas flow in porous media. Probably one of the most significant contributions in the transient pressure analysis theory for fractured wells was made by Gringarten et al.1,2 In the 1974 paper,2 general solutions were made for infinite-conductivity fractures. Cinco et al.3 found a more general solution for the case of finite-conductivity fractures and further extended this analysis in 1978 to present a graphical technique to estimate fracture conductivity.4 For the case of constant pressure at the wellbore, solutions were presented in graphical form by Agarwal et al.5 In his paper, a graph of log (1/qD) vs. log (tDxf) can be used to determine the conductivity of the fracture by using type-curve matching. Although such a contribution is of great interest, unique solutions are difficult to obtain. More recently, Guppy et al.6 showed that the Agarwal et al. solutions may be in error and presented new type curves for the solution to the constant-pressure case assuming Darcy flow in the fracture. That paper developed analytical solutions which can be applied directly to field data so as to calculate the fracture permeability-width (kfbf) product.

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Unique Fall Off Signatures for Stage Fracture Characterization, Actual Field Cases

10.2118/200887-ms ◽

2021 ◽

Author(s):

Ahmed Farid Ibrahim ◽

Mazher Ibrahim ◽

Matt Sinkey ◽

Thomas Johnston ◽

Wes Johnson

Keyword(s):

Flow Regime ◽

Surface Area ◽

Fiber Optics ◽

In Situ Stress ◽

Tensile Fracture ◽

Finite Conductivity ◽

Well Performance ◽

Fracture Geometry ◽

Fracture Conductivity ◽

Diagnostic Plots

Abstract Multistage hydraulic fracturing is the common stimulation technique for shale formations. The treatment design, formation in-situ stress, and reservoir heterogeneity govern the fracture network propagation. Different techniques have been used to evaluate the fracture geometry and the completion efficiency including Chemical Tracers, Microseismic, Fiber Optics, and Production Logs. Most of these methods are post-fracture as well as time and cost intensive processes. The current study presents the use of fall-off data during and after stage fracturing to characterize producing surface area, permeability, and fracture conductivity. Shut-in data (15-30 minutes) was collected after each stage was completed. The fall-off data was processed first to remove the noise and water hammer effects. Log-Log derivative diagnostic plots were used to define the flow regime and the data were then matched with an analytical model to calculate producing surface area, permeability, and fracture conductivity. Diagnostic plots showed a unique signature of flow regimes. A long period of a spherical flow regime with negative half-slope was observed as an indication for limited entry flow either vertically or horizontally. A positive half-slope derivative represents a linear flow regime in an infinitely conductive tensile fracture. The quarter-slope derivative was observed in a bilinear flow regime that represents a finite conductivity fracture system. An extended radial flow regime was observed with zero slope derivative which represents a highly shear fractured network around the wellbore. For a long fall-off period, formation recharge may appear with a slope between unit and 1.5 slopes derivative, especially in over-pressured dry gas reservoirs. Analyzing fall-off data after stages are completed provides a free and real-time investigation method to estimate the fracture geometry and a measure of completion efficiency. Knowing the stage properties allows the reservoir engineer to build a simulation model to forecast the well performance and improve the well spacing.

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Application Investigation of Light Proppant in Hydraulic Fracturing of Marcellus Shale

10.2118/201807-ms ◽

2021 ◽

Author(s):

Aymen Alhemdi ◽

Ming Gu

Keyword(s):

History Matching ◽

Marcellus Shale ◽

In Situ Stress ◽

Production Performance ◽

Well Performance ◽

Fracture Permeability ◽

Fracture Conductivity ◽

Stimulated Reservoir Volume ◽

Conductivity Distribution ◽

Cumulative Production

Abstract Slickwater-sand fracturing design is widely employed in Marcellus shale. The slickwater- sand creates long skinny fractures and maximizes the stimulated reservoir volume (SRV). However, due to the fast settling of sand in the water, lots of upper and deeper areas are not sufficiently propped. Reducing sand size can lead to insufficient fracture conductivity. This study proposes to use three candidate ultra-lightweight proppants ULWPs to enhance the fractured well performance in unconventional reservoirs. In step 1, the current sand pumping design is input into an in-house P3D fracture propagation simulator to estimate the fracture geometry and proppant concentrations. Next, the distribution of proppant concentration converts to conductivity and then to fracture permeability. In the third step, the fracture permeability from the second step is input into a reservoir simulator to predict the cumulative production for history matching and calibration. In step 4, the three ULWPs are used to replace the sand in the frac simulator to get new frac geometry and conductivity distribution and then import them in reservoir model for production evaluation. Before this study, the three ULWPs have already been tested in the lab to obtain their long-term conductivities under in-situ stress conditions. The conductivity distribution and production performance are analyzed and investigated. The induced fracture size and location of the produced layer for the current target well play a fundamental effect on ultra-light proppant productivity. The average conductivity of ULWPs with mesh 40/70 is larger and symmetric along the fracture except for a few places. However, ULWPs with mesh 100 generates low average conductivity and create a peak conductivity in limited areas. The ULW-3 tends to have less cumulative production compared with the other ULWPs. For this Marcellus Shale study, the advantages of ultra-lightweight proppant are restricted and reduced because the upward fracture height growth is enormous. And with the presence of the hydrocarbon layer is at the bottom of the fracture, making a large proportion of ULWPs occupies areas that are not productive places. The current study provides a guidance for operators in Marcellus Shale to determine (1) If the ULWP can benefit the current shale well treated by sand, (2) what type of ULWP should be used, and (3) given a certain type of ULWP, what is the optimum pumping schedule and staging/perforating design to maximize the well productivity. The similar workflow can be expanded to evaluate the economic potential of different ULWPs in any other unconventional field.

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A New Pseudo Steady-State Constant for a Vertical Well with Finite-Conductivity Fracture

Processes ◽

10.3390/pr6070093 ◽

2018 ◽

Vol 6 (7) ◽

pp. 93 ◽

Cited By ~ 2

Author(s):

Yudong Cui ◽

Bin Lu ◽

Mingtao Wu ◽

Wanjing Luo

Keyword(s):

Approximate Solution ◽

Steady State ◽

Analytical Solution ◽

Influence Function ◽

Finite Conductivity ◽

Time Saving ◽

Fracture Conductivity ◽

Type Curves ◽

Wellbore Pressure ◽

The Difference

The Pseudo Steady-State (PSS) constant bDpss is defined as the difference between the dimensionless wellbore pressure and dimensionless average pressure of a reservoir with a PSS flow regime. As an important parameter, bDpss has been widely used for decline curve analysis with Type Curves. For a well with a finite-conductivity fracture, bDpss is independent of time and is a function of the penetration ratio of facture and fracture conductivity. In this study, we develop a new semi-analytical solution for bDpss calculations using the PSS function of a circular reservoir. Based on the semi-analytical solution, a new conductivity-influence function (CIF) representing the additional pressure drop caused by the effect of fracture conductivity is presented. A normalized conductivity-influence function (NCIF) is also developed to calculate the CIF. Finally, a new approximate solution is proposed to obtain the bDpss value. This approximate solution is a fast, accurate, and time-saving calculation.

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Productivity Analysis of Volume Fractured Vertical Well Model in Tight Oil Reservoirs

Mathematical Problems in Engineering ◽

10.1155/2017/9589321 ◽

2017 ◽

Vol 2017 ◽

pp. 1-14 ◽

Cited By ~ 2

Author(s):

Jiahang Wang ◽

Xiaodong Wang ◽

Wenli Xu ◽

Cheng Lu ◽

Wenxiu Dong ◽

...

Keyword(s):

Outer Region ◽

Fracture Network ◽

Oil Reservoirs ◽

Finite Conductivity ◽

Tight Oil ◽

Productivity Analysis ◽

Type Curves ◽

Stimulated Reservoir Volume ◽

Vertical Well ◽

Tight Oil Reservoirs

This paper presents a semianalytical model to simulate the productivity of a volume fractured vertical well in tight oil reservoirs. In the proposed model, the reservoir is a composite system which contains two regions. The inner region is described as formation with finite conductivity hydraulic fracture network and the flow in fracture is assumed to be linear, while the outer region is simulated by the classical Warren-Root model where radial flow is applied. The transient rate is calculated, and flow patterns and characteristic flowing periods caused by volume fractured vertical well are analyzed. Combining the calculated results with actual production data at the decline stage shows a good fitting performance. Finally, the effects of some sensitive parameters on the type curves are also analyzed extensively. The results demonstrate that the effect of fracture length is more obvious than that of fracture conductivity on improving production in tight oil reservoirs. When the length and conductivity of main fracture are constant, the contribution of stimulated reservoir volume (SRV) to the cumulative oil production is not obvious. When the SRV is constant, the length of fracture should also be increased so as to improve the fracture penetration and well production.

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Non-Darcy Flow in Wells With Finite-Conductivity Vertical Fractures

Society of Petroleum Engineers Journal ◽

10.2118/8281-pa ◽

1982 ◽

Vol 22 (05) ◽

pp. 681-698 ◽

Cited By ~ 42

Author(s):

K.H. Guppy ◽

H. Cinco-Ley ◽

H.J. Ramey ◽

F. Samaniego-V.

Keyword(s):

Hydraulic Fracturing ◽

Turbulent Flow ◽

High Flow ◽

Darcy Flow ◽

Finite Conductivity ◽

Gas Wells ◽

Fracture Conductivity ◽

Flow Rates ◽

Vertical Fracture ◽

Constant Rate

Abstract Several methods have been proposed in the literature for analyzing drawdown data for the determination of fracture conductivity of vertically fractured wells. These techniques have paved accurate, but in some cases the fracture conductivity calculated is much smaller than anticipated. This study shows that producing fractured wells at high flow rates will cause nondarcy effects in the fracture, resulting in a pessimistic fracture conductivity.Numerical and semianalytical models were developed to analyze the unsteady flow behavior of finite conductivity fractures producing at high flow rates. Two methods are presented for determining the true fracture conductivity when drawdown data are available at two different flow rates. The amount of turbulent effects also is quantified by the techniques. Examples are presented to illustrate the solution methods. Introduction The increasing use of hydraulic fracturing as a means of improving the productivity of oil and gas wells in low-permeability formations has resulted in many research efforts aimed at increasing fracturing capabilities as well as evaluating the characteristics of the fracture in the postfracturing period. With the advent of the massive postfracturing period. With the advent of the massive hydraulic fracturing (MHF) treatment in recent years, the need for new solutions for evaluating these systems has increased. The problem with the older solutions was the need for many assumptions to arrive at a simple solution. One of the more common assumptions made in these systems was the use of linear flow to describe the flow within the fracture. In gas wells with finite-conductivity fractures producing at high flow rates, the non-Darcy effect is created within the fracture. Hence, new solutions must be developed for these systems. The objective of this paper is to present a new semianalytical solution to this problem that can be applied both to the linear and to the nondarcy flow regimes within the fracture.Over the years. several methods have been developed to analyze postfracture data. Gringarien et al. first solved the fracture system analytically for three special cases: infinite-conductivity vertical fracture, uniform flux vertical fracture, and horizontal fracture. At that time, its application became quite useful. But since not all systems behaved in this manner, the need for further solutions was warranted. Cinco-L. et al. investigated the general case of finite-conductivity vertical fractures, which included the above solution. as well as fracture conductivities as low as 0.1. This research also led to the need to analyze short-time data to obtain unique solutions. Similar results were obtained by Agarwat et al., who presented a finite-difference solution to this problem, considering both the constant rate as well as the problem, considering both the constant rate as well as the constant pressure cases.One of the first papers written on the effects of non-Darcy flow in fractured systems was by Wattenbarger and Ramey. They investigated the effects of non-Darcy flow in the formation and concluded that these effects cannot be felt if the fracture is long or intermediate in size. They further concluded that the effects of turbulent flow within the fracture were more significant.Holditch and Morse investigated the effect of turbulent flow in a fracture and analyzed the transient behavior of specific conductivities (low, medium, and high), giving a qualitative approach to the solution. They stressed the need for greater detail on these solutions and showed that there was indeed a large reduction in the fracture conductivity when non-Darcy flow was included. Although Holditch and Morse gave a detailed descriptive insight into the flow regime problem, they did not develop any general methods for determining the actual conductivity of the fracture. SPEJ P. 681

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Productivity analysis for a horizontal well with multiple reorientation fractures in an anisotropic reservoir

Oil & Gas Science and Technology – Revue d’IFP Energies nouvelles ◽

10.2516/ogst/2020078 ◽

2020 ◽

Vol 75 ◽

pp. 80

Author(s):

Mingxian Wang ◽

Zifei Fan ◽

Lun Zhao ◽

Guoqiang Xing ◽

Wenqi Zhao ◽

...

Keyword(s):

Horizontal Well ◽

Productivity Index ◽

Finite Conductivity ◽

Productivity Analysis ◽

Well Productivity ◽

Fracture Conductivity ◽

Fracture Angle ◽

Fracture Spacing ◽

Anisotropic Factor ◽

Anisotropic Reservoir

Reorientation fractures may be formed in soft and shallow formations during fracturing stimulation and then affect well productivity. The principal focus of this study is on the productivity analysis for a horizontal well with multiple reorientation fractures in an anisotropic reservoir. Combining the nodal analysis technique and fracture-wing method, a semi-analytical model for a horizontal well with multiple finite-conductivity reorientation fractures was established to calculate its dimensionless productivity index and derivative for production evaluation. A classic case in the literature was selected to verify the accuracy of our semi-analytical solution and the verification indicates this new solution is reliable. Results show that for a fixed fracture configuration the dimensionless productivity index of the proposed model first goes up and then remains constant with the increase of fracture conductivity, and optimal fracture conductivity can be determined on derivative curves. Strong permeability anisotropy is a negative factor for well production and the productivity index gradually decreases with the increase of anisotropic factor. As principal fracture angle goes up, horizontal well’s productivity index increases correspondingly. However, the effect of reoriented fracture angle on the productivity index is not as strong as that of principal fracture angle. When reoriented fracture angle is smaller than principal fracture angle, reoriented factor should be as low as possible to achieve optimal productivity index. Meanwhile, well productivity index rises up with the increase of fracture number and fracture spacing, but the horizontal well has optimal reorientation fracture number and fracture spacing to get the economical productivity. Furthermore, the influence of the rotation of one central reorientation fracture on productivity index is weaker than that caused by the rotation of one external reorientation fracture. In addition, the asymmetrical distribution of one or more reorientation fractures slightly affects the productivity index when fracture conductivity is high enough.

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Wood creep data collection and unbiased parameter identification of compliance functions

Holzforschung ◽

10.1515/hf-2019-0268 ◽

2020 ◽

Vol 74 (11) ◽

pp. 1011-1020

Author(s):

Danyang Tong ◽

Susan Alexis Brown ◽

David Corr ◽

Gianluca Cusatis

Keyword(s):

Parameter Identification ◽

Prediction Models ◽

Tall Buildings ◽

Building Design ◽

Parameter Distribution ◽

Experimental Conditions ◽

Global Emission ◽

Wood Construction ◽

Parameter Values

AbstractRising global emission have led to a renewed popularity of timber in building design, including timber-concrete tall buildings up to 18 stories. In spite of this surge in wood construction, there remains a gap in understanding of long-term structural behavior, particularly wood creep. Unlike concrete, code prescriptions for wood design are lacking in robust estimates for structural shortening. Models for wood creep have become increasingly necessary due to the potential for unforeseen shortening, especially with respect to differential shortening. These effects can have serious impacts as timber building heights continue to grow. This study lays the groundwork for wood compliance prediction models for use in timber design. A thorough review of wood creep studies was conducted and viable experimental results were compiled into a database. Studies were chosen based on correlation of experimental conditions with a realistic building environment. An unbiased parameter identification method, originally applied to concrete prediction models, was used to fit multiple compliance functions to each data curve. Based on individual curve fittings, statistical analysis was performed to determine the best fit function and average parameter values for the collective database. A power law trend in wood creep, with lognormal parameter distribution, was confirmed by the results.

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The projected impacts of smart decline on urban runoff contamination levels

Computational Urban Science ◽

10.1007/s43762-021-00002-1 ◽

2021 ◽

Vol 1 (1) ◽

Author(s):

Rui Zhu ◽

Galen Newman

Keyword(s):

Land Use ◽

Green Infrastructure ◽

Prediction Models ◽

Stormwater Runoff ◽

Baseline Scenario ◽

Vacant Land ◽

Smart Decline ◽

Contamination Levels ◽

Indirect Impacts

AbstractThere has been mounting interest about how the repurposing of vacant land (VL) through green infrastructure (the most common smart decline strategy) can reduce stormwater runoff and improve runoff quality, especially in legacy cities characterized by excessive industrial land uses and VL amounts. This research examines the long-term impacts of smart decline on both stormwater amounts and pollutants loads through integrating land use prediction models with green infrastructure performance models. Using the City of St. Louis, Missouri, USA as the study area, we simulate 2025 land use change using the Conversion of Land Use and its Effects (CLUE-S) and Markov Chain urban land use prediction models and assess these change’s probable impacts on urban contamination levels under different smart decline scenarios using the Long-Term Hydrologic Impact Assessment (L-THIA) performance model. The four different scenarios are: (1) a baseline scenario, (2) a 10% vacant land re-greening (VLRG) scenario, (3) a 20% VLRG scenario, and (4) a 30% VLRG scenario. The results of this study illustrate that smart decline VLRG strategies can have both direct and indirect impacts on urban stormwater runoff and their inherent contamination levels. Direct impacts on urban contamination include the reduction of stormwater runoff and non-point source (NPS) pollutants. In the 30% VLRG scenario, the annual runoff volume decreases by 11%, both physical, chemical, and bacterial pollutants are reduced by an average of 19%, compared to the baseline scenario. Indirect impacts include reduction of the possibility of illegal dumping on VL through mitigation and prevention of future vacancies.

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