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

1981 ◽  
Vol 21 (03) ◽  
pp. 390-400 ◽  
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.

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

1982 ◽  
Vol 22 (05) ◽  
pp. 681-698 ◽  
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

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

Processes ◽  
2018 ◽  
Vol 6 (7) ◽  
pp. 93 ◽  
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.

Transient Rate Decline Analysis for Wells Produced at Constant Pressure

1981 ◽  
Vol 21 (01) ◽  
pp. 98-104 ◽  
Author(s):  
C.A. Ehlig-Economides ◽  
H.J. Ramey
Keyword(s):  
Pressure Drop ◽  
Flow Rate ◽  
Constant Pressure ◽  
Well Test ◽  
Well Test Analysis ◽  
Test Analysis ◽  
Type Curve ◽  
Type Curves ◽  
Constant Rate ◽  
Cumulative Production

Abstract Although constant-rate production is assumed in the development of conventional well test analysis methods, constant-pressure production conditions are not uncommon. Conditions under which constant-pressure flow is maintained at a well include production into a constant-pressure separator or pipeline, steam production into a backpressured turbine, or open flow to the atmosphere.To perform conventional well test analysis on such wells, one common procedure is to flow the well at a constant rate for several days before performing the test. This procedure is not always effective, and often the delay could be avoided by performing transient rate tests instead. Practical methods for transient rate analysis of wells produced at constant pressure are presented in this paper. The most important test is the analysis of the rate response to a step change in producing pressure. This test allows type-curve analysis of the transient rate response without the complication of wellbore storage effects. Reservoir permeability, porosity, and the wellbore skin factor can be determined from the type-curve match. The reservoir limit test is also important. Exponential rate decline can be analyzed to determine the drainage area of a well and the shape factor.The effect of the pressure drop in the wellbore due to flowing friction is investigated. Constant wellhead-pressure flow causes a variable pressure at the sandface because the pressure drop from flowing friction is dependent on the transient rate. Finally, for testing of new wells, the effect of a limited initial flow rate due to critical flow phenomena is examined. Introduction Fundamental considerations suggest that conventional pressure drawdown and buildup analysis methods developed for constant-rate production should not be appropriate for a well produced at a constant pressure. However, a well produced at a constant pressure exhibits a transient rate decline which can be analyzed using techniques analogous to the methods for constant-rate flow. In this paper, analytical solutions for the transient rate decline for wells produced at constant pressure are used to determine practical well test analysis methods.Many of the basic analytical solutions for transient rate decline have been available for some time. The first solutions were published by Moore et al. and Hurst. Results were presented in graphical form for bounded and unbounded reservoirs in which the flow was radial and the single-phase fluid was slightly compressible. Tables of dimensionless flow rate vs. dimensionless time were provided later by Ferris et al. for the unbounded system and by Tsarevich and Kuranov for the closed-boundary circular reservoir. Tsarevich and Kuranov also provided tabulated solutions for the cumulative production from a closed-boundary reservoir. Van Everdingen and Hurst presented solutions and tables of the cumulative production for constant-pressure production. Fetkovich developed log-log type curves for transient rate vs. sine in the closed-boundary circular reservoir. Type curves for rate decline in closed-boundary reservoirs with pressure-sensitive rock and fluid properties were developed by Samaniego and Cinco. A method for determining the skin effect was given by Earlougher. Type curves for analysis of the transient rate response when the well penetrates a fracture were developed by Prats et al. and Locke and Sawyer. SPEJ P. 98^

scholarly journals Productivity Analysis of Volume Fractured Wells under Different Working Systems

Geofluids ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-21
Author(s):  
Hongfei Ma ◽  
Wenqi Zhao ◽  
Meng Sun ◽  
Xiaodong Wang ◽  
Lun Zhao ◽  
...  
Keyword(s):  
Prediction Models ◽  
Finite Conductivity ◽  
Productivity Analysis ◽  
Well Performance ◽  
Fracture Conductivity ◽  
Initial Flow ◽  
Stimulated Reservoir Volume ◽  
Constant Rate ◽  
Wellbore Pressure

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.

Interference Between Constant-Rate and Constant-Pressure Reservoirs Sharing a Common Aquifer

1985 ◽  
Vol 25 (03) ◽  
pp. 419-426 ◽  
Author(s):  
Abraham Sageev ◽  
Roland N. Horne
Keyword(s):  
Boundary Conditions ◽  
Line Source ◽  
Infinite System ◽  
Constant Pressure ◽  
Oil Field ◽  
Oil Fields ◽  
Internal Boundary ◽  
Finite Radius ◽  
Pressure Behavior ◽  
Constant Rate

Abstract A practical pressure transient analysis method is presented for interpreting interference between two oil fields or an oil field and a gas field sharing a common aquifer. One oil field is approximated as a constant-rate line source. The other interfering field is represented by a finite-radius circular source producing at constant rate or constant pressure. pressure. A rigorous application of the superposition principle is discussed, making use of a new model where a constant rate line source produces exterior to a circular boundary. Both constant pressure and impermeable internal boundaries are considered. Dimensionless pressure drop curves for both boundary conditions are presented. For the case of a line source producing near a constant-pressure internal boundary, producing near a constant-pressure internal boundary, dimensionless curves for the instantaneous rate and the cumulative injection from this internal boundary are given. These curves may be used to forecast the actual injection/production rate and the cumulative injection/ production at the interfering reservoir as a function of time. production at the interfering reservoir as a function of time. Introduction Pressure interference between hydrocarbon reservoirs Pressure interference between hydrocarbon reservoirs situated in a common aquifer is important in understanding and forecasting the behavior of these reservoirs under exploitation. The fluid driving energy stored in a reservoir is a function of its average pressure. Production in one reservoir causes a pressure drawdown at another reservoir and, hence, changes its deliverability and economic value over a long period of time. Bell and Shepherd I considered the pressure behavior of the Woodbine sand in east Texas, which contains several reservoirs. They presented a pressure loss map that shows that production from the east Texas field affected an extensive area of the Woodbine aquifer. Moore and Truby, using an electric analyzer, described the pressure behavior of five producing fields sharing a pressure behavior of five producing fields sharing a common aquifer. They presented pressure histories for each of the five reservoirs. Every pressure history consisted of five pressure drops. The first pressure drop at a reservoir was caused by its own production, to which four interfering pressure drops caused by the neighboring reservoirs were added. The interfering effect of the TXL field on the average pressure at Wheeler field was larger than the drawdown at Wheeler field caused by its own production. production. In describing interference between two reservoirs sharing a common infinite aquifer, some assumptions as to the shape of these reservoirs must be made. Theis presented the solution for a constant-rate line source in presented the solution for a constant-rate line source in an infinite system. Staliman modified this solution for a semi-infinite system bounded by a linear boundary. If the two reservoirs may be approximated by two line sources, their pressure effects may be superposed in space to yield the pressure interference between them. super-position in space is used to assemble the effects of several producing/injecting reservoirs in the same aquifer. producing/injecting reservoirs in the same aquifer. Carslaw and Jaeger presented solutions for a single finite-radius source in an infinite medium producing at either constant rate or constant pressure. Van Everdingen and Hurst applied those solutions to flow in reservoirs. Mortada used those solutions to describe interference between oil fields and, using superposition in space, calculated the pressure response of a reservoir to its own production and to production from an interfering production and to production from an interfering reservoir. If the reservoirs are of finite radii and are not approximated by line sources, the method of superposition in space must be used with care so that the inner boundary conditions are not violated. By superposing a finite-radius source in an infinite system onto another finite-radius source in an infinite system, the inner boundary conditions at both sources are violated. Mortada's results, therefore, are only approximate. Hursts presented a method for calculating pressure interference between finite-radius reservoirs that includes the material-balance equations. Hursts and Mortada also considered interference between oil fields connected to an aquifer with two permeability regions. Mueller and Witherspoon used the finite-radius constant-rate solution and normalized the time scale to describe interference pressure changes. They concluded that, for practical pressure changes. They concluded that, for practical purposes, interference points at a distance larger than 20 times purposes, interference points at a distance larger than 20 times the radius of the source have a line-source response. Uraiet and Raghavan presented interference log-log type curves for a finite-radius source producing at a constant pressure. In this study, two circular reservoirs in an infinite system are considered. One reservoir is approximated as a constant-rate line source. The other reservoir is considered to be a finite-radius source producing at either a constant rate or a constant pressure. Only single-step changes in rate or pressure are discussed, since they are the basis for superposition in time. SPEJ P. 419

Determination of Fracture Conductivity in Tight Formations With Non-Darcy Flow Behavior

SPE Journal ◽  
2013 ◽  
Vol 19 (01) ◽  
pp. 34-44 ◽  
Author(s):  
Feng Zhang ◽  
Daoyong Yang
Keyword(s):  
Mathematical Model ◽  
Characteristic Length ◽  
Flow Behavior ◽  
Fracture Network ◽  
Darcy Flow ◽  
Flow Number ◽  
Fracture Conductivity ◽  
Type Curves ◽  
Relative Minimum ◽  
Tight Formations

Summary In this paper, a mathematical model has been developed and successfully applied to accurately determine the fracture conductivity in tight formations with non-Darcy flow behavior. A new non-Darcy flow number is first defined to account for the effect of characteristic length in a hydraulic fracture. A semianalytical method is then applied to solve the newly formulated mathematical model by discretizing the fracture into small segments, assuming that there exists unsteady flow between the adjacent segments. The newly developed model has been validated by simplifying it to the traditional Forchheimer (i.e., non-Darcy) model and by performing numerical simulation with a reservoir simulator as well. The pressure response and its corresponding derivative type curves have been reproduced to examine non-Darcy flow behavior under different fracture conductivities. Both relative minimum permeability and characteristic length are found to impose a negative effect on the fracture conductivity. Compared with relative minimum permeability, characteristic length is a strong function dominating the non-Darcy flow behavior in the fractures. It is obvious that the fracture conductivity can be accurately determined when non-Darcy flow behavior in the fracture network is taken into account.

Type Curves Analysis for Asymmetrically Fractured Wells

2013 ◽  
Vol 136 (2) ◽  
Author(s):  
Lei Wang ◽  
Xiaodong Wang
Keyword(s):  
Asymmetry Factor ◽  
Fracture Conductivity ◽  
Linear Flow ◽  
Type Curves ◽  
Starting Time ◽  
Wellbore Storage ◽  
Constant Rate ◽  
Pressure Depletion ◽  
Storage Effects ◽  
New Type

In this paper, a new constant rate solution for asymmetrically fractured wells was proposed to analyze the effect of fracture asymmetry on type curves. Calculative results showed that for a small wellbore storage coefficient or for the low fracture conductivity, the effect of fracture asymmetry on early flow was very strong. The existence of the fracture asymmetry would cause bigger pressure depletion and make the starting time of linear flow occur earlier. Then, new type curves were established for different fracture asymmetry factor and different fracture conductivity. It was shown that a bigger fracture asymmetry factor and low fracture conductivity would prolong the time of wellbore storage effects. Therefore, to reduce wellbore storage effects, it was essential to keep higher fracture conductivity and fracture symmetry during the hydraulic fracturing design. Finally, a case example is performed to demonstrate the methodology of new type curves analysis and its validation for calculating important formation parameters.

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

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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