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

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.

New Analytical Approach to Operational Assessment of Fractured Well Productivity with Variable Permeability

2021 ◽  
Author(s):  
Evgeniy Viktorovich Yudin ◽  
George Aleksandrovich Piotrovskiy ◽  
Maria Vladimirovna Petrova ◽  
Alexey Petrovich Roshchektaev ◽  
Nikita Vladislavovich Shtrobel
Keyword(s):  
Hydraulic Fracturing ◽  
Hydraulic Fracture ◽  
Free Parameter ◽  
Numerical Solutions ◽  
Analytical Models ◽  
Productivity Index ◽  
Finite Conductivity ◽  
Well Productivity ◽  
Fracture Conductivity ◽  
Variable Permeability

Abstract Requirements of targeted optimization are imposed on the hydraulic fracturing operations carried out in the conditions of borderline economic efficiency of fields taking into account geological and technological features. Consequently, the development of new analytical tools foranalyzing and planning the productivity of fractured wells, taking into account the structuralfeatures of the productive reservoir and inhomogeneous distribution of the fracture conductivity, is becoming highly relevant. The paper proposes a new approach of assessing the vertical hydraulic fracture productivityin a rectangular reservoir in a pseudo-steady state, based on reservoir resistivity concept described in the papers of Meyer et al. However, there is a free parameter in the case of modeling the productivity of a hydraulic fracture by the concept. The parameter describes the distribution of the inflow along the plane of the fracture. This paper presents a systematic approach to determining of the parameter. The resulting model allows to conduct an assessment of the influence of various complications in the fracture on the productivity index. During the research a method of determining the free parameter was developed,it was based on the obtained dependence of the inflow distribution on the coordinate along the fracture of finite conductivity. The methodology allowed to refine existent analytical solution of the Meyer et al. model, which, in turn, allowed to assess the influence of different fracture damages in the hydraulic fracture on the productivity index of the well. The work includes the cases of the presence of fracture damages at the beginning and at the end of the fracture. A hydraulic fracture model was built for each of the types of damages, it was based on the developed method, and also the solution of dimensionless productivity ratio was received. The results of the obtained solution were confirmed by comparison with the numerical solutions of commercial simulators and analytical models available in the literature. The advantage of the methodology is the resulting formulas for well productivity are relatively simple, even for exotic cases ofvariable conductivity fractures. The approaches and algorithms described in the paper assume the calculation of the productivity of a hydraulic fracture with variable conductivity and the presence of other complicatingfactors.The methodology of the paper can be used for analysis and diagnosis problems with formation hydraulic fracturing. The efficiency of the calculations allows using the presented methodology to solve inverse problems of determining the efficiency of the hydraulic fracturing operation.

Evaluation of Fracture Asymmetry of Finite-Conductivity Fractured Wells

2010 ◽  
Vol 132 (1) ◽  
Author(s):  
Djebbar Tiab ◽  
Jing Lu ◽  
Hung Nguyen ◽  
Jalal Owayed
Keyword(s):  
Hydraulic Fracturing ◽  
Production Rate ◽  
Radial Flow ◽  
Asymmetry Factor ◽  
Hydraulic Fractures ◽  
Finite Conductivity ◽  
Asymmetry Ratio ◽  
Pressure Derivative ◽  
Fracture Conductivity ◽  
The Asymmetry

Nearly all commercial hydraulic fracture design models are based on the assumption that a single fracture is initiated and propagated identically and symmetrically about the wellbore, i.e., the fracture growth and proppant transport occurs symmetrically with respect to the well. However, asymmetrical fractures have been observed in hundreds of hydraulic fracturing treatments and reported to be a more realistic outcome of hydraulic fracturing. The asymmetry ratio (length of short fracture wing divided by length of long wing) influenced the production rate adversely. In the worst case, the production rate could be reduced to that of an unfractured well. Several authors observed asymmetrically propagated hydraulic fractures in which one wing could be ten times longer than the other. Most pressure transient analysis techniques of hydraulically fractured wells assume the fracture is symmetric about the well axis for the sake of simplicity in developing mathematical solution. This study extends the work by Rodriguez to evaluate fracture asymmetry of finite-conductivity fracture wells producing at a constant-rate. The analysis presented by Rodriguez only involves the slopes of the straight lines that characterize the bilinear, linear and radial flow from the conventional Cartesian and semilog plots of pressure drop versus time. This study also uses the Tiab’s direct synthesis (TDS) technique to analyze the linear and bilinear flow regimes in order to find the asymmetry factor of the fractured well. With the fracture conductivity estimated from the bilinear flow region, dimensionless fracture conductivity and the asymmetry ratio are calculated. A technique for estimating the fracture asymmetry ratio from a graph is presented. An equation relating the asymmetry ratio and dimensionless fracture conductivity is also presented. This equation assumes that the linear and/or bilinear flow regime is observed. However, using the TDS technique, the asymmetry ratio can be estimated even in the absence of bilinear or linear flow period. It is concluded that the relative position of the well in the fracture, i.e., the asymmetry condition, is an important consideration for the fracture characterization. A log-log plot of pressure derivative can be used to estimate the fracture asymmetry in a well intersected with a finite-conductivity asymmetric fracture. The analysis using pressure derivative plot does not necessarily require the radial flow period data to calculate the asymmetric factor.

Non-Darcy Porous-Media Flow According to the Barree and Conway Model: Laboratory and Numerical-Modeling Studies

SPE Journal ◽  
2011 ◽  
Vol 17 (01) ◽  
pp. 70-79 ◽  
Author(s):  
Bitao Lai ◽  
Jennifer L. Miskimins ◽  
Yu-Shu Wu
Keyword(s):  
Numerical Model ◽  
Flow Behavior ◽  
Experimental Studies ◽  
Transient Behavior ◽  
General Purpose ◽  
High Flow ◽  
Darcy Flow ◽  
Porous Media Flow ◽  
Laboratory Findings ◽  
Flow Rates

Summary This paper presents the results of our new experimental studies conducted for high flow rates through proppant packs, which show that the Barree and Conway (2004) flow model is capable of overcoming limitations of the Forchheimer non-Darcy equation at very high flow rates. To quantify the non-Darcy flow behavior using the Barree and Conway model, a numerical model is developed to simulate non-Darcy flow. In addition, an analytical solution is presented for steady-state linear non-Darcy flow and is used to verify the numerical-simulation results. The numerical model incorporates the Barree and Conway model into a general-purpose reservoir simulator for modeling multidimensional, single-phase non-Darcy flow in porous and fractured media and supplements the laboratory findings. The numerical model is then used to perform sensitivity analysis of the Barree and Conway flow model's parameters and to investigate transient behavior of non-Darcy flow at an injection well.

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.

scholarly journals Revising Transient-Pressure Solution for Vertical Well Intersected by a Partially Penetrating Fracture with Non-Darcy Flow Effect

Geofluids ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-17
Author(s):  
Shuheng Cui ◽  
Jie Kong ◽  
Hongwei Yu ◽  
Cheng Chen ◽  
Junlei Wang
Keyword(s):  
Flow Regime ◽  
Flow Regimes ◽  
Pressure Response ◽  
Darcy Flow ◽  
Transient Pressure ◽  
Fracture Conductivity ◽  
Flow Effect ◽  
Vertical Fracture ◽  
Dimensional Flow ◽  
Penetration Ratio

The principle purpose of this work is to formulate an accurate mathematical model to evaluate the transient pressure behavior of a well intercepted by a partially penetrating vertical fracture (PPVF) with non-Darcy flow effect. Fracture conductivity is taken into account by coupling the three-dimensional flow in reservoir and the two-dimensional flow within fracture; the Barree-Conway model is incorporated into the model to analyze non-Darcy flow behavior in fracture, which leads to the nonlinearity of the governing equations. A high-effective iterative algorithm using a combined technique of fracture-panel discretization and dimension transform is developed to render the nonlinear equations amenable to analytical linear treatment. On the basis of the solutions, the pressure response and its derivative type curves were generated to identify the evolution of flow regimes with time. Furthermore, the influences of fracture conductivity, penetration ratio, and non-Darcy characteristic parameters on pressure response are investigated. The results show that PPVF exhibits five typical flow regimes, and analytical solutions for each flow regime are similar to that for a fully penetrating vertical fracture (FPVF) that can be correlated with the penetration ratio and apparent conductivity. The non-Darcy flow effect is found to have more significant effect on the low and moderate conductivity, especially in early-stage flow regimes. When the penetration ratio is smaller than 0.5, the pressure behavior exhibit a more remarkable variation with penetration ratio. This study provides a better insight into understanding the influence of non-Darcy flow on flow regime identification.

Monitoring Effects of Catchment Management Practices on Phosphorus Loads into the Eutrophic Peel-Harvey Estuary, Western Australia

1986 ◽  
Vol 18 (4-5) ◽  
pp. 53-61 ◽  
Author(s):  
P. B. Birch ◽  
G. G. Forbes ◽  
N. J. Schofield
Keyword(s):  
Management Practices ◽  
Major Change ◽  
High Flow ◽  
Catchment Management ◽  
Flow Rates ◽  
Early Results ◽  
Phosphorus Loads ◽  
Time Of Year ◽  
High Runoff

Early results from monitoring runoff suggest that the programme to reduce application of superphosphate to farmlands in surrounding catchments has been successful in reducing input of phosphorus to the eutrophic Peel-Harvey estuary. In the estuary this phosphorus fertilizes algae which grow in abundance and accumulate and pollute once clean beaches. The success of the programme has been judged from application of an empirical statistical model, which was derived from 6 years of data from the Harvey Estuary catchment prior to a major change in fertilizer practices in 1984. The model relates concentration of phosphorus with rate of flow and time of year. High phosphorus concentrations were associated with high flow rates and with flows early in the high runoff season (May-July). The model predicted that the distribution of flows in 1984 should have resulted in a flow-weighted concentration of phosphorus near the long-term average; the observed concentration was 25% below the long-term average. This means that the amount of phosphorus discharged into the Harvey Estuary could have been about 2 5% less than expected from the volume of runoff which occurred. However several more years of data are required to confirm this trend.

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