Low-Conductivity and Short Fracture Half-Length Type Curves and Analysis for Hydraulically Fractured Wells Exhibiting Near Radial Flow Profile

1992 ◽  
Author(s):  
M. Azari ◽  
J.W. Knight ◽  
L.E. Coble ◽  
M.Y. Soliman
Keyword(s):  
Radial Flow ◽  
Flow Profile ◽  
Type Curves ◽  
Half Length

Unsteady-State Spherical Flow With Storage and Skin

1985 ◽  
Vol 25 (06) ◽  
pp. 804-822 ◽  
Author(s):  
Jeffrey A. Joseph ◽  
Leonard F. Koederitz
Keyword(s):  
Boundary Condition ◽  
Radial Flow ◽  
Linear Partial Differential Equation ◽  
Flow Profile ◽  
Unsteady State ◽  
Well Test ◽  
Linear Flow ◽  
Dimensionless Groups ◽  
Short Time ◽  
Suitable Expression

Abstract This paper presents short-time interpretation methods for radial-spherical (or radial-hemispherical) flow in homogeneous and isotropic reservoirs inclusive of wellbore storage, wellbore phase redistribution, and damage skin effects. New dimensionless groups are introduced to facilitate the classic transformation from radial flow in the sphere to linear flow in the rod. Analytical expressions, type curves (in log-log and semilog format), and tabulated solutions are presented, both in terms of pressure and rate, for all flow problems considered. A new empirical equation to estimate the duration of wellbore and near-wellbore effects under spherical flow is also proposed. Introduction The majority of the reported research on unsteady-state flow theory applicable to well testing usually assumes a cylindrical (typically a radial-cylindrical) flow profile because this condition is valid for many test situations. Certain well tests, however, are better modeled by assuming a spherical flow symmetry (e.g., wireline formation testing, vertical interference testing, and perhaps even some tests conducted in wellbores that do not fully penetrate the productive horizon or are selectively penetrate the productive horizon or are selectively completed). Plugged perforations or blockage of a large part of an openhole interval may also promote spherical flow. Numerous solutions are available in the literature for almost every conceivable cylindrical flow problem; unfortunately, the companion spherical problem has not received as much attention, and comparatively few papers have been published on this topic. papers have been published on this topic. The most common inner boundary condition in well test analysis is that of a constant production rate. But with the advent of downhole tools capable of the simultaneous measurement of pressures and flow rates, this idealized inner boundary condition has been refined and more sophisticated models have been proposed. Therefore, similar methods must be developed for spherical flow analysis, especially for short-time interpretations. This general problem has recently been addressed elsewhere. Theory The fundamental linear partial differential equation (PDE) describing fluid flow in an infinite medium characterized by a radial-spherical symmetry is (1) The assumptions incorporated into this diffusion equation are similar to those imposed on the radial-cylindrical diffusivity equation and are discussed at length in Ref. 9. In solving Eq. 1, the classic approach is illustrated by Carslaw and Jaeger (later used by Chatas, and Brigham et al.). According to Carslaw and Jaeger, mapping b=pr will always reduce the problem of radial flow in the sphere (Eq. 1) to an equivalent problem of linear flow in the rod for which general solutions are usually known. (For example, see Ref. 17 for particular solutions in petroleum applications.) Note that in this study, we assumed that the medium is spherically isotropic; hence k in Eq. 1 is the constant spherical permeability. This assumption, however, does not preclude analysis in systems possessing simple anisotropy (i.e., uniform but unequal horizontal and vertical permeability components). In this case, k as used in this paper should be replaced by k, an equivalent or average (but constant) spherical permeability. Chatas presented a suitable expression (his Eq. 10) obtained presented a suitable expression (his Eq. 10) obtained from a volume integral. It is desirable to transform Eq. 1 to a nondimensional form, thereby rendering its applicability universal. The following new, dimensionless groups accomplish this and have the added feature that solutions are obtained directly in terms of the dimensionless pressure drop, PD, not the usual b (or bD) groups. ......................(2) .......................(3) .........................(4) The quantity rsw is an equivalent or pseudospherical wellbore radius used to represent the actual cylindrical sink (or source) of radius rw. SPEJ p. 804

Welltest analysis of hydraulically fractured tight gas reservoirs: a field example from Perth Basin, Western Australia

2012 ◽  
Vol 52 (1) ◽  
pp. 587 ◽  
Author(s):  
Hassan Bahrami ◽  
Vineeth Jayan ◽  
Reza Rezaee ◽  
Dr Mofazzal Hossain
Keyword(s):  
Radial Flow ◽  
Second Derivative ◽  
Tight Gas ◽  
Transient Pressure ◽  
Gas Reservoirs ◽  
Type Curves ◽  
Tight Gas Reservoirs ◽  
Diagnostic Plots ◽  
Reservoir Permeability ◽  
Reservoir Flow

Welltest interpretation requires the diagnosis of reservoir flow regimes to determine basic reservoir characteristics. In hydraulically fractured tight gas reservoirs, the reservoir flow regimes may not clearly be revealed on diagnostic plots of transient pressure and its derivative due to extensive wellbore storage effect, fracture characteristics, heterogeneity, and complexity of reservoir. Thus, the use of conventional welltest analysis in interpreting the limited acquired data may fail to provide reliable results, causing erroneous outcomes. To overcome such issues, the second derivative of transient pressure may help eliminate a number of uncertainties associated with welltest analysis and provide a better estimate of the reservoir dynamic parameters. This paper describes a new approach regarding welltest interpretation for hydraulically fractured tight gas reservoirs—using the second derivative of transient pressure. Reservoir simulations are run for several cases of non-fractured and hydraulically fractured wells to generate different type curves of pressure second derivative, and for use in welltest analysis. A field example from a Western Australian hydraulically fractured tight gas welltest analysis is shown, in which the radial flow regime could not be identified using standard pressure build-up diagnostic plots; therefore, it was not possible to have a reliable estimate of reservoir permeability. The proposed second derivative of pressure approach was used to predict the radial flow regime trend based on the generated type curves by reservoir simulation, to estimate the reservoir permeability and skin factor. Using this analysis approach, the permeability derived from the welltest was in good agreement with the average core permeability in the well, thus confirming the methodology’s reliability.

scholarly journals Two-dimensional numerical investigations on the termination of bilinear flow in fractures

2013 ◽  
Vol 5 (1) ◽  
pp. 391-425
Author(s):  
◽  
R. Jung ◽  
J. Renner
Keyword(s):  
Flow Field ◽  
Master Curve ◽  
Radial Flow ◽  
Dimensionless Time ◽  
Linear Flow ◽  
Type Curves ◽  
Straight Line ◽  
The Matrix ◽  
Line Characteristic ◽  
Fourth Root

Abstract. Bilinear flow occurs when fluid is drained from a permeable matrix by producing it through an enclosed fracture of finite conductivity intersecting a well along its axis. The terminology reflects the combination of two approximately linear flow regimes, one in the matrix with flow essentially perpendicular to the fracture and one along the fracture itself associated with the non-negligible pressure drop in it. We investigated the characteristics, in particular the termination, of bilinear flow by numerical modeling allowing an examination of the entire flow field without prescribing the flow geometry in the matrix. Fracture storage capacity was neglected relying on previous findings that bilinear flow is associated with a quasi-steady flow in the fracture. Numerical results were generalized by dimensionless presentation. Definition of a dimensionless time that other than in previous approaches does not use geometrical parameters of the fracture permitted identifying the dimensionless well pressure for the infinitely long fracture as the master curve for type curves of all fractures with finite length from the beginning of bilinear flow up to fully developed radial flow. In log-log-scale the master curve's logarithmic derivative initially follows a 1/4-slope-straight line (characteristic for bilinear flow) and gradually bends into a horizontal line (characteristic for radial flow) for long times. During the bilinear flow period, isobars normalized to well pressure propagate with fourth and second root of time in fracture and matrix, respectively. The width-to-length ratio of the pressure field increases proportional to the fourth root of time during the bilinear period and starts to deviate from this relation close to the deviation of well pressure and its derivative from their fourth-root-of-time relations. At this time, isobars are already significantly inclined with respect to the fracture. The type curves of finite fractures all deviate counterclockwise from the master curve instead of clockwise or counterclockwise from the 1/4-slope-straight line as previously proposed. The counterclockwise deviation from the master curve was identified as the arrival of a normalized isobar reflected at the fracture tip sixteen times earlier. Nevertheless, two distinct regimes were found regarding pressure at the fracture tip when bilinear flow ends. For dimensionless fracture conductivities TD < 1, a significant pressure increase is not observed at the fracture tip until bilinear flow is succeeded by radial flow at a fixed dimensionless time. For TD > 10, the pressure at the fracture tip has reached substantial fractions of the associated change in well pressure when the flow field transforms towards intermittent formation linear flow at times that scale inversely with the fourth power of dimensionless fracture conductivity. Our results suggest that semi-log plots of normalized well pressure provide a means for the determination of hydraulic parameters of fracture and matrix after shorter test duration than for conventional analysis.

scholarly journals Production decline type curves analysis of a finite conductivity fractured well in coalbed methane reservoirs

Open Physics ◽  
2017 ◽  
Vol 15 (1) ◽  
pp. 143-153 ◽  
Author(s):  
Mingqiang Wei ◽  
Ming Wen ◽  
Yonggang Duan ◽  
Quantang Fang ◽  
Keyi Ren
Keyword(s):  
Flow Regime ◽  
Coalbed Methane ◽  
Radial Flow ◽  
Production Model ◽  
Finite Conductivity ◽  
Type Curves ◽  
State Diffusion ◽  
Diffusion And Convection ◽  
Fractured Well ◽  
Advanced Production

AbstractProduction decline type curves analysis is one of the robust methods used to analyze transport flow behaviors and to evaluate reservoir properties, original gas in place, etc. Although advanced production decline analysis methods for several well types in conventional reservoirs are widely used, there are few models of production decline type curves for a fractured well in coalbed methane (CBM) reservoirs. In this work, a novel pseudo state diffusion and convection model is firstly developed to describe CBM transport in matrix systems. Subsequently, based on the Langmuir adsorption isotherm, pseudo state diffusion and convection in matrix systems and Darcy flow in cleat systems, the production model of a CBM well with a finite conductivity fracture is derived and solved by Laplace transform. Advanced production decline type curves of a fractured well in CBM reservoirs are plotted through the Stehfest numerical inversion algorithm and computer programming. Six flow regimes, including linear flow regime, early radial flow in cleat systems, interporosity flow regime, late pseudo radial flow regime, transient regime and boundary dominated flow regime, are recognized. Finally, the effect of relevant parameters, including the storage coefficient of gas in cleat systems, the transfer coefficient from a matrix system to the cleat system, the modified coefficient of permeability, dimensionless fracture conductivity and dimensionless reservoir drainage radius, are analyzed on type curves. This paper does not only enrich the production decline type curves model of CBM reservoirs, but also expands our understanding of fractured well transport behaviors in CBM reservoirs and guides to analyze the well's production performance.

scholarly journals Two-dimensional numerical investigations on the termination of bilinear flow in fractures

Solid Earth ◽  
2013 ◽  
Vol 4 (2) ◽  
pp. 331-345 ◽  
Author(s):  
A. E. Ortiz R. ◽  
R. Jung ◽  
J. Renner
Keyword(s):  
Flow Field ◽  
Master Curve ◽  
Radial Flow ◽  
Dimensionless Time ◽  
Linear Flow ◽  
Type Curves ◽  
Straight Line ◽  
The Matrix ◽  
Line Characteristic ◽  
Fourth Root

Abstract. Bilinear flow occurs when fluid is drained from a permeable matrix by producing it through an enclosed fracture of finite conductivity intersecting a well along its axis. The terminology reflects the combination of two approximately linear flow regimes: one in the matrix with flow essentially perpendicular to the fracture, and one along the fracture itself associated with the non-negligible pressure drop in it. We investigated the characteristics, in particular the termination, of bilinear flow by numerical modeling allowing for an examination of the entire flow field without prescribing the flow geometry in the matrix. Fracture storage capacity was neglected relying on previous findings that bilinear flow is associated with a quasi-steady flow in the fracture. Numerical results were generalized by dimensionless presentation. Definition of a dimensionless time that, other than in previous approaches, does not use geometrical parameters of the fracture permitted identifying the dimensionless well pressure for the infinitely long fracture as the master curve for type curves of all fractures with finite length from the beginning of bilinear flow up to fully developed radial flow. In log–log scale the master curve's logarithmic derivative initially follows a 1/4-slope straight line (characteristic for bilinear flow) and gradually bends into a horizontal line (characteristic for radial flow) for long times. During the bilinear flow period, isobars normalized to well pressure propagate with the fourth and second root of time in fracture and matrix, respectively. The width-to-length ratio of the pressure field increases proportional to the fourth root of time during the bilinear period, and starts to deviate from this relation close to the deviation of well pressure and its derivative from their fourth-root-of-time relations. At this time, isobars are already significantly inclined with respect to the fracture. The type curves of finite fractures all deviate counterclockwise from the master curve instead of clockwise or counterclockwise from the 1/4-slope straight line as previously proposed. The counterclockwise deviation from the master curve was identified as the arrival of a normalized isobar reflected at the fracture tip 16 times earlier. Nevertheless, two distinct regimes were found in regard to pressure at the fracture tip when bilinear flow ends. For dimensionless fracture conductivities TD < 1, a significant pressure increase is not observed at the fracture tip until bilinear flow is succeeded by radial flow at a fixed dimensionless time. For TD > 10, the pressure at the fracture tip has reached substantial fractions of the associated change in well pressure when the flow field transforms towards intermittent formation linear flow at times that scale inversely with the fourth power of dimensionless fracture conductivity. Our results suggest that semi-log plots of normalized well pressure provide a means for the determination of hydraulic parameters of fracture and matrix after shorter test duration than for conventional analysis.

scholarly journals Solution and type curves for the seepage model of the water-bearing coalbed with leakage recharge

2017 ◽  
Vol 21 (1) ◽  
pp. 17 ◽  
Author(s):  
Wangang Chen ◽  
Yu Yang ◽  
Hansen Sun ◽  
Chengwei Zhang ◽  
Qin Wen ◽  
...  
Keyword(s):  
Coalbed Methane ◽  
Radial Flow ◽  
Curve Matching ◽  
Pressure Derivative ◽  
Type Curve ◽  
Type Curves ◽  
Reservoir Permeability ◽  
Leakage Coefficient ◽  
Seepage Theory ◽  
Seepage Model

To analyze the effects of the leakage recharge of the aquifer on the initial dewatering of coalbed methane wells, the mathematical seepage model of water in the coalbed considering the aquifer leakage was established by using the leakage coefficient according to the unsteady seepage theory. The model was solved after Laplace transform and the Stehfest numerical reverse inversion was used to obtain the solution in right space. Then, the log-log type curves of pressure and pressure derivative were created with new combinations of parameters. Based on the natural seepage mechanism, the influence of aquifer leakage on curve shape was judged. It is found that the radial flow ends earlier as the leakage coefficient increases. Moreover, it was proposed to obtain reservoir permeability, skin factor, and leakage coefficient by using type curve matching. The type curves are useful for quantitatively evaluating the level of leakage, thereby guiding the adjustment of the following production system for CBM wells. Curvas de solución y tipo para el modelo de filtración de capas carboníferas acuíferas con recarga de fugasResumenEste estudio estableció el modelo matemático de filtración de agua en una capa carbonífera al estimar la salida acuífera con el uso del coeficiente de fuga, de acuerdo con la teoría de filtración inestable, para analizar los efectos en la recarga de pérdida de fluidos de un acuífero en el drenado inicial para pozos de gas metano.  El modelo se resolvió tras usar la transformación Laplace y la inversión numérica Stehfest para encontrar la respuesta en el lugar indicado. Luego, se creó la representación algorítmica de la presión y la presión derivativa con nuevas combinaciones de parámetros. Se evaluó la influencia de la pérdida de fluido del acuífero en la forma de la curva con base al mecanismo físico de filtración. Se estableció que el flujo radial finaliza antes de que el coeficiente de pérdida de fluido se incremente. Además, se propone el uso de la curva tipo correspondiente para obtener la permeabilidad del reservorio, el factor de daño y el coeficiente de pérdida de fluido. Las curvas tipo son útiles para evaluar cuantitativamente el nivel de la pérdida de fluido, y de esta manera guiar el ajuste de un sistema de producción consecuente para pozos de gas metano de carbón.

scholarly journals Numerical Well Testing Interpretation Model and Applications in Crossflow Double-Layer Reservoirs by Polymer Flooding

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Haiyang Yu ◽  
Hui Guo ◽  
Youwei He ◽  
Hainan Xu ◽  
Lei Li ◽  
...  
Keyword(s):  
Double Layer ◽  
Oil Recovery ◽  
Radial Flow ◽  
Polymer Flooding ◽  
Flow Section ◽  
Well Testing ◽  
Type Curves ◽  
Wellbore Storage ◽  
Numerical Well Testing ◽  
Interpretation Model

This work presents numerical well testing interpretation model and analysis techniques to evaluate formation by using pressure transient data acquired with logging tools in crossflow double-layer reservoirs by polymer flooding. A well testing model is established based on rheology experiments and by considering shear, diffusion, convection, inaccessible pore volume (IPV), permeability reduction, wellbore storage effect, and skin factors. The type curves were then developed based on this model, and parameter sensitivity is analyzed. Our research shows that the type curves have five segments with different flow status: (I) wellbore storage section, (II) intermediate flow section (transient section), (III) mid-radial flow section, (IV) crossflow section (from low permeability layer to high permeability layer), and (V) systematic radial flow section. The polymer flooding field tests prove that our model can accurately determine formation parameters in crossflow double-layer reservoirs by polymer flooding. Moreover, formation damage caused by polymer flooding can also be evaluated by comparison of the interpreted permeability with initial layered permeability before polymer flooding. Comparison of the analysis of numerical solution based on flow mechanism with observed polymer flooding field test data highlights the potential for the application of this interpretation method in formation evaluation and enhanced oil recovery (EOR).

scholarly journals A Novel Radial-Composite Model of Pressure Transient Analysis for Multistage Fracturing Horizontal Wells with Stimulated Reservoir Volume

Geofluids ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Yunpeng Hu ◽  
Xiaoling Zhang ◽  
Ziyun Cheng ◽  
Wei Ding ◽  
Liangchao Qu ◽  
...  
Keyword(s):  
Horizontal Well ◽  
Storage Capacity ◽  
Radial Flow ◽  
Horizontal Wells ◽  
Outer Zone ◽  
Middle Zone ◽  
Linear Flow ◽  
Type Curves ◽  
Stimulated Reservoir Volume ◽  
Reservoir Volume

In the process of stimulated reservoir volume of tight reservoir, horizontal well can form three zones, the inner zone is multistage fracturing zone, the middle zone is skin damage zone, and the outer zone is undamaged zone. In this paper, a transient well test analysis model of multistage fracturing horizontal well in three area composite reservoir is proposed. Based on Laplace transformation, point source integration, and superposition principle, the infinite conductivity multifracture model of three area composite reservoir is obtained. The linear equations of finite conductivity multifracture in Laplace space are established by using the equal conditions of flow and pressure at the fracture wall. Gauss-Newton iteration method and Stehfest number are used to obtain the solution of wellbore pressure. The accuracy of the results is verified by numerical simulation. Then, the flow characteristics of multistage fracturing horizontal wells in three area composite reservoirs are analyzed by type curves. The flow is divided into ten stages, which are the bilinear flow, the linear flow, the first radial flow stage, the inner zone linear flow, the inner zone radial flow, the middle zone linear flow, the middle zone radial flow, the outer zone linear flow, the outer zone radial flow, and the boundary dominated flow. The pressure derivative curves show different characteristics in different flow stages. The influences of fracture conductivity, fracture spacing, radius ratio of the middle zone to inner zone, radius ratio of the outer zone to the middle zone, permeability ratio of inner zone to the middle zone, permeability ratio of inner zone to outer zone, storage capacity ratio of inner zone to the middle zone, and storage capacity ratio of inner zone to outer zone on type curves are analyzed. Finally, the application and reliability of the proposed model are verified by a case example.

Pre-Frac Injection Test Analysis: A Unified Approach to the Application of Conventional Techniques in an Unconventional Play

2015 ◽  
Author(s):  
P.. Smith ◽  
E.. Pinto
Keyword(s):  
Radial Flow ◽  
Field Tests ◽  
Design Parameters ◽  
Reservoir Pressure ◽  
Unified Approach ◽  
Test Analysis ◽  
Type Curves ◽  
Injection Test ◽  
Test Execution ◽  
Diagnostic Plot

Abstract Pre-fracture injection tests have been commonly used, across the industry, in order to estimate the required hydraulic fracture design parameters and associated reservoir pressure. However, evidence would suggest that industry approaches to both the injection execution and the post-injection analyses are not as equally consistent. The result could potentially be an erroneous and inaccurate interpretation, which could lead to over estimation of these reservoir characteristics and subsequent inefficient fracture design and placement. This paper demonstrates how a unified approach to the analysis of pre-frac injection tests can lead to the valid application of this technique in obtaining reliable estimates of both the reservoir pressure and the matrix permeability in a tight unconventional shale play (Utica play fairway). Analyses of the pressure fall off data, from pre-frac injection tests that were performed in a number of wells, will be discussed here. These analyses included the use of a conventional log-log diagnostic plot, as well as Pressure Decline Analysis using the SQRT (square root time), G function and G dP/dG plots. Finally, the results were also interpreted utilizing the ACA (after closure analysis) approach by employing type curves and flow regime time functions. The results of the formation permeability, the initial reservoir pressure, the closure time and the closure pressure from three of these field tests will be presented in this paper. Two of these tests achieved pseudo-radial flow, whilst one test failed to reach either pseudo-linear or pseudo-radial flow, resulting in a demonstrable overestimation of the reservoir parameters. The paper will present the injection test execution and analysis, as well as confirming the importance of achieving pseudo radial flow in order to obtain reliable and consistent test results.

scholarly journals A Semianalytical Solution for Multifractured Horizontal Wells in Box-Shaped Reservoirs

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Lei Wang ◽  
Xiaodong Wang ◽  
He Zhang ◽  
Yunpeng Hu ◽  
Chen Li
Keyword(s):  
Radial Flow ◽  
Flow Characteristics ◽  
Horizontal Wells ◽  
Flow Region ◽  
Linear Flow ◽  
Type Curves ◽  
Production Ratio ◽  
Dirac Function ◽  
Sensitive Parameters ◽  
First Time

This paper presented a 3D point sink model through using Dirac function. Then, 3D point sink solution in boxed reservoirs was obtained through using Laplace transform and Fourier transform methods. Based on the flux and pressure equivalent conditions in Laplace space, a semianalytical solution for multifractured horizontal wells was also proposed for the first time. The production rate distribution was discussed in detail for multifractured horizontal wells. The calculative results show the outermost fractures had higher production ratio due to larger drainage area and the inner fractures were lower due to the strong interface between fractures. Type curves were established to analyze the flow characteristics, which would be divided into six stages, for example, bilinear flow region, the first linear flow region, the first radial flow region, the second linear flow region, the second radial flow region, and the boundary dominated flow region, respectively. Finally, effects of some sensitive parameters on type curves were also analyzed in detail.

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