Transient-Inflow-Performance Modeling From Analytic Line-Source Solutions for Arbitrary-Trajectory Wells

SPE Journal ◽  
2018 ◽  
Vol 23 (03) ◽  
pp. 906-918
Author(s):  
R. D. Hazlett ◽  
D. K. Babu
Keyword(s):  
Line Source ◽  
Flux Line ◽  
Early Time ◽  
Time Behavior ◽  
Dimensionless Time ◽  
Pressure Derivative ◽  
Local Flow ◽  
Full Characterization ◽  
Storage Effects ◽  
Arbitrary Trajectory

Summary We present two easily computable, equally valid, semianalytic, single-phase, constant-rate solutions to the diffusivity equation for an arbitrarily oriented uniform-flux line source in a 3D, anisotropic, bounded system in Cartesian coordinates. With the addition of superposition, these become inflow solutions for wells of arbitrary trajectory. In addition, we produce analytic time derivatives for pressure-transient analyses (PTAs) of complex wells. If we extract solution components for 2D systems from the general solution, we can construct discrete complex-fracture-inflow and PTA capability for vertical, fully penetrating fractures, suitable for use as the basis solution in modeling complex phenomena, such as pressure-constrained production or development of fracture interference. For a 3D slanted well, the full characterization of dimensionless pressure over 10 decades of dimensionless time behavior can be produced in 1.5 seconds. With a fast-computing analytic solution for pressure anywhere in the system, we can also produce dense pressure maps at scalable resolution where any point could represent an observation well for convolution and enhanced interpretation. Likewise, the pressure derivative and the slope of the logarithmic temporal derivative of pressure can be mapped throughout to indicate local flow regime in a complex system. In particular, we compare and contrast the PTA signatures from symmetrical and asymmetrical horizontal, slanted, and diagonal line sources and examine when the behavior of a thin 3D reservoir collapses to the equivalent of a 2D fully penetrating fracture. Once the reservoir-thickness/length ratio reaches 1:100, all wells with the same projection onto the x–y plane are indistinguishable except for very early time, probably masked by wellbore/fracture-storage effects.

scholarly journals Explicit Deconvolution of Well Test Data Dominated by Wellbore Storage

2014 ◽  
Vol 2014 ◽  
pp. 1-12
Author(s):  
K. Razminia ◽  
A. Hashemi ◽  
A. Razminia ◽  
D. Baleanu
Keyword(s):  
Test Data ◽  
Material Balance ◽  
Early Time ◽  
Time Behavior ◽  
Well Test ◽  
Deconvolution Method ◽  
Pressure Data ◽  
Practical Applications ◽  
Wellbore Storage ◽  
Storage Effects

This paper addresses some methods for interpretation of oil and gas well test data distorted by wellbore storage effects. Using these techniques, we can deconvolve pressure and rate data from drawdown and buildup tests dominated by wellbore storage. Some of these methods have the advantage of deconvolving the pressure data without rate measurement. The two important methods that are applied in this study are an explicit deconvolution method and a modification of material balance deconvolution method. In cases with no rate measurements, we use a blind deconvolution method to restore the pressure response free of wellbore storage effects. Our techniques detect the afterflow/unloading rate function with explicit deconvolution of the observed pressure data. The presented techniques can unveil the early time behavior of a reservoir system masked by wellbore storage effects and thus provide powerful tools to improve pressure transient test interpretation. Each method has been validated using both synthetic data and field cases and each method should be considered valid for practical applications.

Type Curves for a Reservoir Subject to Active Bottom Water Drive

2013 ◽  
Vol 824 ◽  
pp. 373-378
Author(s):  
I. Eiroboyi ◽  
E. Steve Adewole
Keyword(s):  
Steady State ◽  
Bottom Water ◽  
Early Time ◽  
Dimensionless Time ◽  
Pressure Derivative ◽  
Test Analysis ◽  
Type Curves ◽  
Well Completion ◽  
Dimensionless Pressure ◽  
Large Pressure

The use of dimensionless pressure and dimensionless pressure derivative type curves has fully overcome the challenges experienced in the use of straight line methods and has brought about major successes in well tests analyses. Flow periods and reservoir boundary types are easily delineated and identified with the use of these curves. Furthermore, near wellbore characterization results are now more reliable. In this study, type curves for a reservoir subject to bottom water energy and a vertical well completion are developed to reveal specific signatures that can be used to achieve efficient pressure test analysis. Both early and late flow periods were considered for a wellbore of negligible skin and wellbore storage influences. Results obtained show that dimensionless pressures depart from infinite-acting behavior and attain steady state at dimensionless time of order proportional to the square of dimensionless reservoir thickness. Wellbore dimensionless radius affects dimensionless time of attainment of steady state inversely, which is rather accelerated by large fluid withdrawal rates (large pressure drawdown). On the other hand, dimensionless pressure derivatives show gradual collapse to zero after expiration of infinite flow. The rate of collapse is strongly affected by wellbore properties and pressure drawdown. Radial flow is generally characterized by a constant slope of 1.151 during which period the dimensionless pressure derivative gave a value of 0.5. Following assumption of negligible wellbore skin and storage, no early time hump is observed on dimensionless derivative curves.

A Noniterative Blind Deconvolution Approach to Unveil Early Time Behavior of Well Testings Contaminated by Wellbore Storage Effects

2012 ◽  
Vol 134 (2) ◽  
Author(s):  
Arash Moaddel Haghighi ◽  
Peyman Pourafshary
Keyword(s):  
Blind Deconvolution ◽  
Storage Period ◽  
Early Time ◽  
Test Duration ◽  
Well Testing ◽  
Time Behavior ◽  
Rate Data ◽  
Deconvolution Method ◽  
Wellbore Storage ◽  
Storage Effects

Deconvolution method is generally used to eliminate wellbore storage dominant period of well testing. Common Deconvolution techniques require knowledge of both pressure and rate variations within test duration. Unfortunately, accurate rate data are not always available. In this case, blind deconvolution method is used. In this work, we present a new approach to improve the ability of blind deconvolution method in well testing. We examined the behavior of rate data by comparing it with a special class of images and employed their common properties to represent gross behavior of extracted rate data. Results of examinations show ability of our developed algorithm to remove the effect of wellbore storage from pressure data. Our Algorithm can deal with different cases where wellbore storage has made two different reservoirs behave identical in pressure response. Even if there is no wellbore effect or after wellbore storage period is passed, proposed algorithm can work routinely without any problem.

scholarly journals A Method of Differentiating the Early-Time and Late-Time Behavior in Pressure-Pulse Decay Permeametry

Geofluids ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-9
Author(s):  
Yu Zhao ◽  
Chaolin Wang ◽  
Yongfa Zhang ◽  
Qiang Liu
Keyword(s):  
Pressure Pulse ◽  
Critical Time ◽  
Volume Ratio ◽  
Early Time ◽  
Real Data ◽  
Late Time ◽  
Time Behavior ◽  
Dimensionless Time ◽  
Time Data ◽  
Decay Test

The pressure-pulse decay is a preferred technique for determining permeability of unconventional gas reservoir rocks. The pressure-pulse decay often shows quite different characteristics during the early time and the later time. Most approaches for estimating the permeability proposed in the literature are required to use the later-time pressure-pulse decay measurements. However, the later-time data are often selected subjectively, lacking a universal criterion. In this paper, a method of differentiating the early-time and late-time behavior for pressure-pulse decay test is proposed. The analytical results show that the critical time (dimensionless time) of early-/late-time decay characteristics mainly depends on the volume ratios, and it increases first and then decreases with the volume ratios. The critical time for cases with same chamber sizes is much less than that for cases with unequal chamber sizes. Applicability of the proposed methods is examined using a numerical simulator, TOUGH+REALGASBRINE. The numerical results show that the pressure gradient along the sample varies nonlinearly at the early time and becomes a constant at the late time. Then, the proposed method is applied to real data for permeability estimation. It is found that the early-time behavior is negligible as the volume ratio takes on small values. As the volume ratios increase, the deviation becomes significant and considerable permeability errors will be produced if these early-time data are used.

Characteristics of Dimensionless Pressure Gradients and Derivatives of Horizontal and Vertical Wells Completed within Inclined Sealing Faults

2021 ◽  
Author(s):  
A V Ogbamikhumi ◽  
E S Adewole
Keyword(s):  
Pressure Drop ◽  
Horizontal Well ◽  
Superposition Principle ◽  
Early Time ◽  
Pressure Gradients ◽  
Vertical Wells ◽  
Pressure Derivative ◽  
Vertical Well ◽  
Dimensionless Pressure ◽  
Horizontal And Vertical Wells

Abstract Dimensionless pressure gradients and dimensionless pressure derivatives characteristics are studied for horizontal and vertical wells completed within a pair of no-flow boundaries inclined at a general angle ‘θ’. Infinite-acting flow solution of each well is utilized. Image distances as a result of the inclinations are considered. The superposition principle is further utilized to calculate total pressure drop due to flow from both object and image wells. Characteristic dimensionless flow pressure gradients and pressure derivatives for the wells are finally determined. The number of images formed due to the inclination and dimensionless well design affect the dimensionless pressure gradients and their derivatives. For n images, shortly after very early time for each inclination, dimensionless pressure gradients of 1.151(N+1)/LD for the horizontal well and 1.151(N+1) for vertical well are observed. Dimensionless pressure derivative of (N+1)/2LD are observed for central and off-centered horizontal well locations, and (N+1)/2 for vertical well are observed. Central well locations do not affect horizontal well productivity for all the inclinations. The magnitudes of dimensionless pressure drop and dimensionless pressure derivatives are maximum at the farthest image distances, and are unaffected by well stand-off for the horizontal well.

scholarly journals Anisotropic evolution of D-dimensional FRW spacetime

2019 ◽  
Vol 79 (12) ◽  
Author(s):  
Chad Middleton ◽  
Bret A. Brouse ◽  
Scott D. Jackson
Keyword(s):  
Early Time ◽  
Scale Factor ◽  
Accelerated Expansion ◽  
Late Time ◽  
Time Behavior ◽  
Einstein Field Equations ◽  
Fluid Regime ◽  
Field Equations ◽  
Higher Dimensional ◽  
Walker Metric

AbstractWe examine the time evolution of the $$D=d+4$$D=d+4 dimensional Einstein field equations subjected to a flat Robertson-Walker metric where the 3D and higher-dimensional scale factors are allowed to evolve at different rates. We find the exact solution to these equations for a single fluid component, which yields two limiting regimes offering the 3D scale factor as a function of the time. The fluid regime solution closely mimics that described by 4D FRW cosmology, offering a late-time behavior for the 3D scale factor after becoming valid in the early universe, and can give rise to a late-time accelerated expansion driven by vacuum energy. This is shown to be preceded by an earlier volume regime solution, which offers a very early-time epoch of accelerated expansion for a radiation-dominated universe for $$d=1$$d=1. The time scales describing these phenomena, including the transition from volume to fluid regime, are shown to fall within a small fraction of the first second when the fundamental constants of the theory are aligned with the Planck time. This model potentially offers a higher-dimensional alternative to scalar-field inflationary theory and a consistent cosmological theory, yielding a unified description of early- and late-time accelerated expansions via a 5D spacetime scenario.

A New Method for Estimating Average Reservoir Pressure: The Muskat Plot Revisited

2008 ◽  
Vol 11 (02) ◽  
pp. 298-306 ◽  
Author(s):  
James G. Crump ◽  
Robert H. Hite
Keyword(s):  
Direct Synthesis ◽  
New Method ◽  
Theoretical Ground ◽  
Time Behavior ◽  
Reservoir Pressure ◽  
Reservoir Properties ◽  
Pressure Derivative ◽  
Pressure Buildup ◽  
Heterogeneous Reservoirs ◽  
Fluid Properties

Summary This paper describes a new method for estimating average reservoir pressure from long-pressure-buildup data on the basis of the classical Muskat plot. Current methods for estimating average reservoir pressure require a priori information about the reservoir and assume homogeneous reservoir properties or use empirical extrapolation techniques. The new method applies to heterogeneous reservoirs and requires no information about reservoir or fluid properties. The idea of the method is to estimate from the pressure derivative the first few eigenvalues of the pressure-transient decay modes. These values are characteristic of the reservoir and fluid properties, but not of the pressure history or well location in the reservoir. The smallest eigenvalue is used to extrapolate the long-time behavior of the transient to estimate the final reservoir pressure. The second eigenvalue can be used to estimate the quality of the estimate. Numerical tests of the method show that it estimates average reservoir pressure accurately, even when the reservoir is heterogeneous or when partial-flow barriers are present. Examples with real data show that the behavior predicted by the theory is actually observed. We expect the method to have value in reservoir limits testing, in making consistent estimates of average reservoir pressure from permanent downhole gauges, and in characterizing complex reservoirs. Introduction Several different methods of interpreting pressure-buildup data to obtain average reservoir pressure have been proposed (Muskat 1937; Horner 1967; Miller et al. 1950; Matthews et al. 1954; Dietz 1965) in the past, and in recent years some new techniques have appeared in the literature (Mead 1981; Hasan and Kabir 1983; Kabir and Hasan 1996; Kuchuk 1999; Chacon et al. 2004). Larson (1963) revisited the Muskat method and put it on a firm theoretical ground for a homogeneous cylindrical reservoir. Some of the existing techniques depend on knowledge of the reservoir size and shape and assume homogeneous properties (Horner 1967; Miller et al. 1950; Matthews et al. 1954; Dietz 1965). Such methods may result in uncertain predictions when reservoir data are unavailable or reservoir heterogeneity exists. The inverse time plot by Kuchuk (1999) is essentially a modification of Horner's method (1967) and works well in reservoirs that can be treated as infinite during the time of the test. The hyperbola method proposed by Mead (1981) and further developed by Hasan and Kabir (1983) is an empirical technique, not based on fundamental fluid flow principles for bounded reservoirs (Kabir and Hasan 1996). Chacon et al. (2004) develop the direct synthesis technique, in which conventional theory is used to derive an average pressure directly from standard log-log plots. Homogeneous properties and radial symmetry are assumed. Muskat's original derivation was a wellbore storage model. Larson reinterpreted Muskat's method and derived relationships showing how Muskat's plot could be used to estimate average reservoir pressure in a cylindrical, homogeneous reservoir. This paper revisits the ideas underlying Larson's paper. Similar ideas are shown to hold for heterogeneous reservoirs of any shape. A new analysis technique replacing the Muskat plot by a plot of the pressure derivative simplifies the determination of average reservoir pressure. It is shown that parameters from analysis of a long buildup on a reservoir can be used in subsequent buildup tests to shorten the required time of the subsequent buildups. Finally, estimates for time required for a buildup in homogeneous reservoirs of any shape are given.

DETERMINATION OF THE VAPOR-LIQUID CRITICAL POINT FROM THE SHORT-TIME DYNAMICS

2001 ◽  
Vol 15 (12n13) ◽  
pp. 369-374 ◽  
Author(s):  
SHENG-YOU HUANG ◽  
XIAN-WU ZOU ◽  
ZHI-JIE TAN ◽  
ZHUN-ZHI JIN
Keyword(s):  
Critical Point ◽  
Early Time ◽  
Dynamic Scaling ◽  
Time Behavior ◽  
Time Dynamic ◽  
Time Dynamics ◽  
Dynamics Simulations ◽  
Average Potential Energy ◽  
Short Time ◽  
Vapor Liquid

Considering the average potential energy per particle as the parameter, we investigate the early-time dynamics of vapor-liquid transition in the critical region for 2D Lennard-Jones fluids by using NVT molecular dynamics simulations. The results verify the existence of short-time dynamic scaling in the fluid systems and show that the critical point Tc can be determined by the universal short-time behavior. The obtained value of Tc = 0.540 from the short-time dynamics is very close to the value of 0.533 from the Monte Carlo simulations in the equilibrium state of the systems.

A general E-pulse scheme arising from the dual early-time/late-time behavior of radar scatterers

1994 ◽  
Vol 42 (9) ◽  
pp. 1336-1341 ◽  
Author(s):  
E.J. Rothwell ◽  
Kun-Mu Chen ◽  
D.P. Nyquist ◽  
P. Ilavarasan ◽  
J.E. Ross ◽  
...  
Keyword(s):  
Early Time ◽  
Late Time ◽  
Time Behavior
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