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.

A New Deconvolution Technique Based on Pressure-Derivative Data for Pressure-Transient-Test Interpretation

SPE Journal ◽  
2011 ◽  
Vol 17 (01) ◽  
pp. 307-320 ◽  
Author(s):  
Mustafa Onur ◽  
Fikri J. Kuchuk
Keyword(s):  
Small Error ◽  
New Method ◽  
Late Time ◽  
Reservoir Pressure ◽  
Test Interpretation ◽  
Pressure Derivative ◽  
Pressure Transient ◽  
Significant Difference ◽  
Time Periods ◽  
Pressure Transient Test

Summary In this paper, we present a new deconvolution method that removes the dependency of the deconvolved constant-rate drawdown responses on the initial reservoir pressure. It is well known that the late-time periods in particular of the deconvolved responses from the recent pressure-rate deconvolution methods are dependent on the initial reservoir pressure. A small error in the initial reservoir pressure could make a significant difference in the late-time periods of the deconvolved responses that can lead to an incorrect interpretation model, particularly misinterpretation of the boundaries. The new method presented is based on pressure-derivative data rather than pressure data that are used in all published deconvolution algorithms. Using pressure-derivative data in deconvolution leads to a nonlinear least-squares objective function that is different from those used in the earlier deconvolution methods and eliminates the dependency of the deconvolved responses on the initial reservoir pressure. Therefore, the new method minimizes incorrect interpretation because of an error or uncertainty in the initial reservoir pressure. We apply the new method to both simulated and field pressure-transient data sets. The results show that the new method offers a significant advantage over the earlier deconvolution methods for pressure-transient-test interpretation in cases where the initial reservoir pressure is unknown or uncertain.

Determining Average Reservoir Pressure From Pressure Buildup Tests

1974 ◽  
Vol 14 (01) ◽  
pp. 55-62 ◽  
Author(s):  
Hossein Kazemi
Keyword(s):  
Oil Reservoirs ◽  
Reservoir Engineering ◽  
Reservoir Pressure ◽  
Well Test ◽  
Gas Well ◽  
Pressure Buildup ◽  
Line Section ◽  
Straight Line ◽  
Buildup Curve

Abstract Two simple and equivalent procedures are suggested for improving the calculated average reservoir pressure from pressure buildup tests of liquid or gas wells in developed reservoirs. These procedures are particularly useful in gas well test procedures are particularly useful in gas well test analysis, irrespective of gas composition, in reservoirs with pressure-dependent permeability and porosity, and in oil reservoirs where substantial gas porosity, and in oil reservoirs where substantial gas saturation has been developed. A knowledge of the long-term production history is definitely helpful in providing proper insight in the reservoir engineering providing proper insight in the reservoir engineering aspects of a reservoir, but such long-term production histories need not be known in applying the suggested procedures to pressure buildup analysis. Introduction For analyzing pressure buildup data with constant flow rate before shut-in, there are two plotting procedures that are used the most: the procedures that are used the most: the Miller-Dyes-Hutchinson (MDH) plot and the Horner plot. The MDH plot is a plot of p vs log Deltat, whereas the Horner plot is a plot of p vs log [(t + Deltat)/Deltat]. Deltat is the shut-in time and t is a pseudoproduction time equal to the ratio of total produced fluid to last stabilized flow rate before shut-in. This method was first used by Theis in the water industry. Miller-Dyes-Hutchinson presented a method for calculating the average reservoir pressure, T, in in 1950. This method requires pseudosteady state before shut-in and was at first restricted to a circular reservoir with a centrally located well. Pitzer extended the method to include other Pitzer extended the method to include other geometries. Much later, Dietz developed a simpler interpretation scheme using the same MDH plot: p is read on the extrapolated straight-line section of the pressure buildup curve at shut-in time, Deltat,(1) where C is the shape factor for the particular drainage area geometry and the well location; values for C are tabulated in Refs. 5 and 13. For a circular drainage area with a centrally located well, C = 31.6, and for a square, C = 30.9.Horner presented another approach, which depended on the knowledge of the initial reservoir pressure, pi. This method also was first developed pressure, pi. This method also was first developed for a centrally located well in a circular reservoir.Matthews-Brons-Hazebroek (MBH) introduced another average reservoir pressure determination technique, which has been used more often than other methods: first a Horner plot is made; then the proper straight-line section of the buildup curve is proper straight-line section of the buildup curve is extrapolated to [(t + Deltat)/Deltat] = 1 (this intercept is denoted p*); finally, p is calculated from(2) m is the absolute value of the slope of the straightline section of the Horner plot:(3) pDMBH (tDA) is the MBH dimensionless pressure pDMBH (tDA) is the MBH dimensionless pressure at tDA, and tDA is the dimensionless time:(4) tp k a pseudoproduction time in hours:(5) PDMBH tDA) for different geometries and different PDMBH tDA) for different geometries and different well locations are given in Refs. 6 and 13.The second term on the right-hand side of Eq. 2 is a correction term for finite reservoirs that is based on material balance. Thus, for an infinite reservoir, p = pi = p*, where pi is the initial reservoir pressure. SPEJ P. 55

Conditional Statistical Moment Equations for Dynamic Data Integration in Heterogeneous Reservoirs

2006 ◽  
Vol 9 (03) ◽  
pp. 280-288 ◽  
Author(s):  
Liyong Li ◽  
Hamdi A. Tchelepi
Keyword(s):  
Statistical Moment ◽  
Limited Data ◽  
Pressure Data ◽  
Moment Equations ◽  
Reservoir Properties ◽  
Incomplete Knowledge ◽  
Heterogeneous Reservoirs ◽  
Knowledge Uncertainty ◽  
Available Information ◽  
Permeability Field

Summary An inversion method for the integration of dynamic (pressure) data directly into statistical moment equations (SMEs) is presented. The method is demonstrated for incompressible flow in heterogeneous reservoirs. In addition to information about the mean, variance, and correlation structure of the permeability, few permeability measurements are assumed available. Moreover, few measurements of the dependent variable are available. The first two statistical moments of the dependent variable (pressure) are conditioned on all available information directly. An iterative inversion scheme is used to integrate the pressure data into the conditional statistical moment equations (CSMEs). That is, the available information is used to condition, or improve the estimates of, the first two moments of permeability, pressure, and velocity directly. This is different from Monte Carlo (MC) -based geostatistical inversion techniques, where conditioning on dynamic data is performed for one realization of the permeability field at a time. In the MC approach, estimates of the prediction uncertainty are obtained from statistical post-processing of a large number of inversions, one per realization. Several examples of flow in heterogeneous domains in a quarter-five-spot setting are used to demonstrate the CSME-based method. We found that as the number of pressure measurements increases, the conditional mean pressure becomes more spatially variable, while the conditional pressure variance gets smaller. Iteration of the CSME inversion loop is necessary only when the number of pressure measurements is large. Use of the CSME simulator to assess the value of information in terms of its impact on prediction uncertainty is also presented. Introduction The properties of natural geologic formations (e.g., permeability) rarely display uniformity or smoothness. Instead, they usually show significant variability and complex patterns of correlation. The detailed spatial distributions of reservoir properties, such as permeability, are needed to make performance predictions using numerical reservoir simulation. Unfortunately, only limited data are available for the construction of these detailed reservoir-description models. Consequently, our incomplete knowledge (uncertainty) about the property distributions in these highly complex natural geologic systems means that significant uncertainty accompanies predictions of reservoir flow performance. To deal with the problem of characterizing reservoir properties that exhibit such variability and complexity of spatial correlation patterns when only limited data are available, a probabilistic framework is commonly used. In this framework, the reservoir properties (e.g., permeability) are assumed to be a random space function. As a result, flow-related properties such as pressure, velocity, and saturations are random functions. We assume that the available information about the permeability field includes a few measurements in addition to the spatial correlation structure, which we take here as the two-point covariance. This incomplete knowledge (uncertainty) about the detailed spatial distribution of permeability is the only source of uncertainty in our problem. Uncertainty about the detailed distribution of the permeability field in the reservoir leads to uncertainty in the computed predictions of the flow field (e.g., pressure).

A Novel Method for the Direct Synthesis of Symmetrical and Unsymmetrical Sulfides and Disulfides from Aryl Halides and Ethyl Potassium Xanthogenate

Synlett ◽  
2018 ◽  
Vol 29 (07) ◽  
pp. 986-992 ◽  
Author(s):  
M. Soleiman-Beigi ◽  
Z. Arzehgar
Keyword(s):  
Direct Synthesis ◽  
Aryl Halides ◽  
New Method ◽  
Alkyl Aryl ◽  
Novel Method ◽  
Aryl Sulfides ◽  
Bunte Salts

An efficient and new method for the synthesis of disulfides and sulfides via the reaction of aryl halides with ethyl potassium xanthogenate in the presence of MOF-199 is described. O-Ethyl-S-aryl ­carbonodithioate has a key role as an intermediate in this procedure; it was converted into symmetrical diaryl disulfides in DMF. Additionally, this could be applied to the synthesis of unsymmetrical aryl alkyl(aryl′) disulfides by the reaction with S-alkyl(aryl) sulfurothioates (Bunte salts) as well as unsymmetrical aryl alkyl(aryl′) sulfides in DMSO.

A Novel Deliverability Equation for Shallow Layer and Low Permeability Reservoirs with Horizontal Fracture

2012 ◽  
Vol 616-618 ◽  
pp. 1000-1007
Author(s):  
Yue Yang ◽  
Xiang Fang Li ◽  
Ke Liu Wu ◽  
Jian Yang ◽  
Jun Tai Shi ◽  
...  
Keyword(s):  
Low Permeability ◽  
Oil Viscosity ◽  
Reservoir Properties ◽  
Vertical Well ◽  
Horizontal Fracture ◽  
Vertical Permeability ◽  
Shallow Layer ◽  
Fluid Properties ◽  
Fracture Distribution ◽  
Low Permeability Reservoirs

In order to predict the productivity of vertical well for shallow layer and low permeability reservoirs with horizontal fracture, based on the theory of horizontal fracture distribution and oil seepage in reservoir, establish the reservoir seepage physical model for shallow layer and low permeability reservoirs with horizontal fracture, and derive a novel deliverability equation, considering the effect of reservoir properties, fluid properties, horizontal fracture parameters and working systems. Furthermore, the equation was applied and performed sensitivity analysis to the productivity of a vertical well in Yanchang Chang 6 layer reservoir. Results show that vertical permeability, oil viscosity and the semiminor axis of horizontal fracture have more significant impact on well productivity. With real cases, it is demonstrated the established deliverability equation is simple and practical and meets the engineering accuracy requirements.

Preparation of Lead Iodide as Input Material for X-Ray Detectors

2005 ◽  
Vol 480-481 ◽  
pp. 477-482 ◽  
Author(s):  
M. Matuchová ◽  
Olga Prochazková ◽  
K. Zdanský ◽  
J. Zavadil ◽  
J. Maixner
Keyword(s):  
Direct Synthesis ◽  
New Method ◽  
Lead Iodide ◽  
X Ray ◽  
New Methods ◽  
Input Material ◽  
Zone Purification

The aim of this work is to study the new method of direct synthesis of lead and iodine as the input material of PbI2. This method has not been studied for this material till now, and seems to be one of the new methods for preparation of the input material. The photoluminescence measurement and measurement of resistivity has been done and compared with the measurements done by precipitation and zone purification.

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