Finite-Wellbore-Radius Solution for Gas Wells by Green's Functions

SPE Journal ◽  
2015 ◽  
Vol 20 (04) ◽  
pp. 842-855 ◽  
Author(s):  
Emilio P. Sousa ◽  
Abelardo B. Barreto ◽  
Alvaro M. Peres
Keyword(s):  
Line Source ◽  
Significant Loss ◽  
Computational Effort ◽  
Test Problems ◽  
Well Test ◽  
Gas Reservoirs ◽  
Gas Well ◽  
The Difference ◽  
Diffusivity Equation ◽  
Reservoir Simulator

Summary Even when written in terms of a pseudopressure function, the diffusivity equation for flow of gases through porous media is, rigorously speaking, nonlinear because the viscosity/compressibility product is pseudopressure-dependent. However, several techniques and analysis procedures neglect such nonlinearity. A new methodology for constructing solutions for gas reservoirs through the Green's-function (GF) technique was recently proposed in the literature. Such methodology handles the viscosity/compressibility product variation rigorously, and it was successfully applied to solve several gas-well-test problems. In those problems, the wellbore is always represented by a line source. This work extends the theory a little further by considering a finite-wellbore-radius (FWR) boundary condition for a single vertical well producing at constant rate from an isotropic homogeneous and infinite gas reservoir. The proposed solution does not consider non-Darcy-flow effects, wellbore storage, and skin. Results from our FWR solution are compared with a commercial finite-difference reservoir simulator that shows a very close agreement. We also compared the FWR solution to the correspondent line-source solution to study the difference between the two solutions. As expected, the pseudopressure solutions by use of line-source and FWR boundary conditions do not match at early times, but they do agree at long times, which is exactly how FWR and line-source well solutions for slightly compressible fluids behave. It seems that, even for gas-well problems, the wellbore can be satisfactorily represented by a line source without significant loss of generality. The line-source assumption greatly simplifies the mathematics and the computational effort. This aspect is especially attractive for complex nonlinear gas-well problems that remain to be solved by the GF approach.

Analytical Treatment of Pressure-Transient Solutions for Gas Wells With Wellbore Storage and Skin Effects by the Green's Functions Method

SPE Journal ◽  
2016 ◽  
Vol 21 (05) ◽  
pp. 1858-1869 ◽  
Author(s):  
Emilio P. Sousa ◽  
Abelardo B. Barreto ◽  
Alvaro M. Peres
Keyword(s):  
Green's Functions ◽  
Green’S Functions ◽  
Approximate Solutions ◽  
Test Problems ◽  
Well Testing ◽  
Well Test ◽  
Gas Reservoirs ◽  
Analytical Treatment ◽  
Wellbore Storage ◽  
Diffusivity Equation

Summary Even when written in terms of a pseudopressure function, the diffusivity equation for flow of gases through porous media is, rigorously speaking, nonlinear because the viscosity-compressibility product is pseudopressure-dependent. However, several techniques and analysis procedures neglect such nonlinearity. A new methodology for constructing solutions for gas reservoirs through the Green's functions (GF) technique was recently proposed in the literature. Such methodology handles the viscosity-compressibility product variation rigorously, and it was applied to solve several gas-well test problems successfully. However, wellbore storage and skin effects were not considered yet by this new approach. In this work, the GF technique is applied to obtain a new solution for an infinite, homogeneous, isotropic gas reservoir being produced through a single vertical well represented by a line-source with wellbore storage and skin. The solution, however, does not consider non-Darcy flow effects. Even though the wellbore storage introduces a new nonlinearity to an already nonlinear problem, this work presents two accurate approximate solutions compared with the results from a commercial numerical well-testing simulator. This work also shows that the wellbore pseudopressure dimensionless solution is a function of the correlating groups CDexp(2S) and tD/CD, exactly similar to the way that wellbore dimensionless liquid solutions are. Liquid and gas dimensionless solutions under these correlating groups are not equal, though.

The Validity of Approximate Boundary Conditions for Natural Convection With Thermal Radiation in Open Cavities

2020 ◽  
Vol 142 (9) ◽  
Author(s):  
Om Singh ◽  
Shireesh B. Kedare ◽  
Suneet Singh
Keyword(s):  
Natural Convection ◽  
Boundary Conditions ◽  
Significant Loss ◽  
Computational Effort ◽  
Computational Domain ◽  
Maximum Difference ◽  
Open Cavities ◽  
Shallow Cavities ◽  
Approximate Boundary Conditions ◽  
The Difference

Abstract The use of approximate boundary conditions at the opening of the cavities leads to restriction of the computational domain and, hence, the reduction in computational effort. However, the accuracy of the restricted domain approach (RDA) had been evaluated only for the natural convection inside open cavities and that too only for one aspect ratio (AR). The validity of the approach had not been evaluated for inclined, as well as, shallow cavities. This study focuses on the analysis of the accuracy of RDA against extended domain approach (EDA) in open cavities of different ARs, at different inclinations and different Rayleigh numbers (Ra). The results show that the difference between the approaches is only significant in very shallow cavities (AR is defined as the height of the hot wall divided by the depth of the cavity) at low Ra. For Ra higher than  106 and an AR greater than 0.2, the maximum difference between the two approaches is around 5% and hence RDA can be recommended in these ranges, resulting in increased computational efficiency without significant loss in the accuracy. Moreover, the maximum difference in the results for the two methods is for intermediate inclinations. Even there, an increase in the difference is more pronounced at lower Ra. Furthermore, distribution of the exit velocity and temperature at the opening as well as the distribution of the Nusselt number at the hot wall is compared for RDA and EDA to explain the behavior of error at different ARs and inclinations.

Tidal Pressure Response and Surveillance of Water Encroachment

2006 ◽  
Vol 9 (04) ◽  
pp. 335-344 ◽  
Author(s):  
Kare Langaas ◽  
Knut I. Nilsen ◽  
Svein M. Skjaeveland
Keyword(s):  
Fluid Flow ◽  
Petroleum Reservoirs ◽  
Efficiency Factor ◽  
Tidal Effect ◽  
Pressure Response ◽  
Ocean Tide ◽  
Well Test ◽  
Gas Well ◽  
Reservoir Simulator ◽  
Tidal Response

Summary A review of the tidal response in petroleum reservoirs is given. Tidal response is caused by periodic changes in overburden stress induced by the ocean tide; the "tidal efficiency factor" is derived by two different approaches and is in line with a recent well test in the Ormen Lange gas field. For small geomechanical pertubations like the tidal effect, we show that a simplified coupling of geomechanics and fluid flow is possible. The coupling is easy to implement in a standard reservoir simulator by introducing a porosity varying in phase with the tide. Simulations show very good agreement with the theory. The observation of the tidal response in petroleum reservoirs is an independent information provider [i.e., it provides information in addition to the (average) pressure and its derivative from a well test]. The implementation of the tidal effect in a normal reservoir simulator gives us the opportunity to study complex multiphase situations and to evaluate the potential of the tidal response as a reservoir-surveillance method. The case studies presented here focus on the possibility of observing water in the near-well region of a gas well. Introduction The main objective of this work is to investigate whether the tidal pressure response in petroleum reservoirs can be used for reservoir surveillance, in particular to detect saturation changes in the near-well region (e.g., to detect water encroachment toward a gas well). The literature seems sparse in this area. Also, our approach of simplified coupling of geomechanics and fluid flow for small geomechanical effects, and the possibility to implement this in a normal reservoir simulator, has not (to our knowledge) been discussed in the literature. Several authors have derived a tidal efficiency factor, but a review and comparison study seems to be missing.

The Seepage Pressure Distribution and the Capacity of Low-Permeability Reservoirs Gas

2013 ◽  
Vol 734-737 ◽  
pp. 1317-1323
Author(s):  
Liang Dong Yan ◽  
Zhi Juan Gao
Keyword(s):  
Mathematical Model ◽  
Pressure Distribution ◽  
Low Permeability ◽  
Flow State ◽  
Klinkenberg Effect ◽  
Gas Reservoirs ◽  
Gas Well ◽  
Seepage Pressure ◽  
Slippage Effect ◽  
Low Permeability Reservoirs

Low-permeability gas reservoirs are influenced by slippage effect (Klinkenberg effect) , which leads to the different of gas in low-permeability and conventional reservoirs. According to the mechanism and mathematical model of slippage effect, the pressure distribution and flow state of flow in low-permeability gas reservoirs, and the capacity of low-permeability gas well are simulated by using the actual production datum.

A Study of Downhole Drillable Pulsing Cementing Device with Low Frequency Self-Excited Hydraulic Oscillation and its Field Application

2012 ◽  
Vol 450-451 ◽  
pp. 1536-1539
Author(s):  
Cui Ping Nie ◽  
Deng Sheng Ye
Keyword(s):  
Setting Time ◽  
Low Frequency ◽  
Field Application ◽  
Displacement Efficiency ◽  
Cement Slurry ◽  
Gas Reservoirs ◽  
Gas Field ◽  
Gas Well ◽  
Hydraulic Oscillation ◽  
Injection Technology

Abstract: Usually we pay more attention on how to improve gas well cementing quality in engineering design and field operations, and there are so many studies on cement agents but few researches on cement slurry injection technology. The field practice proved that conventional cementing technology can not ensure the cementing quality especially in gas well and some abnormal pressure wells. Most of the study is concentrated on cement agents and some cementing aspects such as wellbore condition, casing centralization etc. All the factors analysis on cementing quality has pointed out that a combination of good agents and suitable measurements can improve cementing quality effectively. The essential factor in cementing is to enhance the displacement efficiency, but normal hole condition and casing centralization are the fundamental for cementing only. Pulsing cementing is the technology that it can improve the displacement efficiency especially in reservoir well interval, also it can shorten the period from initial to ultimate setting time for cement slurry or improve thickening characteristics, and then to inhibit the potential gas or water channeling. Based on systematically research, aiming at improving in 7″ liner cementing, where there are multi gas reservoirs in long interval in SiChuan special gas field, well was completed with upper 7″ liner and down lower 5″ liner, poor cementing bonding before this time. So we stressed on the study of a downhole low frequency self-excited hydraulic oscillation pulsing cementing drillable device and its application, its successful field utilization proved that it is an innovative tool, and it can improve cementing quality obviously.

No Need for Radio Active Tracer When Mother Nature Helps Detecting the Effective Hydraulic Fracture Height

2022 ◽  
Author(s):  
Rinat Lukmanov ◽  
Said Jabri ◽  
Ehab Ibrahim
Keyword(s):  
Hydraulic Fracture ◽  
Natural Radioactivity ◽  
Gamma Ray ◽  
Fracture Propagation ◽  
Radioactive Isotopes ◽  
Main Element ◽  
Tight Gas ◽  
Well Test ◽  
Gas Reservoirs ◽  
Fracture Height

Abstract The tight gas reservoirs of Haima Supergroup provide the majority of gas production in the Sultanate of Oman. The paper discusses a possibility of using the anomalies from natural radioactivity to evaluate the fracture height for complex tight gas in mature fields of Oman. The standard industry practice is adding radioactive isotopes to the proppant. Spectral Gamma Ray log is used to determine near wellbore traced proppant placement. Spectral Noise log in combination with Production logs helps to identify the active fractures contributing to production. These methods complement each other, but they are obviously associated with costs. Hence, majority of wells are fracced without tracers or any other fracture height diagnostics. However, in several brown fields, an alternative approach to identify fracture height has been developed which provides fit-for-purpose results. It is based on the analysis of naturally occurring radioactive minerals (NORM) precipitation. The anomalies were observed in the many gas reservoirs even in cases when tracers were not used. At certain conditions, these anomalies can be used to characterize fracture propagation and optimize future wells hydraulic Fracture design. A high number of PLTs and well test information were analyzed. Since tight formations normally don't produce without fracturing, radioactive anomalies flag the contributing intervals and hence fracture propagation. The main element of analysis procedure is related to that fact that if no tracers applied, the discrepancy between normalized Open Hole Gamma Ray and Gamma Ray taken during PLT after 6-12 months of production can be used instead to establish fracture height. This method cannot be applied for immediate interpretation of fracture propagation because time is required to precipitate NORM and using the anomalies concept. The advantage of this method is that it can be used in some fields to estimate the frac effectiveness of wells without artificial tracers. It is normally assumed that the Natural radioactivity anomalies appear mainly due to co-production of the formation water. However, in the fields of interest the anomalies appear in wells producing only gas and condensate. This observation provides an opportunity for active fracture height determination at minimum cost.

Stress Sensitivity of Low Permeable and Water-Bearing Gas Reservoir without Gas Slippage Effect

2014 ◽  
Vol 962-965 ◽  
pp. 570-573
Author(s):  
Jian Yan ◽  
Xiao Bing Liang ◽  
Qian Wu ◽  
Qing Guo
Keyword(s):  
Water Saturation ◽  
Stress Sensitivity ◽  
Testing Methods ◽  
Gas Reservoirs ◽  
Gas Reservoir ◽  
Gas Well ◽  
Well Production ◽  
Gas Slippage ◽  
Slippage Effect ◽  
Function Relationship

Because of the gas slippage, the testing methods of stress sensitivity for gas reservoir should be different from that for oil reservoir. This text adopts the method that imposing back pressure on the outlet of testing core to weaken the gas slippage effect and tests the stress sensitivity of low permeability gas reservoirs, then analyzes the influence of permeability and water saturation on stress sensitivity. The results show that: low permeable and water-bearing gas reservoirs have strong stress sensitivity; the testing permeability has the power function relationship with net stress, compared to the exponential function, the fitting correlation coefficient is larger and more suited to the actual; the lower the permeability is and the higher water saturation is, the stronger the stress sensitivity is. The production of gas well is affected when considering the stress sensitivity, so the pressure dropping rate should be reasonable when low permeable gas reservoirs are developed. The results provide theoretical references for analyzing the well production and numerical simulation.

Reserves Determination Using Type Curve Matching and Extended Material Balance Methods in the Medicine Hat Shallow Gas Field

1994 ◽  
Author(s):  
S. L. West ◽  
P. J. R. Cochrane
Keyword(s):  
Material Balance ◽  
Poor Quality ◽  
Curve Matching ◽  
Pressure Data ◽  
Gas Reservoirs ◽  
Shallow Gas ◽  
Gas Field ◽  
Type Curve ◽  
Balance Analysis ◽  
Diffusivity Equation

Tight shallow gas reservoirs in the Western Canada Basin present a number of unique challenges in accurately determining reserves. Traditional methods such as decline analysis and material balance are inaccurate due to the formations' low permeabilities and poor pressure data. The low permeabilities cause long transient periods not easily separable from production decline using conventional decline analysis. The result is lower confidence in selecting the appropriate decline characteristics (exponential or harmonic) which significantly impacts recovery factors and remaining reserves. Limited, poor quality pressure data and commingled production from the three producing zones results in non representative pressure data and hence inaccurate material balance analysis. This paper presents the merit of two new methods of reserve evaluation which address the problems described above for tight shallow gas in the Medicine Hat field. The first method applies type curve matching which combines the analytical pressure solutions of the diffusivity equation (transient) with the empirical decline equation. The second method is an extended material balance which incorporates the gas deliverability theory to allow the selection of appropriate p/z derivatives without relying on pressure data. Excellent results were obtained by applying these two methodologies to ten properties which gather gas from 2300 wells. The two independent techniques resulted in similar production forecasts and reserves, confirming their validity. They proved to be valuable, practical tools in overcoming the various challenges of tight shallow gas and in improving the accuracy in gas reserves determination in the Medicine Hat field.

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