The Propagation of Depletion — The Inclusion of Inertia in the Derivation of the Diffusivity Equation

2020 ◽  
Author(s):  
Fred Goldsberry ◽  
Chris Fair ◽  
Don Nguyen ◽  
Venera Zhumagulova
Keyword(s):  
Diffusivity Equation

scholarly journals Semi-Analytical Solution to Assess CO2 Leakage in the Subsurface through Abandoned Wells

Energies ◽  
2021 ◽  
Vol 14 (9) ◽  
pp. 2452
Author(s):  
Tian Qiao ◽  
Hussein Hoteit ◽  
Marwan Fahs
Keyword(s):  
Analytical Solution ◽  
Storage Site ◽  
Co2 Leakage ◽  
Transient Pressure ◽  
Flow Paths ◽  
Abandoned Wells ◽  
Diffusivity Equation ◽  
Carbon Dioxide Co2 ◽  
Good Agreement

Geological carbon storage is an effective method capable of reducing carbon dioxide (CO2) emissions at significant scales. Subsurface reservoirs with sealing caprocks can provide long-term containment for the injected fluid. Nevertheless, CO2 leakage is a major concern. The presence of abandoned wells penetrating the reservoir caprock may cause leakage flow-paths for CO2 to the overburden. Assessment of time-varying leaky wells is a need. In this paper, we propose a new semi-analytical approach based on pressure-transient analysis to model the behavior of CO2 leakage and corresponding pressure distribution within the storage site and the overburden. Current methods assume instantaneous leakage of CO2 occurring with injection, which is not realistic. In this work, we employ the superposition in time and space to solve the diffusivity equation in 2D radial flow to approximate the transient pressure in the reservoirs. Fluid and rock compressibilities are taken into consideration, which allow calculating the breakthrough time and the leakage rate of CO2 to the overburden accurately. We use numerical simulations to verify the proposed time-dependent semi-analytical solution. The results show good agreement in both pressure and leakage rates. Sensitivity analysis is then conducted to assess different CO2 leakage scenarios to the overburden. The developed semi-analytical solution provides a new simple and practical approach to assess the potential of CO2 leakage outside the storage site. This approach is an alternative to numerical methods when detailed simulations are not feasible. Furthermore, the proposed solution can also be used to verify numerical codes, which often exhibit numerical artifacts.

Asymptotic Solutions of the Diffusivity Equation and Their Applications

2016 ◽  
Author(s):  
Michael J. King ◽  
Zhenzhen Wang ◽  
Akhil Datta-Gupta
Keyword(s):  
Asymptotic Solutions ◽  
Diffusivity Equation

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.

scholarly journals Parametric analysis of diffusivity equation in oil reservoirs

2016 ◽  
Vol 7 (1) ◽  
pp. 169-179 ◽  
Author(s):  
Reza Azin ◽  
Mohamad Mohamadi-Baghmolaei ◽  
Zahra Sakhaei
Keyword(s):  
Parametric Analysis ◽  
Oil Reservoirs ◽  
Diffusivity Equation
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