An improved analytical solution for interface upconing around a well

Nordbotten, Jan Martin; Celia, Michael A.

doi:10.1029/2005wr004738

Cited by 56 publications

(50 citation statements)

References 23 publications

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“…The vertically averaged model is based on the assumption of vertical equilibrium, while the analytical model for wellbore flow is an extension of the classic upconing model that was presented by Nordbotten and Celia [24]. We will present a brief overview of both methods herein.…”

Section: Methodsmentioning

confidence: 99%

“…The embedded or local analytical solution used to solve for wellbore flow between two aquifers is taken from Nordbotten and Celia [24]. We refer to this solution as an upconing model because it extends early classic solutions that solve the problem of extracting a light fluid residing over a dense fluid using Dupuittype assumptions [26,28].…”

Section: Analytical Solution For Wellbore Flowmentioning

confidence: 99%

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Vertical equilibrium with sub-scale analytical methods for geological CO2 sequestration

2009

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Large-scale implementation of geological CO 2 sequestration requires quantification of risk and leakage potential. One potentially important leakage pathway for the injected CO 2 involves existing oil and gas wells. Wells are particularly important in North America, where more than a century of drilling has created millions of oil and gas wells. Models of CO 2 injection and leakage will involve large uncertainties in parameters associated with wells, and therefore a probabilistic framework is required. These models must be able to capture both the large-scale CO 2 plume associated with the injection and the small-scale leakage problem associated with localized flow along wells. Within a typical simulation domain, many hundreds of wells may exist. One effective modeling strategy combines both numerical and analytical models with a specific set of simplifying assumptions to produce an efficient numerical-analytical hybrid model. The model solves a set of governing equations derived by vertical averaging with assumptions of a macroscopic sharp interface and vertical equilibrium. These equations are solved numerically on a relatively coarse grid, with an analytical model embedded to solve for wellbore flow occurring at the sub-gridblock scale. This vertical equilibrium with sub-scale analytical method (VESA) combines the flexibility of a numerical method, allowing for heterogeneous and geologically complex systems, with the efficiency and accuracy of an analytical method, thereby eliminating expensive grid refinement for sub-scale features. Through a series of benchmark problems, we show that VESA compares well with traditional numerical simulations and to a semi-analytical model which applies to appropriately simple systems. We believe that the VESA model provides the necessary accuracy and efficiency for applications of risk analysis in many CO 2 sequestration problems.

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Section: Methodsmentioning

confidence: 99%

Section: Analytical Solution For Wellbore Flowmentioning

confidence: 99%

Vertical equilibrium with sub-scale analytical methods for geological CO2 sequestration

2009

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“…Later works on upconing in leaky aquifers were conducted by Bower et al (1999) and Dagan and Zeitoun (1998), which addressed upconing in heterogeneous aquifers. Analytical solutions on sharp interfaces may be divided into two categories: the first category is based on the Dupuit assumption and only allows horizontal flows, such as solutions presented by Bear (1972), Chappelear and Hirasaki (1976), Lake (1989), Kacimov (2002), Bakker (1999) and Nordbotten and Celia (2006); the second category is mainly based on the small-perturbation approach whereby a multidimensional solution is derived, such as the works done by Muskat (1949), Dagan and Bear (1968), Bear (1972) and Bower et al (1999). Bear and Dagan (1964), Bear (1979) and Bower et al (1999) studied interface upconing below a vertical water well.…”

Section: Introductionmentioning

confidence: 99%

Steady critical discharge rates from vertical and horizontal wells in fresh–saline aquifers with sharp interfaces

et al. 2016

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In this study, the critical (or maximum) discharge rates before saline water enters a well were determined for vertical and horizontal wells in a freshwater aquifer which is separated from a static saline aquifer by a sharp interface. Flow around the well was solved by integration of a point sink solution along the well axis, and both the critical discharge rate and critical interface rise were determined through a comparison of the heads and vertical gradients at the saline-fresh water interface. The rates were determined for vertical and horizontal wells with various lengths and depths for different aquifer salinities. Results were generalized by drawing dimensionless type curves. The results showed that the dimensionless total critical discharge rates are higher for the longer horizontal wells and longer vertical wells with a certain bottom depth, and they almost linearly decrease with well depth at rates of 0.7-0.9. For the dimensionless well length of 0.2, the dimensionless total discharge rate of a horizontal well is about 0.1 more than that of a vertical well with the same length and well-top depth. Also, the critical discharge rates per unit length of well are inversely proportional to well length and remarkably higher for shallower wells. Additionally, the critical pumping rate is proportional to the salinity difference of the aquifers. These results were confirmed by comparison to existing solutions for vertical wells with dimensionless lengths of 0.2, 0.5 and 0.6, and for critical interface rises in the range of 0.75-0.9.

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“…While the modifications presented above alter the implementation of the pressure solution, its fundamental form, defined by Equation (1), remains the same. Also, the upconing solution [34] and F' offset term defined above with Equation (7) are neglected for the purpose of simplifying the following analyses. All passive wells permeabilities, k pw , were randomly generated having a 50% chance of being either "intact"…”

Section: The Estimating Leakage Semi-analytically (Elsa) Algorithmmentioning

confidence: 99%

“…This algorithm creates a set of linear equations describing the pressure distribution throughout the domain by superimposing pressure changes caused by each source or sink in each aquifer. The general algorithm presented in [38] in conjunction with the development of a multiphase pressure response function [33,34,35,38] has led to a semi-analytical CO 2 leakage algorithm, presented in [40] and expounded upon in [7] and [36], which estimates both brine and CO 2 flux across confining layers resulting from the injection of CO 2 . While there are multiple pathways for the leakage of sequestered CO 2 from subsurface storage reservoirs (e.g.…”

Section: Introductionmentioning

confidence: 99%

An iterative global pressure solution for the semi-analytical simulation of geological carbon sequestration

Baù

Cody²,

González‐Nicolás

2015

Comput Geosci

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Successful large-scale implementation of geological CO 2 sequestration (GCS) will require the preliminary assessment of multiple potential injection sites. Risk assessment and optimization tools used in this effort typically require large numbers of simulations. This makes it important to choose the appropriate level of complexity when selecting the type of simulation model. A promising multiphase semi-analytical method proposed by [40] to estimate key system attributes (i.e. pressure distribution, CO 2 plume extent, and fluid migration) has been found to reduce computational run times by three orders of magnitude when compared to other standard numerical techniques. The premise of the work presented herein is that the existing semi-analytically leakage algorithm proposed by [40] may be further improved in computational efficiency by applying a fixed point type iterative global pressure solution to eliminate the need to solve large sets of linear equations at each time step. Results show that significant gains in computational efficiency are obtained with this new methodology. In addition, this modification provides the same enhancement to similar semi-analytical algorithms that simulate singe-phase injection into multi-layer domains.

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An improved analytical solution for interface upconing around a well

Cited by 56 publications

References 23 publications

Vertical equilibrium with sub-scale analytical methods for geological CO2 sequestration

Vertical equilibrium with sub-scale analytical methods for geological CO2 sequestration

Steady critical discharge rates from vertical and horizontal wells in fresh–saline aquifers with sharp interfaces

An iterative global pressure solution for the semi-analytical simulation of geological carbon sequestration

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