Comment on “A closed‐form analytical solution for thermal single‐well injection‐withdrawal tests” by Jung and Pruess

Maier, Friedrich; Kocabaş, İbrahim

doi:10.1029/2012wr012621

Cited by 6 publications

(9 citation statements)

References 7 publications

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“…Concerning our statement that the variation of fluid return temperatures with time is independent on the flow velocity, we wish to clarify several points. As pointed out by Maier and Kocabas [], the pumping rate directly controls the flow velocity in the fracture and therefore affects temperature‐return curves. When the ratio of the injection to the withdrawal flow rate is λ , similar to the approach in Kocabas [], the analytical solution (equation (15)) in Jung and Pruess [] can be readily revised as follows:

\begin{matrix} left \\ T_{f 3 D} (x_{D}, t_{3 D}) = \int_{0}^{\min (\frac{t_{3 D}}{λ}, t_{D q} - x_{D})} true \frac{\sqrt{θ} λ^{2} ξ}{2} true \frac{exp true(- \frac{θ λ^{2} ξ^{2}}{4 true(t_{3 D} - λ ξ true)} true)}{\sqrt{π {(t_{3 D} - λ ξ)}^{3}}} \cdot T_{f 3 D} (x_{D} + ξ, 0) d ξ \\ + \int_{0}^{t_{3 D}} true \int_{0}^{\min true(true \frac{τ}{λ}, t_{D q} - x_{D} true)} true \frac{\sqrt{θ} λ^{2} ξ}{2} \cdot true \frac{exp true(- \frac{θ λ^{2} ξ^{2}}{4 true(τ - λ ξ true)} true)}{\sqrt{π {(τ - λ ξ)}^{3}}} θ \int_{0}^{\infty} T_{m 3 D} true(x_{D} + ξ, η, 0 true) true \frac{\sqrt{θ} η}{2} \\ \cdot \end{matrix}

…”

Section: Insensitivity Of Return Temperatures To the Flow Velocitymentioning

confidence: 96%

“…Regarding the computational efficiency of the analytical solutions, we agree that the solutions developed by Kocabas [] and Maier and Kocabas [] using the iterated Laplace transform have a simpler form than our solutions and therefore need a shorter computation time. For a simple single‐well injection‐withdrawal (SWIW) test with no quiescent time, the solution presented in Kocabas [] or Maier and Kocabas [] can be used to reduce computation time, and, as stated in Maier and Kocabas [], it would particularly be useful for parameter estimation problems in which repeated calculations are required.…”

Section: Efficiency Of the Analytical Solutionmentioning

confidence: 99%

“…Another point claimed by Maier and Kocabas [] is that the value λ can account for changes in the fracture geometry during the runtime of SWIW tests. This statement may be true if all the properties of the fractured rocks, including the fracture geometry and the thermal diffusivity of the matrix, are known before thermal SWIW tests, or if a monitoring well located along the flow path and sufficiently close to the injection well is available, additional information on changes in the fracture geometry may be obtained from temperatures measured at the monitoring well.…”

Section: Insensitivity Of Return Temperatures To the Flow Velocitymentioning

confidence: 99%

“…Finally, in addition to the comments on the insensitivity of return temperatures to the flow velocity, Maier and Kocabas [] assert that thermal breakthrough curves can be better interpreted when the pumping rate is smaller than the injection rate applied, with which we do agree. For simplicity, if we disregard the effect of conductive heat transfer from the rock matrix, it will take

λ \cdot t_{D i}

to completely recover the cold water injected, where

t_{D i}

is the dimensionless total injection time.…”

Section: Insensitivity Of Return Temperatures To the Flow Velocitymentioning

confidence: 99%

“…We appreciate the comment by Maier and Kocabas [] on our research article [ Jung and Pruess , ]. In their comment, they raised the following issues: (1) their solutions presented in Kocabas [] and Maier and Kocabas [] are mathematically simpler and computationally more efficient than our analytical solutions, and (2) the insensitivity of thermal breakthrough curve to the flow velocity, which is one of the important conclusions of our study, only holds for the special case where the injection and the withdrawal flow rate is identical. We address each of these comments, along with a few other relatively minor comments and suggestions, below.…”

Section: Introductionmentioning

confidence: 99%

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Reply to comment by Maier and Kocabas on “A closed‐form analytical solution for thermal single‐well injection‐withdrawal tests”

Jung

Pruess

2013

Water Resources Research

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\begin{matrix} left \\ T_{f 3 D} (x_{D}, t_{3 D}) = \int_{0}^{\min (\frac{t_{3 D}}{λ}, t_{D q} - x_{D})} true \frac{\sqrt{θ} λ^{2} ξ}{2} true \frac{exp true(- \frac{θ λ^{2} ξ^{2}}{4 true(t_{3 D} - λ ξ true)} true)}{\sqrt{π {(t_{3 D} - λ ξ)}^{3}}} \cdot T_{f 3 D} (x_{D} + ξ, 0) d ξ \\ + \int_{0}^{t_{3 D}} true \int_{0}^{\min true(true \frac{τ}{λ}, t_{D q} - x_{D} true)} true \frac{\sqrt{θ} λ^{2} ξ}{2} \cdot true \frac{exp true(- \frac{θ λ^{2} ξ^{2}}{4 true(τ - λ ξ true)} true)}{\sqrt{π {(τ - λ ξ)}^{3}}} θ \int_{0}^{\infty} T_{m 3 D} true(x_{D} + ξ, η, 0 true) true \frac{\sqrt{θ} η}{2} \\ \cdot \end{matrix}

…”

Section: Insensitivity Of Return Temperatures To the Flow Velocitymentioning

confidence: 96%

Section: Efficiency Of the Analytical Solutionmentioning

confidence: 99%

Section: Insensitivity Of Return Temperatures To the Flow Velocitymentioning

confidence: 99%

λ \cdot t_{D i}

to completely recover the cold water injected, where

t_{D i}

is the dimensionless total injection time.…”

Section: Insensitivity Of Return Temperatures To the Flow Velocitymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Reply to comment by Maier and Kocabas on “A closed‐form analytical solution for thermal single‐well injection‐withdrawal tests”

Jung

Pruess

2013

Water Resources Research

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Site Characterization

Niemi¹,

Edlmann²,

Carrera³

et al. 2017

Geological Storage of CO2 in Deep Saline Formations

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The study of horizontal well excavation technology of point bar during ultra-high water-cut stage based on flow field intensity evaluation

Guo¹,

Wang

Meng³

2018

J Petrol Explor Prod Technol

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The Ming Huazhen group of Gang Dong Oilfield is a medium-high permeability reservoir of meandering stream deposits. It has a high areal and vertical heterogeneity and has entered the stage of extra-high water-cut. Point bar is an important development area for oil sands in meandering stream deposits and the development of a lateral layer is an important factor controlling the distribution of residual oil. The change rule of water displacement in medium-high permeability reservoirs was clearly determined by laboratory experiments. A numerical simulation method was used to determine the time-varying physical properties of the reservoir. Based on the internal configuration of the meandering river point bar, the horizontal well excavation method for residual oil development of point bars during the ultra-high water-cut stage is employed on the basis of the evaluation of flow field intensity. The results show that this method can well reflect the distribution of the flow field in a point bar sand body. The degree of extraction increases by 3.2% if horizontal wells are drilled in the weak flow field rather than in other places.Keywords Medium high permeability reservoir · Ultra-high water-cut stage · Point bar deposit · Internal configuration · Strength of flow field Publisher's Note Springer Nature remains neutral with regardtojurisdictional claims in published maps and institutional affiliations.

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Comment on “A closed‐form analytical solution for thermal single‐well injection‐withdrawal tests” by Jung and Pruess

Cited by 6 publications

References 7 publications

Reply to comment by Maier and Kocabas on “A closed‐form analytical solution for thermal single‐well injection‐withdrawal tests”

Reply to comment by Maier and Kocabas on “A closed‐form analytical solution for thermal single‐well injection‐withdrawal tests”

Site Characterization

The study of horizontal well excavation technology of point bar during ultra-high water-cut stage based on flow field intensity evaluation

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