Progress in Analytical Modeling of Water Hammer

Urbanowicz, Kamil; Jing, Haixiao; Bergant, Anton; Stosiak, Michał; Lubecki, Marek

doi:10.1115/1.4062290

Cited by 10 publications

(2 citation statements)

References 43 publications

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“…And the formula derived by Brereton and Jiang [43], which was quoted in Urbanowicz et al's paper [44]:…”

Section: Other Series and Their Possible Solutionsmentioning

confidence: 98%

Infinite Series Based on Bessel Zeros

Urbanowicz

2023

Applied Sciences

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An interesting series based on Bessel function roots (zeros) is discussed and numerically analyzed. The novel-derived simplified general solutions are based on Lommel polynomials. This kind of series can have a large practical use in many scientific areas, such as solid mechanics, fluid mechanics, thermodynamics, electronics, physics, etc. Some practical examples connected with fluid mechanics are provided in this paper. The errors in Afanasiev solutions are corrected. In addition, the main solution for the series analyzed by Baricz and Angel is presented.

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“…And the formula derived by Brereton and Jiang [43], which was quoted in Urbanowicz et al's paper [44]:…”

Section: Other Series and Their Possible Solutionsmentioning

confidence: 98%

Infinite Series Based on Bessel Zeros

Urbanowicz

2023

Applied Sciences

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“…Water hammer fracture diagnostics [10], an emerging technique for fracturing diagnosis, evaluate the diversion effectiveness using the cepstrum analysis and error function of water hammer signals [11]. Water hammer, a sudden pressure pulsation occurring upon pump shutdown, propagates along the wellbore and interacts with fractures or other downhole events [12][13][14]. These interactions alter the pressure signal feature, conveying valuable subsurface information that can be identified using water hammer diagnostics [3,[15][16][17].…”

Section: Introductionmentioning

confidence: 99%

Oscillation Times in Water Hammer Signatures: New Insights for the Evaluation of Diversion Effectiveness in Field Cases

Liu,

Yue,

Wang

et al. 2024

Processes

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Diversion is a crucial technique for effectively improving shale reservoir production by creating more complex fracture networks. Evaluating diversion effectiveness is necessary to optimize the parameters in hydraulic fracturing. Water hammer diagnostics, an emerging fracturing diagnosis technique, evaluate diversion effectiveness by analyzing water hammer signals. The water hammer attenuation, as indicated by the oscillation time, correlates with the complexity of fracture networks. However, it remains unclear whether the oscillation time is associated with diversion effectiveness. This paper elucidates the relationship between the water hammer oscillation time and diversion effectiveness by taking the probability of diversion and the treating pressure response as the evaluation criteria. Initially, a high-frequency pressure sensor was installed at the wellhead to sample the water hammer signals. Next, the oscillation times were determined using the feature extraction method. Simultaneously, the probability of diversion and the treating pressure response were calculated using the cepstrum error function and treating pressure curve, respectively. Then, the relationship between the oscillation time and diversion effectiveness was analyzed. Finally, a rapid judgment method for evaluating diversion effectiveness based on the water hammer oscillation time was proposed. The results indicated a negative correlation between the probability of diversion and the oscillation time, with higher probabilities resulting in lower oscillation times. The oscillation times exhibited a negative correlation with the treating pressure response, including the treating pressure increases and diversion pressure spikes, wherein a greater pressure differential led to lower oscillation times. Drawing from the statistics of a shale gas horizontal well in Sichuan, a better diversion effectiveness is associated with fewer oscillations, demonstrating a negative correlation between the diversion effectiveness and the oscillation time in water hammer signatures. Finally, a rapid judgment method for evaluating diversion effectiveness was proposed, utilizing the 95% confidence interval of the mean oscillation time. This paper offers useful insights into evaluating diversion performance in field cases.

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Unsteady flow rate in transient, incompressible pipe flow

Brumand‐Poor,

Kotte,

Pasquini

et al. 2024

Z Angew Math Mech

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Knowledge regarding current flow rates through pipes and other components is crucial for most hydraulic systems. The hydraulic power can be computed in combination with the pressure, which may be used in many applications, such as predictive maintenance. Most flow rate sensors used in the field of fluid power operate invasively. Therefore, the measurement process itself alters the flow rate. Furthermore, most sensors operate accurately for stationary flow but produce inaccurate measurements for transient flow. A well‐known method of determining the flow rate is to measure the pressure difference between two points along a pipeline and calculate the flow rate based on the law of Hagen and Poiseuille. However, since the relation mentioned above only applies to laminar, steady, and incompressible flow, its usefulness for transient flows is limited. This paper derives a system equation based on the fundamental laws of fluid mechanics, which describe transient, incompressible pipe flow. As a result, the fundamental equations are solved in the Laplace domain and subsequently transformed back into the time domain. The four‐pole theorem relates the pressure difference and the volumetric flow rate. The analytical solution consists of a convolution integral containing a weighting function and the pressure difference. Compared to a simulation, the novel equation displays high accuracy for transient and stationary incompressible pipe flow. This equation paves the way for a soft sensor, which allows the noninvasive measurement of arbitrary volumetric flow rates within pipes.

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Progress in Analytical Modeling of Water Hammer

Cited by 10 publications

References 43 publications

Infinite Series Based on Bessel Zeros

Infinite Series Based on Bessel Zeros

Oscillation Times in Water Hammer Signatures: New Insights for the Evaluation of Diversion Effectiveness in Field Cases

Unsteady flow rate in transient, incompressible pipe flow

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