Asymptotics of the Filtration Problem With Almost Constant Coefficients

Кузьмина, Людмила Ивановна; Osipov, I. L.

doi:10.22337/2587-9618-2021-17-2-43-49

Cited by 3 publications

(1 citation statement)

References 21 publications

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“…Calculation using an explicit difference scheme allows you to quickly make calculations, but the presence of discontinuities significantly complicates finding a solution. If an exact solution in an implicit closed form or its asymptotics is known, it is used to numerically calculate the solution in an explicit form [21,22]. For the problem of filtering a bidisperse suspension in a porous medium, an exact implicit solution is obtained.…”

Section: Introductionmentioning

confidence: 99%

Analysis of the Filtration Problem by Bitwise Search Method

Кузьмина¹,

Osipov²,

Astakhov³

2022

IJCCSE

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During the construction of ground and underground structures, filtration of a liquid grout in loose soil makes it possible to strengthen the foundation and create underground waterproof partitions. A one-dimensional problem of filtering a bidisperse suspension in a homogeneous porous medium with size-exclusion particle capture mechanism is considered. The article is devoted to the calculation of the exact solution of the problem given as the upper limit of the integral with a singularity. The proposed bitwise search method for calculating integrals makes it possible to smooth out fluctuations of the solution near the singularity. Partial and total retention profiles are analyzed.

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Section: Introductionmentioning

confidence: 99%

Analysis of the Filtration Problem by Bitwise Search Method

Кузьмина¹,

Osipov²,

Astakhov³

2022

IJCCSE

Self Cite

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An Approximate Analytical Solution for Damage Radius Prediction in Water Injection Wells Based on Langmuirian Blocking: Derivation, Comparison and Field Applications

Liu

Bedrikovetsky

Osipov

et al. 2022

Day 2 Thu, February 24, 2022

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Water flooding is extensively used in the industry to develop the mature oilfields. However, after several years’ of injection, the injectivity usually declines and the injection pressure increases. This is because the solid or liquid particles in the injected water are retained in the pores and block the flow channel in the near wellbore region. The prediction of the particle retention and permeability damage is important for the design of damage removal methods like acidizing. Previous researchers including M. Nunes, P. Bedrikovetsky, Feike J. Leij, et al. have done some work on the analytical solutions of the flow of particulate suspension in porous media with particle retention and consequent permeability reduction. However, they either assumed one-dimensional linear flow in the porous media or took the filtration coefficient as a constant. These are not always true because the flow of the injected water near the wellbore is radial and the filtration coefficient tends to decline with more and more particles being retained in the pores and ultimately reaches zero when all channels are blocked. In this paper, we established a near-wellbore axisymmetric suspension flow and particle retention model based on Langmuirian blocking, obtained the approximate analytical solution and compared it with the numerical solution. The results showed that the error of our approximate solution for the retained particle concentration is within 5%. Then we incorporated the analytical expression into the Darcy's law equation and derived the expression of pressure drop as well as skin factor caused by particle retention. Damaged zone radius was also defined so as to estimate the acid volume needed to remove the damage. We also checked our models and solutions using field cases of water injection and acidizing from Tarim Oilfields, western China. The results showed that the injection pressure drop due to particle retention and the injection pressure recover after acidizing calculated from our models are basically consistent with the actual situation. Our models can be further used to predict the damage zone radius and design the acid volume for damage removal. The analytical solution can also be used to perform sensitivity analysis for the parameters involved.

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Prediction of Formation Damage Caused by Suspend Solids from Injected Water and a Guideline for TSS Control

Liu,

Xu,

Yuan

et al. 2024

Day 3 Thu, March 07, 2024

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During waterflooding, suspend solids are usually contained in the injected water, which may gradually block pores and cause formation damage after flowing into a formation and being trapped there. Water treatment is usually conducted on the surface to reduce TSS (Total Suspended Solids) before being injected. However, to what extent the TSS should be controlled depends on specific water injection conditions and there are no methods in industry to quantitatively evaluate it. Meanwhile, the corrections between the injection parameters and the extent of formation damage are not clear. In this paper, a near-wellbore axisymmetric suspension flow and particle retention model is established based on the Langmuirian Pore Blocking mechanism. This model is solved numerically by Shampine's code developed in MATLAB using an explicit central finite deference method. Based on this model, pressure drop, damage factor, damage zone radius and damage time are defined and the methods to obtain them are described. With assumed injection parameters, the basic tendencies of particle retention as well as the influences of TSS, injection rate, initial filtration coefficient and maximum formation retention capacity are investigated. A general guideline is given in the end, suggesting the determination of three formation-related parameters and control of four operational parameters. A workflow for determining the TSS of injection water based on these models is also proposed. The modelling results using the assumed water injection parameters lead to deep understandings on the particle retention-caused formation damage. The concentration of retained particles is the highest near a wellbore and gradually declines to zero. Most of the particle retention occurs within five meters to the wellbore. The concentration of retained particles gradually increases with time, and the rate of increase is relatively high at the beginning of water injection but slows down with injection time. The damage zone radius increases continuously with the injection time, and it can reach 4.0-6.0m after 10 years of water injection. Most of the damage occurs in the first three years, which accounts for at least 60% of the 10 years’ cumulative damage. Higher TSS in injection water causes quicker and deeper damage to a formation. When TSS increases from 10mg/L to 100 mg/L, the damage zone radius with three years of water injection is doubled and the damage time is decreased by 30%. A higher injection rate will result in a larger damage zone radius. When the injection rate increases from 1.0bbl/(day·ft) to 6.0bbl/(day·ft), the damage zone radius is deepened by 30% after five years’ water injection and the damage time is shortened by 31.5%. The initial filtration coefficient has big influence on the damage zone radius. With 10 years of water injection, the damage zone radius is much higher for a bigger initial filtration coefficient. However, there is an optimal initial filtration coefficient to obtain the longest damage time. The maximum retention capacity has a significant impact on the damage zone radius. The smaller the maximum retention capacity, the larger the damage zone radius and the shorter the damage time. The novelty of this study is that an axisymmetric suspension flow model based on Langmuirian blocking is established and a method of quantitatively evaluating the particle retention-caused formation damage is obtained. Based on this method, the influences of TSS in injected water, rate of injection, initial filtration coefficient and maximum formation retention capacity on the damage zone radius and damage time are investigated. The proposed guideline and workflow for water injection parameter control can be a reference for designing of waterflooding scenarios in a matrix-type reservoir. The prediction results of the damage zone radius will also be a reference for acidizing job design.

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Asymptotics of the Filtration Problem With Almost Constant Coefficients

Cited by 3 publications

References 21 publications

Analysis of the Filtration Problem by Bitwise Search Method

Analysis of the Filtration Problem by Bitwise Search Method

An Approximate Analytical Solution for Damage Radius Prediction in Water Injection Wells Based on Langmuirian Blocking: Derivation, Comparison and Field Applications

Prediction of Formation Damage Caused by Suspend Solids from Injected Water and a Guideline for TSS Control

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