﻿ 微粒沉积导致孔喉尺寸变化的Lattice Boltz-Mann模拟研究 LBM Simulation of Pore-Throat Radius Variation Due to Particle Deposition

Vol.07 No.02(2017), Article ID:21158,8 pages
10.12677/APF.2017.72002

LBM Simulation of Pore-Throat Radius Variation Due to Particle Deposition

Xiaodong Han

CNOOC Ltd, Tianjin Branch, Tianjin

Received: Jun. 8th, 2017; accepted: Jun. 22nd, 2017; published: Jun. 28th, 2017

ABSTRACT

During the developing process of oil and gas reservoirs, particles deposited in pore-throats may result in the decrease of its effective radius and capability for fluid flowing through. For studying the influence of deposited particles on the pore-throat radius and its changing rule, the formula for calculating the effective radius is obtained based on the capillary model and theoretical derivation. Besides, sensitive analysis is conducted for various parameters. The simulation results show that, the effective radius of pore-throats gets smaller with the increase of deposited particle radius and the decreasing rate is higher at the bigger particle size; the closer the particle deposits from the inlet face, the smaller of the effective radius is; besides, the effective radius of the pore- throat will be much greater when the pore-throat has a bigger ratio value between the length and its width. In addition, a mathematical model for calculating the effective radius is proposed based on the regression fitting, which may provide a useful guidance for research on the formation damage.

Keywords:Porous Media, Particle Deposition, LBM, Capillary Model, Effective Radius

1. 引言

2. 微粒沉积后有效半径计算

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Figure 1. Schematic figure of particle depositing in pore-throat

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3. 格子Boltzmann方法模拟实现

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Figure 2. D2Q9 lattice structure model

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① 定x、y方向的网格数目：由于网格步长相同，的比值即为孔喉的长度与宽度比；

② 边界条件设置：上下边界为反弹边界，左右边界为速度边界且保持流体流量恒定；

③ 孔喉内无微粒时孔喉入口、出口间压差计算：应用式9和式11得到入口和出口处的压力值，计算可得出入口与出口间压差为

④ 将微粒添加进孔喉：设置微粒在孔喉内距入口的距离以及微粒半径值，微粒所在网格设置为固体边界，且微粒边界同样采用反弹边界；

⑤ 孔喉内有沉积微粒时孔喉入口、出口间压差计算：同样应用公式9和公式11得到入口和出口处的压力值，计算出入口与出口间压差为

⑥ 微粒沉积后有效半径计算：在得到微粒沉积前后孔喉两端压差后，应用公式4即可计算得到微粒沉积后孔喉后有效半径与原始半径的比值

4. 不同因素下有效半径变化规律

4.1. 微粒粒径的影响

4.2. 微粒沉积位置的影响

4.3. 孔喉长宽比的影响

5. 孔喉有效半径计算模型

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Figure 4. Effective radius vs location of the deposited particle

Figure 5. Effective radius vs ratio between the length and the width of the pore-throat

Table 1. Comparison between the simulated effective radius and predicted value

6. 结论

1) 以毛细管模型为基础推导了微粒沉积后孔喉有效半径的计算公式，得到有效半径与原半径比值的四次方与对应压差比值呈反比；且应用格子Boltzmann方法对孔喉有效半径进行模拟求解可行。

2) 通过模拟结果得出：沉积微粒粒径越大，孔喉有效半径越小；微粒沉积位置越靠近孔喉入口端，孔喉的有效半径越小；微粒的长度和宽度之比越小，微粒沉积后孔喉有效半径越小。也就是说，微粒粒径越大、微粒越靠近孔喉入口段、孔喉长度越短，微粒沉积导致的伤害程度越大，孔喉有效半径越小。

3) 在大量模拟的基础上，通过回归得到了微粒沉积后孔喉有效半径的计算模型。通过对比公式估算值及模拟值确定该计算模型能较好地对微粒沉积后有效半径进行预测计算。

LBM Simulation of Pore-Throat Radius Variation Due to Particle Deposition[J]. 渗流力学进展, 2017, 07(02): 13-20. http://dx.doi.org/10.12677/APF.2017.72002

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