﻿ 多层合采阶梯井产能计算模型的建立与求解

Development and Solution to the Coupling Model of the Productivity of Interbeded Reserviors in Stepped Horizontal Wells
Ma Shuai, Zhang Fengbo, Hong Chuqiao, Liu Shuangqi, Zhong Jiajun, Wang Shichao
Zhanjiang Branch of CNOOC Ltd., Zhanjiang, Guangdong, 524057, China
Abstract:It is difficult to forecast the production capacities of stepped horizontal wells when producing multiple reservoirs at multiple sections. On the basis of the relevant theories such as seepage mechanics, engineering fluid mechanics, reservoir engineering and numerical analysis, a new detailed coupled model of stepped wells and thin interbedded reservoirs was established by utilizing discretization processing and considering factors such as anisotropy, filtering interference, pipe flow pressure drop and contamination caused by drilling and/or completion. This productivity calculation model of multilayer commingled production of stepped wells has a unique solution. Taking a three thin interbedded reservoir as an example, we analyzed with this model the wellbore radial flow rate, wellbore flow and wellbore flow pressure distribution rules of stepped horizontal wells. Numerical simulation results showed that flow friction in the wells should not be overlooked, and the stepped horizontal well flow rate distribution presented the shape of a high-order polynomial, the flow rate distribution adhered to cubic polynomial law, flow pressure distribution stayed within parabolic limits, and pressure dropped faster at the heel section. The entire well production calculated by this model is just 1.79% less than Joshi's. It demonstrated that the calculation results for production were reasonable and provided a new method for productivity prediction of stepped horizontal wells.
Key words: stepped horizontal well    thin interbed    coupling    mathematical model    productivity forecast

1 模型的建立

1.1 假设条件

1.2 离散化处理

1.3 油藏渗流模型

1) 第1阶段,流体从油藏边界流向近井地带(理想渗流压降)[8, 9]，表达式为：

2) 第2阶段，流体在近井地带流经钻完井污染带(表皮附加压降)，表达式为：

3) 第3阶段，流体通过井壁和完井管柱之间的环空流入井筒内部压降(完井管柱压降)[10, 11]，其表达式为：

1.4 井筒管流模型

1.4.1 沿程摩阻压降

i,j微元段内管流流量的表达式为：

1.4.2 加速压降

1.4.3 重力压降

1.5 稳态耦合模型

 图1 三层合采阶梯井产能计算模型示意 Fig.1 Diagram of the productivity forecast model of stepped horizontal wells’ commingled production in 3 layers
2 模型求解

2.1 具备唯一解条件验证

A为线性方程组的系数矩阵，可表示为：

Ai的具体表达式为：

X为方程组的未知数矩阵，具体形式为：

B为方程组的常数矩阵，具体形式为：

2.2 迭代求解

3 实例计算

 层号 油层厚 度/m 油层压 力/MPa 水平渗透 率/mD 垂向渗透 率/mD 原油密度/ (kg·m-3) 原油黏度/ (mPa·s) 1 11 18.0 722 491 880 37.62 2 9 18.1 638 477 875 37.01 3 8 18.2 715 498 869 33.42

 井段 井筒半径/ m 井筒长度/ m 井筒垂深/ m 污染带半径/ m 污染带渗透率/ mD 跟端 趾端 跟端 趾端 跟端 趾端 1号水平段 0.088 90 357 1 807.0 1 807.0 0.57 0.54 136 155 1号连接段 0.088 90 58 1 807.0 1 817.0 2号水平段 0.069 85 546 1 817.0 1 817.0 0.49 0.43 227 268 2号连接段 0.069 85 49 1 817.0 1 825.5 3号水平段 0.069 85 308 1 825.5 1 825.5 0.33 0.28 470 493

Lws取5 m，NM取4，ξ取0.5%，给定跟端流压16 MPa，可计算得到流率、流量和流压沿井筒方向的剖面。同时，Joshi公式虽然难以反映井筒入流规律，但具有对水平井全井段产量预测准确度高的特点，因此采用Joshi公式对3个水平段的生产进行了离散化模拟对比。

 图2 井筒径向流率分布规律 Fig.2 Radial flow rate distribution profiles

 图3 井筒流量分布规律 Fig.3 Cumulative flow distribution profiles

 图4 井筒流压分布规律 Fig.4 Flowing pressure distribution profiles

4 结论与建议

1) 采用离散化手段建立了多层合采阶梯井产能计算模型，该模型考虑了表皮系数、完井方式、层间原油物性差异等的影响，且能够对任意层合采的阶梯井进行产量计算。

2) 求解多层合采阶梯井产能计算模型得到了阶梯井井筒入流规律，即呈高阶偶次多项式的形态，且每个阶梯中，跟端流率通常达到中间段的3倍，这表明在该类井完井或调剖设计时有必要对井筒进行分段处理。

3) 全井产量计算值与Joshi公式的计算结果相差仅为1.79%，流压剖面与Joshi公式一致，说明了该模型的合理性；流量剖面呈三次多项式分布，流压剖面呈抛物线状分布；由于跟端流体大量汇集，导致大部分流压消耗在靠近跟端的井段，故开发边底水油藏时应预防水体在跟端突破。

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#### 文章信息

Ma Shuai, Zhang Fengbo, Hong Chuqiao, Liu Shuangqi, Zhong Jiajun, Wang Shichao

Development and Solution to the Coupling Model of the Productivity of Interbeded Reserviors in Stepped Horizontal Wells

Petroleum Drilling Techniques, 2015, 43(05): 94-99.
http://dx.doi.org/10.11911/syztjs.201505016