深水钻井溢漏同存条件下温压分析及溢漏层位判别

高永海，于鑫，李昊，赵欣欣，孙小辉，孙宝江; GAO Yonghai; YU Xin; LI Hao; ZHAO Xinxin; SUN Xiaohui; SUN Baojiang

引 en

深水钻井溢漏同存条件下温压分析及溢漏层位判别

高永海^1,2
，于鑫¹
，李昊¹
，赵欣欣¹
，孙小辉¹
，孙宝江^1,2

1. 深层油气全国重点实验室（中国石油大学（华东）），山东青岛 266580； 2. 中国石油大学（华东）石油工程学院，山东青岛 266580；

Temperature and pressure analysis under coexistence of overflow and drilling fluid loss conditions and determination of overflow and loss locations in deep water drilling

GAO Yonghai^1,2
， YU Xin¹
， LI Hao¹
， ZHAO Xinxin¹
， SUN Xiaohui¹
， SUN Baojiang^1,2

1. State Key Laboratory of Deep Oil and Gas, China University of Petroleum (East China), Qingdao 266580 , China； 2. School of Petroleum Engineering, China University of Petroleum (East China), Qingdao 266580 , China；

作者简介:

高永海（1977-），男，教授，博士，博士生导师，研究方向为井筒多相流与传热、深水钻井与井控。E-mail: upcgaoyh@163.com。

通信作者:

孙宝江（1963-），男，教授，博士，博士生导师，研究方向为井筒压力控制、多相流理论及工程应用。E-mail: sunbj1128@vip.126.com。

中图分类号:TE 21

文献标识码:A

文章编号:1673-5005(2025)05-0093-09

DOI:10.3969/j.issn.1673-5005.2025.05.008

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目录contents

摘要Abstract
关键词Keywords
1 深水钻井溢流同存理论模型
1.1 溢漏同存条件下瞬态多相流模型
1.1.1 质量守恒方程
1.1.2 动量守恒方程
1.1.3 能量守恒方程
1.1.4 气侵模型
1.1.5 漏失模型
1.2 模型数值离散与求解过程
1.3 基于温压分布规律的溢漏层位判断方法
1.3.1 溢漏层位判断方法及流程
1.3.2 模型方法的验证
2 结果讨论
2.1 溢漏共存工况
2.2 上漏下溢工况
2.3 上溢下漏工况
3 结论
参考文献

摘要

针对深水钻井溢漏复杂工况下温压变化规律认识不清和溢漏层位判断难度大的问题，在分析溢漏循环过程中传热的基础上，考虑井筒环空内的变质量流动对井筒内温压变化影响，建立溢漏循环条件下井筒瞬态温压模型。通过定义环空沿程温差和环空沿程压差的概念，进行溢漏共存工况的模拟分析。结果表明：对于溢漏共存工况，上溢下漏工况的温差整体上大于上漏下溢工况下的温差，而上漏下溢工况的压差整体上大于上溢下漏工况下的压差；裸眼段环空温差突变位置对应着气侵层位，裸眼段环空温差转折位置对应着漏失层位；初始气侵压差越大，井口处环空温差越大；初始漏失压差越大，井口处环空温差越小，且降低的幅度呈增加趋势。

Abstract

In deep water drilling, there are challenges to work out the temperature and pressure variation patterns in wellbore and it is difficult to determine the gas influx (overflow) and drilling fluid loss positions, especially under the complex coexistence of overflow and loss conditions. In this study, a transient wellbore temperature and pressure model under the coexistence of overflow and circulation loss conditions was established, based on heat transfer analysis and accounting for the impact of variable mass flow in wellbore annulus on temperature and pressure changes. The analysis of the gas influx and circulation loss coexistence was conducted by defining and calculating the temperature and pressure differences along the annulus. The simulation results indicate that the temperature difference is generally greater under the condition of upper gas influx and lower circulation loss positions compared to that with upper circulation loss and lower gas influx, while the pressure difference is generally greater under the condition of upper circulation loss and lower gas influx compared to upper gas influx and lower circulation loss. An abrupt change of annular temperature difference in an open hole section mostly corresponds to a gas influx position, while a transition in annular temperature difference in an open hole section corresponds to a circulation loss position. A larger initial gas invasion pressure difference can result in a greater annular temperature difference at the wellhead. As the initial circulation loss pressure difference increases, the annular temperature difference at the wellhead decreases.

关键词

深水钻井；溢漏同存；井筒温压预测；溢漏位置判断

Keywords

deep water drilling ； coexistence of gas influx and circulation loss ； wellbore temperature and pressure prediction ； determination of gas influx and circulation loss positions

随着油气资源勘探开发进程的推进，深水区域已经成为了油气资源开发的主战场之一^[1-2]。在深水钻井条件下，由于海水段的存在，地层破裂压力梯度偏低，安全作业窗口较窄。当存在多压力层系时，极易发生溢流、漏失或溢漏共存等钻井作业事故^[3-4]。溢漏发生之后，对于溢漏位置和溢漏速率的初步判断是安全钻进的重要前提，有利于缩短压井或堵漏的时间，降低钻井综合成本^[5-6]。而建立准确而高效的井筒温压预测模型，是探究深水钻井溢漏发展规律、判断溢漏层位的重要前提之一。目前，井筒温压场的研究涉及多相流流动传热^[7-9]、多相多组分流体相变迁移^[10-16]、井筒-地层的耦合流动^[9，17]等多个方面。针对钻井溢漏问题，学者们的研究主要包括不同地层、不同井型的溢漏早期监测^[18-19]、溢漏发展规律^[20-26]及溢漏控制方案^[27]等。然而，上述研究多集中于陆地井、溢流或漏失工况，鲜有针对深水钻井期间不同地层溢漏共存工况的研究^{[3-4，28-29]}。因此有必要针对深水钻井过程中可能发生的不同层位的溢漏共存现象展开研究。笔者基于建立的深水钻井井筒-地层非稳态温压耦合模型，进行溢漏共存现象的模拟，探究溢漏共存工况下井筒温压的发展趋势，得到不同溢漏位置和强度条件下井筒沿程温压变化规律，建立基于温压分布规律的溢漏位置判断方法，为井控措施的落实提供一定的理论指导，从而降低海上钻井作业的风险。
1 深水钻井溢流同存理论模型
深水钻进过程中，当钻遇多压力体系时，由于裸眼段不同层位存在多个压力层系，可能存在溢漏共存现象。相较于正常钻井循环状态，溢漏同存时，井筒温压变化还需要考虑地层流体侵入环空及环空流体漏失至地层导致的变质量流动，这也是导致井筒温压重新分布的主要原因。根据溢漏的相对位置，可以分为上漏下溢和上溢下漏工况，如图1所示。
图1 深水钻井溢漏共存工况示意图
Fig.1 Schematic diagram of coexistence of gas influx and loss circulation in deep water drilling
1.1 溢漏同存条件下瞬态多相流模型
深水钻井高温高压气体侵入井筒后，环空流体流动由液固两相流转变为气液固三相流动。此外，当钻遇裂缝性地层时，一旦环空压力大于地层压力，极易发生钻井液漏失事故，导致漏失点上下发生变质量流动，影响井筒对流传热和压力的沿程变化。为了精细表述深水钻井期间溢漏事故对于井筒多相流动传热的影响，在建立深水钻井多相流瞬态温压预测模型时，考虑了井筒环空流体流动和传热特性，假设：①井筒内流动为一维可压缩的；②忽略钻杆、地层、套管、水泥环的热物性参数的变化；③采用水基钻井液，忽略侵入气在水基钻井液中的溶解；④低速钻进过程中忽略进尺对井深的影响。
1.1.1 质量守恒方程
在深水钻井期间，受溢漏共存流动安全风险的影响，环空内可能同时存在液固两相和气液固三相流动。为了精确刻画溢漏相对位置的变化对井筒环空内多相流动的影响，需要分别建立气相、钻井液相和岩屑相的质量守恒方程。
（1）气相质量守恒方程。对于溢漏共存工况，在计算井筒环空单元内的气相质量变化时，除了需要考虑高压气藏侵入气的影响，还需要考虑井漏时的气相损失。根据质量守恒定律，气相连续性方程为

\frac{\partial}{\partial t} (A α_{g} ρ_{g}) + \frac{\partial}{\partial s} (A α_{g} ρ_{g} v_{g}) = q_{g} - q_{g l o s s} .

(1)

式中，t为时间，s；s为该位置到井底的距离，m；ρ_g为侵入气密度，kg·m^-3；A为横截面积，m²；α_g为截面含气率，无量纲；v_g为自由气流速，m·s^-1；q_g为气侵井段单位长度的气体侵入速率，kg·m^-1·s^-1；q_gloss为漏失井段单位长度气体漏失速率，kg·m^-1·s^-1。
（2）液相质量守恒方程。环空单元中的液相质量变化主要受井漏速率的影响。根据质量守恒方程，可得液相连续性方程为

\frac{\partial}{\partial t} (A α_{1} ρ_{1}) + \frac{\partial}{\partial s} (A α_{1} ρ_{1} v_{1}) = - q_{loss} .

(2)

式中，ρ_l为钻井液密度，kg·m^-3； α_l为钻井液截面占比，无量纲；v_l为钻井液流速，m·s^-1；q_loss为漏失井段单位长度的钻井液漏失速率，kg·m^-1·s^-1。
（3）岩屑质量守恒方程。井底处环空单元内岩屑相的增量由机械钻速决定，机械钻速决定了岩屑生成速度。根据质量守恒方程，岩屑相的连续性方程为

\frac{\partial}{\partial t} (A α_{c} ρ_{c}) + \frac{\partial}{\partial s} (A α_{c} ρ_{c} v_{c}) = q_{c} .

(3)

式中，ρ_c为岩屑密度，kg·m^-3； α_c为岩屑截面占比，无量纲；v_c为岩屑流速，m·s^-1；q_c为井底处井筒单元的岩屑生成速度，kg·m^-1·s^-1。
1.1.2 动量守恒方程
环空单元内的动量增量主要包括流入环空单元的流体动量和外界力产生的动量增量。外力方面主要考虑重力和摩擦力的影响，综合考虑井斜角的影响，根据牛顿第二定律，环空单元内多相流动量守恒方程为

\begin{matrix} \frac{\partial}{\partial t} (A α_{g} ρ_{g} v_{g} + A α_{l} ρ_{l} v_{l} + A α_{c} ρ_{c} v_{c}) + \frac{\partial}{\partial s} (A α_{g} ρ_{g} v_{g}^{2} + \\ A α_{l} ρ_{l} v_{l}^{2} + A α_{c} ρ_{c} v_{c}^{2}) + A g c o s θ (α_{g} ρ_{g} + α_{l} ρ_{l} + α_{c} ρ_{c}) + \\ \frac{\partial (A p)}{\partial s} + A f \frac{ρ_{m} v_{m}^{2}}{2 d_{c}} = 0 . \end{matrix}

(4)

式中，θ为井斜角，rad；p为环空压力，Pa；ρ_m为混合物密度，kg·m^-3；v_m为混合物流速，m·s^-1；f为摩擦因子，无量纲；d_c为水力直径，m；g为重力加速度，m·s^-2。
1.1.3 能量守恒方程
对于深水钻井，能量增量主要受环境温压、摩擦热以及储层流动耦合等效应影响。在计算环空单元内流体能量增量时，主要考虑流入环空单元的流体能量、热传导产生的能量、重力做功、压力做功以及黏性力做功5项。根据能量守恒定律，井筒内多相流动能量守恒方程为

\begin{matrix} \frac{\partial}{\partial t} [A α_{g} ρ_{g} (e_{g} + \frac{v_{g}^{2}}{2}) + A α_{1} ρ_{1} (e_{1} + \frac{v_{1}^{2}}{2}) + A α_{c} ρ_{c} (e_{c} + \frac{v_{c}^{2}}{2})] + \\ \frac{\partial}{\partial s} [A α_{g} ρ_{g} v_{g} (e_{g} + \frac{v_{g}^{2}}{2}) + A α_{l} ρ_{l} v_{1} (e_{1} + \frac{v_{1}^{2}}{2}) + \\ A α_{c} ρ_{c} v_{c} (e_{c} + \frac{v_{c}^{2}}{2})] = - A (α_{g} ρ_{g} v_{g} + α_{l} ρ_{l} v_{1} + α_{c} ρ_{c} v_{c}) g c o s θ - \\ \frac{\partial [A p (α_{g} v_{g} + α_{1} v_{1} + α_{c} v_{c})]}{\partial s} + Q_{t} + Q_{f r} . \end{matrix}

(5)

式中，e_g、 e_l、 e_c分别为单位质量气体、液体和岩屑的内能，J·kg^-1；Q_t和Q_fr分别为井筒与环境间的热交换和摩擦热，J·m^-1·s^-1。
1.1.4 气侵模型
在气体渗流过程中，考虑到气层温度的下降很快会被周围地层所补偿，因此忽略渗流过程中气藏温度的变化^[30]。在气体径向渗流的过程中，随着渗流面积的减小，气体渗流速度必然增大，可能在井壁附近出现非达西渗流。综合考虑上述因素，建立气体渗流模型为

\begin{matrix} p_{e}^{2} - p_{w}^{2} = \frac{\bar{μ} p_{s c} \bar{Z} T}{2 π h k T_{s c}} I n (\frac{4 k t}{1.781 φ \bar{μ} c_{t} r_{w}^{2}}) Q_{s c} + \\ \frac{p_{s c} ρ_{s c} β \bar{Z} T}{2 π^{2} h^{2} T_{s c}} (\frac{1}{r_{w}} - \frac{1}{r_{n - d}}) Q_{s c}^{2} . \end{matrix}

(6)

式中，p_e为气藏边界压力，MPa；p_w为井底流动压力，MPa； $\bar{μ}$ 为气藏流体的平均黏度，Pa·s；p_sc为标准压力，0.101 MPa； $\bar{Z}$ 为气藏流体的平均压缩因子，无量纲；h为气藏厚度，m；k为气藏渗透率，m²；t为时间，s；r_n-d为非达西渗流半径，m；r_w为裸眼段半径，m；Q_sc为标准条件下的气体体积流量，m³·s^-1；ρ_sc为标准条件下侵入气密度，kg·m^-3； φ为气藏孔隙度；c_t为储层综合压缩系数，Pa^-1；β为福西海默系数，m^-1。
1.1.5 漏失模型
在深水钻井过程中，深部地层多为碳酸盐岩地层，缝洞较为发育，由天然裂缝引起的井漏最为常见。由于地层裂缝型态极其复杂，难以精确表征。为了简化计算，将缝网简化为径向的等效单裂缝形态并忽略井漏过程中裂缝开度的变化，采用的基于H-B流变模式的径向等效单裂缝漏失模型^[25]为

\begin{matrix} Q_{loss} = \\ \frac{{[Δ p - \frac{2 n + 12 τ_{y}}{n + 1} w_{h} (r_{f} - r_{w})]}^{\frac{1}{n}} {[\frac{w_{h} (1 - n)}{2}]}^{\frac{1}{n}} (π w_{h}^{2} \frac{n}{2 n + 1})}{{[K (r_{f}^{1 - n} - r_{w}^{1 - n})]}^{\frac{1}{n}}} \end{matrix} .

(7)

式中，Q_loss为钻井液漏失的体积流量，m³·s^-1；Δp为漏失层位与对应深度井筒环空的压差，MPa；r_f为漏失层边界半径，m；r_w为裸眼井段的半径，m；w_h为裂缝的水力学开度，m； n为流型指数，无量纲；K为稠度系数，Pa·sⁿ；τ_y为动切力，Pa。
1.2 模型数值离散与求解过程
根据式（4），采用隐式差分格式可得环空压力的表达式为

\begin{matrix} (A_{j} p_{j}^{n + 1} - A_{j + 1} p_{j + 1}^{n + 1}) = Δ s A_{j + 1} g c o s θ_{j + 1} {(\sum_{i = g, l, c} α_{i} ρ_{i})}_{j + 1}^{n + 1} + \\ Δ s A_{j + 1} {(2 f_{f} \frac{ρ_{m} v_{m}^{2}}{d_{c}})}_{j + 1}^{n + 1} + \frac{Δ s A_{j + 1}}{2 Δ t} [{(\sum_{i = g, l, c} α_{i} ρ_{i} v_{i})}_{j + 1}^{n + 1} - \\ {(\sum_{i = g, l, c} α_{i} ρ_{i} v_{i})}_{j + 1}^{n} + {(\sum_{i = g, l, c} α_{i} ρ_{i} v_{i})}_{j}^{n + 1} - {(\sum_{i = g, l, c} α_{i} ρ_{i} v_{i})}_{j}^{n}] + \\ \frac{A_{j + 1}}{2} [{(\sum_{i = g, l, c} α_{i} ρ_{i} v_{i})}_{j + 1}^{n + 1} - {(\sum_{i = g, l, c} α_{i} ρ_{i} v_{i}^{2})}_{j}^{n + 1} + \\ {(\sum_{i = g, l, c} α_{i} ρ_{i} v_{i}^{2})}_{j + 1}^{n} - {(\sum_{i = g, l, c} α_{i} ρ_{i} v_{i}^{2})}_{j}^{n}] . \end{matrix}

(8)

由于内能和焓存在关系式：

e = h - \frac{p}{ρ} .

(9)

将式（9）代入式（5）可得

\begin{matrix} \frac{\partial}{\partial t} [A \sum_{i = g, l, c} α_{i} ρ_{i} (e_{i} + \frac{v_{i}^{2}}{2})] + \\ \frac{\partial}{\partial s} [A \sum_{i = g, l, c} α_{i} ρ_{i} v_{i} (h_{i} + \frac{v_{i}^{2}}{2})] = Q_{t} + Q_{f r} - \\ A (\sum_{i = g, l, c} α_{i} ρ_{i} v_{i}) g c o s θ . \end{matrix}

(10)

各相流体焓表示为

\{\begin{matrix} d h_{g} = c_{p g} d T - c_{p g} c_{J} d p, \\ d_{l} = c_{p l} d T, \\ d h_{c} = c_{p c} d T . \end{matrix}

(11)

式中，c_p_g为气相比定压热容，J·kg^-1·℃^-1；c_p_l为钻井液相比定压热容，J·kg^-1·℃^-1；c_p_c为岩屑相比定压热容，J·kg^-1·℃^-1；c_J为气体焦汤系数，K·Pa^-1；h_g、 h_l、 h_c分别为单位质量气体、液体和岩屑的焓，J·kg^-1。
将式（11）代入式（10），并展开交换热项和摩阻热项可得井筒环空内流体能量方程计算式为

\begin{matrix} A (\sum_{i = g, 1, c} α_{i} ρ_{i} c_{p i}) \frac{\partial T}{\partial t} + A (\sum_{i = g, 1, c} α_{i} ρ_{i} v_{i} c_{p i}) \frac{\partial T}{\partial s} - \\ A α_{g} ρ_{g} c_{p g} c_{J} \frac{\partial p}{\partial t} - A α_{g} ρ_{g} v_{g} c_{p g} c_{J} \frac{\partial p}{\partial s} - \frac{\partial (A p)}{\partial t} + \\ \frac{1}{2} \frac{\partial}{\partial t} [A (\sum_{i = g, 1, c} α_{i} ρ_{i} v_{i}^{2})] + \frac{1}{2} \frac{\partial}{\partial s} [A (\sum_{i = g, 1, c} α_{i} ρ_{i} v_{i}^{3})] = \\ - A (\sum_{i = g, 1, c} α_{i} ρ_{i} v_{i}) g c o s θ + h_{g} q_{g loss} + h_{1} q_{loss} - h_{g} q_{g} - \\ h_{c} q_{c} + A f_{f} \frac{2 ρ_{m} v_{m}^{2}}{d_{c}} v_{m} + \frac{1}{A^{'}} (T_{e} - T) + \frac{1}{B^{'}} (T_{t} - T) . \end{matrix}

(12)

根据式（12），可得环空温度差分格式为

\begin{matrix} A_{j + 1} {(\sum_{i = g, 1, c} α_{i} ρ_{i} v_{i} c_{p i})}_{j + 1}^{n + 1} (T_{j + 1}^{n + 1} - T_{j}^{n + 1}) = \\ \frac{Δ s}{2 Δ t} A_{j + 1} {(\sum_{i = g, 1, c} α_{i} ρ_{i} c_{p i})}_{j + 1}^{n + 1} (T_{j + 1}^{n} + T_{j}^{n} - T_{j + 1}^{n + 1} - T_{j}^{n + 1}) + \\ \frac{Δ s}{2 Δ t} A_{j + 1} {(α_{g} ρ_{g} c_{p g} c_{J})}_{j + 1}^{n + 1} (p_{j + 1}^{n + 1} + p_{j}^{n + 1} - p_{j + 1}^{n} - p_{j}^{n}) + \\ \frac{1}{2} A_{j + 1} {(α_{g} ρ_{g} c_{p g} c_{J})}_{j + 1}^{n + 1} (p_{j + 1}^{n + 1} - p_{j}^{n + 1} + p_{j + 1}^{n} - p_{j}^{n}) + \\ \frac{Δ s}{2 Δ t} A_{j + 1} (p_{j + 1}^{n + 1} + p_{j}^{n + 1} - p_{j + 1}^{n} - p_{j}^{n}) + Δ s {(q_{g l o s s} h_{g})}_{j + 1}^{n + 1} + \\ Δ s {(q_{loss} h_{1})}_{j + 1}^{n + 1} - Δ s {(q_{g} h_{g})}_{j + 1}^{n + 1} - Δ s {(h_{c} q_{c})}_{j + 1}^{n + 1} - \\ \frac{Δ s}{4 Δ t} A_{j + 1} [{(\sum_{i = g, 1, c} α_{i} ρ_{i} v_{i}^{2})}_{j + 1}^{n + 1} - {(\sum_{i = g, 1, c} α_{i} ρ_{i} v_{i}^{2})}_{j + 1}^{n} + \\ {(\sum_{i = g, 1, c} α_{i} ρ_{i} v_{i}^{2})}_{j}^{n + 1} - {(\sum_{i = g, 1, c} α_{i} ρ_{i} v_{i}^{2})}_{j}^{n}] - \\ \frac{1}{4} A_{j + 1} [{(\sum_{i = g, 1, c} α_{i} ρ_{i} v_{i}^{3})}_{j + 1}^{n + 1} - {(\sum_{i = g, 1, c} α_{i} ρ_{i} v_{i}^{2})}_{j}^{n + 1} + \\ {(\sum_{i = g, 1, c} α_{i} ρ_{i} v_{i}^{2})}_{j + 1}^{n} - {(\sum_{i = g, 1, c} α_{i} ρ_{i} v_{i}^{2})}_{j}^{n}] - \\ Δ s A_{j + 1} {(\sum_{i = g, 1, c} α_{i} ρ_{i} v_{i})}_{j}^{n + 1} g c o s θ_{j} + Δ s A_{j + 1} {(f \frac{ρ_{m} v_{m}^{3}}{2 d_{c}})}_{j + 1}^{n + 1} - \\ Δ s T_{j + 1}^{n + 1} j + 1 {(\frac{1}{A^{'}} + \frac{1}{B^{'}})}_{j + 1}^{n + 1} + \\ Δ s [{(\frac{T_{e j}}{A^{'}})}_{j + 1}^{n + 1} + {(\frac{T_{t j}}{B^{'}})}_{j + 1}^{n + 1}] . \end{matrix} .

(13)

式中，A′为环空流体与地层或海水间的热阻，m·℃·W^-1；B′为环空流体与钻杆内流体间的热阻，m·℃·W^-1。
采用全隐式差分方法对井筒温压控制方程离散后，模型的求解过程包括三层循环：第一层循环为根据温压场分布确定瞬时气侵量和漏失量，并利用漂移模型计算各控制单元内的各相真实速度和空隙率；第二层循环为通过迭代更新井筒压力场；第三层循环为通过耦合压力场和空隙率分布，迭代更新井筒温度场。具体求解过程如图2所示。
图2 求解过程示意图
Fig.2 Schematic diagram of solution process
1.3 基于温压分布规律的溢漏层位判断方法
1.3.1 溢漏层位判断方法及流程
文献^[29]中已经详细探讨了不同气侵速率、气侵位置、漏失速率、漏失位置对深水钻井井筒温压场变化的影响，结果表明气侵发生后井口温度增加，井漏发生后井口温度降低，一定程度上可以区分溢流和漏失事故。然而气侵速率、位置和井漏位置的改变对环空温压的变化影响很小，难以分辨。
相较于正常循环工况，溢流或漏失发生后，时间域下温度计算过程中明显差异项为：地层高温流体侵入携带的焓和钻井液漏失后井筒对流传热量。发生溢流后，由于地层高温流体的侵入，在气侵层位处的井筒温度存在突增现象，且井筒环空温度整体上呈现增加趋势；发生漏失后，由于漏失点上下环空内流体流量的变化，导致漏失点以上和漏失点以下的环空对流传热存在差异，因此沿程的环空温差变化梯度会存在明显差异。
将环空温差定义为溢漏工况下的井筒环空温度与正常循环时环空温度的差值，环空压差定义为实际工况下井筒环空压力与正常循环时环空压力的差值。通过分析时移过程中不同溢漏条件下环空温差、环空压差沿程分布，总结不同溢漏压差、深度下环空温差、压差分布特征，实现对溢漏位置的判断。具体判断流程如图3所示。
图3 基于温压分布规律的气侵和漏失位置判断方法
Fig.3 Judgment method of gas influx and loss circulation position based on temperature and pressure distribution law
1.3.2 模型方法的验证
为了验证本文中井筒多相流温压场的准确性，利用所建立的深水钻井溢漏共存条件下的瞬态多相流模型，计算实例井正常循环期间及溢流发展阶段的井口环空出口处的温度，并将模拟结果与南海某深水井钻井溢流期间的实测数据进行比对，如图4所示。深水井的具体参数如下：井深4430 m，水深846 m，钻井液注入温度和环境温度均为25℃，地温梯度为2.98℃·hm^-1，钻杆内径为0.127 m，外径为0.1397 m，循环期间的钻井泵排量为60 L·s^-1，增压泵排量为40 L·s^-1
由图4可以看出，本文中模型对正常循环阶段和气侵发展阶段的温度预测效果较好，环空出口处温度变化趋势基本一致，总体误差小于5%。
图4 实测值与模型计算值的对比验证
Fig.4 Validation of experimental data against model calculations
2 结果讨论
实例井模拟参数如下：井深为3000 m，水深为1000 m，钻井液注入温度和井口环境温度均为25℃，地温梯度为3.73℃·hm^-1，气藏厚度为10 m。钻井液的排量为30 L·s^-1，密度为1200 kg·m^-3，比定压热容为1675 J·kg^-1·℃^-1。在所有的模拟实例中，井筒的初始温压条件为正常循环钻进4 h时的温压场，气侵初始压差为1.0 MPa，漏失初始压差为1.0 MPa。上溢下漏工况：气侵位置为2600 m，漏失位置为2800 m。上漏下溢工况：漏失位置为2600 m，气侵位置为2800 m。
2.1 溢漏共存工况
上溢下漏工况下气侵压差和漏失压差变化如图5所示。以上溢下漏工况为例，溢漏发生后，井口于0.89 h时见气。可以发现，井口见气之前，气侵压差呈现增加趋势，而漏失压差呈减小的趋势，且在临近见气时间时，气侵压差和漏失压差均会出现剧烈变化。因地层气运移过程中，主要在靠近井口位置发生剧烈膨胀，导致井筒环空压力变化幅度较大；井口见气之后，逐渐建立起稳定循环，气侵压差和漏失压差均趋于稳定。
图5 上溢下漏工况下气侵压差和漏失压差变化
Fig.5 Variation of gas invasion pressure difference and leakage pressure difference under condition of upper gas influx and lower loss circulation
不同工况下温差沿井筒分布如图6所示。从图6可以发现，上溢下漏工况的温差整体上大于上漏下溢工况下的温差。在气侵深度处，环空温差存在突变。上溢下漏工况的温差突变位置位于2591~2600 m，上漏下溢的温差突变位置位于2791~2800 m，均是气藏所处位置。这是因为在气藏位置处，由于地层高温流体侵入井筒，导致侵入位置处井段的环空温差明显增加。在漏失深度处，环空温差变化曲线存在明显转折点。上溢下漏工况下温差曲线转折点位于2800 m，上漏下溢工况的转折点位于2600 m。因为受钻井液漏失的影响，漏失点以上井段和漏失以下井段的钻井液流量不同，导致环空流体与外界的对流传热量存在明显差异，因此温差曲线存在明显转折。
图6 不同工况下温差沿井筒分布
Fig.6 Temperature difference under different working conditions
不同工况下压差沿井筒分布如图7所示。上漏下溢工况的环空压差整体上大于上溢下漏工况下的压差。首先上漏下溢工况的环空温度整体上要小于上溢下漏工况的环空温度，因此上漏下溢工况的钻井液密度要略大；此外，由于上漏下溢工况会发生气液同比例漏失的情况，导致该工况下的截面含气率要低于上溢下漏工况下的截面含气率。因此上漏下溢工况的环空压力要略大于上溢下漏工况的环空压力。此外，发生漏失的压差曲线在海水段均存在明显转折点。这是因为发生漏失后，海水段的环空温度会出现明显下降，钻井液密度、黏度均明显增加，一方面钻井液密度增加会导致静液柱压力有所增加；另一方面钻井液黏度的增加一定程度上改变了因钻井液环空返量减小导致流动摩阻减小的变化趋势。因此海水段上部的压差变化趋势会出现明显转折。
图7 不同工况下压差沿井筒分布
Fig.7 Pressure difference under different working conditions
2.2 上漏下溢工况
上漏下溢工况下沿程温差分布如图8所示。由图8可知：当气侵深度由3000 m减小到2800 m时，井口处温差由0.354℃降低至0.329℃，井口温差降低0.025℃；随着初始漏失压差的增加，井口温差降低，且降低幅度呈现增加趋势；随着初始气侵压差的增加，环空温差总体上呈现线性增加趋势，初始气侵压差每增加0.5 MPa，井口处温差增加0.519℃。
图8 上漏下溢工况下沿程温差分布
Fig.8 Temperature difference under upper loss circulation and gas influx conditions
2.3 上溢下漏工况
上溢下漏工况下沿程温差分布如图9所示。由图9可知：当漏失深度由3000 m减小到2800 m时，井口处温差由0.505℃降低到0.476℃，井口温差降低0.029℃；随着初始漏失压差的增加，井口温差降低，降低的幅度呈现增加趋势；随着初始气侵压差的增加，环空温差总体上呈现线性增加趋势，初始气侵压差每增加0.5 MPa，井口处温差增加0.552℃。
图9 上溢下漏工况下沿程温差分布
Fig.9 Temperature difference under upper gas influx and loss circulation conditions
可以发现，基于环空温差、环空压差分布规律的分析，可实现对溢流深度、漏失深度以及溢漏相对位置的准确判断。此外，通过对环空温差和压差的分析，同样实现了对气侵和漏失相对强度的判断。
3 结论
（1）上溢下漏工况的温差整体上大于上漏下溢工况下的温差，上漏下溢工况的压差整体上大于上溢下漏工况下的压差，两者在井口处环空温差的差值为0.147℃；裸眼段环空温差突变位置对应着气侵层位，环空温差转折位置对应着漏失层位。
（2）对于上漏下溢工况，气侵深度越小，环空温差越小，气侵深度减小200 m，井口温差降低0.025℃；初始漏失压差越大，井口处的温差越小，且变化幅度呈现递增趋势；初始气侵压差越大，环空温差越大，初始气侵压差每增加0.5 MPa，井口处温差增加0.519℃。
（3）对于上溢下漏工况，漏失深度越小，环空温差越小，漏失深度减小200 m，井口温差减小了0.029℃；初始漏失压差增加后，井口温差呈现减小趋势，且井口温差变化的幅度呈现递增的趋势；初始气侵压差增加后，井口温差呈现增加趋势，初始气侵压差每增加0.5 MPa，井口处温差增加0.552℃。
参考文献
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- [27] 李大奇.裂缝性地层钻井液漏失动力学研究[D].成都:西南石油大学,2012.LI Daqi.Study on the dynamics of drilling fluid leakage in fractured formations[D].Chengdu:Southwest Petroleum University,2012.
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基本信息

中图分类号: TE 21
文献标识码: A
DOI: 10.3969/j.issn.1673-5005.2025.05.008
文章编号: 1673-5005(2025)05-0093-09

基金信息

国家自然科学基金项目（U21B2069，52274022，52074325）；
国家重点研发计划项目（2022YFC2806502）；

引用信息

高永海，于鑫，李昊，等.深水钻井溢漏同存条件下温压分析及溢漏层位判别[J].中国石油大学学报（自然科学版），2025,49（5）：93-101.

GAO Yonghai, YU Xin, LI Hao, et al. Temperature and pressure analysis under coexistence of overflow and drilling fluid loss conditions and determination of overflow and loss locations in deep water drilling[J].Journal of China University of Petroleum(Edition of Natural Science),2025,49(5):93-101.

稿件历史

收稿日期: 2024-11-15

参考文献

[1] 舟丹.世界海洋油气资源分布[J].中外能源,2017,22(11):55.ZHOU Dan.Distribution of marine oil and gas resources in the world[J].Sino-Global Energy,2017,22(11):55.
[2] WEN Z,WANG J,WANG Z,et al.Analysis of the world deepwater oil and gas exploration situation[J].Petroleum Exploration and Development,2023,50(5):1060-1076.
[3] ZHANG R,LI J,LIU G,et al.Analysis of coupled wellbore temperature and pressure calculation model and influence factors under multi-pressure system in deep-water drilling[J].Energies,2019,12(18):3533.
[4] 张锐尧,李军,柳贡慧,等.深水钻井多压力系统条件下的井筒温度场研究[J].石油机械,2021,49(7):77-85.ZHANG Ruiyao,LI Jun,LIU Gonghui,et al.Research on the wellbore temperature field under the multiple pressure system during deep water drilling[J].China Petroleum Machinery,2021,49(7):77-85.
[5] 葛以德.钻井泥浆漏失层位识别方法研究[D].西安:西安石油大学,2023.GE Yide.Research on identification method of drilling mud leakage layer[D].Xi’an:Xi’an Shiyou University,2023.
[6] 夏安迪.基于模式识别的气侵早期诊断与地层信息反演[D].青岛:中国石油大学(华东),2019.XIA Andi.Gas invasion early diagnosis and formation information inversion based on pattern recognition[D].Qingdao:China University of Petroleum(East China),2019.
[7] ETTEHADI O R,OZBAYOGLU M E,OZBAYOGLUA M,et al.Three phase flow characteristics in inclined eccentric annuli[R].SPE 166687,2013.
[8] LAGE A C V M,TIME R W.An experimental and theoretical investigation of upward two-phase flow in annuli[R].SPE 64525,2000.
[9] SUN B,SUN X,WANG Z,et al.Effects of phase transition on gas kick migration in deepwater horizontal drilling[J].Journal of Natural Gas Science and Engineering,2017,46:710-729.
[10] HE M,LIU G,LI J,et al.Study of sour gas kicks taken during managed pressure drilling operations[R].SPE 176337-MS,2015.
[11] BERTHEZENE N,DE HEMPTINNE J C,AUDIBERTA,et al.Methane solubility in synthetic oil-based drilling muds[J].Journal of Petroleum Science and Engineering,1999,23(2):71-81.
[12] THOMAS D C,Jr LEA J F,TUREK E A.Gas solubility in oil-based drilling fluids:effects on kick detection[J].Journal of Petroleum Technology,1984,36(6):959-968.
[13] GOMEZ L E,SHOHAM O,SCHMIDT Z,et al.Unified mechanistic model for steady-state two-phase flow:horizontal to vertical upward flow[J].SPE Journal,2000,5(3):339-350.
[14] ZHANG Z,SUN B,WANG Z,et al.Intelligent well killing control method driven by coupling multiphase flow simulation and real-time data[J].Journal of Petroleum Science and Engineering,2022,213:110337.
[15] BHAGWAT S M,GHAJAR A J.A flow pattern independent drift flux model based void fraction correlation for a wide range of gas-liquid two phase flow[J].International Journal of Multiphase Flow,2014,59:186-205.
[16] WANG N,SUN B,WANG Z,et al.Numerical simulation of two phase flow in wellbores by means of drift flux model and pressure based method[J].Journal of Natural Gas Science and Engineering,2016,36:811-823.
[17] 宋亚港.碳酸盐岩地层溢漏同存井筒多相流状态及井筒压力控制方法研究[D].北京:中国石油大学(北京),2023.SONG Yagang.Study on multiphase flow state and wellbore pressure control method of overflow and leakage coexistence wellbore in carbonate formation[D].Beijing:China University of Petroleum(Beijing),2023.
[18] 戴永寿,岳炜杰,孙伟峰,等.“三高”油气井早期溢流在线监测与预警系统[J].中国石油大学学报(自然科学版),2015,39(3):188-194.DAI Yongshou,YUE Weijie,SUN Weifeng,et al.Online monitoring and warning system for early kick foreboding on "three high" wells[J].Journal of China University of Petroleum(Edition of Natural Science),2015,39(3):188-194.
[19] 许玉强,金衍,管志川,等.深水钻井气侵溢流发展规律及隔水管气侵监测优势[J].中国石油大学学报(自然科学版),2019,43(1):60-67.XU Yuqiang,JIN Yan,GUAN Zhichuan,et al.Evolution of gas kick and overflow in wellbore during deepwater drilling and advantage analysis of early gas kick detection in riser[J].Journal of China University of Petroleum(Edition of Natural Science),2019,43(1):60-67.
[20] 毕书博.裂缝性地层漏失机理研究[D].荆州:长江大学,2023.BI Shubo.Study on leakage mechanism of fractured formation[D].Jingzhou:Yangtze University,2023.
[21] 付群超,董振国.莺琼盆地高温高压井漏失原因及漏层深度确定方法[J].录井工程,2021,32(4):43-46.FU Qunchao,DONG Zhenguo.Analysis of the causes of leakage in high temperature and high pressure wells in Yingqiong Basin and methods for determining the depth of leakage zone[J].Mud Logging Engineering,2021,32(4):43-46.
[22] 舒刚.裂缝性地层钻井溢漏同存流动规律及模型研究[D].成都:西南石油大学,2012.SHU Gang.Drilling overflow and leakage coexistence flow in fractured formation[D].Chengdu:Southwest Petroleum University,2012.
[23] 王明波,郭亚亮,方明君,等.裂缝性地层钻井液漏失动力学模拟及规律[J].石油学报,2017,38(5):597-606.WANG Mingbo,GUO Yaliang,FANG Mingjun,et al.Dynamics simulation and laws of drilling fluid loss in fractured formations[J].Acta Petrolei Sinica,2017,38(5):597-606.
[24] MEHRABI M,ZEYGHAMI M,SHAHRI M P.Modeling of fracture ballooning in naturally fractured reservoirs:a sensitivity analysis[R].SPE 163034,2012.
[25] MAJIDI R,MISKA S Z,AHMED R,et al.Radial flow of yield-power-law fluids:numerical analysis,experimental study and the application for drilling fluid losses in fractured formations[J].Journal of Petroleum Science and Engineering,2010,70(3/4):334-343.
[26] 翟晓鹏,鞠鹏飞,谢志涛,等.页岩诱导性裂缝漏失压力动力学模型[J].天然气工业,2018,38(3):81-86.ZHAI Xiaopeng,JU Pengfei,XIE Zhitao,et al.A dynamic model for the leakage pressure of induced fractures in shale reservoirs[J].Natural Gas Industry,2018,38(3):81-86.
[27] 李大奇.裂缝性地层钻井液漏失动力学研究[D].成都:西南石油大学,2012.LI Daqi.Study on the dynamics of drilling fluid leakage in fractured formations[D].Chengdu:Southwest Petroleum University,2012.
[28] 娄文强,王金堂,贺艳祥,等.逆流条件下基于能量守恒的Taylor泡运移速度预测模型[J].中国石油大学学报(自然科学版),2023,47(6):60-71.LOU Wenqiang,WANG Jintang,HE Yanxiang,et al.Taylor bubble migration velocity prediction model based on energy conservation under countercurrent condition[J].Journal of China University of Petroleum(Edition of Natural Science),2023,47(6):60-71.
[29] YU X,GAO Y,ZHAO X,et al.Research on heat transfer law of multiphase flow in wellbore under coexistence of overflow and lost circulation in deepwater drilling[J].Case Studies in Thermal Engineering,2024,55:104103.
[30] LI D,JUNBIN C.Mechanics of oil and gas flow in porous media[M].Singapore:Springer Singapore,2021:171-181.

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深水钻井溢漏同存条件下温压分析及溢漏层位判别

Temperature and pressure analysis under coexistence of overflow and drilling fluid loss conditions and determination of overflow and loss locations in deep water drilling

摘要

Abstract

关键词

Keywords

1 深水钻井溢流同存理论模型

1.1 溢漏同存条件下瞬态多相流模型

1.1.1 质量守恒方程

(1)

(2)

(3)

1.1.2 动量守恒方程

(4)

1.1.3 能量守恒方程

(5)

1.1.4 气侵模型

(6)

1.1.5 漏失模型

(7)

1.2 模型数值离散与求解过程

(8)

(9)

(10)

(11)

(12)

(13)

1.3 基于温压分布规律的溢漏层位判断方法

1.3.1 溢漏层位判断方法及流程

1.3.2 模型方法的验证

2 结果讨论

2.1 溢漏共存工况

2.2 上漏下溢工况

2.3 上溢下漏工况

3 结论

参考文献

基本信息

基金信息

引用信息

稿件历史

参考文献