Downward directional drilling nitrogen foam power-law multiphase flow slag unblocking technology
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摘要:
为了解决下行定向钻孔煤屑堵塞、瓦斯抽采有浓度无流量技术瓶颈难题,提出下行定向钻孔氮气泡沫幂律多相流携渣、解堵技术,采用理论分析、数值模拟、现场工业试验等方法,对煤矿井下下行定向钻孔瓦斯抽采引起煤屑堵塞的原因、下行定向钻孔环空氮气泡沫幂律多相流携渣理论及实践应用进行了研究。通过含壁函数的湍流模型数值模拟耦合瓦斯流动和煤体变形,钻孔抽采后流体压力变化引起的孔壁弹性位移。通过三维库仑失效准则模型数值模拟求解抽采引起的压力变化以及压力变化引发的应力、应变、位移变化及下行定向钻孔塌孔风险。通过幂律多相流理论分析氮气泡沫的稳定性、泡沫在钻杆内、钻头处、环空间隙的流动性、泡沫中煤粉悬浮性能、环空间隙泡沫排渣的压力损失、泡沫向上排渣受力情况。在下行定向钻孔环空氮气泡沫幂律多相流携渣理论分析的基础上,设计了稳定氮气泡沫发生器、泡沫发生灌注系统、下行定向钻孔氮气泡沫钻进工艺、瓦斯抽采钻孔氮气泡沫二次解堵工艺,并进行下行定向钻孔氮气泡沫排渣现场工业试验。研究结果表明:钻孔壁摩擦曳力和弯曲处的离心力会造成煤屑颗粒聚集及孔壁坍塌风险增大,瓦斯携带的煤粉颗粒会撞击孔壁使孔壁变形或剥离,进而导致抽采钻孔塌孔堵塞;建立的涵括氮气泡沫稳定性、流动性、煤粉悬浮性能、环空间隙泡沫压力损失、排渣受力分析的下行定向钻孔环空氮气泡沫幂律多相流携渣、解堵技术理论体系能很好的为下行定向钻孔氮气泡沫排渣提供理论支撑;现场工业试验中氮气泡沫排渣钻孔相比水排钻孔,初始混合量和纯量分别提高了6.5倍和6.4倍,40 d混合量和纯量分别提高了10倍左右,说明氮气泡沫携渣、解赌技术可显著提高下行定向钻孔的瓦斯抽采效率。
Abstract:In order to solve the technical bottleneck problem of downward directional drilling coal cuttings blockage and gas drainage with concentration but no flow, the nitrogen foam power law multiphase flow slag carrying and unblocking technology of downward directional drilling was proposed. Theoretical analysis, numerical simulation, om-site industrial experiments and other methods were used to research the causes of coal cuttings blockage caused by downward directional drilling gas drainage in coal mines, and the theory and practical application of nitrogen foam power law multiphase flow slag carrying in downward directional drilling annular. Numerical simulation was carried out by a turbulence model containing wall function coupled with gas flow and coal deformation, and the elastic displacement of the borehole wall caused by the fluid pressure after drilling extraction was analyzed. Numerical simulation with a three-dimensional Coulomb failure criterion model solved for the pressure changes caused by extraction, as well as the stress, strain, and displacement changes induced by the pressure changes, and the collapsing risk of downward directional drilling. The stability of nitrogen foam, the fluidity of foam in drill pipe, at the drill bit, in the annulus, the suspension performance of coal powder in foam, the pressure loss of foam slagging in the annulus, and the upward slagging stress on the foam were analyzed by the power law multiphase flow theory. Based on the theoretical analysis of downward directional drilling annulus nitrogen foam power law multiphase flow slag carrying theory, the stable nitrogen foam generator, foam generating injecting system, downward directional drilling nitrogen foam drilling process, and gas drainage drilling nitrogen foam secondary unblocking process were designed, and the downward directional drilling nitrogen foam slag removal on-site industrial experiment was conducted. The results indicated that, the frictional drag force of the borehole wall and the centrifugal force at the bends could cause the aggregation of coal particles and increase the risk of borehole wall collapse. The coal powder particles carried by the gas will collide with the borehole wall to deform or detach the borehole wall, which would lead to the collapse and blockage of the extraction borehole. The theoretical system of downward directional drilling annulus nitrogen foam power law multiphase flow slag carrying and unblocking technology, which included nitrogen foam stability, fluidity, coal powder suspension performance, annular space foam pressure loss, and analysis of slag removal force, can well provide theoretical support for downward directional drilling nitrogen foam slag removal. In the on-site industrial experiments, the initial mixing and pure amount of the nitrogen foam slag removal drilling hole increased by 6.5 and 6.4 times, respectively, compared with the water drainage drilling hole, and the mixing and pure amount increased by about 10 times in 40 days, which indicated that the nitrogen foam slag carrying and unblocking technology can significantly improve the gas drainage efficiency of the downward directional drilling hole.
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0. 引 言
随着煤矿开采深度的不断增加,防治煤与瓦斯突出的任务变得越来越艰巨[1-3]。利用定向钻孔进行瓦斯抽采是防止瓦斯事故的有效技术途径[4-6],下行定向钻孔施工过程排渣、排水难度大,易造成孔内积渣、积水[7-8],孔壁长时间浸泡会导致钻孔坍塌[9-11],严重降低瓦斯抽采效率。国内外学者和现场技术人员对排渣工艺进行了大量研究[12-16],伍清等[17]、朱亚飞[18]、蒋志刚[19]提出用铁磁粉作为排渣介质,提高了瓦斯抽采效果;杨虎伟等[20]、王国飞[21]提出高转速压风排渣技术,提高了钻孔深度及成孔率,降低了钻进过程中卡钻、埋钻几率;韩晓明等[22]、周宗勇[23]、任仲久[24]采用CFD-DEM耦合方法对瓦斯抽采钻孔反循环气力排屑过程进行数值模拟,得出合适的排屑气速在节约能耗的条件下可提高排屑效率;付孟雄等[25]、高建成等[26]、刘建林[27]对巷道锚固孔排渣机理进行了研究,发现钻渣平均粒径随着岩石单轴抗压强度的增加而增加;袁志坚[28]研究了气举反循环钻进技术,研制出了气举反循环工艺施工大直径工程井所需钻具;孟晓红[29]研究了钻孔坍塌失效的线弹性力学模型,发现瓦斯压力越来越大,钻孔塌坍应力越大;刘春[30]研究了孔隙流体渗流的钻孔坍塌失效模型,得出了松软煤层坍塌压力随着瓦斯渗流的衰减规律。左伟芹等[31]研发了向下钻孔水渣运输抽采一体化装备,实现了排渣、排水、抽采3种作业的快速切换和循环作业。
泡沫钻进技术首先被应用于石油天然气钻井、地矿勘探钻井[32-33],具有润滑降温、捕集排粉效果好的优点[34]。GOTOVTSEV [35]、AMIT等[36]、BLAUER等[37]研究高温高压下的泡沫流动,并提出了泡沫欠平衡钻井预测井底压力的封闭水力方程及圆管泡沫流动模型。KUTAY[38]、AHMED等[39]、HERZHAFT等[40]提出了环空泡沫流动数学模型与垂直井泡沫洗井数学模型,并将膨润土加入到泡沫体系中。李丽红等[41]、亚巴儿[42]、张端琴等[43]对泡沫半衰周期、发泡体积及泡沫钻进技术展开了研究,建立了水平井岩屑运移模型。张君亚[44]、朱继东[45]研究了泡沫增压钻进和碎软煤层泡沫钻进技术,研制出抗高温性能的泡沫剂。郝从猛[46]研究下向钻孔机械破煤造穴技术,强化了瓦斯抽采效果。
综上,以往的研究主要集中于水、气的排渣方法机理及钻井装备的研发上,对泡沫洗井方法的研究不足,钻孔内多相流运动规律以及泡沫携粉机理[47]的研究还不完善,缺乏适合于煤矿井下煤层特殊地质条件氮气泡沫钻进携渣解堵的机理研究。为解决钻孔瓦斯抽采引起煤屑堵塞问题,从塌孔风险分析入手,综合考虑分析各种洗井、解堵技术手段,优选出氮气泡沫洗井、解堵方法。针对煤矿下行定向钻孔施工的特点,研究下行定向钻孔氮气泡沫幂律多相流携渣解堵技术机理。考虑钻孔施工时的孔壁弹性形变的影响,构建钻孔变形的力学模型,对其变形情况进行数值模拟,得出钻孔易塌孔的位置。
1. 定向钻孔孔壁变形、塌孔风险分析
下向钻孔施工期间及开始抽采后,钻孔塌孔风险相对较高[48],利用达西定律在多孔弹性仿真中获取钻孔中流体流动状态,与通过应力−应变分析得到的结构位移相耦合,分析钻孔抽采后流体压力变化引起的弹性位移。煤层边缘的位移受到约束,但钻孔壁可以自由变形。将达西速度代入连续性方程(1),可求解瓦斯抽采引起的钻孔内瓦斯气体压力、应力、应变和位移的变化。
$$ \nabla \left[-\frac{k}{\mu} \nabla p\right]=0 $$ (1) 式中:$\nabla $为矢量微分算符哈密顿算子;k为渗透率;μ为动力黏度;p为煤层中瓦斯的压力。
实体变形描述,准静态变形的方程组为
$$ {{ - }}\nabla \sigma {\text{ = }}F $$ (2) 式中:σ为应力张量;F为体积力,Nm−3。由于孔隙压力的变化,应力张量随着压力载荷的增大而增大。
线性材料的应力−应变关系通过弹性矩阵C将应力张量和应变张量联系起来,对于各向同性材料,弹性矩阵是杨氏模量ε和泊松比v的函数,应变张量的分量取决于位移矢量u,它具有方向分量u,v,w :
$$ \begin{array}{ll} \varepsilon_x=\dfrac{\partial \boldsymbol{u}}{\partial x} & \varepsilon_{x y}=\dfrac{1}{2}\left(\dfrac{\partial \boldsymbol{u}}{\partial {y}}+\dfrac{\partial \boldsymbol{v}}{\partial x}\right) \\ \varepsilon_y=\dfrac{\partial \boldsymbol{v}}{\partial {y}} & \varepsilon_{y {\textit{z}}}=\dfrac{1}{2}\left(\dfrac{\partial \boldsymbol{v}}{\partial {\textit{z}}}+\dfrac{\partial \boldsymbol{w}}{\partial {y}}\right) \\ \varepsilon_{\textit{z}}=\dfrac{\partial \boldsymbol{w}}{\partial {\textit{z}}} & \varepsilon_{x {\textit{z}}}=\dfrac{1}{2}\left(\dfrac{\partial \boldsymbol{u}}{\partial {\textit{z}}}+\dfrac{\partial \boldsymbol{w}}{\partial x}\right) \end{array} $$ (3) 张量σ和ε通过胡克定律 $ {\boldsymbol{\sigma}} $ = C·ε线性相关。
假设条件如下:①煤层均质分布且各向同性;②煤层气密度和黏度保持不变;③入口处的流体通量为已知量;④流场为稳态[49]。模型参数如下:
下行定向钻孔多孔弹性法模拟耦合瓦斯流动和煤变形的结果如图1所示。最大位移发生在定向钻孔弯曲处。图中显示的瓦斯流动和煤体变形仿真结果表明钻孔易塌孔的位置。
不考虑不同地质构造对瓦斯抽采孔稳定性的影响,把抽采孔周围煤体看成均质的单一介质体,孔周围煤体所受应力超过煤体本身的强度而产生剪切破坏就会发生坍塌,当煤体中孔隙压力为pρ时,基于库仑−摩尔准则的有效应力可用于主应力σ1和σ3表示为
$$ \sigma_1=\sigma_3 \cot\; x^2\left(45-\frac{\varphi}{2}\right)+2 C \cot \left(45-\frac{\varphi}{2}\right) $$ (4) 式中:C为煤体的固有剪切强度(黏聚力),MPa;φ为煤体的内摩擦角。从式(4)可以看出,煤体剪切破坏与否主要受最大、最小应力控制。σ3与σ1的差值越大,孔壁越易坍塌失效[30]。
渗透率k/μm 1×10−16 流体动力黏度μ/(Pa·s) 6.9×10−4 煤层瓦斯压力p/Pa 4.21×105 煤岩弹性模量ε/Pa 2.00×109 泊松比$\nu $ 0.16 三维库仑失效准则涉及岩石失效、3个主应力(σ1、σ2和σ3)和流体压力,如式(5)所示。
$$ \begin{gathered} {l }=\left(\sigma_3+p\right)-Q\left(\sigma_1+p\right)+N\left[1+\frac{\left(\sigma_2-\sigma_1\right)}{\left(\sigma_3-\sigma_1\right)}\right] \\ Q=\frac{1+\sin \;\phi}{1-\sin \;\phi} \quad N=\frac{2 \cos \;\phi}{1-\sin \;\phi} { S o } \end{gathered} $$ (5) 式中:l为失效准则函数,l=0为岩石开始失效,l<0为严重失效,l>0预测稳定性;So为库仑黏聚力;ϕ为库仑摩擦角。失效准则的l函数值如图2a所示。随着l的绝对值越来越大,塌孔风险越高。l函数估算值表明钻孔弯曲处发生塌孔现象的可能性最大。
使用COMSOL Multiphysics多物理场耦合数值模拟软件,采用含壁函数的湍流模型,对瓦斯携带煤屑颗粒进行模拟[50]。这些煤屑颗粒会撞击孔壁,使孔壁变形或剥离[51-52],进而导致抽采钻孔塌孔。得到的速度分布如图2b所示。流动以壁摩擦曳力和弯管中的离心力形成了涡流。
钻孔弯管处的压力云图如图2c所示,携带煤粉颗粒的瓦斯流在弯管处上下壁形成巨大压差;颗粒轨迹如图2d所示。系统受到重力作用,流动以2种方式作用在管上:壁摩擦曳力和弯曲处的离心力。2种力会造成煤屑颗粒聚集及孔壁坍塌风险增大。
2. 下行定向钻孔环空氮气泡沫幂律多相流携渣理论分析
2.1 泡沫的稳定性
泡沫在钻进过程中的流动规律、钻进煤粉在环空间隙内的受力情况等是影响煤层氮气泡沫钻进的关键因素。泡沫中液体的流失是气泡相互挤压和重力作用的结果,用Laplace(拉普拉斯)方程表示
$$ {P_\delta } - {P_A} = \frac{\delta }{R} $$ (6) 式中:Pδ为B处的液体压力;PA为A处液体压力;δ为表面张力,R为3个气泡的半径。
气泡间的气体扩散,会导致泡沫液膜总表面积的降低,如下式
$$ A\left( t \right) = \frac{{3V}}{{2\sigma }}(\Delta {P_\infty } - \Delta {P_t}) $$ (7) 式中:A(t)为t时刻泡沫液膜的总面积;V为封闭体系的体积;$ \Delta {P}_{\infty } $为泡沫完全破灭后体系的压力增量;ΔPt为t时刻时泡沫外部空间的压力增量。测出不同时间的压力增量就可以计算出A(t),进而得出泡沫寿命Lf 。
$$ {L_{\mathrm{f}}} = \int_0^\infty {{A(t)}{\mathrm{d}}t} $$ (8) 评价发泡剂性能优劣的指标主要有发泡体积V0、半衰期t1/2和出液时间ta。Waring-Blender法是美、日等国使用最多的一种方法,如图3所示。高速搅拌一定时间后,读取泡沫体积,然后记录从泡沫中析出液体所需的时间,作为泡沫的半衰期。
2.2 煤层钻进泡沫流动性
煤层钻进泡沫流动划分为钻杆内流动、钻头处流动、环空间隙流动等阶段。
1)钻杆内的流动。泡沫在钻杆内孔的流动可以近似视为在圆管内的幂律流体流动。圆管内黏性流体流速分布的一般表达形式为
$$ u = \frac{R_Z}{{{\tau _w}}}\int_\tau ^{{\tau _w}} {f\left( \tau \right)} {\mathrm{d}}\tau $$ (9) 式中:u为钻杆内黏性流体流速;RZ为钻杆内壁半径;τ为流体切应力;τw为流体在圆管内壁处的切应力。
根据幂律流体本构方程的应变速度为
$$ f(\tau ) = {\left(\frac{\tau }{k}\right)^{\tfrac{1}{n}}} $$ (10) 式中:k为黏度系数,Pa·s。
综合以上算式可得:
$$ u = \frac{n}{{n + 1}}\left({{R_Z}^{1 + \tfrac{1}{n}}} - {r^{1 + \tfrac{1}{n}}}\right)\dfrac{{\Delta {p^{\frac{1}{n}}}}}{{2kZ}} $$ (11) 式中:r为流体到钻杆中轴线的半径;Z为钻杆内轴向长度。
考虑钻进给进速度的叠加,总的合速度可以表示为
$${V_{\rm{H}}} = {\left\{ \begin{array}{l} {\left(\omega r\right)^2} + u_{\rm{G}}^{\rm{2}} + {\left(\dfrac{n}{{n + 1}}\right)^2}{\left[ {{R_{\rm{Z}}}^{\left(1 + \tfrac{1}{n}\right)} - {r^{\left(1 + \tfrac{1}{n}\right)}}} \right]^2}{\rm{ \times }}\\ {\left(\dfrac{p}{{2k}}\right)^{\tfrac{2}{n}}} + \left(\dfrac{{2n{u_{\rm{G}}}}}{{n + 1}}\right)\left[ {{R_{\rm{Z}}}^{\left(1 + \tfrac{1}{n}\right)} - {r^{\left(1 + \tfrac{1}{n}\right)}}} \right]{\left(\dfrac{p}{{2k}}\right)^{\tfrac{1}{n}}} \end{array} \right\}^{\tfrac{1}{2}}} $$ (12) 式中:ω为角速度;uG—钻进给进速度,m/s。
正常钻进时,钻杆内孔中泡沫的轴向速度与旋转角速度无关,所以泡沫的流量表达式为
$$ \begin{array}{c} Q=\displaystyle {\int }_{\tau }^{{\tau }_{\omega }}f(\tau ){\mathrm{d}}\tau =\pi {R_{\rm{Z}}^{2}}{u}_{{\mathrm{G}}}+\\ 2\pi \left(\dfrac{n}{n+1}\right){\left(\dfrac{p}{2k}\right)}^{\tfrac{1}{n}}\left(\dfrac{n}{3n+1}-\dfrac{1}{2}\right){R_{\rm{Z}}^{3+\tfrac{1}{n}}} \end{array} $$ (13) 泡沫在钻进过程中流经钻杆内孔的压力梯度表达式为
$$ P = {( - 1)^n}\left[ {\frac{{2K{{({V_H} - {u_{\mathrm{G}}})}^n}}}{{{R^{n + 1}}}}} \right]{\left(3 + \frac{1}{n}\right)^n} $$ (14) 2)钻头处的流动。泡沫在钻头处的流动场包括了钻头水眼、切削齿等结构。泡沫流经钻头水眼时,与气液两相流通过喷嘴的原理类似,都遵循机械能守恒定律。假设此时气体和液体混合均匀,建立能量守恒方程为
$$ \frac{{v{\mathrm{d}}v}}{{{g_{\mathrm{c}}}}} - \frac{{g{\mathrm{d}}x}}{{{g_{\mathrm{c}}}}} + {V_{\mathrm{m}}}{\mathrm{d}}p + \frac{{2{v_n^2}{f_n}{\mathrm{d}}x}}{{{g_c}x}} = 0 $$ (15) 式中:vn为泡沫流经水眼的速度,m/s;Vm为泡沫的比容,m3/kg;gc为重力加速度;fn为混合物流经水眼的摩擦系数;x为水眼长度,m。
由于钻头的水眼较短,在进行近水平钻进时,可以忽略钻头水眼入口和出口髙度差变化带来的重力影响,则能量守恒方程可以简化为
$$ \frac{{v{\mathrm{d}}v}}{{{g_{\mathrm{c}}}}} + {V_{\mathrm{m}}}{\mathrm{d}}p = 0 $$ (16) 通过对上式进行积分,可得
$$ \frac{1}{{{g_{\mathrm{c}}}}}\int_0^{{v_{\mathrm{n}}}} {v{\mathrm{d}}v + \int_{{p_1}}^{{p_2}} {{V_{\mathrm{m}}}{\mathrm{d}}p = 0} } $$ (17) 式中:P1为钻头上游压力,Pa;P2为钻头下游压力,Pa。
以质量分数表示的泡沫比容为
$$ {V_{\mathrm{m}}} = {\chi _{\mathrm{g}}}{V_{\mathrm{g}}} + (1 - {\chi _{\mathrm{g}}}){V_{\mathrm{l}}} $$ (18) 式中:χg为气相的质量分数;Vg为气相的比容,m3/kg;${V_l}$为液相的比容,m3/kg。
混合物中气相的质量分数可以表示为
$$ {\chi _{\mathrm{g}}} = \frac{{{\rho_{\mathrm{g}}}{V_{\mathrm{l}}}}}{{{\rho_{\mathrm{g}}}{V_{\mathrm{l}}} + {\rho_{\mathrm{l}}}{V_{\mathrm{g}}}}} $$ (19) 式中:ρg为气相密度,kg/m3;ρl为液相密度,kg/m3。
气相的比容可以表示为
$$ {V_{\text{g}}} = \frac{{xRT}}{{{M_{\mathrm{g}}}p}} $$ (20) 式中:x为气体的质量;Mg为气体的摩尔质量;R为气体常数;T为气体的绝对温度。
将式(18)代入式(17),后可得
$$ \frac{{{v_{\mathrm{n}}^2}}}{{{g_{\mathrm{c}}}}} + {V_l}(1 - {\chi _{\mathrm{g}}})({p_2} - {p_1}) + {\chi _{\mathrm{g}}}\frac{{xRT}}{{{M_{\mathrm{g}}}}}\ln \left(\frac{{{p_2}}}{{{p_1}}}\right) = 0 $$ (21) 煤层钻进钻头有多个水眼,泡沫流经水眼的速度为
$$ {v_{\mathrm{n}}} = \frac{{{Q_{\mathrm{g}}}{\rho _{\mathrm{g}}} + {Q_{\mathrm{l}}}{\rho _{\mathrm{l}}}}}{{{A_{\mathrm{n}}}}}{V_{\mathrm{m}}} $$ (22) 3)环空间隙的流动。泡沫在环空间隙的流动,幂律流体环形空间螺旋溜的视黏度分布函数可写为
$$ \eta = \eta (\xi ) = {K^{\tfrac{1}{n}}}{\left[ {\frac{{{\beta ^2}}}{{{\xi ^4}}} + \frac{{{p^2}{R_0}^2{{({\xi ^2} - {\lambda ^2})}^2}}}{{4{\xi ^2}}}} \right]^{\tfrac{{n - 1}}{{2n}}}} $$ (23) 式中:K为稠度系数,或称为幂律系数,Pa·Sn。
泡沫在环空中的速度分布可以参考幂律流体在环形空间中的螺旋流的速度分布函数,对于幂律流体,可以用迭代法数值求解β和λ值。
环空中泡沫的流量计算公式为
$$ \begin{array}{c} Q = \displaystyle\int_{{R_1}}^{{R_{\text{0}}}} {2\pi ru(r){\mathrm{d}}r} \quad=\displaystyle \int_{k_{\textit{z}}}^1 {2\pi {R_0}^2\zeta u(\xi ){\mathrm{d}}\xi } \\ \quad = - \pi P{R_{\text{0}}}^4 \displaystyle \int_{k_{\textit{z}}}^1 {\xi {\mathrm{d}}\xi } \displaystyle\int_{k_{\textit{z}}}^1 {\dfrac{{{\xi ^2} - {\lambda ^2}}}{{\xi \eta (\xi )}}{\mathrm{d}}\xi } \\ \end{array} $$ (24) 式中:kz为内管转数。
将以下边界条件
$$ \int_{k_{\textit{z}}}^1 {\frac{{{\zeta ^2} - {\lambda ^2}}}{{\zeta \eta (\zeta )}}} {\mathrm{d}}\zeta = 0 $$ (25) 代入式(24)后,得到幂律流体环形空间的流量为
$$ Q = \int_{{R_1}}^{{R_0}} {2\pi ru(r){\mathrm{d}}r = \frac{{ - \pi P{R_0}^4}}{2}} \int_{k_{\textit{z}}}^1 {\frac{{\xi {{({\xi ^2} - {\lambda ^2})}^2}}}{\eta }} {\mathrm{d}}\xi $$ (26) 根据平均速度的定义,幂律流体环形空间螺旋流的平均速度可表示为
$$ V = \frac{Q}{A} = \frac{{ - P{R_0}^2}}{{2(1 - {k^2})}}\int_{k_{\textit{z}}}^1 {\frac{{\xi ({\xi ^2} - {\lambda ^2})}}{\eta }} {\mathrm{d}}\xi $$ (27) 环空泡沫压力梯度方程为
$$ P = \frac{{2({K^2} - 1)V}}{{{R_0}^2\int_{k_{\textit{z}}}^1 {\frac{{\xi ({\xi ^2} - {\lambda ^2})}}{\eta }{\mathrm{d}}\xi } }} $$ (28) 2.3 泡沫中煤粉悬浮性能
泡沫中煤粉的沉降速度可由以下经验公式计算。
$$ {\mu }_{\mathrm{max}}\text=\frac{2{r}_{{\mathrm{c}}}}{\eta ({\rho }_{{\mathrm{c}}}+{\rho }_{{\mathrm{f}}})} $$ (29) 式中:μmax为煤粉颗粒沉降速度,m/s;η为泡沫的动力粘度,mPa·s;ρc为煤粉密度,kg/m3;ρf为泡沫密度,kg/m3;rc为煤粉颗粒半径,m。
稳定泡沫在管道内流变性能符合幂律流体的流动,其流体切应力与应变速度间的本构方程,可以表示为
$$ \tau = K{\gamma ^{n_{\mathrm{m}} - 1}} $$ (30) 式中:nm为流动性指数,无量纲。
2.4 向上排渣钻屑受力分析
泡沫在孔内环间隙中上返速度为Va为
$$ {V_{\mathrm{a}}} = \frac{{318.5\pi {d^2}V \times {{10}^{ - 3}}}}{{{d_1^2} - {d_2^2}}} $$ (31) 泡沫中钻渣受力如图4所示,泡沫施加一个拽力F,钻屑浮力Ff,泡沫压力梯度对钻渣作用力Fp,以及钻屑自身重力G,当钻屑处于平衡状态时有
$$ F + {F_{\mathrm{f}}} + {F_{\mathrm{p}}} = G $$ (32) 式中:F为泡沫绕钻渣颗粒阻力;Fp为泡沫流动压力梯度对颗粒的作用力;Ff为钻渣颗粒的浮力;G为钻渣颗粒的重力。
在重力作用下钻渣下落,设钻渣的下落速度为Vs,则钻渣上返的速度Vt为
$$ {V_{\mathrm{t}}} = {V_{\mathrm{a}}} - {V_{\mathrm{s}}} $$ (33) 整理后可得钻渣的滑落速度为
$$ {V_{\mathrm{s}}} = {\left[ {\frac{8}{3}\frac{{{r_0}({\rho _0}g + {P_1} - {\rho _{\mathrm{f}}}g}}{{{\rho _{\mathrm{f}}}{C_{\mathrm{d}}}}}} \right]^{\tfrac{1}{2}}} $$ (34) 式中:ρf为泡沫密度,kg/m3;ρ0为钻渣密度,kg/m3;Cd为绕流阻力系数。
整理以上公式可得钻渣的上返速度为
$$ {V_t} = \frac{{318.5\pi {d^2}V}}{{{d_1^2} - {d_2^2}}} - {\left[ {\frac{8}{3}\frac{{{r_0}({\rho _0}g + {P_1} - {\rho _{\mathrm{f}}}g)}}{{{\rho _{\mathrm{f}}}{C_{\mathrm{d}}}}}} \right]^{\tfrac{1}{2}}} $$ (35) $$ {P_1} = \frac{{{d^2}({p_0} - \Delta {p_1})}}{{{d_1^2} - {d_2^2}}} $$ (36) 将参数代入式(35)中得钻渣上返的速度Vt和钻渣颗粒的大小r0、泡沫流速Va及压力的关系P1的关系,即
$$ {V_t} = {V_a} - {\left[ {\left(6 + \frac{8}{3} \times {{10}^{ - 4}} \cdot {P_t}\right)\frac{{{r_0}}}{{{C_{\mathrm{d}}}}}} \right]^{\tfrac{1}{2}}} $$ (37) 将上述参数代入雷诺数式(43)得出钻孔环间隙的流速,当钻孔环形间隙中的泡沫上返处于不同流速时,将相应的雷诺数代入式(37)中得到钻渣输送情况。
2.5 环空间隙泡沫排渣的压力损失
泡沫的压力损失$ \Delta {P}_{1}$
$$ \Delta {P}_{1}=\sum \Delta {P}_{{\mathrm{n}}}\text+\sum \Delta {P}_{{\mathrm{j}}}\text+\sum \Delta {P}_{{\mathrm{t}}}\text+\Delta {P}_{{\mathrm{h}}} $$ (38) 其中,钻杆中心摩擦沿程损失$\Delta {P}_{{\mathrm{n}}} $为
$$ \sum \Delta {P}_{{\rm{n}}}\text=\gamma {h}_{f}=\gamma {\lambda }_{1}\frac{\sum l}{d} \frac{{V}^{2}}{2g} $$ (39) 钻杆接头处局部损失$\Delta {P}_{{\mathrm{j}}} $为
$$ \sum \Delta {P}_{{\mathrm{j}}}\text=\sum \gamma \left[({\xi }_{1}\text+{\xi }_{2})\text+{\lambda }_{1}\frac{{l}_{D}}{D}\right] \frac{{V}^{2}}{2g} $$ (40) 钻头处局部损失$\Delta {P}_{{\mathrm{t}}} $为
$$ \Delta {P}_{{\rm{t}}}\text=n\gamma {\xi }_{3}\frac{{V}^{2}}{2g} $$ (41) 孔壁摩擦损失$\Delta {P}_{{\mathrm{h}}} $为
$$ \sum \Delta {P}_{{\rm{h}}}\text=\gamma {h}_{f1}=\gamma {\lambda }_{2}\frac{\sum l}{{d}_{1}-{d}_{2}} \frac{{V}_{a}{}^{2}}{2g} $$ (42) 式中:l为钻杆的长度,m;γ为流体容重,t/m3;V为钻杆内流体的平均流速,m/s;d为钻杆接头处直径,m;Va为流体在环间隙中的平均流速,m/s;ζ1为局部阻力系数(流道突然增大);ζ2为局部阻力系数(流道突然缩小);ζ3为钻头出水口的阻力系数,ζ3=0.6;其中,λ1和λ2为沿程阻力系数,根据临界雷诺数Re确定,即:
$$ {Re} = \frac{{Vd}}{v} $$ (43) 式:v为泡沫的运动黏度,m2/s;
若Re<2320流体为层流区,根据尼古拉试验得沿程阻力系数为
$$ \lambda = \frac{{65}}{{{Re}}} $$ (44) 若Re>2320流体为紊流区,根据安礼特苏里试验得沿程阻力系数为
$$ \lambda = 0.11\left( {\frac{\varepsilon _{\mathrm{c}}}{d} + \frac{{68}}{{{Re}}}} \right) $$ (45) 式中:$\varepsilon _{\mathrm{c}}$为管壁当量粗糙度,孔壁为0.75 mm。
通过以上分析可以看出下行定向钻孔氮气泡沫幂律多相流排渣、解堵理论上可行。
3. 下行定向钻孔氮气泡沫幂律多相流现场试验设计
在下行定向钻孔环空氮气泡沫幂律多相流携渣理论分析的基础上,设计稳定氮气泡沫发生器、泡沫发生灌注系统、氮气泡沫钻进工艺及瓦斯抽采钻孔氮气泡沫二次解堵工艺。
3.1 氮气泡沫发生器设计
在泡沫发生装置中分别输入调配好的泡沫液和氮气,泡沫液和氮气输入方向相反,氮气经分散板后为多股气体,以加强混合效果,保证形成稳定连续的泡沫,如图5所示。
3.2 泡沫发生灌注系统设计
泡沫发生灌注系统主要包括井下移动式制氮机(中煤科工集团沈阳研究院有限公司研制生产的DMJ-900/20 高压智能制氮装置,该制氮装置输出额定流量900 m3/h,输出压力2.0 MPa[53])、泡沫泵、泡沫液池、泡沫发生器、气体流量计、泡沫流量计和配套管路、阀门等部件,如图6所示。
3.3 下行定向钻孔氮气泡沫钻进工艺设计
下行定向钻孔钻进时,在孔口的钻杆上固定一个密封部件,在孔内形成封闭空间,再向孔内通入氮气泡沫,排出孔内煤屑,如图7所示。
3.4 下行定向钻孔抽采时氮气泡沫二次排渣工艺设计
下行定向钻孔抽采一段时间后,煤岩层裂隙水会集聚在钻孔内。为解决该问题,需要在定向钻孔封孔时,加入预留氮气泡沫注入管,打钻后,封孔前,下入氮气泡沫注入管,注入管随打钻过程进入煤体,再封孔。预留管延伸至孔底不远处,有利于氮气泡沫进入孔底排渣。抽采时,若遇流量急剧下降,向预留管内注入氮气泡沫进行排渣、排水处理,如图8所示。
3.5 下行定向钻孔氮气泡沫排渣现场工业试验
阳泉煤业集团安泽登茂通煤业有限公司2号煤层厚度1.25~1.53 m,平均厚度为1.38 m。3号煤层厚度0.90~1.83 m,平均1.49 m。2号、3号煤层平均间距为13.10 m。矿井最大绝对瓦斯涌出量为32.98 m3/min,最大相对瓦斯涌出量为17.42 m3/t,回采工作面最大绝对瓦斯涌出量为11.99 m3/min,掘进工作面最大绝对瓦斯涌出量为2.86 m3/min,属高瓦斯矿井。瓦斯相对压力为0.54 MPa,坚固性系数f=0.40。
为对比氮气泡沫排渣与水排渣方法的瓦斯抽采效率,选择在2号煤层巷道使用下行定向钻孔抽采3号煤层瓦斯进行对比试验,在3个抽采区内设置3组对比钻孔分别使用水和氮气泡沫排渣方法,其中①②③号钻孔使用水排渣方法,④⑤⑥号钻孔使用氮气泡沫排渣方法。抽采区及钻孔位置如图9所示。现场试验过程如图10所示。
3组对比钻孔瓦斯抽采数据如图11所示,从浓度的变化趋势上看,抽采开始后④⑤⑥号钻孔瓦斯抽采浓度整体高于①②③号钻孔的瓦斯抽采浓度,后者在10 d内的瓦斯抽采平均浓度从最初的86.23%快速下降为32.95%,其后瓦斯浓度大约稳定在25%~30%。④⑤⑥号钻孔的瓦斯抽采平均浓度从最初的74.34%在3 d内逐渐上升达到最高浓度89.11%,在第3天至第15天时间里逐渐下降到约50%,最后稳定在45%~50%。
由图可知,①②③号钻孔的瓦斯抽采混合量均值随着抽采时间增加从0.0576 m3/min逐步下降到0.000513 m3/min,而④⑤⑥号钻孔抽采混合量均值从0.376 m3/min快速下降到0.195 m3/min,后逐步稳定在约0.130~0.150 m3/min。
从抽采纯量的变化趋势看,2类钻孔的瓦斯抽采纯量随着抽采时间的增加都呈下降趋势,流量大小差别也十分明显。在抽采初期,①②③号钻孔及④⑤⑥号钻孔的初始瓦斯抽采纯量均值分别是0.041 m3/min和0.262 m3/min,使用氮气泡沫洗井方法使得初始瓦斯抽采纯量显著提高了6.4倍。随着抽采时间的延长,④⑤⑥号井的抽采纯量逐渐下降并稳定在0.06~0.07 m3/min。40 d时,2组钻孔的瓦斯抽采纯量均值分别是0.063 m3/min和0.0059m3/min,随着抽采时间的增加,氮气泡沫洗井钻孔的瓦斯抽采纯量始终显著大于水洗井钻孔。
综上,氮气钻孔相比水排钻孔,抽采浓度优势明显,初始混量和纯量差距达6.5倍和6.4倍,40 d混量和纯量差距达10倍左右。
4. 结 论
1)利用三维库仑失效准则模型求解了抽采引起的压力变化以及压力变化引发的应力、应变和位移;利用Fail函数估算值表明钻孔弯曲处发生塌孔现象的可能性最大,对瓦斯携带煤屑颗粒的运移情况进行模拟,模拟结果表明煤屑颗粒会撞击孔壁,使孔壁变形或剥离,进而导致抽采塌孔。
2)对泡沫在钻进过程中的流动规律及钻进煤粉在环空间隙的受力情况进行理论分析,推导出幂律流体环形空间的流量公式;对泡沫中钻渣受力情况进行分析,得出钻渣在泡沫流中的输送情况,结果说明定向钻孔氮气泡沫幂律多相流排渣、解堵理论上可行。
3)设计了下行定向钻孔氮气泡沫幂律多相流现场工业性试验,使用氮气泡沫洗井方法使得初始瓦斯抽采初始混量及纯量从使用水力洗井方法的0.0576、0.041 m3/min提高到0.376、0.262 m3/min,显著提高了6.5、6.4倍。说明氮气泡沫幂律流体钻井工艺避免了水排渣的水锁效应,使得煤体裂隙中瓦斯渗流持续、稳定、畅通,结果表明使用氮气泡沫洗井方法可显著提高瓦斯抽采效率。
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渗透率k/μm 1×10−16 流体动力黏度μ/(Pa·s) 6.9×10−4 煤层瓦斯压力p/Pa 4.21×105 煤岩弹性模量ε/Pa 2.00×109 泊松比$\nu $ 0.16 -
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