应用马氏漏斗测定钻井液流变参数

第31卷第5期 2014年 9月

钻井液与完井液

DRILLING FLUID & COMPLETION FLUID

V ol. 31 No.5Sept. 2014

doi: 10.3969/j.issn.1001-5620.2014.05.017

应用马氏漏斗测定钻井液流变参数

刘扣其，　邱正松，　罗洋，　刘云峰，　周国伟

（中国石油大学（华东）石油工程学院，山东青岛）

刘扣其等. 应用马氏漏斗测定钻井液流变参数[J].钻井液与完井液，2014，31（5）：60-62.

摘要　马氏漏斗通常仅仅能表征钻井液的平均黏度，无法表征钻井液的其他流变参数。为此，基于马氏漏斗测定原理，测量不同体积钻井液流出马氏漏斗所需的时间，建立马氏漏斗中钻井液的剪切应力随剪切速率的变化关系，并最终给出了钻井液流变参数（表观黏度、塑性黏度、动切力）的关系式。最后应用具体实例，通过测量2种组分不同的钻井液体系的流变参数，进一步阐述了应用马氏漏斗测量和计算钻井液流变参数的步骤和过程。

关键词　马氏漏斗；钻井液；模型；流变参数

中图分类号：TE254.2　　　　文献标识码：A 　　　　文章编号：1001-5620（2014）05-0060-03

在现场钻井条件下，准确、简单地测量钻井液的流变参数，对于现场的一些决策非常重要[1]。马氏漏斗是广泛应用于现场测量流体流变性能的一种装置，但是通常我们只测量一个时间点来了解钻井液的平均黏度，无法获得更多关于钻井液流变性能方面的知识[2]，为此在过去的一段时间内，一些国内外学者进行了研究，并建立了多种模型[1-8]。在分析钻井液在马氏漏斗中受力情况的基础上，建立了钻井液剪切应力与剪切速率的关系模型，求解得到剪切应力随剪切速率的变化曲线，并最终得到了钻井液的流变参数表达式。

的时间，建立马氏漏斗中液体高度与时间的函数关系，并且通过分析求解，最终得到剪切应力和剪切速率的物理方程，得到剪切应力随剪切速率的变化关系。为此进行如下假设：①测试流体密度一定，不可压缩，且流体通过马氏漏斗属于层流并且是恒温的；②不考虑液体的弹性性能，假设钻井液为纯黏性流体；③钻井液流经喷嘴时属于稳态泊肃叶流[1]。1.1　剪切应力方程

分h ＞0和h ＜0两种情况考虑，当h ＞0时，将马氏漏斗中的钻井液分为上下2部分，则漏斗中钻井液的压降表达式如下。

△P 总=△P 圆台+△P 圆柱（1）其中根据马氏漏斗下端圆柱单元中钻井液的受力平衡条件得到ΔP 圆柱，具体表达式如下。

△P 圆柱πR 2=2πRh 2τw →△P 圆柱=2τw h 2/R

（2）

LτR P △圆台=w /w

式中，△P 圆台为马氏漏斗上端圆台单元中的压降。R w =R +h tan α，可以得到：结合L =h /cosα；

（/R cos α+hsin α）（3）△P 圆台=hτw

所以漏斗中钻井液的总压降为：△P 总=△P 圆柱+△P 圆台=

2h 2τw h τw h ＞0+（）

+又由于△P 总=ρg （h +h 2），所以此时的剪切应力为：

1　模型建立

R 为马氏漏斗下端圆马氏漏斗主要参数如下：

h 2为马氏漏斗下端圆柱体的高度，柱体的半径，cm ；

h 1为筛孔为0.90 mm筛子到圆柱体顶端的距离，cm ；

R o 为筛孔为0.90 mm筛子所在位置对应的马氏cm ；

h 为马氏漏斗中剩余流体上液面距离漏斗半径，cm ；

R w 为漏斗中剩余流体上端对圆柱顶端的距离，cm ；

α为马氏漏斗上部圆台曲面应的马氏漏斗半径，cm ；

L 为马氏漏斗中剩余流体和竖直方向的夹角，（°）；上液面沿圆台曲面到圆柱顶端的距离，cm 。

通过测量不同体积钻井液流过马氏漏斗喷嘴所需

基金项目：博士后基金（2012M521385）、教育部创新团队（IRT1086）联合资助。

第一作者简介：刘扣其，在读研究生，主要从事油基钻井液体系研究。地址：山东省青岛市经济技术开发区长江西路66号中国石油大学石油工程学院工科楼B 座502；邮政编码 266555；E-mail ：[email protected]。

第31卷第5期

r g(h +h ) 2+a +a

刘扣其等：应用马氏漏斗测定钻井液流变参数

（h ＞0）（4）

1.3　钻井液流变参数的确定

τw =

根据求解得到的剪切应力和剪切速率方程，作钻井液在马氏漏斗中流动时壁面剪切应力随剪切速率的变化曲线，结合以下关系式，求解钻井液的流变参数。

ττ-τ511

m a =1022, m p =1022（13）

关于钻井液的切力，则取决于最终静止后钻井液

残留在马氏漏斗中的体积，具体关系式如下。

r h 2) τ014）2+

式中，h 可以根据体积守恒进行求解，漏斗中原来的钻井液体积=漏出去的钻井液体积+漏斗内剩下的钻井液体积。

由于h ＞0，此时的V ＜1500-πR 2h 2，公式中的h 可以根据下面的公式进行求解。

（V 0-V -πR 2h 2=πh (R w +R w R +R 2) 5）

V V 为流式中，0为起初实验时漏斗中的体积，mL ；出漏斗的体积，mL 。

（5）中可以得到如下公式。将R w =R +h tan α带入式

V 0-V -πR 2h 2=πhR 2+tan 2a h 3+πR tan a h 2

对上述一元三次方程进行求解[9]

，得

h 式中，πR2h 2＜V ＜V 0

τ0=ρg R /2 （0＜V ＜πR2h 2）（15）τ0=0 （V =0）（16）

（6）

将h 带入公式（4

）可以得到以下公式。

r h 2) τw 2+

2　室内验证

（7）

配制油基和水基钻井液体系，其配方如下。油基钻井液　240 mL5#白油+3 g主乳+6 g副乳（CaCl 2）为20%）+2%润湿剂+60 mLCaCl2水溶液（w

+0.5%氧化钙+2%提切剂+3%降滤失剂+2%有机土+144 g重晶石（密度为1.2 g/cm3）

水基钻井液　海水+0.5%增黏剂+3%阳离子淀粉+1.5%润滑剂+2.5%降滤失剂+130 g 重晶石（密度为1.3 g/cm3）

分别将1 500 mL上述2种体系加入到马氏漏斗中，记录不同体积的2种钻井液流过马氏漏斗所需的时间，2种钻井液流出体积随时间的变化曲线见图1

。

上面的公式表明，当马氏漏斗形状一定时，钻井液在马氏漏斗中流动时受到的壁面剪切应力只取决于钻井液的密度，而与钻井液的类型无关。

当h ＜0时，此时，钻井液仅仅存在于马氏漏斗下端的圆柱体单元中，此时：△P 总=△P 圆柱=2hτw /R 。对应的钻井液在马氏漏斗中受到的剪切应力为：

τw =ρg R /2 (h ＜0) （8）1.2 　剪切速率方程

使用Brydson 提出的公式来预测马氏漏斗壁面剪切速率[10]，

R R R

Q =2πòrv h d r =π(v h r 2-òr 2d v h ) （9）000

式中，v h 指当马氏漏斗中剩余流体的高度为h 时对应的剪切速率，m/s。当r =R 时，v h =0，带入上式得到：

R τw d v 2

Q =-πòr d v h =-πòR 2h d r （10）

00 . τw d v h τ

, τ=w ，得到以下公式。结合d τ=d r ,γ=

3τw .Q τ=-òγτ2d τ（11）0π

进一步对上述公式进行处理，最终得到：. 34Q 14Q dlg(4Q /πR 3) （12）γw =-() -´´

ππτw

图1　不同钻井液流出马氏漏斗的体积随时间的变化

求出不同测试点对应的壁面剪切应力，作出剪切应力随马氏漏斗内钻井液流出体积的变化关系曲线，见图2。图2表明油基钻井液和水基钻井液的剪切应力随流出体积的增加而降低。

随lg τ的变化曲线，如图3所示。作出lg （4Q /πR 3）根据公式（12），结合图3算出一定体积的钻井液流

62钻井液与完井液

度、塑性黏度和切力。

2014年 9月

出马氏漏斗时对应的剪切速率。作出剪切应力随剪切速率的变化关系曲线，如图4

所示。

2. 当马氏漏斗的形状一定时，钻井液在马氏漏斗中受到的剪切应力仅仅与钻井液的密度有关，与钻井液的种类无关。

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图2

　马氏漏斗中钻井液壁面剪切应力随流出体积的变化

图3　 lg（4Q /πR 3）随lg τ

的变化关系

[4] 刘孝良，刘崇建，谢应权，等. 应用漏斗黏度计测定塑

性流体的流变参数研究[J]．天然气工业，2004，24（1）：47-49．

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度的关系[J]．钻井液与完井液，2012，29（1）：12-14．[6] Yang Li， Li Jiaxue， Liu Huifeng. Study on relationship

图4 　漏斗内钻井液剪切应力随剪切速率的变化关系

between Mash Funnel Viscosity and Apparent Viscosity of Drilling Fluids [J]. Drilling Fluid & Completion Fluid， 2012， 29（1）： 12-14.

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（收稿日期2014-04-11；HGF=1403N2；编辑　王小娜）

根据图4结合公式（13）～（16）计算出这2种钻井液的流变参数，并与Fann35六速黏度计测量结果进行对比，实验结果如表1所示。表1数据表明，采用马氏漏斗建立的模型求得的钻井液流变参数与采用Fann35六速黏度计测得的流变参数值较接近。

表1　不同仪器测量钻井液的流变参数计算结果

马氏漏斗

钻井液油基水基

w Pa 14.7815.13

a mPa ·s 63.5755.93

p mPa ·s 43.6138.20

Fann35六速黏度计w Pa 1617

a p mPa ·s mPa ·s 6354

4737

3　结论

1. 基于马氏漏斗黏度计建立了钻井液剪切应力随剪切速率的变化关系，从而能够计算钻井液的表观黏

V ol.31， No.5

ABSTRACT 99

Authors LIU Lei, LUO Yue, LIU Qingyun, LIU Pianpian, LI Fan, ZHENG Miao

Abstract Caking plays an important negative role in the application of organic salts. Studies show that factors such as composition, temperature, humidity, pressure and particle size all contribute to the caking of organic salt. Of these factors humidity and pressure are the most important ones, thus anticaking can be achieved by sealing and humidity control, minimizing pressure, controlling particle sizes, and maintaining storage temperature etc. The effect of an anticaking additive, AK-3, was tested on potassium formate, showing that the breakdown pressure of the potassium formate is 3.2 kg at AK-3 concentration of 0.3%, and the pressurized salt sample is fluffy, and can be pulverized almost to its original state. This test shows that AK-3 can be used in field application to prevent organic salt from caking.

Key words Organic salt; Anti-caking; Hydroscopicity; Breakdown pressure

First author’s address College of Chemistry and Environmental Engineering, Yangtze University, No.1 Nanhuan Lu, Jingzhou, Hubei 434023, China.E-mail: [email protected].

Laboratory Study on Plastic LCM for Use in Chuan-Yu Area.DFCF , 2014, 31(5) :52-55

Authors WAN Wei, LI Maosen, HUANG Ping, LUO Yufeng, QIN Zonglun

Abstract Cost spent in dealing with severe mud losses in Chuan-Yu area (Sichuan and Chongqing) had reached 50% of the total cost spent in dealing all kinds of mud losses in this area. A plastic lost circulation material (LCM ) was developed with binding agent, light weight agent, rheological controller, plasticizing agent and gelling agent to control mud losses in this area. This LCM has these characteristics: adjustable density, plastic creeping, a certain level of resistance to compression, and can stand for a long time. The “loss of gravity” of the LCM column minimized the drive force for mud losses. In laboratory study, this LCM was 100% successful in mud loss control, and was compatible with other mud additives. An operation techniques were also developed for the effective use of this LCM.

Key words Severe mud loss; Plastics; Mud loss control; Operation technique

First author’s address No. 83, 1st Section of Jianshe North Road, Chengdu, Sichuan 610051, China.E-mail: [email protected].

Mud Loss Control under Pressure in No. 1 Structure of Nanpu: Study and Application.DFCF , 2014, 31(5) :56-59

Authors LI Zhanwei, WANG Wei, ZHAO Yongguang, DENG Wei, WANG Gaojie

Abstract The Structure No.1 of Nanpu, an artificial island, has found formation pressure depletion because of long period of production. Mud losses have been a major problem for safe and economic drilling operation. A high performance LCM slurry, which is aimed at controlling mud losses under pressure, is recently developed. This LCM slurry uses large bridging particles, flake LCM NTS-M and NTS-S and fiber LCM SQD-98 as well as sized packing LCM in a certain mass ratio, can hold pressures up to 7 MPa in laboratory test. Mud losses in well Nanpu13-1170 was completely controlled at the first use of this LCM slurry, and subsequent jobs such as casing running, cementing were all successful.

Key words Mud losses in adjustment well drilling; Pressure depletion in reservoir formation; Mud loss control under pressure; Well completion; Pressure bearing capacity

First author’s address Exploration and Development Project Department, Xincheng Dajie, Tanghai County, Tangshan, Hebei 063200, China.E-mail: [email protected].

Measure Rheology of Drilling Fluids with Marsh Funnel Viscometer.DFCF , 2014, 31(5) :60-62

Authors LIU Kouqi, QIU Zhengsong, LUO Yang, LIU Yunfeng, ZHOU Guowei

Abstract Marsh funnel viscometer is widely used in field measurement of the viscosity of drilling fluid. Though simple and cheap, the Marsh funnel can only measure the parameter that characterizes the average viscosity of drilling fluids. Based on the working principle of Marsh Funnel, the relationship of change in shearing stress and change in shear rate of mud in the Marsh funnel was calculated by measuring the time spent by the mud flowing out of the funnel, and an equation characterize the relation among apparent viscosity, plastic viscosity and yield point. By measuring two drilling fluids of different compositions, the procedure and process of using Marsh

100DRILLING F LUID & COMPLETION F LUID Sept. 2014

funnel to measure and calculate the rheological parameters were demonstrated.Key words Marsh funnel; Drilling fluid; Model; Rheological parameter

First author’s address No. 66 Changjiang West Road, Huangdao District, Qingdao City, Shandong 266555, China.E-mail: [email protected].

Temperature Pattern Modelling and Calculation and Analysis of ECD for Horizontal Wellbore. DFCF , 2014, 31(5) :63-66

Authors YANG Xueshan, LI Sheng, YAN Jienian, LIN Yongxue, WANG Xianguang

Abstract Precise prediction of circulation temperatures in horizontal wellbore plays a significant role in bottom hole pressure control and safe, fast drilling because of the narrow safe mud density window in horizontal drilling. A model for mud circulation temperature prediction in vertical, buildup and horizontal sections of a well is established based on conventional borehole temperature calculation and modeling, the basic principle of heat transfer, and energy equilibrium theory. An error of 0.6% was produced of this model compared with temperatures actually measured for the studied borehole. The calculation and analysis show that annular temperature gradually increases above the end of kick-off point, and the ESD gradually decreases from the start point of the horizontal section, and ECD , on the contrary, gradually increases along the horizontal section, and reaches a maximum at the bottom of the hole.Key words Borehole temperature; Horizontal well; Prediction model; ECD

First author’s address Research Institute of Petroleum Engineering of Jiangsu Oilfield, No. 188 Weiyang Road, Yangzhou, Jiangsu 225012, China.E-mail: [email protected].

Development and Performance of CO2 Resistant Compound Cementing Material.DFCF , 2014, 31(5) :67-70

Authors GUO Xinyang, BU Yuhuan, GUO Shenglai, MA Cong, HE Yingjun

Abstract A phosphoaluminate is selected for use in well cementing because of its good performance in CO2 rich environment. Based on acid-base hydrothermal reaction principle, a phosphate, SHP, was added to the phosphoaluminate to optimize the composition of the hydrate of the phosphoaluminate and to improve the anti-corrosion performance of the set cement. The phosphoaluminate was further treated with compound retarder CBS and a polymer fluid reducer AADI to improve the performance of the phosphoaluminate. The thickening capacity and filtration characteristics of the phosphoaluminate are adjustable, and the sensitiveness of change of performance to the amount of the additives added can satisfy the engineering requirements. The formulated phosphoaluminate has a short transient time, a fluid loss of less than 50 mL, and excellent performance of anti-corrosion by CO2.

Key words Compound cementing material resistant to corrosion by CO 2; Phosphoaluminate; Acid-base hydrothermal reaction; Phosphate; Performance

First author’s address Department of Oil and Gas Well Engineering, College of Petroleum Engineering, China University of Petroleum, Qingdao, Shandong 266580, China.E-mail: [email protected].

Study on and Application of Aluminate Cement Slurry in Cementing Heavy Oil Thermal Recovery Well.DFCF , 2014, 31(5) :71-74

Authors LI Zaoyuan, WU Peng, WU Dongkui, WU Shuang, XIAO Yunfeng, CHENG Xiaowei, GUO Xiaoyang

Abstract In heavy oil thermal recovery wells, the cement slurry is required of fast hardening at low temperatures, and long-term high temperature performance when producing the wells. Aluminate cement slurry is planned to be used in cementing heavy oil thermal recovery wells because of its good properties required, such as fast hardening, high strength and high temperature tolerance. A filtrate reducer, J73S, and a retarder, SR, have been developed through laboratory experiment with aluminate cement. A cement slurry, having density between 1.70 g/cm3 and 1.90 g/cm3, was prepared with J73S and SR for using at temperatures of 30-80 ℃. Variation of the density of the cement slurry can be adjusted to less than 0.02 g/cm3. Other properties of the cement slurry are as follows: Filtration rate ＜50 mL, Thickening time 30-300 min adjustable, compressive strength after 24 hours 14 MPa, and the compressive strength of the set cement reaches 25 MPa after aging twice at high temperature. This cement slurry was used to cement the sidetracked liner section in Well 40-18-38C2, a heavy oil thermal recovery well, and good cement job quality was obtained, satisfying the need for