Wellbore Mud Invasion Depth Determination Method Based on Fluid Loss Experiment

Cai Jun1,2, Sun Jian-meng3, Chen Yuanfang1, Liang Hao1 1 .School of Engineering in China University of Petroleum. Qingdao

266580, Shandong, China; 2. Zhanjiang constituent company of CNOOC, Zhanjiang 524057 Guangdong, China; 3 .School of Geosciences in China University of Petroleum. Qingdao 266580, Shandong, China) e-mail: [email protected]

ABSTRACT The density of the applied in the gas field A with high temperature and high pressure 3 (HPHT) located in the South China Sea can be up to 2.1 g / cm . This high density of the drilling fluid can cause reservoir pollution, damage and other issues. In order to determine the invasion depth by the drilling fluid, a multi-cores measurement of drilling fluid contamination experimental device under formation temperature and pressure conditions has been developed. First of all, based on the analysis of real time data of drilling fluid loss, the filtration law with three typical stages is proposed and a drilling fluid loss calculation model is developed. Second, a new model which can calculate the fluid filtration inversion under the wellbore conditions is developed by using Darcy flow characteristics and fluid filtration equation. Finally, the new built model is applied to calculate the filtration invasion depth of the drilling fluid under wellbore conditions. The results are compared with those obtained from the resistivity inversion. The comparison proves the efficiency and accuracy of the new model. KEYWORDS: Mud filtration; filtration law; three stages; invasion depth; Darcy law

INTRODUCTION During the reservoir exploration and development, drilling fluid invasion can cause formation damage problems. The invasion of the solid particles and filtration fluid can be influenced by different factors such as rock pore structures, formation soaking time and reservoir development environment. Till now, many mathematical models have been developed to determine the invasion depth. Fan et al. [1-5] discussed the damage caused by the drilling fluid and its impact on the effectiveness of oil exploration and development. Also Fan et al. [1-5] proposed the damage radius- permeability reservoir model to evaluate the formation damage. Based on the principle of chemical analysis, Li [6] proposed a method to determine the invasion of the fluid by calculating the changes of ion content from the test oil. Zhang et al. [7-11] analyzed the changes of the electrical and physical performance due to the invasion and predicted the invasion depth by applying the bilateral logging and other engineering data. Yu et al. [12] calculated the drilling fluid invasion radius based on test oil and . By using radial friction and mass conservation equations, Wang and Yan [13]

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Vol. 21 [2016], Bund. 25 9974 deduced a model to quantify the invasion of solid particles and filtration fluid under the consideration of mud cake. These studies provide different methods to calculate the invasion depth. However, these methods are based on the traditional theory of drilling mud invasion model, which can not accurately predict the invasion characteristics under the real wellbore conditions. In this study, we carried out the filtration tests for core samples with different permeability and recorded the filtration in real time. Based on the assumption that the liquid be regarded as Newtonian fluids, function of fluid invasion amount, invasion depth, permeability and pressure difference is developed. Thus, the invasion depth of the drilling fluid can be determined by the amount of fluid filtration estimated by the exposure time. Gas filed A is a high temperature and high pressure gas filed in the South China Sea. Drilling fluid with high density (up to 2.1 g / cm3 ) was applied in the development of this gas filed. This high density makes the reservoir exploration to face the risk of the formation damage. In order to determine the invasion depth under wellbore reservoir conditions, a multi-cores measurement of drilling fluid contamination experimental device was developed. First, the filtration volume in real time during the experiment was recorded, and the dynamic filtration characteristics were identified by analyzing the experiment data. A new invasion calculation model was built considering three stages. Thus, the amount of filtration loss under wellbore conditions was obtained by applying the Darcy flow characteristics and fluid filtration equation. Finally, the volume method was used to calculate the invasion radius of the drilling fluid under wellbore conditions. Also, the calculated results were compared with those obtained by using resistivity inversion. The comparison shows the accuracy of the drilling fluid filtrate loss model based on the three -stages drilling fluid law.

THREE-SECTION FILTRATION LAW AND NEW MODEL FOR FILTRATION LOSS Gas field A with high temperature and pressure can be easily influenced by the filtration and have formation damage problem. In this study, drilling fluid filtration experiments were conducted on different cores under formation pressure and temperature conditions. The amount of filtration was recorded in the real time.

5 DF-11(17.36md)filtration volume 4 DF-2(0.87md)filtration volume DF-13-1(29.5md)filtration volume DF-14-1(34.98md)filtration volume 3

filtration volume,ml 2

1

0

0 10 20 30 40 50 root of time, min1/2

Figure 1: Relation diagrams of mud filtrates and mud invasion time Vol. 21 [2016], Bund. 25 9975

As shown in the Fig.1, a linear relationship can be found between the filtration volume and root of exposure time. When t is less than 2.5 min, this linear relationship is not obvious. However, when t is greater than 2.5 min, filtration volume changes linearly as t increases. The slope of the linear part does not change until t is larger than 25 min. Based on the filtration characteristics illustrated above, the filtration process can be divided into three stages, namely Section A, Section B and Section C as shown in Fig.2. Section A can be regarded as the instant filtration section and in this section, no linear relationships can be found between the filtration and t . In Section B and Section C, filtration volume changes linearly with t , and the slope in Section C is larger than Section B.

5 DF-11(17.36md)filtration volume 4 DF-2(0.87md)filtration volume DF-13-1(29.5md)filtration volume DF-14-1(34.98md)filtration volume 3

filtration volume,ml 2 B C A 1

0

0 10 20 30 40 50 root of time, min1/2

Figure 2: Three steps of mud filtrate change with invasion time Fig.2 shows the drilling fluid filtration in gas field A can change with time in three stages, and the total amount of the drilling fluid filtration volume is the sum of the filtration volume of each stage. Based on the change of three stages, the new model to calculate the filtration loss is built as shown below: Q = Q + Q + Q (1)

Based on the analysis of experimentTOTAL data, filtrationA BvolumeC of Section A has no relationship with t . However, when t equals to 2.5min, a power law relation exists between filtration and permeability. The parameters in the power law function depend on the permeability of the core samples. By considering the reality that t normally is larger than 2.5 min, we can characterize the instant filtration volume at t equals to 2.5min as the input model for Section A, which can be described as: Q = 0.1483 × k . , k (0.1,1.5) （2） 1. 0828 （ ） Q A = 0.2103 × k , k ∈ [1.5,10. ) 3 0.2213 （ ） QA = 0.1483 × k , k ∈ [10. ,100) 4 0 1091 A ∈ Vol. 21 [2016], Bund. 25 9976

For the Section B ( t is less than 20), the filtration volume changes linearly with t and the slope of the linear part is influenced by the permeability of the , the filtration volume of section B can be calculated as: Q = Q + × ( t 2.5) （5） . = 0.0425 × k filtration A where . α √ − 0 109 For αthe Section C ( t is larger than 20), the amount of the drilling fluid invasion is linearly changed with t and the slope is also related to the permeability of the core sample as in section B. Compared with Section B, the slope in section C is larger. Eq. (6) can be used to calculate the filtration volume in C Section: Q = Q + × (20 2.5) + × ( t 20) （6） . = 0.0425filtration× k A， = 0.0148 × ln(k) + 0.0544 . Where, α − β √ − 0 109 α β CALCULATION OF DRILLING FILTRATION AND DEPTH OF INVASION UNDER WELLBORE CONDITIONS Drilling fluid loss is a penetration process. Under the actual wellbore conditions, the principle of drilling fluid filtrates into the formation can be regarded same as the principle of reservoir fluid flows through the porous medium, both them are based on the Darcy law. Normally, it assumes that the drilling fluid is incompressible with a constant thickness value, the permeability of the cake is constant and the liquid phase (filtration fluid) is a Newtonian fluid. Thus, under the wellbore conditions, the fluid filtration rate can be described by Darcy's law under as shown in Eq. 7: = (7) 𝑑𝑑Q 𝑘𝑘A∆p Then the static filtration and dynamic filtration𝑑𝑑t can𝜇𝜇ℎmc be derived as shown below:

Q = A 2 p( 1) (8) 𝑓𝑓𝑠𝑠𝑠𝑠 √𝑡𝑡 𝑠𝑠𝑠𝑠 �Q𝑘𝑘=∆ k 𝑓𝑓 − √ 𝜇𝜇 (9) 𝐴𝐴∆pt The dynamic filtration equation (Eq. 9) describes that∙ under𝜇𝜇𝜇𝜇 the differential pressure ∆p , the fluid with viscosity flows through the sample with the cross-sectional area A and sand column length L during time t, the total flow volume is Q. When the permeability and the column length is constant, 𝜇𝜇 , and at the same value of ∆p and t the fluid filtration volume is proportional to the cross section area. Thus, when the experiments are conducted under the same pressure difference and invasion time by using the same drilling fluid, based on the above analysis, the experiment results can be transferred to well bore condition results. The ratio between the filtration volume through the core samples in the experiment and the real filtration volume in the reservoir formation is equal to their area ratio as shown in Fig 3. This criterion can be applied to calculate the real filtration in the formation based on the core filtration experiments. Vol. 21 [2016], Bund. 25 9977

Figure 3: Comparison between core mud filtration loss model and borehole mud filtration loss model The equation to calculate the filtration volume under reservoir conditions can be derived as shown below: = = 2 (10) Qcore Score πrcore × Q wellbore S=wellbore 2πRwellDcore (11) 𝑄𝑄core 2𝜋𝜋𝑅𝑅well𝐷𝐷core wellbore 2 Where, r = , R 𝑄𝑄 = . 𝑟𝑟core Dcore CAL By using thecore calculation2 modelwell proposed2 above, a code module was built to do the logging interpretation. Fig.4 shows the analysis results of the real well in the field based on the new model considering three stages. As the figure shows, column 6 and column 7 respectively represent the exposure time and the filtration loss volume under the wellbore conditions. It can be seen that the exposure time for the well depth from 3130m and 3162m ranges from 28 to 36 hours and the related filtration loss volume is about 100-120 ml. As the well depth increases to 3180m-3220m, the exposure time varies from 16 to 25 hours and the related drilling fluid filtration ranges from 60 ml -85 ml. The filtration volume increases as the exposure time continues. Vol. 21 [2016], Bund. 25 9978

Figure 4: Result map of three-steps mud filtration calculation

INVASION DEPTH CALCULATION USING VOLUME METHOD In the reservoir formation, the drilling fluid can change the reservoir fluid composition and content during the filtration process. Based on the volume method, It can be regarded that the filtration volume of the drilling fluid equals to the change of the formation fluid volume. Thus, the filtration volume of the drilling fluid under the wellbore conditions can be illustrated as below: Q = ( R R ) h S (12) 2 2 where, R - invasion depth,filtrate in; R -wellbored radius,well in; S filtrate-filtration saturation ; d wellπ − π ∙ ∙ ∅filtration∙ -porosity.

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Due to the equation shown below: = (13)

It can be written as: wellbore filtration 𝑄𝑄 𝑄𝑄 × = ( ) (14) 𝑄𝑄core 2𝜋𝜋𝑅𝑅well𝐷𝐷core 2 2 2 Thus the invasion depth𝑟𝑟core can be described𝜋𝜋𝑅𝑅𝑑𝑑 − as:𝜋𝜋 𝑅𝑅well ∙ ℎ ∙ ∅ ∙ 𝑆𝑆𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓

R = + R (15) 2πRwellDcoreQcore 2 d 2 well where, core radius ，in； � π∅Sfiltrationcore rdiametercore ， in； core filtration. 𝑟𝑟core − 𝐷𝐷core − 𝑄𝑄core − Fig.5 demonstrates the calculation results of the invasion depth using volume method. Column 6, 7 and 8 shows the exposure time between the drilling fluid and formation, the filtration volume and the invasion depth, respectively. The invasion depths of the well depth from 3130 to 3162 m range from 20 to 35 inches, while the invasion depths of well depth from 3180 to 3220 vary from 13 to 20 inches. The result proves that the invasion depth of the drilling fluid has a positive correlation with the exposure time.

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Figure 5: Invasion depth inversion using three-section mud filtration model By analyzing the characteristics and limitations of the classical model for calculating the invasion depth proposed by Tan, Fan(2004) modified the model and proposed the correction equation of Tan equation to calculate the invasion depth based on the practical applications:

D = 0.6202 × D × × e . （ ） Rd−RT 16 8 2 9967Rxo−RT i 0 where, D0-wellbore radius, in ; Bits- diameter ofBits bit, in；RT- real formation resistivity; Rd- apparent formation resistivity；Rxo- flushed zone resistivity；Di-invasion radius, in. In this paper, we used both the filtration model established above and the model proposed by Fan to calculate the same real case. The results were compared as shown in Fig.6. Vol. 21 [2016], Bund. 25 9981

Figure 6: Invasion depths from experimental method and resistivity inversion method As Fig.6 shows, column 6, 7 represents the exposure time and drilling fluid filtration volume under the wellbore conditions by using three-section model, respectively. Column 8 shows the comparison of the invasion depth calculated from the two models, the purple line in column 8 illustrates the invasion depth of drilling fluid based on the drilling fluid invasion experiment. As for the well depth from 3130m to 3162m, the invasion depths calculated by both models are the same, ranging from 20 to 35 inches. As for the well bore depth from 3180m to 3220m, the invasion depths calculated from the model established in this paper are from 13 to 20 inches, while the invasion depths derived from the Fan’s model is from 10 to 20 inches. The results from the new model built in this paper are similar to the results from Fan’s model. This shows the efficiency and accuracy of the new model considering the three stages filtration law. Vol. 21 [2016], Bund. 25 9982

CONCLUSIONS Based on the research about the determination of invasion depth in gas field A in the South China Sea, following conclusions can be obtained: (1)The total filtration loss can be divided into three stages: A section, B section and C section. A section is related with instant filtration. And it shows no obvious linear relation between filtration volume and the root of exposure time. For B section and C section, filtration volume changes linearly with the root of the exposure time. The slope in C section is larger than that in B section. (2)According to Darcy flow characteristics and the drilling fluid dynamic filtration equation, the filtration under wellbore conditions can be calculated directly based on the amount of fluid filtration under experimental conditions. (3)Based on the new model considering the three stages, the invasion depth can be calculated by using volume method. The results obtained by new model are similar to the results of Fan’s model. This proves the efficiency and accuracy of the new model.

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Editor’s note. This paper may be referred to, in other articles, as: Cai Jun, Sun Jian-meng, Chen Yuanfang, and Liang Hao: “Wellbore Mud Invasion Depth Determination Method Based on Fluid Loss Experiment” Electronic Journal of Geotechnical Engineering, 2016 (21.25), pp 9973- 9983. Available at ejge.com.