Wellbore Flow Analysis of a Gas-Kick Well During Shut-In

Send Orders for Reprints to reprints@benthamscience.ae The Open Fuels & Enery Science Journal, 205, 8, 63-67 63 Wellbore Flow Analysis of a Gas-Kick Well Durin Shut-In Sun Shihui *, Yan Tie, Bi Xuelian, Chen Xun and Zhan Nan Open Access Institute of Petroleum Enineerin, Northeast Petroleum University, Daqin 6338, China Abstract: Due to the effects of wellbore storae, shut-in period allows additional inflow of as bubbles into the annulus. Wellbore and casin pressures rise durin shut-in of a as kick as a consequence of as upward miration and as compressibility, which will threaten the safety of well control. Therefore, the variation law of surface and wellbore pressures for a as kick well durin shut-in should be investiated. Based on wellbore storae effect, a new model to the wellbore and casin pressure build-up durin shut-in for a as kick well is developed in this paper. Simulation results show that at different as kick volumes, the rate of bottom-hole pressure rise increases as the permeability decreases. And surface casin pressure stabilizes quickly for low permeable formations. However, at equal initial annular aseous volume, the rates of rise of the bottom-hole and surface casin pressures for low permeable formations are slower than for hih permeability formations. Keywords: Bottom hole pressure, casin pressure, as kick, well shut-in, wellbore storae effects.. INTRODUCTION Due to the effect of wellbore storae, shut-in period allows additional inflow of as bubbles into the annulus. Gas bubbles mirate upward, wellbore and casin pressures rise with increase in shut-in time that can lead to weak formation leakae, wellhead equipment breakdown and other drillin accidents [-3]. All of the currently existin models for pressure analysis are based on as upward miration approach [4, 5]. However, as compressibility also play a sinificant role in the pressure build-up. Because of the compressibility of as phase in annular fluid system, the initial total annular volume occupied by the as is reduced. Therefore, the pressurization by the formation would introduce an equivalent volume of as bubble into the annulus to retain the initial annular volume of the aseous phase at all times. By this action, the annular as phase volume is kept constant with increased mass of the aseous phase. This causes the as density to correspondinly increase with time. Surface casin and the bottom hole or wellbore pressures stabilized until the bottom-hole pressure equalizes the as reservoir pressure. Therefore, the variation laws of surface and wellbore pressures which are caused by upward as miration and as compressibility at well shut-in should be investiated. The primary objective of this paper is to implement the wellbore storae concept to analyzin pressure rise in the wellbore and at the surface when the well is shut-in. 2. ANNULAR PRESSURE MODEL OF A GAS-KICK WELL DURING SHUT-IN For the wellbore pressure modelin, the followin hypotheses are considered in this study.. The continuous phase, drillin mud is static, while the dispersed phase, as is allowed to mirate upward with no further expansion after well complete closure. 2. Drillin mud is assumed incompressible, while the as phase is considered hihly compressible. 3. The effect of the weiht of cuttins on the bottom hole pressure is nelected. 4. The time taken to shut in the well is assumed to be known. Since the annulus comprises mostly of incompressible drillin mud and some hihly compressible aseous phase, the annular fluid system is considered to be slihtly compressible. That is, not as compressible as when the entire annulus is filled with as. For slihtly compressible fluid system, the standard compressibility expression under isothermal condition can be expressed as follow [6]. ) By applyin Chain Rule, Eq. ) can be expressed as follow [7]. 2) Re-arranin Eq. 2), we have: Gas density is expressed as follows: 3) m 4) 876-973X/5 205 Bentham Open

64 The Open Fuels & Enery Science Journal, 205, Volume 8 Shihui et al. where, is as compressibility, Pa - ; is as density, k/m 3 ; P bh is bottomhole pressure, Pa; m is mass of as bubble, k; and is the portion of the annular volume occupied by the as, m 3 /min. Differentiatin Eq. 4) with respect to time, t, yields: dm q dq m 2 At any instantaneous time, t, any pressure imposed on the annular as compresses a constant as mass that causes additional as inflow from the reservoir. Such compression results in increased as mass of the entire annular aseous phase at instantaneous time t+δt for the constant annular as volume. However, the mass of each already existin as bubble, before the additional inflow, is assumed to remain the same. Therefore, the increase in the entire annular aseous mass is as a result of the additional as inflow by the wellbore storae effect. It should be noted that the consequential chane in density for each of the as bubble is due to the chane in its volume only. Thus, at any instant, the reservoir pressurizes a constant annular aseous mass for additional inflow. At that instant of reservoir pressurization, dm 5) 0 6) Also, since the successive additional as bubbles are as a result of reduction in the entire annular aseous volume, substitutin Eq. 6) into Eq. 5) yields an expression in terms of the as density and volume: ρ dq When Eq. 7) is substituted into Eq. 3), we have: d Gas inflow rate is expressed as: KhP 2 P 2 p bh )B T µ Z ) res so re-arranin Eq. 8) yields: 2 P bh 2 KhB µ Z 7) 8) [8], 9) Two constant parameters could be defined as follows: K I c 2 φ µ r w and, ln I c + 0.8 where, K is formation permeability, m 2 ; h is formation interval or heiht drilled, m; B is as formation volume factor, m 3 /m 3 ; µ is as viscosity, Pa s; Z is as compressibility factor, ; is dimensionless wellbore pressure parameter, ; is formation pore pressure, Pa; T is wellbore temperature, K; is bottom hole temperature, K; φ is formation porosity, ; r w is wellbore radius, m. Therefore, dimensionless pressure term simplifies to: 2 J c ) 0) Substitutin Eq. 0) into Eq. 9) and interatin results, we have: dp bh P 2 2 p P bh KhB µ Z 2 ) where the Left-Hand-Side of Eq. ) is interated as: dp bh P 2 2 p P bh Let, tanh P bh 2) u 3) Differentiatin Eq. 3) with respect to time, t, we have: du 4) t Then, tdu 5) From Eq. 3), lnt u t Then, u ) e 6) Therefore, substitutin Eq. 5) and 6) into the Riht- Hand-Side of Eq. ), we have: e u Jc du u e e u u du 7) The Riht-Hand-Side interand is evaluated as: e u du lnu + u u! + u2 2 2! + u3 3 3! + u4 4 4! + u5 + 8) So, substitution of Eq. 8) into Eq. 7) yields: ln e + J c 3 3! + J c ) 3 If a parameter is defined as: + J c ) δ ln! 4 + J c 4 4! + J c ) 2 2 2!! ) 5 + + J c ) 2 2 2! 5 + J c + J ) 3 c 3 3! + 9) + J ) 4 c + 4 4! Then, substitutin Eqs. 2) and 9) into the solution of the model Eq. ), completely solves for the model.

Wellbore Flow Analysis of a Gas-Kick Well Durin Shut-In The Open Fuels & Enery Science Journal, 205, Volume 8 65 Therefore, we have the complete solution expressed as follows: tanh P bh 2 e KhB µ Z + C 20) For simplicity sake, another arbitrary parameter can be defined as: 2 e KhB µ Z Therefore, Eq. 20) is re-written as: P bh tanh δ + C 2) When P P hy is substituted into Eq. 2), the constant of interation is solved for as: C tanh P hy δ ttshut 22) Accordin to Eq. ), as density in bottom hole is determined as: e P bh C 2) 23) where C 2 is another constant of interation, and it is expressed in terms of the reservoir conditions as: C 2,res ln,res 24) Annular as volumetric fraction is represented as follow [9]. 3. DYNAMIC SIMULATION OF A GAS-KICK WELL DURING SHUT-IN 3.. Simulation of Gas Miration at Different Gas Kick Volumes At the same rate of penetration and for the same interval drilled into the reservoir of different permeability values of 50-md, 300-md and 400-md, Fis. -3) show the trends of bottom hole pressure, inflow as volume and surface casin pressure with shut-in time for a wellbore shut-in durin a as kick. As seen in Fi. ), as bubbles mirate upward and expand in wellbore, due to the limitation of annular volume, bottom hole pressure build-up as shut-in time increases. And when bottom hole pressure increases to balance with formation pressure, wellbore pressure will be stable. Also, the rate of bottom-hole pressure rise increases as the permeability decreases. This is because at the time of noticin a as-kick on surface equipment, drillin a low permeable reservoir would have caused a smaller volume of as inflow into the annulus than drillin the same interval into a hiher permeable reservoir. The smaller the as fraction is, the hiher the bottom hole pressure is. In the meantime, for the same reservoir pressure imposed on different annular as volumes, it takes a shorter time to compress a smaller as volume to its maximum density than compressin a larer as volume to the same maximum density. Therefore, low permeable formations would build-up its wellbore pressure faster than hihly permeable formations. Surface casin pressure observed in the field should be expected to stabilize quickly for low permeable formations. λ + q l 25) Implementin a volumetric averain technique, the averae density of the annular fluid system is estimated as follow [0]. ρ f ρ q + ρ l l ρ + λ + ρ l λ l 26) Therefore, the hydrostatic pressure of the annular fluid system can be estimated from: P hy ρ f H 27) Fi. ). Bottom hole pressure for different permeability values durin shut-in. where, q l is drillin fluid flow rate, m 3 /min; ρ l is liquid density, k/m 3 ; is ravity acceleration, m/s 2. The annular fluid hydrostatic pressure in Eq. 27) is computed for every wellbore buildup pressure value to obtain the correspondin surface casin pressure rise. P c P bh P hy 28) Eq. 2) and 28) can be used to predict bottom-hole pressure and surface casin pressure when as kick volume is. Fi. 2). Inflow as volume for different permeability values durin shut-in.

66 The Open Fuels & Enery Science Journal, 205, Volume 8 Shihui et al. hole and surface casin pressures for the 50-md reservoir are slower than for the 300 or 400-md permeability formations, which are opposite to the results presented in Fis., 3). This is because for the same reservoir pressurization and equal initial annular as volume at the time of complete well shut-in, the hiher rate of as inflow from the 300 or 400-md formations would continuously introduce larer quantity of as mass into the annulus than the 50-md formation. Since the annular as volume is the same for all the permeability cases, the introduction of larer as mass by the 300 or 400- md formation would result in rapid increase in the annular as density up to the maximum as density. Fi. 3). Surface casin pressure for different permeability values durin shut-in. Since the as bubbles in annular fluid system are capable of further compression, shut-in period allows additional inflow of as bubbles into the annulus with the effect of wellbore storae. Under the same reservoir pressure for all the permeability cases, Fi. 2) shows that as shut-in time increases, the rate of inflow decline. This is because wellbore pressure buildup durin shut-in of a as kick, pressure difference between the wellbore and formation decreases, and the subsequent inflow rate decline. And as shown in Fi. 2), lower as flow rate from the low permeability formation would result in lower total wellbore storae durin shut-in. Fi. 3) shows a trend of radual surface casin pressure buildup, but different permeability have different rates to achieve the initial pressure stabilization. That is, with smaller annular as volume and the same reservoir pressure, low permeable formations would build-up its wellbore pressure faster than hihly permeable formations. Fi. 5). Inflow as volume for an assumed as kick volume at well shut-in. 3.2. Simulation of Gas Miration at Nominal Gas Inflow Volume.5 m 3 of as is assumed to flow into the annulus, the trends of bottom hole pressure, inflow as volume and surface casin pressure with shut-in time are shown in Fis. 4-6). Fi. 6). Surface casin pressure for an assumed as kick volume at well shut-in. Such rapidity of as density increase also causes rapid decline in the subsequent inflow rate from the 300 or 400-md formations. A shut-in time is reached when the rates of inflow from the formations are equal, as shown by the intersection point in Fi. 5). When the maximum annular as density is attained, initial pressure stabilization occurs at the surface and downhole. 4. MODEL VALIDARION Fi. 4). Bottom hole pressure for an assumed as kick volume at well shut-in. Fis. 4, 6) shows that wellbore and casin pressure increase with increase in shut-in time as a consequence of as upward miration. When wellbore pressure equalizes the reservoir pressure, surface casin and bottom hole pressures stabilized. On the other hand, the rates of rise of the bottom- In order to validate the model, the experimental results of Goldkin No. Well at Louisiana State University LSU) [] is used, which is presented in Fi. 7). As shown in Fi. 7), pressure rise slowly in the system durin the first shut-in period. Such period is considered as the wellbore storae period because more as could be injected into the closed annulus to attain the initial wellbore

Wellbore Flow Analysis of a Gas-Kick Well Durin Shut-In The Open Fuels & Enery Science Journal, 205, Volume 8 67 And the rates of rise of the bottom-hole and surface casin pressures for low permeable formations are slower than for hih permeability formations. CONFLICT OF INTEREST The authors confirm that this article content has no conflict of interest. ACKNOWLEDGEMENTS Fi. 7). Plots of the as kick experimental results at LSU-Goldkin NO. Well. pressure rise durin shut-in. After attainin a desired casin pressure, the as injection was stopped, and the casin pressure was maintained by bleedin the mud from the well. Durin this period, the drop in the bottom-hole pressure is as a result of as bubble expansion, which consequently lowers the equivalent hydrostatic pressure of the as-mud mixture in the annulus with constant casin pressure. When as bubble reaches the surface choke line, there is a sharp increase in the casin pressure, which also causes sharp increase in the bottom-hole pressure as shown the final shut-in period in Fi. 7). That is because the as bubbles exert the hih internal pressure on the surface choke. Comparison results show that the simulation results of the proposed model have a ood areement with the experimental results. CONCLUSION ) Based on wellbore storae effect, a new model to the wellbore and casin pressure build-up durin shut-in for a as kick well is developed. And the accuracy of the model has been validated with experimental results. 2) At different as kick volumes, as shut-in time increases, wellbore and casin pressure increase. The rate of bottom-hole pressure rise increases as the permeability decreases. And surface casin pressure stabilizes quickly for low permeable formations. 3) At equal initial annular aseous volume, as shut-in time increases, wellbore and casin pressure increase. The support of the National Natural Science Foundation of China No. 5374077) is ratefully acknowleded. REFERENCES [] Ronron, S.; Baojian, S.; Xiaolan, L.; Zhiyuan, W. Calculation and analysis of bottomhole pressure in wellbore after as invasion. Fault-Block Oil Field, 20, 84), 486-488. [2] Grace, R.D. Advanced Blowout and Well Control. Gulf Publishin Company: Houston, Texas, 994. [3] Li, X.F.; Zhuan, X.Q.; Sui, X.; Gan, T. Study on two-phase asliquid flow durin as kick. J. En. Thermophys., 2004, 25), 73-76. [4] Hasan, A.R.; and Kabir, C.S. Modelin Chanin Storae Durin a Shut-in Test. SPE 2477, 67th Annual Technical Conference and Exhibition, Washinton, Oct. 4-7, 992. [5] Lu, Z.; Gao, X.; Cao, X. Simulation study on two-phase as-liquid flow durin as kick. Oil Dril. Prod. Technol., 2008, 230), 25-28. [6] Terry, R.E.; Roers, J.B.. Applied Petroleum Reservoir Enineerin. 3rd ed.; Prentice-Hall: London, 99. [7] Spieel, M.R.; Liu, J. Mathematical Handbook of Formulas and Tables - Schaum s Outline Series. McGraw-Hill Companies: NewYork, 997. [8] Nickens, H.V. A Dynamic Computer Model of a Kickin Well: Part I-The Theoretical Model. SPE 483, SPE Drillin Enineerin, Part II-Model Predictions and Conclusions. SPE 484, SPE Annual Technical Conference and Exhibition, Las Veas, Sep. 22-26, 985. [9] Butler, G. Multiphase Flow Consideration in Underbalanced Drillin of Horizontal Well, 7 th International Conference on Multiphase Production, Cannes, France, June 7-9, 995. [0] Bes, H.; Brill, J. A study of two phase flow in inclined pipes. J. Petrol. Technol., 973, 255), 607-67. [] Mathews, J.L.; Bouroyne, A.T. Well Control - How to Handle a Gas Kick Movin up a Shut-in Well. SPE Reprint Series, No. 42, 996. Received: November 26, 204 Revised: January 28, 205 Accepted: February 6, 205 Shihui et al.; Licensee Bentham Open. This is an open access article licensed under the terms of the Creative Commons Attribution Non-Commercial License http://creativecommons.or/licenses/by-nc/3.0/) which permits unrestricted, non-commercial use, distribution and reproduction in any medium, provided the work is properly cited.