ON THE SAFETY OF HYDRATE REMEDIATION BY ONE-SIDED DEPRESSURIZATION

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1 Proceedings of the 7th International Conference on Gas Hydrates (ICGH 2011), Edinburgh, Scotland, United Kingdom, July 17-21, ON THE SAFETY OF HYDRATE REMEDIATION BY ONE-SIDED DEPRESSURIZATION Ricardo Camargo, Marcelo Gonçalves Petrobras Rio de Janeiro, RJ BRAZIL Claudio Barreto, Rafael Faraco and Angela O. Nieckele SIMDUT, Det. Mech. Eng., Catholic University of Rio de Janeiro, PUC-Rio Rio de Janeiro, RJ BRAZIL ABSTRACT This aer resents a new model to accurately redict hydrate lug dislacement during a onesided deressurization. This model is both simle to handle and rigorous in the hysical reresentation of the henomenon, and was imlemented as a finite volume transient simulator caable of calculating the lug dislacement dynamics after its detachment. It takes into consideration a number of imortant variables such as ressure and temerature rofiles across chambers ustream and downstream the lug at each instant of time, as well as ie deformation due to ressure variations along the fluid. Some tyical cases for dee offshore roduction are analyzed. Results show that, deending on the conditions and rovided a careful revious analysis is erformed, it may be safe to remediate hydrate lug by one-sided deressurization in a number of tyical situations in offshore roduction scenario. Keywords: gas hydrates, one-sided deressurization, hydrate remediation NOMENCLATURE A Cross section area [m 2 ] c Secific heat at constant ressure [J/(kg.K)] C dyn Dynamic force coefficient [kg/s] D Diameter [m] e Wall thickness [m] E Young's modulus of elasticity [Pa] f Friction factor [-] F f Friction force [N] g Gravity [9.81 m/s 2 ] m Plug mass [kg] M w Molecular weight [kg/kgmol], ch Pressure, Chamber ressure [Pa] s Flow direction coordinate - Distance [m] t Time [s] T Temerature [K] U Global heat transfer coefficient [W/(m 2.K)] v Velocity [m/s] V Volume [m 3 ] Z Gas comressibility factor [-] α Pie inclination [rad] β Thermal exansion coefficient [1/K] χ Poisson s ration [-] µ Viscosity [mpa.s] ρ Density [kg/m 3 ] R Gas universal constant [8314 J/(kgmol K)] INTRODUCTION Flow assurance is a major concern in deewater offshore hydrocarbon roduction rojects. The most frequent flow assurance issue in this environment is the ossibility of ieline blockage Corresonding author: Phone: Fax: ricardo.camargo@etrobras.com.br

2 by gas hydrate lugs, due to the high ressure and low temerature conditions. Hydrate lugs interrut flow in ielines causing substantial economic losses due to roduction deferment and oerational exenditures to clean out the ieline. The oil industry usual strategy is to design the system to avoid hydrate formation during the whole field roductive life. This is tyically achieved by conservative subsea flowlines thermal insulation and oerational rocedures that revent fluids to reach hydrate region. However, sometimes it is not ossible to avoid hydrate formation, esecially during shutdowns and restarts. Thus, safe hydrate lug dissociation becomes a very imortant subject. One of the most usual methods to dissociate hydrate is to deressurize the ieline, moving the fluid to a thermodynamic condition in which the solid hase is no longer stable. Figure 1 shows a hydrate dissociation curve for a given gas comosition, bounding the hydrate region (to the left of the hydrate dissociation curve). For this examle, to dissociate a hydrate lug in thermal equilibrium with a surrounding environment at 280 K, one should deressurize the hydrate lug to a value below 1.9 MPa. Plug two-sided deressurization is always referred when comared to one-sided deressurization. From an economic standoint, lug dissociation in this way is faster because it eliminates the Joule-Thomson cooling that may stabilize the downstream end of the lug [1] and also increases the length of the lug below the hydrate equilibrium ressure. However, the main reason to recommend two-sided deressurization for hydrate lug dissociation in a ieline is safety. One-sided deressurization can bring risk of equiment damage and even fatal accidents have been reorted [2]. Pieline deressurization reduces the temerature at the hydrate interface to the equilibrium temerature. Since the equilibrium is below the environment temerature, there will be a radial heat influx from the sea to melt the hydrate lug. Hydrate dissociation starts at the ie wall and therefore the lug can be suddenly released [1]. Moreover, if the differential ressure across the lug is high enough, it can be dislaced at high velocities through the ieline. A hydrate lug moving at high velocities can ruture a ieline wall either by imact at a bend, or by increasing the ressure of the downstream ie chamber to a value higher than maximum allowed ressure (due to the kinetic energy of the moving lug). These risks are often referred [1, 2, 3]. Nevertheless, when it comes to flexible flowlines, there is another risk that is not often addressed: the temeratures the fluids may reach at both sides of the dislacing lug (due to fast comression/exansion), may be outside the flowline secification. Another concern relates to the allowed limits of ressurization and deressurization rates for these flowlines. Figure 1: Tyical hydrate dissociation curve. Desite the indubitable advantage of two-sided deressurization, sometimes it is oerationally difficult, or even imossible, to erform it. In these cases one-sided deressurization is the most suitable otion. However, it is essential to reviously erform a careful risk evaluation, in order to avoid the hazards described above. A widely known model often used to evaluate the risk of such oeration is described by McMullen in reference [3]. It is based on gas laws alied to two chambers searated by the hydrate block mass, as resented in Figure 2. Just after lug detachment the mass (m) undergoes an acceleration (dv /dt) due to the balance force between high ( ch1 ) and low ressure ( ch2 ) chambers (Eq. 1). In some models a friction force (F f ), oosite to the motion direction, is also included. As the lug moves, the volumes of two chambers (V 1 and V 2 ) change due to exansion at one side and comression at the other one (Eq. 2). This model assumes the ressure is the same along all the extent of each chamber. Hydrate lug ch1,v 1 ch2,v 2 High Pressure Chamber Low Pressure Chamber Figure 2 Simlified model reresentation.

3 dv m dt ch1 Z 1 V ( ch ch ) A Ff = 2 1 (1) 1 ch2 2 = (2) Z 2 V However, the differential ressure across the lug may be high enough to accelerate it to a velocity close to the seed of sound. For lug motion at this level of velocity, the henomenon of fast transient ressure wave dislacement along ie length can not be neglected, as it is in this simlified model. The simlified model may be considered accurate enough when the lug velocity is much lower than the seed of sound. For high lug velocities, the assumtion of constant ressure along each chamber (as in the simlified model), leads to a over evaluation of the risk, because the lug is considered to be submitted to an instantaneous differential ressure higher than it really is, as shown in Figure 3. Another asect is that the simlified model assumes a constant temerature, while the sudden exansion/comression can cause either low or high gas temeratures, which in turn also affect the ressure. Pressure (MPa) Distance (m) Initial state Simlified - t=1s This work - t=1s Figure 3 Pressure rofiles along ieline and through hydrate lug (initially located at 5,000 m). This aer resents a more rigorous model to accurately redict the hydrate lug dislacement during a one-sided deressurization. This model includes a number of imortant variables such as ressure and temerature rofile across both chambers at each instant of time, as well as ie deformation due to ressure variations along the fluid. Some tyical cases for offshore roduction are analyzed using both the simlified model and the one roosed in this work and results are comared. FLUID FLOW AND PLUG MODELING The dynamics of a hydrate lug dislacement inside a ie can be obtained by the solution of the fluid flow roblem, couled with a model to redict the lug motion. The fluid inside the ieline is natural gas, a Newtonian fluid with density ρ calculated by ρ = M w /( Z R T ) (3) where and T are the ressure and temerature. R is the gas universal constant, M w is the molecular weight and Z the gas comressibility factor, which deends on ressure and temerature and is determined based on the Peng-Robinson correlation [4]. Gas viscosity µ is obtained from Lee et al correlation [5], as a function of ressure and temerature, and the secific heat at constant ressure c is calculated by a fifth order temerature olynomial [6]. The flow roblem is governed by the conservation of mass, momentum and energy equations. It is assumed that the flow is one-dimensional; however, the ie can be inclined with the horizontal at an angle α. Pie deformation due to ressure variations along the fluid are also considered [7]. The ie diameter can be determined from the reference diameter at atmosheric ressure, by integrating A/ =A D (1-χ 2 )/(ee), where A is the cross section area, D is the ie diameter, e is the ie wall thickness, E the Young's modulus of elasticity of the ie material and χ the Poisson's ratio. The mass conservation equation can be written as D v v A DT + ξ + β = 0 (4) Dt s A s Dt where Z ξ = ; β = 1 + Y / (5) 1 + ( / A)( A/ ) X / Z T X = ( Z / ) ; Y = T ( / T ) (6)

4 where v,, T are the velocity, ressure and temerature, resectively, s and t are the flow direction coordinate and time. The material derivative is D/Dt = / t + v / s. The momentum equation can be written as Dv Dt 1 f v v = ρ s 2 D g sinα ; (7) where g is gravity and f the friction factor, which is determined from the Colebrook correlation [8], assuming the flow to be locally fully develoed. The energy conservation equation is c D T Dt 2 β T D f v v 4U = + T ρ Dt 2 D ρ D ( T ) ; (8) where U is the global heat transfer coefficient between the fluid inside the ie and the ambient, at a temerature T, including the ie wall conduction as well as internal and external convection. Convective heat transfer coefficients are calculated by Hilert and Gnielinski correlations [9]. The couling of the lug motion with the fluid flow in the ieline is obtained through a balance of forces acting on the lug, which can be written as dv m dt = ( )A mg sinα F 1 2 f (9) where v and m are the lug velocity and mass, 1 and 2 the ressure on the ustream and downstream faces of the lug. F f is the contact force between the lug and the ie wall. When the lug is not in motion, the contact force is equal to the static force. The lug will move only if the force due to the ressure difference across the lug is larger than the static force. Once the lug is set in motion, the contact force becomes the dynamic friction force, which can be set constant or it can vary linearly with the lug velocity as F f = C dyn v (10) where C dyn is the dynamic force coefficient. It is assumed a constant lug mass during the dislacement eriod, so hydrate melting is not considered. This assumtion is based on the fact that the fast transient lasts just a few seconds, during which hase change can be neglected. NUMERICAL METHOD To better account for the motion of the lug in the ieline the governing equations were re-written in terms of a coordinate system that stretches and contracts in the ie, deending on the ig osition. The set formed by equations (4), (7), (8) and (9), together with the aroriate boundary and initial conditions, requires a numerical method to obtain the desired time-deendent ressure and velocity fields. These equations were discretized by a finite difference method. A staggered mesh distribution was selected to avoid unrealistic oscillatory solutions, as recommended by reference [10]. The equations where integrated in time using a totally imlicit method. The sace derivatives were aroximated by the central difference method around the mesh oint. The resulting coefficient matrix is heta-diagonal, and can be easily solved by a direct heta-diagonal algorithm. The total number of grid oints inside the ie is ket constant in the numerical calculations. The initial distribution of the number of grid oints ustream and downstream of the lug was made roortional to the length of the ie at each side of the lug. However, as the lug moves along the ie, an adative mesh technique is emloyed to rearrange the node distribution, i.e., the mesh moves with the lug, and when the lug dislacement is larger than a certain distance, grid oints migrate from one side of the lug the other side. CASE ANALYSIS Hydrates may form in subsea ielines due to several different conditions, therefore the lug location, mass and ressure will vary for each case. In some deewater installations, however, a set of tyical hydrate formation conditions can be defined, corresonding to the more common ractical occurrences. This work is focused in gas flow ies because this corresonds to a more critical situation than multihase flow, in which liquid has a damening effect. Therefore, gas lift flowlines and gas exort ielines are analyzed. We defined for this study three scenarios: gas lift

5 in subsea well with short and long tiebacks and gas exort ieline. Gas lift in short tieback. It consists of a 6 km flexible flowline with 4 internal diameter, and the lug is initially located 1 km from ie downstream boundary. The initial ressure at ustream chamber is set to 200 kgf/cm 2 (19.6 MPa), corresonding to the ie normal oeration condition. The ressure in the shorter chamber is set to 7 kgf/cm 2 (0.69 MPa) to reresent the deressurization at the latform side to dissociate hydrate. Figure 5 resents the results for lug velocity. The maximum velocity calculated by the simlified model is considerably higher than the calculated by this work model. This is an exected result, rovided the fact that in simlified model the lug is submitted to a higher ressure dro (Figure 3). A lower hydrate lug velocity means a lower risk related to thrust on bends and fittings. The flowline structure resistance analysis is beyond the scoe of this aer. Gas lift in long tieback This scenario is similar to the first one and the only difference is the total ie length, here set to 12 km. All the other arameters remain, including distance between initial lug osition and flowline extremity at the low ressure side. Gas exort ieline It consists of a 38 km steel ie with internal diameter, and the lug initially located 4 km from ie downstream boundary. The initial ressure at ustream chamber is set to 125 kgf/cm 2 (12.3 MPa), corresonding to the ie normal oeration condition. The ressure in the shorter chamber is also set to 7 kgf/cm 2 (0.69 MPa). In the three scenarios the hydrate lug length was assumed m and the fluids at initial conditions are in thermal equilibrium with the environment at 4 o C. For each one of the three scenarios it is erformed an analysis using both simlified and this work model and their results are comared. For both models the dynamic force coefficient, C dyn, was set to 230 kg/s. Figure 4 shows ustream and downstream lug ressure trends for gas lift in short tieback scenario. Given the fact that for this work model ressure varies along ie length for each time ste, the lotted values reresent ressure at both ieline extremities. The transient calculated by this work model is considerably slower and more stable than the one calculated by simlified model. Even considering calculated ressure behavior is different between models, in terms of maximum ressure they both agree that there is no risk for this scenario, for the maximum ressure achieved is lower than ie maximum allowed ressure. Figure 4 - Pressure trend ustream and downstream hydrate lug for gas lift in short tieback scenario. Figure 5 - Plug velocity trend for gas lift in short tieback scenario.

6 Figure 6 shows fluid temerature trend at both flowline extremities calculated by this work model. Fluid temerature reaches extreme values, increasing due to gas comression at the downstream chamber and decreasing at the ustream chamber. Flexible and steel flowlines have different ranges of working temeratures. Further calculation must be erformed to evaluate temerature radial rofile along ie wall in order to verify if these limits are resected and, if not, to assess the consequences. difference between models results is even more remarkable. Figure 8 shows that for simlified model the ressure downstream the lug is high enough to cause flowline ruture, while for this work model the maximum calculated ressure does not exceed ustream ressure at initial conditions. Again, the transient calculated by this work model is considerably slower and more stable. This is an examle showing that using simlified model could lead to exceedingly conservative assessment related to ressure limits. Figure 6 - Temerature trend at both flowline boundaries for gas lift in short tieback scenario. Figure 7 - Sensitivity analysis for friction coefficient on the model roosed in this work. The dynamic force coefficient, C dyn, has a strong influence on the simlified model results. Since this arameter is not easy to obtain, a sensitivity analysis is erformed to assess its influence on the model roosed in this work. Figure 7 shows lug velocity results for C dyn = 230 kg/s and C dyn = 50 kg/s. By examining Fig. 7, it can be seen that some differences can be observed but only at the early eriod of the movement, with the lower friction lug reaching higher velocities. As a consequence, the ressure just downstream lug rises raidly, increasing force oosite to the motion direction and slowing lug motion to aroach the higher friction case. Therefore C dyn influence on this work model results is not as strong as on the simlified model. Concerning gas lift in long tieback scenario, the Figure 8 - Pressure trend ustream and downstream hydrate lug for gas lift in long tieback scenario.

7 The conclusions for lug velocity are similar to those for short tie back scenario (Fig. 9): lower maximum velocity and slower and more stable transient for this work model. Figure 10 - Plug velocity comarison for gas lift in short and long tieback scenarios. Figure 9 - Plug velocity trend for gas lift in long tieback scenario. One interesting asect to be discussed can be arisen from lug velocity comarison for short and long tieback scenarios, as calculated by this work model. As shown in Figure 10 both velocities are exactly the same for the initial hase of lug dislacement. This can be exlained by examining Eq. (9) and Fig. 11, where the ressure distribution along the flowline can be seen for both cases at different time instants. It is imortant to remark that the only difference among these cases is the flowline length ustream the lug. The lug movement is governed by the ressure difference across the lug, which is almost the same because for long distances the ressure remains constant. This means that the ie chambers can be considered as infinite regarding lug reference because lug is not subjected to any influence from boundaries for the lengths and times analyzed. The main difference among the cases is the time required to equalize the ustream ressure with the downstream one. The long tieback takes around 105 s, while the short tieback equalizes the ressures after 60 s. (a) short tieback b) long tieback Figure 11 Axial ressure for gas lift in short and long tieback scenarios at different time instants.

8 Figure 12 shows ressure trend ustream and downstream the lug for the gas exort scenario. Results for simlified and this work models are comletely different for this case. According to simlified model the maximum ressure downstream the lug could reach over 150 MPa, more than an order of magnitude higher than ustream at initial conditions! On the other hand, this work model shows a smooth downstream ressure increase, not surassing ustream initial ressure, and a very slow transient. While in the simlified model everything haens within the initial 20 s, this work model assesses more than 150 seconds for ressure equalization on both sides of hydrate lug. Examining Figure 14, it can be seen that due to the initial high ressure difference, the lug reaches 372 m/s. However, since the contact force is roortional to the velocity, it is also high forcing the lug to decelerate. After 60s the lug resents a very small velocity, but due to the still existing ressure difference (Fig. 12), it still moves, but very slowly. Figure 13 Comarison between simlified and resent model of the lug velocity trend for gas exort ieline scenario. Figure 12 - Pressure trend ustream and downstream hydrate lug for gas exort ieline scenario. Accordingly, lug velocity trends are comletely different for the two models, as can be seen in Figure 13. Figure 14 resents only the lug velocity obtained with the resent model, so that it can be better visualized. The maximum lug velocity redicted by the resent model was 372 m/s, while the simlified model redicted an extremely high and unrealistic value. The simlified models redicted a velocity oscillation, which was not redicted by the resent model. The sizes of the ieline ustream and downstream of the lug are very big, so that the changes in volume, due to the lug movement, which induces changes in ressure, are relatively small, leading to a more stable behavior. Figure 14 - Plug velocity trend for gas exort ieline scenario. Present model.

9 CONCLUSIONS Safety is fundamental. Therefore, it is essential to erform a very rigorous risk analysis before alying one-sided deressurization, taking into consideration the lug characteristics, such as its osition, mass, ustream ressure, etc. The simlified model is too conservative with resect to ressure. For all cases analyzed with the resent model, the resulting ressure was always within the normal oeration limits. Longer and more stable transients were observed with the resent model in relation to the simlified one. For flexible flowline, it is also recommended to investigate the limiting temeratures that the ieline wall will be submitted during the oeration and to evaluate their imact on its integrity. The maximum lug velocities redicted with the resent model were always considerably lower than the velocities redicted by the simlified model. However, the ieline integrity risks due to the high lug velocities inside the ieline were not assessed in the resent work. The lug dynamics is governed by the lug characteristics, such as mass, friction force, and ressure difference across it. The ieline length ustream and downstream the lug is only relevant if the ieline is very short or if the lug is very close to one of the extremities. REFERENCES [1] Sloan E.D., Koh C.A. Clathrate Hydrates of Natural Gases. Boca Raton: Taylor and Francis, [2] Sloan, E.D., Hydrate Engineering.Monograh 21, Richardson: Society of Petroleum Engineers, [3] Sloan E.D., Koh C.A., Sum A.K. Natural Gas Hydrates in Flow Assurance. Burlington: Gulf Professional Publishing, 2011 [4] Pratt. R.M., Thermodynamic roerties involving derivatives. Using the Peng-Robinson Equation of State. Chemical Engineering Education, , [5] Lee, A. L., Gonzalez, M.H., Eakin, B. E., The viscosity of Natural Gases, Journal of Petroleum Technology, Vol.18 (8), aer 1340-PA, 1966 [6] Van Wylen, G. J; Sonntag, R. E.; Borgnakke, C., Fundamentals of Thermodynamics. 6th Ed. Edgard Blucher, [7]Wylie, E.B. and Streeter, V.L., Comressible flow in ies, McGraw Hill, New York, [8] Fox, R. W.; Mc Donald, A. T., Pritchard, P. J., Introduction Fluid Mechanics, 6th Edition. John Wiley & Sons, Inc., 2003 [9] Incroera, F.P, Dewitt, P. D., Fundamentals of Heat and Mass Transfer. John Wiley & Sons. NY, 1996 [10] Patankar, S.V., Numerical transfer and fluid flow, Hemishere Publ. Co., New York, The dynamic force coefficient influences the maximum lug velocity, which occurs immediately as the lug starts moving. However, during lug deceleration eriod this arameter influence is no longer significant. Results show that, rovided a careful revious analysis is erformed, it is safe to remediate hydrate lug by one-sided deressurization in a number of tyical situations in offshore roduction scenario that would be considered dangerous if the simlified model is used. ACKNOWLEDGEMENTS The authors wish to thank Petrobras and CNPq for suorting the develoment of this work.