spe/iadc-185276-ms prediction model for gas migration in ... · 4 spe/iadc-185276-ms (13) where ag...

SPE/IADC-185276-MS

Prediction Model for Gas Migration in Well During PMCD Operation

Felipe de Souza Terra, DEM - PUC-Rio/Petrobras; Antonio Carlos Vieira Martins Lage, Petrobras; Kjell Kåre Fjelde,University of Stavanger; Mônica Feijó Naccache and Sidney Stuckenbruck, DEM - PUC-Rio

Copyright 2017, IADC/SPE Managed Pressure Drilling and Underbalanced Operations Conference and Exhibition

This paper was prepared for presentation at the 2017 IADC/SPE Managed Pressure Drilling & Underbalanced Operations Conference & Exhibition held in Rio deJaneiro, Brazil, 28–29 March 2017.

This paper was selected for presentation by an IADC/SPE program committee following review of information contained in an abstract submitted by the author(s).Contents of the paper have not been reviewed by the Society of Petroleum Engineers or the International Association of Drilling Contractors and are subject to correctionby the author(s). The material does not necessarily reflect any position of the Society of Petroleum Engineers or the International Association of Drilling Contractors,its officers, or members. Electronic reproduction, distribution, or storage of any part of this paper without the written consent of the Society of Petroleum Engineers orthe International Association of Drilling Contractors is prohibited. Permission to reproduce in print is restricted to an abstract of not more than 300 words; illustrationsmay not be copied. The abstract must contain conspicuous acknowledgment of SPE/IADC copyright.

AbstractThe use of the Managed Pressure Drilling (MPD) is spreading in offshore operations. The increasingcomplexity in the new exploratory frontiers is demanding for new techniques to reduce costs and increaseoperational safety. MPD appears as an answer for that demand and sometimes it is the only viable way todrill some of the challenging wells. In that way, understanding the gas migration behavior while drilling inPMCD mode allows an optimized well design concerning cost and operational safety.

The present study validates a mathematical model capable of simulating a scenario where loss of drillingfluid in the bottom of the well is present while having an influx from the same reservoir and observing gasmigration to the surface in a PMCD operation. A Drift Flux Two Phase Flow Model is used in associationwith the Advection Upstream Splitting Method (AUSMV). Before the presentation and discussion of thecomplete PMCD scenario, two simple cases were simulated and the results were compared to the onesfrom a computer application considered as a reference to the industry, validating the proposed model. Theresults of the simulations can be used as a base for the elaboration of operational procedures to monitor gasbehavior and optimize bullhead in PMCD scenarios.

IntroductionThe Managed Pressure Drilling (MPD) technic is one of the operational alternatives developed to face theprogressive challenges of incorporating new reserves in the oil industry. The use of this technology onshoreis well established but it is also spreading fast in offshore scenarios. Nowadays, operating in Brazil, thereis the major fleet of Dynamic Position Vessels (DP) adapted for MPD, pioneering the use of the Mud CapDrilling in ultra-deep water [1]

The MPD technology is usually implemented to avoid NPT related to losses of circulation or to increasethe safety of operations in narrow window scenarios, but, in some cases, it is the only way to drill the well.Literature presents a huge number of studies related to gas migration in wells [2], [3], [4], [5], [6], [7], [8],[9], [10], [25]. However, the majority of those studies focus on conventional well control events, whichmeans that fluid losses are not considered. Those works provide a robust input to the present study but,unfortunately, they do not fill all the demands. The dynamic behavior of the fluids in front of the reservoir

2 SPE/IADC-185276-MS

while drilling in Pressurized Mud Cap may result in influxes, gas migration to the surface and drilling fluidlosses.

When the bit reaches a fracture, a massive loss starts. In some cases, as the level of the drilling fluid dropsdown, an underbalance situation occurs at the top of the reservoir [figure 1]. The correct understanding ofthis phenomenon and its evolution can help to optimize the sequence of operations to keep the well undercontrol without unnecessarily increasing costs.

Figure 1—Illustration of the flux condition stablished when hitting themassive loss zone with production in the upper part of the reservoir.

Another important issue consists of monitoring the position of the gas that migrates in the well, stablishingsafety limits for the operation and defining bullhead requirements. However, tracking gas position whilemigrating is, indeed, a challenge. Consequently, bullhead sequences are, usually, intentionally conservativeto avoid risks based on this uncertainty.

The objective of the present study consists of developing a reliable model to reproduce the eventsin a cross flow scenario related to a PMCD operation. The model should predict precisely the transientphenomena that characterize the behavior of such a complex system, helping the early operational planningphases.

From this perspective, the Drift Flux model is combined with the numerical scheme AUSMV (AdvectionUpstream Splitting Method). The validation process consists of comparing the results from the developedmodel to the ones obtained from the multiphase software OLGA Dynamic Multiphase Flow Simulator [11].After the validation of the mathematical model, a representative PMCD scenario is defined and simulatedto analyze as illustrative case of cross flow.

Computational and Mathematical ModelingThe model adopted to simulate the PMCD scenario is based on a unidimensional two-phase flow approach.However, as two phase flow models are highly complex, simplifications are adopted to make it more suitableto simulate the desired well condition, leading to the adoption of the Drift Flux model, which is largely usedfor dealing with bubble and slug two-phase flow patterns [12]. Despite introducing those simplifications,the Drift Flux model is still complex, requiring the use numerical methods. The present study uses theAdvection Upstream Splitting Method (AUSMV) [13], [14], [15] to solve the following system of partialdifferential equations:

(1)

SPE/IADC-185276-MS 3

(2)

(3)

Where α1 is the liquid volumetric fraction, αg is the gas volumetric fraction, ρ1 is the liquid density, ρg

is the gas density, v1 is the liquid velocity, vg is the gas velocity, P is the pressure, which is considered thesame for both liquid and gas, Γ1 and Γg are the mass exchange coefficient between gas and liquid and q isthe source term. For the present paper, the system is considered isothermal and there is no mass exchangebetween the phases:

(4)

The source term is divided in two parts:

(5)

Where Fg is the gravitational term:

(6)

And θ is the well inclination. FW is the viscous component. As a first approach, the friction pressure lossis calculated based on a simplified equation:

(7)

Where ρmix is the mixture density, vmix is the mixture velocity, de and di are the external and internaldiameter of the annular section, respectively, and f is the friction loss coefficient and depends on the flowregime, laminar or turbulent., being a function of the Reynolds Number (Re) defined by the followingequation:

(8)

Where μmix is the mixture viscosity. For Reynolds numbers lower than 2,000, the regime is consideredlaminar and for values greater than 3,000, the regime is considered turbulent. To avoid any discontinuity, alinear interpolation is applied for Reynolds between 2,000 and 3,000.

The friction loss for the laminar regime is:

(9)

And, for the turbulent regime, it is

(10)

Four closure equations are also needed. One is the relation between liquid and gas fractions:

(11)

Two others are the density equations for gas and liquid as functions of P, which are the following:

(12)

Where ρ1,0 is the liquid density at atmospheric pressure (101,325 Pa) and a1 is the sound velocity in theliquid phase. (in water a1 = 1.500m/s). For the gas, the ideal gas law is adopted:


(13)

Where ag is the sound velocity in the gas phase (for ideal gas Finally, the last closure equation is the gas slip, which was proposed by Zuber, N. & Findlay [16]:

(14)

Where vg is the average in–situ gas velocity, S0 is the slip velocity between the gas bubble and thestationary liquid, vmix is the average mixture velocity and K0 is the distribution parameter [16]. The value ofK0 varies between 1.0 and 1.5 according to the flow condition. For both bubble and slug flow, experimentsindicate that a value near 1.2 is adequate [12]. For the bubble rise velocity, the equation proposed byHarmarthy [17] is applied:

(15)

Where g is the gravity acceleration and σ is the surface tension. For large bubbles, almost the size of theduct cross section, the rising velocity is given by the equation proposed by Davies & Taylor [18] with thecorrection for annulus developed by Hasan & Kabir [6]:

(16)

Where Di is the internal diameter of the outer pipe and D0 is the external diameter of the inner pipe foran annular geometry.

The proposed formulation uses the same approach adopted by Nickens [19], which means that the gas slipvelocity for bubble flow is described by equation (15) and K0 is equal to 1. For slug flow, the slip velocityis defined by equation (16) where k0 is equal to 1.2. For gas fractions lower than 25%, or αg < 0.25, the flowpattern is considered to be bubble flow. For gas fractions greater than 85%, or αg > 0.85, the flow pattern isdefined as slug flow. A linear interpolation is used for gas fractions between 25% and 85%, or 0.25 < αg <0.85, avoiding any discontinuity problems may appear during the execution of numerical routines.

The Drift-Flux Model PropertiesThe Drift Flux system, equations (1), (2) and (3), can be also written in a vector form as follow:

(17)

Where:

(18)

The sound velocity for the mixture, cmix, can be obtained by the following equation [20]:

(19)

considering that αg * ρg << α1 * ρ1, where αg ∈ (0,1). The eigenvalues are given by the following expressions:


(20)

The first and the third eigenvalue are the pressure pulses propagating in both directions and the secondone represents the mass transport (gas volume wave: e.g. a migrating kick). In places where there is onlyliquid, αg = 0, and the eigenvalues are:

(21)

On the other hand, if only gas is present, the eigenvalues are given by

(22)

It is also worth to mention that the distribution parameter, K0, may cause numerical problems by inducingdiscontinuities in the model for larger gas volume fractions. As mentioned previously, K0 varies from 1.0,for gas fraction below 0.25, to 1.2, for gas fractions greater than 0.85. A linear interpolation is used between1.0 and 1.2, avoiding numerical problems in that range.

For higher gas fractions, near or greater than 0.85, the relation 1 - (K0 * αg) tends to 0, creating adiscontinuity. Figure 2 illustrates the solution adopted to eliminate this potential problem.

Figure 2—Distribution Parameter, K0 – Theoretical Value × Modified Value to avoid discontinuity

The Numerical Method - Advection Upstream Splitting Method (AUSMV)The AUSMV is a numerical method proposed to solve the Drift Flux system of partial differential equations[13]. It can be easily implemented and literature has interesting examples of its application, such asconventional well control situations and MPD scenarios [14], [15], [21], [22].

The domain is divided into a pre-defined number of elements, as illustrated in figure 3. All the averageproperties of the elements are calculated and stored in the center of the element, but the fluxes betweenelements are calculated and stored at the interface between elements. The numerical scheme requires a CFLlower than 1 in accordance with [23]:

(23)


Where λ1, λ2, λ3 where defined in (20). Additional details about the AUSMV can be obtained from [13],[14].

Figure 3—AUSMV typical mesh discretization.

Model ValidationThe validation process of the presented model consists of comparing the results obtained to the ones fromthe software OLGA [11], considering two distinct scenarios. Those two cases of study present differencesrelated to the flow rates used and the boundary conditions, but they are similar in terms of well geometryand fluids properties.

The adopted well geometry is composed of a drilling riser, a casing and an extension of open hole withexposed formation, with the following characteristics: (1) water depth = 2,070 m; (2) casing shoe at 4,050m; and (3) bottom hole at 4,500 m. There is a drilling string inside the well, but the OD is considered thesame for its whole extension. The diameters are: (1) OD of the drilling string = 5.5;″ (2) Riser ID = 19.5;″ (3) Casing ID = 12.375;" (4) Open hole ID = 12.250″.

The simulation involves the flow of a liquid inside the well and a gas. The liquid is a brine, a Newtonianfluid, with constant viscosity, 1.0 cp, and surface tension, 70.0 dyna/cm, but the density is defined by theequation of state expressed by equation (12), having 8.55 ppg at the atmospheric pressure. The gas is anideal one, following equation (13) in terms of density and constant viscosity, 0.0172 cp.

The first case illustrates a typical well control situation. A limited amount of gas enters at the bottom ofthe well and is circulated out with a small surface casing pressure increase. The boundary condition at theexit of the annular space, at surface, starts with constant pressure, equal to the atmospheric pressure. Lateron, during the circulation of the gas out of the well, surface pressure reaches the maximum value of 200 psi.During the whole simulation, the liquid injection rate is kept constant with 30 kg/s. The gas flow rate startsfrom zero to 4 kg/s in 30 seconds, following a linear interpolation. It is kept constant at value of 4 kg/s for300 seconds, then, it drops down to zero in 30 seconds following a straight line.

The simulations are performed in 3 steps. The first one focuses on evaluating the ideal mesh to be used.After each simulation the pressure and the gas fraction are plotted and compared to define the optimum pointwhere increasing the number of elements does not improve precision significantly. For this comparison,the following grids are used: 75, 225, 675, 1,325 and 2,025 elements. The second step is performed with aconstant grid, composed of 75 elements, and changing the time step to observe how the results change.


The last step consists of comparing the output of the model with the one from the software OLGA.From Fig. 4, it is possible to observe that the grid space causes significant influence on the precision of

the model. As the grid is getting finer and finer, from 75 to 2,025 elements, the gas region becomes lessand less dispersed in the well. In other words, the transition between the regions with and without gas inthe annular space becomes sharper and sharper as the grid is getting finer. On the other hand, the pressureoutput, in Fig. 5, is not influenced by the grid space as the distribution of the gas region in the annulus is.Considering the results presented in Fig 4, it is adopted the grid with 1,325 elements because the results arevery similar to the ones from the 2,025 elements grid and the computational time is still feasible.

Figure 4—Comparative Chart Gas Fraction × Time by changing only the mesh. Scenario 1.

Figure 5—Comparative Chart Pressure × Time by changing only the mesh. Scenario 1.

Fig. 6 and Fig. 7 compare the results from the proposed model to the ones obtained from the SoftwareOLGA. The pressure results, Fig. 7, present a very good match, having almost no significant differences.The maximum pressure differences, at about 35 psi, represent less than 1% of the values. Considering the


gas fraction distribution, Fig. 6, the proposed model tends to have less gas dispersion than the commercialsoftware package. In other words, the gas transition from the liquid to the two-phase region in the annulusfor the proposed model is sharper than the one obtained from the OLGA.

Figure 6—Comparative Chart Gas Fraction × Time simulated by themodel and by the software OLGA. Scenario 1 – Mesh 1,325 elements.

Figure 7—Comparative Chart Pressure × Time simulated by themodel and by the software OLGA. Scenario 1 – Mesh 1,325 elements.

The second scenario considered for the validation consists of simulating the migration of a gas bubblein a well, closed at surface. A small amount of gas is introduced at the bottom of the well while circulating


liquid. After the introduction of the gas volume into the well, the liquid injection stops and the well is closedat surface. The total simulation lasts for a total time of 6,000 s.

The simulation starts with the injection of liquid at 30 kg/s. This liquid rate is kept constant up to the totalentrance of gas in the well. After that, the liquid injection is stopped. The gas flow rate starts from zero to 4kg/s in 30 seconds, following a straight line. It is kept constant at 4 kg/s for 300 seconds, then, it drops downto zero in 30 seconds in accordance with a linear interpolation. The exit of the annular space, at surface,starts with constant pressure, equal to the atmospheric pressure, but it changes after the well closure.

The simulation of the second scenario is performed in 2 steps. The first one focuses on evaluating theoptimum numerical scheme in terms of grid space, considering the following: 225, 675, 1,325 and 2,025elements. The second step consists of comparing the output from the proposed model to the ones from thesoftware OLGA.

Fig. 8 and Fig. 9 present the results related to the first step of the second scenario. As observed previouslywhile analyzing the results of first scenario, in Fig. 5, the pressure match occurs without refining too muchthe grid, as can be observed in Fig. 8. On the other hand, the match of the gas fraction distribution demandsa much higher grid refinement, which agrees with what is observed already in Figure 4, related to thefirst scenario. In other words, pressure match requires much less refinement then gas distribution match.Consequently, the grid with 1,365 elements is chosen based on the requirement for matching the gas fractiondistribution with a good computational performance. One could note that for the lowest number of elements,the numerical diffusion is large and this will have impact on the pressure build up in a closed well [25]

Figure 8—Comparative Chart Gas Fraction × Time by changing only the mesh. Scenario 2.


Figure 9—Comparative Chart Pressure × Time by changing only the mesh. Scenario 2.

Fig. 10 and Fig. 11 compare the results from the proposed model to the ones from the commercial softwareOLGA. As shown in Fig. 11, the pressure curves present a good match, the highest differences betweenthose pressure curves are around 1.3%. However, regarding the gas distribution curves, the differences aresignificant, as can be observed in Fig. 10. It is also worth to mention that the gas migration velocity inthe proposed model is slightly higher than the one obtained from the OLGA. This difference in terms ofmigration velocity is noticeable from the pressure curves in Fig. 11, in which the pressure curve obtainedfrom the proposed model is, most of the time, above the curve from the OLGA.

Figure 10—Comparative Chart Gas Fraction × Time simulated bythe model and by the software OLGA. Scenario 2 – Mesh 1325.


Figure 11—Comparative Chart Pressure × Time simulated by themodel and by the software OLGA. Scenario 2 – Mesh 1325 elements

Pressurized Mud Cap ScenarioThe simulation of a Pressurized Mud Cap scenario demands for modeling both fluid losses through fracturesand production from the reservoir. The following assumptions are adopted to fill those gaps: (1) the fracturedzone, or the loss zone, is always at the bottom of the well; (2) the productivity index is considered constantfor the entire reservoir exposed; (3) there is only one reservoir present in the open hole; (4) there is no lossesthrough any other part of the reservoir, except through the bottom of the well where the fracture zone is;and (5) the reservoir produces only gas.

As a first attempt to simulate the inevitable crossflow during a PMCD operation, a special cell is created,outside the domain already presented previously, to simulate the interaction between the reservoir and thefractured zone. This special cell, also known as a virtual cell, is connected to the bottom of the discretizedwell, as presented in Fig. 12.

Figure 12—Example of the "Virtual Cell" adopted


The virtual cell has to follow some rules to work properly, such as: (1) the pressure at the top of thereservoir is equal to the pressure at the lowest element of the discretized well; (2) for each iteration theaverage density of the mixture in the virtual cell is recalculated, conserving mass, as Figure 13 presents; (3)the pressure in front of the loss zone is calculated considering the hydrostatic column of the updated fluidmixture inside the virtual cell; (4) for each new iteration the volumetric balance is recalculated to stablishthe new gas fraction inside the virtual cell, and (5) the formation compressibility is not considered, meaningthat the virtual cell has a constant volume.

Figure 13—Schematic drawing of the volumetric balance to stablish the gas fraction inside the "Virtual Cell"

The reservoir gas production rate, once an underbalanced condition is stablished at the top of the reservoir,is calculated considering that the whole length of the reservoir inside the virtual cell contributes to theproduction.

The schematic of the mass balance for the "Virtual Cell" is presented in figure 13.[24]Fig. 14 and Fig. 15 present 24,000 seconds, or 400 minutes, of simulation without using bullhead

injections. In figure 14 it is possible to observe that the pressure in the virtual cell is kept constant duringthe whole operation, as expected, because of the mass loss zone. The pressure inside the well, in front ofthe loss zone, is almost the same of the reservoir in the loss zone. Any pressure variation would be causedby changing the injection flow rate.

Figure 14—Chart Pressure × Time – PMCD Circulation – Mesh 1325 elements.


Figure 15—Chart Gas Fraction × Time – PMCD Circulation – Mesh 1325 elements.

Other interesting observation possible if you analyze figures 14 and 15, is the possibility of identifyingthe moment that the gas passes through specific points of the well. It is possible to observe that the pressurein any point of the well keeps rising until the moment that the front of the gas migration passes throughit. After that moment the pressure at the point remains constant. Another interesting observation is that,the pressure increasing rate changes if the gas front passes through an annular section change below themonitored point. These two observations can be used to monitor the process on migration and pressureincrease in a Mud Cap operation.

On figure 15, it is possible to observe that at the moment the gas production from the reservoir starts, thegas fraction in the "virtual cell" and in the base of the discretized well increases until a point of equilibriumis reached. Figure 16, presents the flowrates of gas and liquid from the discretized well to the "virtualcell". Negative values means it flows from the well to the "virtual cell". On the other hand, positive valuesrepresent it flows from the "virtual cell" to discretized well. As the liquid flow rate from the discretized wellincreases due to the gas expansion related to its migration in the well, the gas flow rate starts to decreasebecause a counter flow is stablished. In fact, this behavior is expected based on practical experience in thefield and is confirmed by the simulation.


Figure 16—Chart Mass Flow Rate × Time – PMCD Circulation – Mesh 1325 elements.

Figure 17 shows the gas fraction profile in the closed well in different periods of the simulation process.It is possible to observe that every time you have a change in the well geometry there is a change in thegas fraction distribution inside the well. After arriving at the surface, the gas fraction of this front startsgrowing as more and more gas arrives. Consequently, it is possible to observe that the model is capable ofrepresenting this gas fraction increase and achieving a situation in which its concentration reaches 100%at the surface.

Figure 17—Chart Gas Fraction × Depth – PMCD Circulation – GasFraction profile in the closed well in different times of the simulation.


ConclusionsThe combination of the Drift Flux model with the AUSMV numerical method is capable of successfullysimulating a well control scenario, a gas migration in a closed well and a PMCD operation. This proposedapproach deals properly with different situations, varying from single-phase flow with only liquid to a two-phase mixture composed of liquid and gas in different proportions up to a single phase region only with gas.

The results from the proposed model are also compared to the ones obtained from the software OLGA,showing a good match. Two different scenarios are used for this validation, a well control situation and agas migration in a closed well.

Regarding the simulation of the PMCD operation, the following aspects are noticeable:

1. As expected, the pressure at the bottom of the well in a PMCD operation is kept almost constant allthe time if the drilling flowrate is kept constant;

2. As expected, without bullhead operations, the wellhead pressure increases all the time, reaching apoint in which the top part of the well is full of gas, if no other fracture appears.

3. There are two possibilities of identifying the gas front position: pressure gauges positioned along thewell, that will make possible to identify when the gas front pass through it. (it is worth to mentionthat after that moment, the pressure is constant until the gas arrives at surface). In addition, if there isa considerable geometry change in the well, it also makes possible to identify changes in the pressureincrease rate after the gas front passes through this annular section change.

For future studies, it is recommended to use the source terms from the partial differential equationsto represent the reservoir production and fluid losses to the fractures. This new formulation can be moreeffective than the approach of the virtual cell simulating multiple gas sources with higher precision and thecrossflow in front of the reservoir.

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