Liquid Loading in Gas Wells

Sequence causing liquid loading in a gas well
-  Initially, annular mist flow
   -  With time, gas velocity/ flowrate declines as reservoir pressure declines
       -  Thickness of liquid layer on tubing wall increases
-  Eventually, all liquid is no longer carried to surface by the gas
   -  Accumulated liquid in column adds hydrostatic backpressure on formation
       -  Liquid accumulates at bottom of wellbore (falling film), fed by falling film
       -  Liquid can accumulate at a higher level in the wellbore
                 -  Local condensation at level of aquifer region (cold)  
-  As backpressure increases with liquid accumulation, the gas flow rate declines further
       -  Gas flow eventually stops flowing
       -  See chart below (Lea, et al., 2003) 

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                                                                    Annular  Flow

-  Steady state flow

-  Wall effects result in phase separation
          -  Off-center flux phenomenon
                    -  Anisotropy of carrier phase (gas) velocity flowfield increases near wall
                              -  Results in heavier phase (liquid) concentrating in proximity to wall
                                        -  Liquid (carried phase) film on wall of tubing, with droplets
                                            entrained into gas core
                                        -  Highest velocity gas flows in the center of tube (core)
                                        -  See photo below of flow in live gas well (GEK Engineering)

-  Energy transfer
          -  Interaction between gas phase and liquid phase occurs at their interface
          -  Extent of energy transfer varies according to the nature of the interface                                       
                  -  Shear forces on film surface, and body forces on waves and droplets





                                            Disturbance Waves and Droplet Formation

-  Disturbance waves
          -  Defined as peaks in the thickness of a continuous liquid film on tubing wall
          -  Shear and form drag are described by G. F. Hewitt as the two mechanisms
             of energy transfer from the gas phase to the liquid
                    -  Shear between the phases increases due to these waves
                    -  Form drag increases as waves force the redirection of the gas

-  Droplet entrainment
          -  Mechanisms
                   -  Ligament breakup – ligaments are torn from the tips of the
                       disturbance waves, breaking into small droplets in the gas core
                    -  Bag breakup – disturbance waves are undercut, forming large
                       open-ended bubbles near the wall (occurs at lower gas velocities)
          -  In aggregate, form drag on the liquid phase increases with droplet entrainment

-  Hewitt concluded that tube diameter plays an important role in determining what  
    mechanism lifts the liquid, either wave transport or entrainment
          -  For wave transport to occur, the gas force on the wave must be large
                    -  Small diameter tubes
                              -  Circumferentially coherent, ring-type waves can be formed
                              -  Wave is relatively large proportion of tubing cross-section
                                        -  High form drag
                                        -  Results in greater energy transfer to liquid
                    -  Large diameter tubes
                              -  Waves cover only a small part of the tubing circumference
                                        -  Partial wave is a small proportion of tubing cross-section
                                         -  Form drag is low
                                                  -  Requires high velocity of gas to push wave up

-  Conclusions of Hewitt
          -  Large-diameter tubes: carryover of droplets
              from disintegration of falling film is the
              dominant transport mechanism
          -  Small-diameter tubes: upward transport of
              waves is the dominant mechanism
                 -  Critical velocity is much lower           
-  Energy transfer is more efficient with form drag
    than by shear forces
-  As tubing diameter declines, the extent of
    energy transfer increases

                                                      The Wallis Correlation

-  The Wallis Correlation is the most widely used correlation for determining flooding velocity
             -  Flooding velocity is defined as the minimum gas flow velocity up a vertical tube required
                to prevent flooding, with varying rates of liquid fed through a porous section of the tube
             -  Wallis Correlation has been updated by many researchers to improve predicatability
-  Predicts the onset of flooding in a vertical tube with a falling film
            -  Wallis found that the minimum gas flow velocity declines with declining tube diameter
            -  Theoretically, maintenance of steady state flow can be maintained in a gas well
                by reducing the diameter of production tubing again and again
                          -  As shown, with declining gas flow velocity, from 150mm, to 100mm, to 50mm,
                             to 25mm, etc



                                                                      Slug Flow

-  At low gas flow rates, liquid accumulates at the bottom of gas wells (liquid loading),
    and slug flow typically occurs in this region
          -  In a liquid column, rising Taylor gas bubbles are surrounded by a falling liquid film
                    -  Once a bubble constitutes ~ 75% of the cross-section of a liquid column,
                       the bubble becomes cylindrical
                              -  Cylindrical bubble forms a dome-shaped head and a flat stern
                              -  As the gas flowrate increases, the volume of Taylor bubble increases
                                        -  The bubble length increases but diameter stays the same
                                        -  Shape of head and stern of bubble remain unchanged
                                        -  Rise velocity (drift velocity) is independent of bubble length
                    -  Flow is characterized as discontinuous (intermittent)
                              -  Liquid slugs break the continuity of the gas phase
                                        -  Consecutive liquid slugs mix only by contact through the liquid film
                                                  -  Low axial mixing of the phases
                    -  Slug flow occurs at low to medium flow velocities
                              -  Velocity of Taylor gas bubble is the sum of two components
                                        -  Velocity of a gas bubble rising in still liquid (drift velocity)
                                                  -  Driven by buoyancy                                  
                                        -  Velocity of the liquid, messured at nose of the bubble
                    -  Energy transfer mechanism from carrier phase (gas) to carried phase (liquid)
                              -  Body forces
                                        -  Taylor bubble spans most of the tube diameter, and the
                                            buoyant bubble pushes on the liquid slug ahead of it
                                        -  The better the seal (thinner film), the more efficient the transfer
                    -  Energy losses
                              -  Losses are negligible inside the Taylor gas bubble
                                        -  Low shear forces, given low velocity
                                        -  Pressure in the bubble is uniform
                                                  -  Implies that ∆P over the length of the liquid film is zero
                              -  Most losses are incurred in the liquid slug
                                        -  Losses are due to dynamics of falling film (momentum transfer)
                                               -  Greatest losses occur at the tail of the bubble, where the
                                                      falling film liquid joins the liquid slug
                                                            -  Turbulence is induced in the liquid slug
                                                  -  Film thickness increases as bubble rise velocity increases
                                                            -  Increases flow losses (more recirculation)
                                        -  Shear losses of liquid on the tubing wall can be neglected
                    -  As the bubble velocity approaches zero, flow losses approach zero
                              -  Pressure gradient is then dominated by the gravity term

                                               Effect of Tubing Diameter on Slug Flow

-  Confinement of a bubble is a necessary condition to perform useful work (lifting liquid)
          -  A rising cap bubble in a lake only displaces water as the bubble rises
                    -  Potential energy is simply dissipated - no “useful work” is performed
          -  Confinement of rising bubbles in a tube results in work being performed
                    -  Liquid in a tube is lifted higher than the lake surface
                              -  Increases the potential energy of the liquid (classic air-lift pump)

-  Effects of surface tension when reducing the tubing diameter
          -  “As tube diameter is decreased below 20mm, the effects of surface tension on the
              dynamics of vertical slug flow become increasingly important.” (Zukoski, 1966)
          -  In air/ water systems, surface tension effects begin at ~ 20mm diameter tubing
                    -  Reduces the rise velocity of a Taylor bubble (drift velocity)
                    -  Surface tension effects increase at an increasing rate as diameter is reduced
                              -  The square of the diameter is in the denominator of the formula
                                  for the “surface tension number”, indicated exponential relationship
          -  In air/ water systems, surface tension effects “max out” at tube diameter of 6mm
                    -  Taylor bubble will not rise in a liquid column with a diameter under 6mm
                              -  Drift velocity of a Taylor bubble become zero (6mm and under)
          -  Liquid film thickness
                    -  With tube diameter of 20mm, the liquid film is > 25% of the cross-section
                              -  Greater film thickness is associated with a higher volume of liquid in
                                  falling film, increasing recirculation/turbulence (reducing efficiency)
                    -  As the tubing diameter is reduced below 20mm, the film becomes thinner,
                       occupying less and less of tubing cross-section area, isolating the liquid slugs
                              -  Nose of the Taylor bubble becomes more blunt, more plug-like
                    -  With a tubing diameter less than 6mm, the film layer is very thin
                              -  As defined, once such “Taylor Flow” is achieved, the film thickness
                                  accounts for less than 2% of the cross-section area of the tube
                                        -  The wall is covered by a thin liquid layer, and the gas bubbles
                                            slide over this “ lubricating” layer (Schwartz, 1986)

-  As tubing diameter decreases, it widens the range where the slug flow regime occurs
          -  Transition from bubble flow to slug flow occurs at lower gas flowrates
                    -  Bubbles coalesce more quickly in smaller diameter tubes
                              -  Reynolds number (turbulence) declines linearly with tubing diameter
                    -  To bridge the tube diameter, a smaller-sized bubble is required
                              -  Lower gas proportion at transition from bubble to slug flow
          -  Transition from slug flow to churn flow occurs at higher gas flowrates
                    -  Reynolds number declines linearly with tubing diameter
                              -  Offsets increase in capillary number with increasing velocity

                                                        Small-Diameter Airlift Pumps

“Two important effects become significant when the airlift tube diameter is below
    about 20mm.  The first is the increased importance of surface tension.  The second is
    decreased Reynolds number.” (Reinemann, 1989)
          -  Reinemann examined the effects of tube diameter on the hydrodynamics of airlift
              pumps in the range of tube diameters where surface tension effects are significant
                    -  Tested diameters from 3.18 to 19.1 mm, with a column height of 1.8 m
                    -  Efficiency was determined at different flow rates and submergence ratios
          -  It was determined that as tubing diameter is decreased below 20mm, the effects of
              surface tension act to increase optimal airlift efficiency and submergence ratio
                    -  Maximum attainable efficiency is reached at 6mm
                              -  Below 6mm, efficiency does not change with declining diameter

-  The charts below show results from two tubing diameters (6.35mm and 9.53mm)
          -  Efficiency vs. flowrate is shown at various submergence ratios
                    -  At low gas flowrates, the 6.35 mm diameter tube is more efficient
                              -  Note that the efficiency declines with any increase in the gas flowrate
                                 at all submergence ratios
                    -  At very low gas flowrates, the efficiency is zero for the 9.53 mm tubing
                              -  “Work is done by the expanding gas, and no useful work is being
                                  performed pumping the fluid.”  (Reinemann).

-  “It is instructive to examine the situation in which no frictional losses are included
    in theoretical predictions.  This is an excellent approximation to actual performance
    at low flow rates when frictional losses are small.”  (Reinemann)
          -  Frictional losses increase at an increasing rate with increasing velocity
                    -  Flow losses are near zero at low velocities
Pressure gradient is dominated by the gravity term                 
          - Taylor Flow structure in 6mm tube is intermittent, and film thickness is small,
             so there is no minimum “critical velocity” requirement for gas to lift liquid

-  Flow efficiency vs. tubing diameter
          -  As shown in Fig. 8, drift velocity is zero in tubes with diameters less than 7mm
                    -  No upward gas flow (driven by buoyancy), so no liquid flow
                    -  Gas phase is prevented from rising
                              -  Surface tension effects exceed buoyancy forces
          -  With diameters greater than 7mm, efficiency declines at an exponential rate
                    -  Most efficiency gains are attainable at 7mm to 10mm (the “sweet spot”)
                              -  Efficiency ranges from 83% (7mm) down to 58% (20mm)

                                                    Airlift Pumps with Step Geometry

-  An airlift pump with step geometry was tested for performance (Karimi, 2010)
          -  Step geometry is when a riser has a smaller diameter at the bottom than at the top
          -  Performance was tested in a 918mm riser with a submergence ratio of 0.6 (Fig. 5)
                    -  Ordinary airlift pump (“OALP”)
                              -  10mm diameter riser (same diameter from bottom to top)
                    -  Step airlift pump (“SALP”)
                              -  6mm diameter riser in bottom section of riser (first step)
                                        - Step at 200mm up riser (diameter increases from 6mm to 12mm)
                              -  12mm diameter riser in top section of riser (second step)
                    -  Performance is significantly improved using a step-geometry riser
                              -  At the same gas flow rate, liquid production rate is significantly higher
                                        -  The SALP is much more efficient per unit of input gas
                              -  Authors postulated that the reason SALP is more efficient is that slug
                                  flow is maintained in the upper part of the riser vs. churn in OALP
                                        -  Slug flow is a more efficient flow regime than churn flow

                                                         Tubing Performance Curve

-  Relationship between the pressure drop in gas well tubing and the flowrate
          -  Pressure drop up tubing has two components: hydrostatic head and flow losses
                    -  Hydrostatic head
                              -  “Accumulated liquid” in the column contributes to hydrostatic head
                                        -  Accumulation of liquid in bottom of the wellbore
                                        -  Accumulation of liquid up the wellbore (condensation region)
                              -  Liquid accumulates at low flowrates (left of the minimum ∆P value)
                                        -  Slug flow: flow slightly to left of minimum ∆P value on TPC
                                        -  Bubble flow: flow far to left of minimum ∆P value on TPC
                    -  Flow losses
                              -  Start at zero, and increase exponentially with increases in the flowrate
          -  TPC passes through a minimum value of ∆P near the middle of the curve
                    -  Increases in ∆P to right of minimum value are due to increases in flow losses
                    -  Increases in ∆P to left of minimum value due to increases in liquid holdup

-  Flow stability
          -  Flowrates are unstable to the left of minimum ∆P value
                    -  Low flowrates promote liquid accumulation
                              -  Insufficient gas flow velocity to evacuate all liquid inflow
                              -  Liquid accumulation results in flow velocity declining further
                                  (less ∆P), leading to more liquid accumulation
                                        -  Leads to increasing severity of slugging and longer slug cycle
          -  Flowrates are stable to the right of the minimum ∆P value
                    -  Steady-state flow with no accumulation of liquid
                    -  By design, gas wells are operated (a bit) to the right of minimum ∆P value
                              -  Matched to reservoir inflow performance (IPR) curve



                                                                    Velocity String

-  Conversion to a smaller-diameter of production tubing
          -  Results in a gas velocity sufficient to lift all liquid to surface, unloading the well
                    -  Returns well to steady state flow
          -  Physical mechanism responsible for success of a velocity string
                    -  Increase in flow velocity
                              -  Reduces cross-section area available for flow
                                   -  Higher ratio of volume to flow area, increasing flow velocity
                    -  Effect of reduced diameter on efficiency
                              -  Most velocity strings are from 3/4- to 1 ¼-inch in diameter
                                       -  Reduction from 2-inch diameter
                                             -  Improves efficiency by improving coherence of classic
                                                flow regimes (slug, churn and annular flow)
                                                       -  Reduced Reynolds Number (less turbulence)
                                             -  No meaningful benefits from surface tension effects
                                                       -  Effects only begin at under ~ 20 mm (4/5ths of inch)
-  Net effect
          -  Gas production increases
                    -  Accumulated liquid is expelled, so gas can flow at steady state
                    -  More energy is transferred from the carrier phase (gas) to the liquid
          -  Trade-off: maximum gas flow rate is reduced/ more limited
                    -  Chokes earlier


                                                                             Critical Velocity

-  Concept of a minimum flow velocity in gas wells needed to produce fluid at steady state
          -  If minimum not achieved, water accumulates in the wellbore, and the well will die
          -  Theory pioneered by Turner in 1969 (see formulas below)
                    -  Assumes annular flow regime: droplet entrainment, with falling film
                              -  Found that entrained droplet model best fit empirical test well data
                                        -  Formula assumed spherical-shaped droplets
                    -  Variables and coefficients were determined based on empirical data
                              -  High-pressure wells were used in sample
-  > 800 psi flowing WHP, and Reynolds number > 200,000
                              -  Upward adjustment factor of 20%
                              -  Predicted minimum flow velocity of 25 feet per second at wellhead
          -  Updated by Coleman for lower pressure wells
-  < 500 psi, and Reynolds number 1,000 to 100,000
                    -  Same phenomenological model as Turner
                              -  Same formula, but lower coefficient (no 20% upward adjustment)

          -  Theory updated again by Li (2004)
                    -  Revised theory of droplet shape (less spherical, so higher drag forces)
                    -  < 500 psi, and Reynolds number of 10,000 to 100,000
                    -  Predicts even lower critical velocity (~ one half predicted by Turner)




                                                            Multi-Channel Production String

-  High-strength polymer extrusion having many small-diameter “production tubes”
          -  Hung from the wellhead and extending down to the perforations
          -  Wells up to 5,000 feet deep can utilize low-cost polymer material
                    -  Costs $1.35 to $1.75 per foot, depending on capacity (extrusion diameter)
                    -  With more expensive material, possible to exceed 9,000 feet in depth
                           -  Compared to the performance of traditional production tubing,        
                                the liquid-lifting efficiency of an MCS increases with depth

 -  An MCS decouples decision of tubing diameter from production volume considerations
            -  Permits optimization of the liquid-lifting capability of the gas (carrier) phase
            -  First, the diameter of the MCS internal tubes is selected
                    -  Possible to manage the extent of energy transfer from gas to liquid
                    -  At low flowrates - small MCS tube diameters increase energy transfer
                           -  Emphasis on maximizing flow efficiency at low flow velocity
                    -  At high flowrates - larger MCS diameters will reduce friction/ choking, while
                       still having a much lower minimum critical velocity vs. conventional tubing
                           -  Maintain gas flow velocity within efficient range  
            -  Second, the number of small-diameter MCS tubes is selected
                 -  Number of tubes is based on the potential gas flowrate of reservoir
                      -  Match aggregate flow through all tubes with inflow rate
            -  Third, the design of the MCS extrusion may vary up the well
                    -  Threaded connectors can link several MCS segments up the well
                    -  MCS extrusion design near the bottom of the well
                              -  More internal MCS tubes, each with relatively small diameter
                                  -  Emphasize reducing/ minimizing “critical velocity” 
                    -  MCS extrusion design near the top of the well
                              -  Flow velocity at top is higher due to gas expansion
                                        -  Gas volume doubles each time the pressure declines by half
                                        -  At higher flow velocities, concern becomes
                                            excessive friction, not minimum critical velocity
                                             -  Outside diameter of MCS conduit may be increased
                                                      -  Provide more cross section available for flow
                                             -  Or fewer MCS tubes, each with larger diameter

        -  Pressure ratio (BHP/WHP)
            -  In a conventional gas well, the pressure ratio is very small (often ~ 1.1x)
​                   -  Low pressure drop given low flow resistance in 2-inch tubing
            -  In an MCS string, pressure ratio can be relatively high (3 to 5x)
                   -  Indicates greater utilization of the expansion energy of the gas phase
                   -  Energy wasted at surface choke can instead be utilized to lift liquid


                                                                             Pilot Gas Well MCS Installation

-  A conventional tight gas well 1,930’ down to the perforations
          -  Prior to MCS installation averaged 15 MCF of gas and 2 barrels of water per day
                   -  Two-week slugging cycle, with soap sticks to assist kickoff
          -  Well was liquid loaded prior to MCS installation
                    -  Water level at 360’ above perforations (8 barrels)
                    -  Shut in pressure at surface: 2 3/8-inch tubing (280#) and casing (290#)

-  Installed Multi-Channel Production String in the well   
          -  Installation: required about 3 hours by 2 men with a spooler truck
          -  Materials cost: $1.75 per foot for MCS extrusion, and $500 for surface completion
          -  Well kicked off within 20 hours after installation, without stimulation or assistance
          -  All water accumulated in the wellbore was produced within 3 days
                   -  Water was filled with debris… “It was like cleaning out a rat hole”
                   -  Gas production rate became fully steady-state
                           -  Exceptionally smooth line on the gas production chart
                   -  Pressure steady: casing (250#) and multi-channel production string (70#)
                           -  Differential of 14 against line pressure of 55#

-  Gas production volume increased after the MCS installation
          -  Produced 20 MCF and 2.7 barrels of water for ~ 2 months post MCS installation
          -  Then, production increased to ~ 21 MCF and stayed flat
                    -  Production level maintained for over 2 years, requiring no maintenance
                    -  Fundamental improvement in production decline curve (more flat)
          -  Benefits to near wellbore region using MCS string
                    -  MCS continuously evacuates all liquid at its entrance
                              -  Less liquid in bottom-hole area improves reservoir permeability to gas
                              -  No pressure cycling, so no liquid flow reversals in reservoir                                   
                    -  Less disruption to reservoir integrity in near wellbore region



                                                              Flow Characteristics up MCS String

-  Surface quality benefits of MCS polymer extrusion vs. steel tubing
          -  Friction
                    -  Surface roughness of “MCS tubes” is > 30x less than steel tubing
          -  Solids deposition
                    -  Adhesion of solids on polymers is inhibited vs. steel
                              -  MCS polymer surface does not provide a cold nucleation point
                              -  Other deposition processes are facilitated by steel (not by polymer)
                                        -  Cathodic, magnetic, molecular linking/bridging, etc.
                    -  Polymer is easier to treat with chemicals vs. steel
                              -  Deposits adhere less strongly to polymer and are removed more easily
                    -  Steady state flow in MCS tubes inhibits deposition
                              -  No stagnant or intermittent flow conditions to facilitate deposition
                              -  Shear stress of flow on MCS tubing walls provides scouring effect
                                        -  In test 1,930’ tight gas well, there was no plugging, even with
                                            water salinates in excess of 130,000 ppm NaCl equivalent

-  Production of sand and coal fines
          -  Particulates can damage pumps and accumulate to form blockages
                    -  Sand is especially abrasive for pumps, leading to regular overhauls
                    -  Pumps facilitate agglomeration/ clumping of coal fines
                              -  Coal fines have a small positive electric charge
                              -  Metal to metal contact of pumps creates negative ions
                                        -  Coal fines becomes negatively charged, leading to agglomeration
          -  MCS produces to the surface sand and coal fines together with the liquid
                   -  Particulates have higher form drag vs. liquid, especially in small tubes
                             -  Low critical velocity in small diameter tubes
                    -  No stagnant conditions inside MCS to facilitate accumulation/ agglomeration
                              -  Steady-state flow is constant in an MCS (misty annular flow)
                    - MCS does not promote agglomeration of coal fines
                              -  No production of negative ions, so no attraction between coal fines
-  Wellbore is continuously evacuated of all liquid near MCS entrance
          -  MCS (unlike pumps) has no requirement of net positive suction head (NPSH)
                    -  Pumps cavitate without required positive inlet pressure
                              -  Equivalent to a penalty of pressure loss
          -  Bottom-hole is maintained nearly dry at perforations with an MCS 
                    -  Improves reservoir permeability to gas near perforations

                                                Minimum Critical Flowrate in an MCS
-  Minimum flowrate is needed to continuously remove all liquid from bottom of a gas well
          -  Conventional model: annular flow with entrained droplets (misty annular flow)
                    -  Flow velocity is the primary determinant of achieving steady-state flow
                    -  Given gas expansion, flow velocity is lowest at bottom of the well
                              -  Therefore, velocity at bottom is the determinant of steady-state flow

-  Minimum flowrate in an MCS during kick-off
          -  Kick-off process
                    -  MCS is installed in a gas well loaded with water (no packer)
                    -  Water fills MCS tubes, equalizing its height with the level in casing/ tubing
                    -  Wellhead is completed, and only MCS string is left open to atmosphere
                    -  Gas enters through perforations, pressurizing the casing (no flow up MCS)
                    -  Rising gas is trapped/ concentrated in a space just below the MCS entrance
                              -  Device facilitates gas phase separation and containment
                    -  Given no-flow conditions in the MCS, and equivalent pressure just inside the
                       MCS entrance and the entrapped gas just below, (heavier) water in the MCS
                        tubes falls/ leaks into entrapped gas space below, and gas enters MCS tubes
                              -  Tube diameter must be large enough to permit a bubble to rise,
                                 so that the liquid will fall (> 6mm in air/ water systems)
                                    -  Buoyancy forces must exceed surface tension effects
                              -  Gas-entrapped space is resupplied with gas rising from perforations
                    -  Water leaks down/ out of MCS, and hydrostatic head declines in MCS
                    -  Eventually, enough liquid leaks out of the small MCS tubes to reduce
                       the hydrostatic head sufficiently to initiate upward flow in the MCS
                              -  Clean-out stage (solids are produced along with the liquid)
                                    -  Period of low gas flow volume and high liquid production
                                          -  Slug flow regime until water is evacuated
                                                     -  Highly efficient (negligible friction at low velocity)
                                                     -  Minimum critical flow velocity approaches zero
                                    -  Pilot gas well took almost 3 days to evacuate > 360 feet of water

-  Minimum critical flowrate in an MCS during the steady-state flow stage 
         -  Misty annular flow regime  
                    -  All water above entrance to MCS has been evacuated
                    -  Almost no hydrostatic contribution to the pressure gradient (∆P)
                              -  In 1,930’ test gas well, estimated amount of water in each column
                                 is less than 1 foot (130 bbl/MMcf of water)
                              -  Well projected to produce down to very low flowrates

                                                Modeling the J-Curve of an MCS String

-  First, model the J-curve for one “small diameter” production tube within the MCS
          -  Calculate the same as any J-curve
                  -  Determine the friction vs. flowrate curve (single MCS tube)
                              -  No friction at zero flowrate
                              -  Friction grows exponentially with increasing flowrate
                                        -  Friction is increasingly exponential with reductions in diameter
                  -  Determine the liquid buildup vs. flowrate curve (single MCS tube)
                              -  At zero flowrate, hydrostatic head is at its maximum
                              -  Kick-off stage
                                        -  Slug flow regime up MCS string extending from the bottom
                                             -  Extremely low gas flowrate while accumulated liquid
                                                leaks down into space with accumulated gas
                                             -  With time, the declining hydrostatic head reduces ∆P
                                             -  Slug flow continues until all accumulated liquid above
                                                MCS entrance is evacuated (leaks down or produced up)
                             -  Steady-state flow stage (after accumulated liquid is evacuated)
                                        -  Wispy annular flow is established from bottom to top
                                        -  Fully steady-state flow, with GLR constant
                 -  Then, combine the two curves (friction + hydrostatic head)

-  Second, construct the J-curve for multiple MCS tubes (see chart below on left)
          -  Simple multiplication process (multiple of the J-curve of a single tube)
                    - Curve stretches out on x-axis (flowrate), but y-axis values (∆P) stay the same
                              -  The ∆P at the minimum flowrate is the same for any MCS string
                                  (any # of internal tubes) when all internal tube diameters are the same

                                                              Surface Choke

-  Traditional surface choke constricts flow at the wellhead, reducing the flowrate
          -  All fluid flows through a small diameter orifice
                    -  Orifice diameter can be changed to alter the flowrate
                              -  Typically 1/8th to ¾ inch in diameter
-  Surface choke provides several critical functions
          -  Allows control of pressure at wellhead
                    -  Improves safety downstream
          -  Limits the flowrate in gas wells
                    -  Reduces velocity of the gas flowing up the well
                              -  Controlled to limit erosion of tubing and wellhead equipment
                    -  Reduces the volume of fluid entering the well
                              -  Reduces the amount of sand entering the well
                              -  Reduces water and gas coning
          -  Isolates pressure fluctuations downstream from affecting well performance
                    -  Flow must be critical at choke (sonic barrier)
-  Surface choke dissipates energy
          -  Potential energy of the fluid (pressure) is reduced, but no useful work is done
                    -  Potential energy is wasted
-  MCS performs the functions of a surface choke, but the potential energy is utilized
          -  MCS also constricts the flow, but utilizes a different length/ diameter arrangement
                    -  Traditional surface choke has a small diameter and a very small axial length
                    -  MCS has a much greater length, and larger aggregate cross-section for flow
                               -  Extremely high L / D ratio isolates flow effects  
-  MCS provides the same benefits of limiting the flowrate
                    -  Improves safety
                    -  Reduces the velocity of the fluid up the well
                    -  Reduces the volume of fluid entering the well
          -  MCS also isolates upstream well performance from downstream fluctuations
                    -  Different mechanism of isolation
                              -  Traditional surface choke uses barrier of critical (sonic) velocity
                              -  MCS isolation depends on damping effect
                                        -  Very long tubing length and small diameter of each channel
                                                  -  Extremely high L / D ratio
          -  Useful work is performed in the flow through the MCS “choke”
                    -  Liquid is lifted along with the produced gas
                    -  Increases available pressure ratio in flowing gas well from ~1.1 up to ~3-5
                              -  Indicative of available power to lift liquid
          -  May be employed in conjunction with a traditional surface choke
                    -  MCS “choke” acts like a surface pre-choke with a fixed diameter orifice
                    -  Traditional surface choke provides variable control of flowrate