Flow losses are a function of flow velocity and tubing diameter. At zero velocity, there are no flow losses. As flow velocity increases, flow losses increase exponentially, eventually leading to a choking condition where the flowrate plateaus. And smaller diameter tubing is associated with higher flow losses at the same velocity and becoming choked at a lower flowrate.
Accumulated liquid in the well column contributes to the hydrostatic head. Liquids collect in the well bottom, and sometimes water vapor condenses up the well (typically in the aquifer region), adding to the pressure drop. As can be seen in the TPC chart above, hydrostatic head constitutes all of the pressure drop at zero flowrate, and declines gradually as the flowrate increases.
The TPC passes through a minimum value (delta P) near the middle of
the curve on the flowrate axis. Increases in value to the left are due to increases in liquid holdup (hydrostatic head), and increases to the right are due to increases in flow losses ("friction"). Flowrates are unstable (intermittent) to the left of the minimum TPC value, where liquid accumulation leads to lower flow velocities and even more liquid accumulation, a negative feedback cycle. Flowrates are stable to the right of the minimum TPC value, where higher gas velocities characteristic of annular flow carry the liquid with it as it is produced (steady state flow). In practice, gas wells are produced a bit to the right of the TPC minimum value to maintain flow stability.
Tubing Performance Curve - MCS production Tubing
The following is an attempt to model the TPC curve for MCS production tubing. First, the TPC curve will be calculated for a single MCS passageway, and then this TPC curve will be used to extrapolate multiple-tube performance.
First is the flow losses vs. flowrate component. Universally, flow losses are zero at zero flowrate and increase exponentially with increases in flowrate. But with MCS passageways being so small in diameter (7mm
vs. 2 inches), the increase in flow losses occur at much, much lower flow velocities. When the flow velocity increases to ~20 to 25 feet per second, flow losses become excessive (choking region, i.e. a flowrate plateau).
With respect to the MCS hydrostatic head component, MCS
passageways have two distinct regions of flow performance. To the
right of the TPC minimum value, it is similar to that of conventional
tubing (small amount of liquid holdup, given steady state flow).
But to the left of the TPC minimum value, the
character of the hydrostatic head component within the small MCS passageways is very different from that of conventional production tubing. This is due to the different underlying gas-liquid flow pattern in 7mm vs. 2-inch tubing. With a flow diameter of 7mm, it is easy for the liquid to bridge the entire flow area, capable of forming the capillary bubble flow pattern (intermittent layers of gas pockets and liquid slugs). This flow structure is, 1) highly efficient, with little slippage of the gas past liquid, and 2) forms at low flow velocities and over an extremely high range of gas-liquid ratios. And
once all of the standing liquid has been "bailed out" during capillary bubble flow (intermittent flow), steady state flow begins.
It is important to note that this switch from intermittent flow to steady state flow occurs over a very short range of flowrates (not gradual like
for 2-inch ID tubing) and at a very low flowrate. What this means in practice is that the "bailing out" of standing liquid is a discrete phase of up to a day or two, with no meaningful volume of gas produced... and then like flipping a switch, steady state flow initiates, flowing indefinitely.
Extrapolating the TPC curve of one MCS passageway to multiple MCS passageways is relatively straight forward. Flowing double the volume of gas through two same-diameter MCS passageways results in a similarly shaped TPC curve, only stretched out on flowrate axis by a factor of two.
To summarize, the shape of the Tubing Performance Curve for MCS production tubing is different vs. that of traditional 2-inch tubing.
Liquid is unloaded at much lower gas flowrates in MCS production tubing, and so the
minimum value on the TPC curve occurs at a much lower flowrate. Also, given the higher efficiency of the gas phase in lifting liquid within 7mm passageways, the
pressure at the minimum value of the TPC curve is substantially lower. Together, t
his results in a
TPC curve with a minima that hugs closely to the origin, suggesting a significantly higher ultimate recovery of gas from the reservoir vs. conventional production tubing or velocity strings.
Also, by flowing produced fluids through MCS production tubing having multiple same-diameter passageways, flow volume becomes in a way “digitized”. Each MCS passageway is a discrete flowpath. Therefore, once intermittent flow eventually does start to occur in the MCS passageways as a whole, individual passageways can be closed off one-by-one to match reservoir influx with the optimum cross section available for flow to maintain steady state flow.