DROPPED BHA MAY INDUCE FORMATION BREAKDOWN FROM PRESSURE SURGE

April 24, 1995
Roberto Maglione, Gualtiero Ferrario, Angelo Calderoni Agip SpA Milan A calculation method helps determine the dynamic gradient when a parted drillstring falls to the bottom of a well, possibly inducing formation breakdown. When a drillstring parts above a critical depth, dropping the bottom hole assembly (BHA), formation breakdown can occur from the falling fish. The equations help determine a critical drop velocity, which indicates if the BHA may undergo plastic deformation as it hits
Roberto Maglione, Gualtiero Ferrario, Angelo CalderoniAgip SpA Milan

A calculation method helps determine the dynamic gradient when a parted drillstring falls to the bottom of a well, possibly inducing formation breakdown.

When a drillstring parts above a critical depth, dropping the bottom hole assembly (BHA), formation breakdown can occur from the falling fish.

The equations help determine a critical drop velocity, which indicates if the BHA may undergo plastic deformation as it hits bottom.

Understanding the critical drop velocity and critical depth for a dropping fish could help better prepare drilling crews during fishing operations and possible well control operations should other problems develop.

A formation breakdown could put the well into unsafe conditions, if mud losses decrease the hydrostatic head and lead to influx of water, gas, or oil. Controlling the well under these circumstances can become complicated. In more severe cases, formation breakdown could lead to an internal, uncontrollable blowout.

The downhole pressure variations are a function of the free fall of the fish from a given depth. In this study, the breakdown of the formation was investigated considering the fracture gradient and neglecting the capacity of the formation to absorb, elastically or plastically, energy from the dropped fish.

Two main criteria had to be taken into consideration: the free drop of the fish in a fluid and surge effects. The equations were programmed on a computer for easier analysis, and the results are displayed in the form of a fracture map for the well. Two base cases have been studied, one a shallow well and the other an ultradeep well.

A fracture map for a well gives the depth limit at which a falling fish (parted drillstring) induces a downhole pressure able to exceed the formation breakdown gradient. The main parameters influencing this phenomenon are the cross sectional area and length of the parted string, the hole diameter, the mud rheology, the mud density and the formation breakdown gradient.

The analytical model takes into account the following:

  • The vertical free fall of the parted string, which is immersed in drilling fluid and contained in a definite volume determined by the well geometrical shape and by the fall height

  • The surge pressure occurring on the well bore during the fall.

    Some assumptions have been made to simplify the problem. In particular, with regard to surge pressure calculations, two different approaches are available in the drilling literature:

  • Assume the fluid levels in the annulus and pipe bore are equal at all times. The distribution of fluid displaced by the drillstring is therefore dependent on the relative cross sectional areas of annulus and pipe bore.

  • Assume the pipe bore and the annulus behave as a U-tube. In this case, the sum of hydrostatic and frictional pressures in the pipe bore and through the bit should equal the sum of hydrostatic and frictional pressures in the annulus. Both represent the pressure prevailing immediately below the bit.

In this study, the first method was used. In fact, both the fluid velocity (at the exit of the top of the parted string as it drops) in the annular and in the circular sections are actually the same at all times because there is a constant hydrostatic pressure above this point.

ANALYTICAL MODEL

The following are the basic assumptions used in the development of the analytical model:

  • Vertical well

  • Flow in concentric annulus

  • Newtonian fluid and constant properties

  • Incompressible fluid

  • One-dimensional flow

  • Isothermal flow.

Moreover, the friction force from the stabilizers (on the parted string) on the wall of the well bore has been neglected. The forces acting on the parted string, considered as a cylinder with different sections and lengths, result from the buoyancy, gravity, and friction forces. At all times, the equilibrium of these forces can be written as Equation 1(62686 bytes), or in explicit form as Equation 2.(62686 bytes)

The terms in Equation 2 (62686 bytes) can be expressed as the BHA weight (Equation 3)(62686 bytes), the buoyancy effect (Equation 4)(62868 bytes), the drag force (Equation 5)(62686 bytes), the force from nozzle pressure drop (Equations 6 and 7)(62686 bytes), the force from circular pressure drop (Equation 8)(62686 bytes), and the force from annular pressure drop (Equations 9 and 10)(62686 bytes).

In Equation 5(62686 bytes) for the drag force, the term A is the drag force constant dependent on well parameters.

To calculate the pressure drop at the bit nozzles in terms of downhole force, the pump rate in the circular section must be determined. The assumptions are that the parted string is open-ended and that the clinging constant (k) is equal for each annular section. This circulation rate has to be constant in all circular sections (Equation 6)(62686 bytes). Therefore, the force R2 can be expressed as Equation 7,(62686 bytes) in which B is the nozzle pressure drop constant that depends on well parameters.

The friction force in the circular section can be written as Equation 8(62686 bytes), in which the laminar flow constant C1 and the turbulent flow constant C2 depend on well parameters.

The pump rate passing in a section is given by Equation 9(62686 bytes). The friction force in the annular section can be written as Equation 10(62686 bytes), in which the laminar flow constant D1 and the turbulent flow constant D2 depend on well parameters.

MOTION PARAMETERS

Substituting the expression of the forces above into Equations 1 and 2 (62686 bytes) yields a differential equation (Equation 11)(62686 bytes). The expression of space z(t), velocity v(t), and acceleration a(t) are obtained for the dropping BHA (Equations 12-14,(62686 bytes) respectively). 1 through 7 depend on well constants A through D2.

The limit drop velocity of the BHA can be directly obtained from Equation 2,)62686 bytes) considering a = 0 for the steady condition and neglecting the contribution from laminar flow that occurs at the beginning of motion for a very short time. The velocity can therefore be written as Equation 15.(62686 bytes)

The impact energy of the parted string when it touches the bottom of the well is given by the kinetic energy equation (Equation 16)(62686 bytes). The kinetic energy absorbed by the parted string (without plastic deformation) is commonly approximated as Equation 17(62686 bytes). Neglecting the kinetic energy that could be absorbed by the formation on bottom, a critical drop velocity for the parted string can be derived as Equation 18.(62686 bytes)

This Vlim,c is the value above which plastic deformation can be observed in terms of shortening (s). The equivalent force (Fe), that is subjected to the parted string at the impact, and the relative plastic deformation (s) can be expressed as Equations 19 and 20.(62686 bytes)

For steel commonly used in drill pipe and drill collars (that is, AISI 4145 H with s = 0.5sy), Equations 18-20(62686 bytes) can be rewritten as Equations 21-23,(62686 bytes) respectively.

The shortening can be evaluated and calculated only if the limit drop velocity of the fish exceeds the critical drop velocity (Vlim 9.5 m/s).

FRACTURE MAPS

A vertical shallow well (Well A) located in the Po Valley has been used in a case study to analyze the application of these equations. This well is 2,300-m deep and was drilled in two sections, 12 1/4 in. and 8 1/2 in. in diameter.

It has been assumed that the parted BHA resulted from a connection failure.

The corresponding limit dropping depth has been evaluated for each well depth during the drilling process. Fig. 1 (41105 bytes) shows pore, mud, and fracture gradients for Well A. Table 1 (41156 bytes) lists all well data needed for the calculation as well as the results.

Fig. 2 (35706 bytes) shows the fracture map of Well A and the relevant derived data. This figure also shows that, in both the 12 1/4-in. and 8 1/2-in. sections, the drop of the parted string is almost always critical because of the low safety margin. In any case, it becomes very critical on bottom.

ULTRADEEP WELL

An ultradeep vertical well (Well B) located near the Alps in northern Italy was used for a second case study. The well has a total depth of 5,900 m and had hole (bit) sizes of 23 in., 17 1/2 in., 12 1/4 in., and 8 1/2 in.

Fig. 3 (40346 bytes) shows pore, mud, and fracture gradients of the drilled formations. Table 2 (62798 bytes) lists all well data needed for the calculation and the results.

Fig. 4 (40403 bytes) shows the well's fracture map with the values of the critical parameters as the parted BHA is dropping. The fracture map shows that the 17 1/2-in. and 12 1/4-in. hole sections are critical and have a low safety margin. The 23-in. and 8 1/2-in, hole sections are less critical and have a higher safety margin and, therefore, the chance of fracturing the formation is very small (even on bottom) in each of these two sections.

EXAMPLE

For an example calculation, consider that Well B is drilled with an 8 1/2-in. hole section to total depth (TD) at 5,900 m and the string is pulled out of the hole. The possibility of fracturing the formation when a parted string (BHA) falls from a dropping depth (PSDD) of 3,000 m, 4,500 m, 5,500 m, and 5,700 m down to TD will be evaluated. Table 3 (11077 bytes) and Fig. 5 (55146 bytes) show the results of this investigation.

Table 3 (11077 bytes) shows pressure gradients at the bottom of the dropping string, critical dropping velocity, and total time to reach TD. Fig. 6 (43953 bytes) shows the trend of the dropping parameters (distance, velocity, and acceleration) of the parted string against the time.

The results can be summarized as follows for each depth:

  • PSDD = 3,000 m: The drop of the BHA from this depth would always induce formation breakdown from the 9 5/8-in. casing shoe to 5,560 m (critical dropping depth). In this case, the parted BHA would not be subjected to plastic deformation as the critical velocity would not be reached. Vd,lim = 7.98 m/sec, which is smaller than the critical velocity, Vlim,c = 9.5 m/sec

  • PSDD = 4,500 m: The formation would fracture just below the 9/s-in. casing shoe (4,520 m) up to the critical dropping depth (5,560 m). The BHA is not subjected to plastic deformation.

  • PSDD = 5,500 m: Neither formation breakdown nor plastic deformation would occur when the parted BHA falls from this depth.

  • PSDD = 5,700 m: Neither formation breakdown nor plastic deformation would occur.

As these examples show, when a string parts above the critical depth (5,560 m), breakdown of the formation can occur, resulting in drilling fluid losses and influx of hydrocarbons.

RESULTS

A method to calculate the dynamic gradient when a parted string is dropping to the bottom of a well has been developed. The examined cases have shown that formation breakdown from a parted drillstring falling and hitting the bottom of a well is not an event of negligible probability.

A critical drop velocity has been obtained. This value depends only on the characteristics of the steel of the parted string, and above which the steel, as it hits the hole bottom, endures a plastic deformation.

The dynamic gradient is strongly affected by the well and string geometries, mud weight, and the fracture gradient of the drilled formations. The gradient induced by the parted string when it is dropping must be calculated well-by-well, and the breakdown of the formation must be checked case-by-case.

ACKNOWLEDGMENT

The authors wish to thank Agip SpA for permission to publish this article.

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