2.1 Cover

Cover section is integrated by basic information of the well, such as name, number, classification, objectives, and geographic coordinates of the well.

These data are part of the design or user’s guide used by Petróleos Mexicanos for each of its drilling projects, which is considered a standard in the presentation of projects for service companies. Likewise, this section is complemented by a subsection that welcomes the user and briefly describes the content of the software and its procedures or hydraulic methods, in addition to indicating the technical literature used for its development.

2.2 Hydraulics I

Hydraulics I section is mainly developed by the methodology described by Petróleos Mexicanos (Pemex), [¹¹, ¹², ¹³]. Due to the experience in the field and in trainings by active personnel in the area of oil well drilling, all the above, is integrated as shown in the flow chart shown in Figure 1.

Fig. 1 Drilling fluids Hydraulics I diagram 

Hydraulics I calculations require entering casing and drillstring information such as initial and final lengths (Li and Lf), inside and outside diameters (Do and Di), the grade and type of pipe in terms of its function (drill collar, heavy weight and drill pipe) and according to its strength (yield strength and tensile strength R).

In this regard, the typical grades, from lowest to highest strength, are E, X, G and S. This information allows generating the mechanical condition.

Once the mechanical state is appropriate, the program requests information on: i) The drilling fluid: density (ρf), yield point (σy), gel stress (G) and plastic, Marsh funnel and apparent viscosities (G) (μp, μe and μa), ii) Pump data: piston diameter (Dp), stroke length (Lp), volumetric efficiency (η), the pump operating cost (Q), iii) Cuttings data: length (Lr), diameter (Dr) and thickness (ϵr). With this new information the length of the tools is determined. The program comprises the following three cases depending on the pipe configuration:

where Lag, LDC and LHW are the lengths of the open hole, drill collar pipe and heavy weight pipe, respectively. The program then evaluates the drillstring design.

In general, the drillstring is composed of three types of pipes: drill collar, heavy weight and drill pipe. In particular, drill pipe has two subtypes: new pipe and (premium) used pipe. The calculation procedure determines the design of the drillstring and casing.

From this design, the number of sections, the annular volume (Va), the interior volume of the drillstring (Vi), the internal pressure drops of the string and in the annular volume ΔPi and ΔPa and the fluid velocities in the annular space and optimal (va and vo).

Furthermore, the adjusted weight (Wadj), bit pressure drop (ΔPb) and nozzle variables, such as nozzle diameter (Dt), fluid velocity at the nozzle outlet (vt), hydraulic impact and hydraulic factor (IH and FH), cuttings upward velocity (vr), among other variables and parameters, are estimated.

2.3 Hydraulics II

Similarly, the Hydraulics II section is based on a combination of the methodologies described in [⁴]. Field experience and training material from international companies, which can be found in the flow chart in Figure 2.

Fig. 2 Drilling fluids Hydraulics II diagram 

2.4 Rheological Models

Finally, the section Rheological Models is integrated by the results of the Fann viscometer test with which rheology values are calculated for low and high shear rate using the Bingham plastic and exponential law models [⁶].

Drilling fluid hydraulics refers to the fluid that performs a path that starts its displacement by means of mud pumps, which can be duplex or triplex, which are considered the heart of the circulatory system and that concludes in the settlement dam.

For the realization of the program, it was necessary to know the diagram or fluid circulation circuit during the drilling or circulation stages, as shown in Figure 4. The flow diagram of the calculation processes allows to identify the sections and the sequence of the programming, which have the following order:

Fig. 3 Software cover page with user data and well location 

Fig. 4 Drilling fluid circulation diagram 

In the applied hydraulics calculation procedure, the flow rate and string consistency parameters (ns and ks) are estimated, where the former describes the degree of shear thinning of a fluid and is dimensionless, depends on the viscosifier quality and is controlled with chemical thinners.

On the other hand, the consistency index is considered as plastic viscosity, either by an increase in the concentration of solids or a decrease in the particle size.

Its control is achieved with mechanical solids control and dilution equipment. Additionally, these indices are also calculated for the annular space, denoted as na and ka respectively.

Additionally, the calculations of average propagation velocity, effective viscosity, Reynolds number, Fanning friction factor and pressure loss are determined for each of the drillstring and annular space interior volumes generated from the mechanical state design.

The friction factor is determined by considering the value of the Reynolds number (Re).

Depending on whether the flow regime is predominantly laminar or turbulent, the friction factor (Ff) is calculated by: For the case of predominantly laminar flow (Re<2100):

where n was previously determined for the inner string volume and annular space.

The calculations in the Complementary Hydraulic Calculations section correspond to drilling optimization, i.e., estimating a penetration rate according to bit performance [⁴], since among the many factors that can modify it are, for example:

Bit size, type and characteristics, type and concentration of solids in the formation, and bit hydraulics. However, the latter can be optimized by controlling hydraulic power and nozzle velocity.

Application Examples

To demonstrate the capabilities of the software, two illustrative examples of oil well drilling have been selected. First, a calculation procedure using the national methodology and, subsequently, an exercise developed under the API methodology.

Introduction Section and Description of Hydraulics

Figure 3 corresponds to the front page of the software, which requests basic information from the design guide, in order to know the name, number, location and objective of the well, as well as the name of the technician or design engineer.

To perform the first hydraulic calculations, it is required to enter a set of data whose information is classified into seven elements: casing, borehole, drillstring, pump, mud properties, nozzles and cuttings.

Table 1 provides the necessary information to exemplify the use of this tool using national petroleum engineering methods and procedures.

Technical Data and Mechanical State Section

Figure 5 corresponds to the input of technical data of the casing pipes, drillstring, mud pumps, bits, solids/cuttings and the drilling fluid whose first result corresponds to the generation of the mechanical state, in which it can be identified the number of annular spaces both in the hole section and in the casing pipes.

Fig. 5 Data entry and mechanical state section 

The drillstring is outlined with a color code: the blue color is the drill collar, the gray color is the heavy weight, and the orange, green and brown colors correspond to the drill pipes in the order Tp1, Tp2 and Tp3, respectively.

It is important that the design engineer or technician corroborate the MS schematic in this section as it determines the volume of drilling fluids inside the string and the corresponding hole sections, casing pipes, and drillstring tools.

Hydraulics I Section

Figure 6 begins with the evaluation of the drill pipes (Tp), the pull margin, the flotation factor, and the weight of the floating drillstring.

Fig. 6 Results of: string design, annular and optimal velocity, interior volume, circulation times and system pressure 

Subsequently, the calculations according to the MS design are obtained, such as: hole-string annular volumetry, internal volume of each of the tools that make up the drillstring, expenses and circulation times, annular and optimal speeds, speed and area of nozzles, internal pressure in the drillstring, hydraulic parameters, pressure in annular intervals, transport of cuttings, among others.

Each of the previous points has its respective physical units and four decimal places of precision, as shown in Table 2.

Accurate estimation of pressure drop is important for the design of the drillstring, nozzles and for optimizing fluid circulations, as well as identifying drilling problems such as flushing or clogging of the bit nozzles [²].

Hydraulics II Section

To illustrate the use of the Hydraulics II Section, referring to the hydraulic methodology established in [⁶], the data will be entered as shown in Figure 7.

Fig. 7 Hydraulics II data entry section 

This methodology is used by transnational oil companies, the information indicated in Table 3 is required. The exercise used corresponds to the example of the API manual.

For this procedure it is required to know the results of the Fann viscometer tests and the value of the total pressure of the surface system, and to identify the corresponding case of the types of surface connections with which the drilling equipment is operating.

Figure 7 right, schematizes the mechanical state according to the data of the various casing pipes and tools that make up the drillstring. Figure 8 shows the solution of the exercise.

Fig. 8 Determination of coefficients 

Figure 8 corresponds to the results of the applied hydraulics operations, where initially the readings are determined at different rotational speeds of the viscometer, i.e. 600, 300, 100, and 3 rpm, where the lowest speed corresponds to a low shear stress.

From these data, the flow and consistency indices of both the string and the annular space (ns, ks, na y ka) are calculated.

Once the type of surface connection is identified, it is essential to know that it is integrated by the vertical pipe, the kelly device hose, swivel joint and the kelly ”traveling rotary”; but as there is no standard value for the traveling rotary it is important to know the geometry of each of them, for example, the vertical pipe and hose measure approximately 86 ft in length, with an inside diameter of 3 or 3.8 in and the S-hose is different for each rig, giving a total of four connection cases, as reported in the API manual [⁶]. For this exercise, Table 3 uses case 3 as stated in the manual.

The resulting hydraulic calculations are summarized in Table 4. After the mechanical state is generated, the Fann viscometer readings are entered to determine the n and k parameters for the string and for the annular space.

Finally, to complete the hydraulic design of the well, and regardless of the number of sections and the type of pipe to be used, it is essential to perform complementary calculations, which are summarized in Table 5.

Rheological Models Section

Figure 9 corresponds to the Rheological Models Section, which allow describing the relationship between shear stress and shear velocity. Most drilling fluids are non-Newtonian fluids, which is why Newton’s viscosity law or model does not describe their flow behavior. For this program, the Bingham plastic and exponential law models were implemented.

Fig. 9 Shear rate and shear stress calculations 

In recent years, the Bingham plastic flow model has been one of the most widely used to describe the flow characteristics of drilling fluids; however, this model is characterized by requiring a finite force to initiate the flow to subsequently develop a constant viscosity as the shear rate increases.

The curve or profile of a typical or conventional fluid is obtained from the rotary viscometer data, where this curve does not pass through the origin point, as shown in the graphs in Figure 9 and Figure 11, between shear rate and shear stress.

Fig. 10 Exponential law rheological model 

Fig. 11 Flow diagram of Newtonian and typical mud. Adapted from API Energy Handbook (2001) 

In Figure 10, the exponential law model does not assume that there is a linear relationship between shear stress and shear rate; however, for fluids obeying the exponential law, its curve starts from the origin.

In this model it is confirmed that the shear rate varies according to the change in shear stress. The Bingham rheological and exponential law models are among the most used and important for the determination of pressure loss in the drilling system [¹⁶].

Finally, for the Hydraulics II section, the value of na defines the flow profile formed in the annular space (Figure 12); i.e., na must have a value close to zero for its profile to be flat, which is considered ideal for the transport of cuttings towards the surface.

Fig. 12 Effect of Exponential Law index n on velocity profile. Adapted from API Energy Handbook (2001) 

Nevertheless, if the value of na is very close to 1, the velocity profile will be very steep in the center, resulting in cuttings being displaced towards the annular space walls, thus increasing the possibility of drill string entrapment.

In addition, this methodology allows to contrast the result with the initial surface pressure value, allowing to know more quickly if the applied hydraulics is in accordance with what the surface monitoring equipment indicates.