Structural-mechanical properties

Mechanical properties of drilling fluids (plasticity, toughness, elasticity and durability) are determined by their internal structure and therefore they are called structural-mechanical. Mechanical properties of heterogeneous (multiphase) drilling muds can be: an unstructured (easy dispersed) and structured (bonded dispersed). In unstructured systems (called sols) particles of dispersion phase do not interact with each other and they are not able to create a spatial grid or structure. Mechanical properties of these systems are similar to mechanical properties of their dispersion medium and these properties are equal at rest and in motion. In structured systems, called gels, particles of dispersion phase are related. They form of the spatial structure with certain mechanical durability. Being at rest gels become more durable, and dispersion medium in the cell structure (free water) loses its mobility. However, mixing or heating of the system violates the structure. It takes sols properties back. The phenomenon of transition gel in the sol and back is called thixotropy. It is necessary to destroy the structure with some efforts in order to return the structure liquid properties. The magnitude of this force depends on the adhesion forces between particles of a dispersion phase of drilling mud, (on the strength of the resulting structure) and it is characterized by static shear stress. Static shear stress (SSS) is the force which begins structure destruction and which is referred to the area unit. Static shear stress is expressed in the dPa. The value of the static shear stress specifies the possibility for the retention of drilling cuttings particles and weighting material in suspension when there are drilling mud circulation stops. It is obvious that in order to ensure this possibility the value of the static shear stresses must exceed the value of force which is created by weight of drilling cuttings particles and weighting material. Otherwise, in the absence of drilling mud circulation these particles will settle down in the bottom part of the well, and this fact can lead to the sticking of the drill by drilling cuttings. However, increasing static shear stress worsens the self-cleaning conditions of drilling mud from cuttings on the surface, and the value of pulse pressure on the bottom and the walls of the well when initiating the mud flow (when starting the pump) and during the CPO also increases, which, in its turn, increases the probability of kicks, disturbance of the bore hole walls, fracs and acquisitions of drilling mud. Thus, the value of the static shear stress should be minimal, but enough to keep suspended in rest mud drilling cuttings particles and weighting material. The SNA-2 device, rotational viscometers VSN-3, VSN-2M and viscometer FANN are used for the measurement of static shear stress value (figures 5.3 - 5.5). To assess the nature of the growing strength of the structure in time measurements are made in 1 min (SNS) and 10 min (SNS) in rest. In addition structural-mechanical drilling mud properties are characterized by the thixotropy coefficient

C_T = SNS₁₀ / SNS₁. (5.7)

Required value of static shear stress after 1 min (SNS1, DPA) can be determined by using the following formula

SNS1³ 5 [2 - ехр (- 110 d)] d (rп- r), (5.8)

where: d - conditional diameter of characteristic drilling cuttings particles, m; rп, r- the density of cuttings and drilling mud respectively, kg/m³.

Figure 5.3 The SNA-2 device.

1 - upright;

2 - plug to install threads;

3 - flared sleeve;

4 - elastic thread;

5 - protective metal tube;

6 - the scale with 1 degree interval;

7 - screw for bracing threads;

8 - measuring cylinder;

9 - external cup;

10 - pivoting support;

11 - common plate;

12 - fixing screws;

13 - drive unit;

14 - pointer.

Figure 5.4 - Viscometer VSN-3.

1 - external rotary cylinder;

2 - internal rotary cylinder;

3 - cup;

4 - scale on the vertical line of inspection window;

5 - screw-in crown;

6 - switch;

7 - switch;

8 - lifting table;

9 - fitting.

Figure 5.5 - General scheme of rotation viscometer.

1 - external rotary cylinder;

2 - internal rotary cylinder;

3 - spring;

4 - scale.

5.3 Rheological properties of flushing liquids

All liquids are characterized by the mobility, i.e. ability to flow. The science about liquids flow is called a rheology, and their properties connected with a flow are called rheological.

Rheological properties of flushing liquid play an important role when drilling wells. Unsatisfactory rheological properties can lead to the plug formation in a well bore, to a cuttings blocking of a critical bore area, to the drilling rate decrease, to washing-out of bore walls, to sticking of a drill string, to flushing liquid absorption and even to blowout. The flushing liquid behavior is caused by its flow regime. There are two flow regimes: the laminar regime which prevails at low flow rates (the dependence pressure — velocity is defined by viscous properties of a liquid), and the turbulent regime which prevails at high rates and depends on inertial properties of a liquid (viscosity influences it only indirectly).

Laminar flow. The laminar flow in a round pipe can be visually presented in the form of one very thin cylinder sliding in another (figure 5.6). The velocity of cylinders increases from zero at a pipe wall to the maximum on its axis. The difference ratio in adjacent layers speeds ∆ v to ∆r the distance between them is called as the shear rate

(5.11)

Interaction force between two adjacent layers, moving relatively to each other with a certain speed, depends on a sort of a liquid, the gapping areas of rubbing layers and shear rate (the I. Newton law of internal friction)

(5.12)

where F – the friction force between two adjacent layers of a liquid;

- the dynamic viscosity depending on a liquid origin;

S –the area of contact between layers; -the shear rate.

Figure 5.6 – The sketchy image of a laminar liquid flow in the pipe

If to divide both members of the equation (5.12) into S: F / S = m g,

where F / S = t - shear stress causing a layer shift. [t] = F / S = Н/м2= Pa.

Then in a final form I. Newton's law will be registered in a following way

t = m g (5.13)

The equation (5.13) is a rheological model of the Newtonian (viscous) liquid.

[m] = t / g =Pa/s-1 = Pa×S.

At the temperature of 20,5°С and pressure of 0, 1 MPa the viscosity of water is equal to 1 MPa.

Rheogram (the dependence graph t = f(g) the Newtonian (viscous) liquids represents the straight line passing through the coordinates beginning (figure 5.7).

It is shown on the graph that for the Newtonian liquids the dynamic viscosity remains unchanged at any shear rate (in pipes, in the annular space, in bit shoes) and geometrically represents an inclination angle tangent of a rheological curve to an axis of the shear rate.

m = tg a

a

0 g

Figure 5.7 - Dependence graph t = f(g) the Newtonian (viscous) liquids

Liquids which don't contain particles of the size more than a molecule, for example salt mud, oil, glycerin, etc can be easily defined as Newtonian liquids.

Suspension flow to which flushing liquids belong and containing in a large quantity particles larger than molecules does not submit to Newton laws. Two non-Newtonian types of drilling mud are distinguished: pseudoplastic (PPL); the viscoplastic

(VPL).

Rheogram of a pseudoplastic liquid passes through the coordinates beginning and turned by convexity to a tangent tension axis of a shift (figure 5.8). Ratio t/g (viscosity) of such a liquid decreases at the shear rate increase.

The rheological behavior of PPL is described by Ostwald’s law –de Vaal

t = k(g)n, (5.14)

where: k – a consistency indicator, Pa × s;

n – Non-Newtonian behavior indicator (n < 1).

0 g

Figure 5.8 – Rheogram of pseudoplastic liquid

Dependence of shear stress on the shear rate of non-Newtonian liquids is defined by its composition. Argillaceous flushing liquids with a considerable solid phase fraction behave approximately according to the Bingham ductile flow theory. According to this theory, in order that the Bingham liquid flow began, someultimate effort has to be made; at higher values of made efforts it will flow as the Newtonian liquid. Therefore consistency graph of Bingham ductile liquid has to be described by two parameters — ultimate dynamic shear stress and plastic viscosity, as it is shown in figure 5.9.

Rheogram doesn't pass VPL through the coordinates beginning, and begins from a point on a shear stress axis and has a rectilinear site.

For the shear rates corresponding to a linear site, t = f(g)

it is described by the Bingham – Shvedova’s law

t = t0+ h g, (5.15)

where: t0- dynamic shear stress, Pa (dPa);

h- plastic viscosity, Pa×s (MPa× s).

Bingham’s model describes rheological properties of drilling fluids on a hydrous base with sufficiently high bentonite content.

t

t0

СНС

Figure 5.9 – Rheogram of viscoplastic liquids

In non-Newtonian liquid the relation of shear stress to the shear rate (at any shear rates) is a quantitative characteristic of effective viscosity. In figure 5.10 it is shown, that effective viscosity decreases with increase in shear rate and it is the significant parameter for hydraulic calculations only at shear rate it is measured. The effective viscosity cannot be a reliable parameter for comparison of two various flushing liquids behavior (figure 5.11.)

Shear stress

Shear rate

1 2 3

Figure 5.10 – effective viscosity decrease with shear rate increase

Shear stress

1 2

Shear rate

Figure 5.11 – Comparison of effective viscosity at two shear rates for two various flushing liquids

Flushing liquids which contain only polymers or polymers with a small share of tiny particles of a solid phase at high shear rates behave as if they possess the limited dynamic shear stress, but actually its consistency graph passes through the coordinates beginning. Its behavior is described by the empiric equation which is considered as an ideal extential law. This law establishes the following dependence:

Τ=К(dυ/dr)n (5.16)

where τ – shear rate; K and n - the constants characterizing behavior of a moving liquid (K - the consistency indicator which plays a viscosity role of the Newtonian liquid, but is expressed in dynes on square centimeter; n - the nonlinearity indicator characterizing deviation degree from the Newtonian liquid); dυ/dr – shear rate.

Theextential law (5.16) describes three known flow models in dependence of a value and:

• pseudoplastic at n < 1 - effective viscosity decreases with shear rate increase;

• the Newtonian at n = 1 - viscosity remains constant at a shear rate change, parameter K is equal to viscosity;

• dilatant ny п > 1 - effective viscosity increases with shear rate increase.

The majority of flushing liquids behave as liquids, serving as something average between Bingham plastic liquid and the liquid submitted to the extent law. As a result of forces action between particles at shear rates n and K are changeable. Flushing liquids have a quite uncertain value of a maximum dynamic shear stress which is less than shear stress values received by extrapolation, measured at high shear rates. That circumstance that consistency graphs of argillaceous flushing liquids cross tension axis in points not corresponding to zero, indicates to gel formation in them. The origin of such structures is explained by a clay bands tendency to form up in a way that positively charged ribs adjoined to negatively charged basic surfaces. This charges interaction leads to effective viscosity increase at low shear rates, rendering an impact on parameters n and K values.

Maximum static shear stress of some flushing liquids, especially argillaceous, prepared on fresh water, starts increasing after the mixing cessation.

This phenomenon is called as the thixotropy. If a flushing liquid after staying calm is exposed to a shear with a constant rate, its viscosity decreases over time i.e. there is a structure destruction which proceeds until the balanced state will be reached

Thus, effective viscosity ofthixotropic flushing liquid depends both on time, and on shearing force.

Except the main indicators of Bingham – Shvedova and Ostwald – de Vaal models (t0, h, k, n) for the rheological properties description of drilling fluids a number of additional indicators are being widely applied in recent years: plasticity coefficient; effective viscosity at a shear rate equal to 100 с-1; asymptotic viscosity or effective viscosity at completely destroyed structure (at a shear rate equal to 10000 с-1).

The plasticity coefficient of drilling mud (KP, с-1) is defined by the value of dynamic shear stress to plastic viscosity relation:

КP = t0/ h. (5.17)

Transporting stream ability and hydrodynamic pressure of drilling mud jets from bitnozzles increases with the coefficient growth. That provides more effective rock destruction on the bottom hole and drilling rate growth. Thus it is desirable to support high values of plasticity coefficient due to plastic viscosity decrease of drilling mud, instead of dynamic shear stress increase.

Effective viscosity characterizes that natural viscosity, which drilling mud possesses at a shear rate in ring well space, in drill pipes or in flashing channels of the rock cutting tool.

In a well circulating system the shear rate changes in very wide limits: in a drill string from 100 to 500 с-1, in UBT from 700 to 3000 с-1; in annular ring space from 10 to 500 с-1, more often 100 с-1; in chisels nozzles from 10 000 to 100 000 с-1.

Effective viscosity at a shear rate equal to100 с-1(EV100, PA-s) characterizes drilling mud viscosity in a well annular space and it is the main indicator defining transporting stream ability of which is higher, than values are higher EV100.

EV100= k (100) n - 1 (5.18)

However with growth of EV100 hydraulic resistances at a mud flow in annular space increase and relatively, the differential pressure that leads to drilling rate decrease and bit footage as a result not only the rotted rock particles retention on a bottom hole, but also conditions deteriorations of a prefracture zone formation (macro - and micro fracture origin and development conditions).

Effective viscosity at completely destroyed structure (EV10000) characterizes drilling mud viscosity in bit nozzles and in hydrocyclones. With EV10000 reduction bottom hole desludging degree and cooling of drilling bit cutting structure increase. Drilling rate and operation potential increase.

Besides, with EV10000 reduction cuttings enrichment intensity of drilling mud decreases, as at smaller viscosity the latter easily separates in cleaning devices.

EV10000 = k (10000) n - 1 (5.19)

It is obvious that the application of seven indicators ((t0, h, k, n, KP, EV100, EV10000) allows to characterize rather comprehensively rheological properties and functional drilling mud possibilities.

However, if at a design stage it is an advantage, but in the drilling mud exploitation process, on the contrary, it becomes a disadvantage as to control a large number of indicators, and to operate them simultaneously is extremely difficult.

The turbulent flow. The pipe flow will turn from laminar into turbulent when the stream rate will exceed the ultimate value. Instead of smooth slip of water layers relatively to each other in a stream there are local changes of velocity and particles migration direction at preservation of the general flow direction parallel to a pipe axis. The laminar stream can be compared to the river, smoothly flowing through the plain, and turbulent — with currents, when stream with bottom roughness interaction causes whirlwinds formation (figure 5.12).

Figure 5.12 - Two-dimensional profile of a turbulent stream velocity in a pipe with the Newtonian liquid

Critical velocity at which there is a flow turbulization decreases with pipe diameter increase, with density increase and viscosity reduction. It is expressed by a dimensionless parameter — Reynolds's number.

Reynolds's number considers the main stream indicators in a pipe: a pipe diameter, average liquid rate, liquid density and its viscosity. Reynolds's number is represented by the equation:

Re = (VDρ)/μ

Reynolds showed that in plain-end ring pipes for all Newtonian liquids and with all of pipe diameters the transition from laminar flow into the turbulent flow occurs when Reynolds's number is about 2000. However, turbulent flow arises in the whole liquid when Reynolds's number exceeds 4000.

Therefore a laminar flow is defined by Reynolds's number equal to 2000 and below at the Newtonian liquids. Turbulent flow is defined by Reynolds’s number equal to 4000 or more. The transient condition is defined by Reynolds's number from 2000 to 4000.

Liquid pressure losses at its turbulent flow in a pipe of concrete length depend on inertial factors. They are influenced by liquid viscosity insignificantly. These pressure losses increase in proportion to a speed square with increase in density, dimensionless parameter — Fanning friction coefficient which is the function of Reynolds’s number and pipe wall roughness.

Flow continuity. Many hydraulic calculations demand the application of liquid rate. It is important to realize the distinction between a consumption (volume rate) and liquid rate. We will consider a liquid stream in a pipe at a constant consumption of Q as it is shown on figure 5.13

Figure 5.13 - Flow continuity: Liquid rate is inversely proportional to the area of cross section in the stream direction

The volume flow rate of the liquid flowing in a pipe should be equal to its volume speed at the pipe outlet, because drilling muds are almost incompressible. This is the basic principle of the flow continuity. An important result of this principle is that, while the flow rate remains constant, the fluid speed is inversely proportional to the area, through which it passes. In other words, if the area is reduced, the fluid speed must grow at the constant flow rate.

Rheological properties of drilling muds exert a dominant influence on the following indicators and processes related to drilling wells:

- the degree of cleaning well bottom from hole cuttings;

- the degree of cooling rock cutting tool;

- the stream carrying ability;

- the flow resistance value in all links of a hole circulation systems;

- the hydrodynamic pressure value on the bottom and the hole walls in the drilling process;

- the pressure fluctuations amplitude during the start and stop pumps, performing tripping and well reaming with drill string reciprocation;

- the enrichment intensity of the mud with cuttings;

- the mud replacement completeness with the cementing slurry in the annular space between the casing column and the borehole wall, etc.

Ideal from the rheological point of view drilling mud in the downward flow (in the drilling column, downhole hydraulic motor, bit nozzles), on the bottom and in gas cleaning units must have viscosity close to the water viscosity, and in the upstream it must have viscosity, necessary and sufficient for the cutting transportation to surface without accumulating it in the well.

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