礦用泥漿泵的設(shè)計【5PS型礦用砂泵】,5PS型礦用砂泵,礦用泥漿泵的設(shè)計【5PS型礦用砂泵】,泥漿泵,設(shè)計,ps,型礦用砂泵 Safe Mud Pump Management while Conditioning Mud: On the Adverse Effects of Complex Heat Transfer and Barite Sag when Establishing Circulation Eric Cayeux* *International Research Institute of Stavanger, Stavanger, N-4068, Norway (Tel: +47 51 87 50 07; e-mail: eric.cayeuxiris.no). Abstract: For complex drilling operations with narrow geo-pressure windows, it is not uncommon to have problems with formation fracturing, due to erroneous mud pump management. To assist the driller in managing the circulation, it is possible to limit both the acceleration of the mud pumps whilst changing the flow-rate as well as the actual flow-rate, to avoid generating downhole pressure above the fracturing pressure gradient of the open hole section. Such mud pump operating limits are dependent on the operational parameters (e.g. drill-string axial and rotational velocities), and the in situ conditions downhole. The in situ conditions evolve with time due to the changes of bit and bottom hole depths as well as the variations in temperature, mud properties and cutting concentrations. When starting to condition mud after a long period of time without circulation, the changes in temperature can be very large. Furthermore, in the eventuality of barite sag, lifting up drilling fluids containing a large concentration of high gravity solid can cause much increase of the downhole pressure. This paper presents a methodology that is used in an automatic drilling control system to account for all those factors in order to have a safe mud pump management including circumstances where mud is being conditioned. Keywords: drilling automation, safe guard, physical model, mud pump management, mud pump acceleration, maximum flow-rate, formation fracturing gradient, mud losses, barite sag, heat transfer. 1. INTRODUCTION An excessive mud pump acceleration or a too large flow- rate can generate downhole pressures that exceed the fracturing pressure gradient of the open hole formation therefore causing mud losses and in the worst case scenario, a loss circulation incident. The maximum tolerable pump accelerations and flow-rates are very context dependent (Iversen et al. 2009). Both the drilling operational parameters and the downhole conditions dictate the well safe guards to be used. When drilling is well established, the time dependence of those limits is mostly influenced by the change of depth. But while conditioning mud after a long period of time without mud circulation, the downhole conditions change quickly because of the combined effect of heat exchange happening with the cold fresh mud being pumped into the well and the displacement of the mud in place which properties may have been altered during the period of inactivity. This paper describes an automatic system that attempts at enforcing mud pump safe guards that adapt themselves to the current downhole conditions. 2. AUTOMATION OF MUD PUMP MANAGEMENT In this section, we will first describe the fundamental physical characteristics of the drilling hydraulic system and then we will present the method used to solve the problem of managing the mud pumps during a drilling operation. 2.1 Drilling hydraulics In conventional drilling and with a simple drill-string and BHA (Bottom Hole Assembly), the drilling hydraulic system is composed of two branches connected together at the level of the bit: the drill-string branch and the annulus branch (see Fig. 1). Note that if the bit is off bottom, the annulus branch is longer than the drill-string one. Fig. 1: The drilling hydraulic system can be seen as a network of interconnected branches. But several junction points may exist, if there are components like circulation-subs, hole openers, under- reamers, downhole motors, etc. in the drill-string because such elements provides access from the inside of the drill- string to the annulus at other places than the bit. The result is a network of inter-connected branches. The condition to be respected by this network is that the pressures on both sides of the junction point between the two branches are equal. Proceedings of the 2012 IFAC Workshop on Automatic Control in Offshore Oil and Gas Production May 31 - June 1, 2012. Trondheim, Norway 978-3-902661-99-9/12/$20.00 2012 IFAC 231 10.3182/20120531-2-NO-4020.00018 To describe the behaviour of the drilling fluid in each branch we can use a cross sectional averaging of the Navier- Stokes equation (Fjelde et al., 2003). There are three balance equations that describe the interface exchange of mass, momentum and energy. The mass balance can be written: ( ) ( ) (1) where is time, is the curvilinear abscissa, is the cross- sectional area of a fluid element, is the averaged density, is the average velocity, is the source term, a mass per length per time through the fluid element side walls. In a multi-phase context, it is more complicated to write the momentum balance. The assumption made here is to use a drift-flux formulation where the different phases are mixed together but each phase has a slip velocity compare to a reference one. The momentum balance can then be written as follow: ( ) ( ) ( ( ) (2) where is the pressure, is the friction pressure-loss term, is the average inclination of the fluid element, is the gravitational acceleration of the earth. Finally, the energy conservation can be written (Marshall and Bentsen, 1982): ( ) ( ) , (3) where is the enthalpy per mass unit, is the forced convective term, is the conductive and natural-convective term, is the heat generated by mechanical and hydraulic frictions. The forced convective term can be expressed: , (4) The conductive and natural-convective term does not have a general expression. In the case of purely convective isotropic material, we can use: , (5) where is the thermal conductivity, is the temperature, 2.2 Drilling fluid density The partial differential equations (1), (2) and (3) are all dependent upon the local density of the drilling fluid element. It is therefore important to have a precise estimation of the in situ density of the mud. A drilling fluid is constituted of a liquid, a solid and a gas phase. The liquid phase is either solely based on a brine solution (water-based mud) or on a mix of oil and brine (oil- based mud). The solid components of the mud are low gravity solids (like bentonite clay), high gravity solid (like barite) and rock cuttings. Except for special drilling applications such as using a foam as a drilling fluid (Kuru et al., 2005) or particular dual-gradient managed pressure drilling (MPD) solutions using gas to reduce the mud density within the upper part of the well annulus (Scott, 2009), the presence of gas in the mud is not planned, but arises from contamination of the drilling fluid with air in the surface installation or because of formation gas mixing downhole with the drilling fluid. Accounting for the different components of the drilling fluid, one can express the mud density as: (6) Where is a set of indices representing the different constituents of the drilling fluid (i.e., brine, oil, low-gravity solid, high-gravity solid, cuttings and gas), is the mass fraction of the i component of the drilling fluid, is the density of the i component of the drilling fluid. In addition, the following relationship shall be respected: (7) The thermal expansion and compressibility of the liquid phases (i.e. brine and oil) used in drilling fluids (see Fig. 2) can be well approximated through a 6-parameters model (Ekwere et al., 1990) as defined in the following relationship: ( ) ( ) ( ) , (8) where is the density of the brine or oil phase of the drilling fluid element, is the temperature of the fluid element, is the pressure of the fluid element, , i=0, 1, 2 and j = 0, 1 are the coefficients of the model. Fig. 2: Base oil density in pounds per gallon (ppg) of a typical low viscosity oil-based mud as a function of temperature and pressure. At high pressure, gas may be dissolved in the liquid phase (especially with oil-based mud) and therefore affects the compressibility and thermal expansion of the liquid phase (Monteiro et al., 2010). However, when the pressure decreases below the bubble point, free gas is present in the drilling fluid. Its density is then governed by the ideal gas law: , (9) where is the molar mass of the gas, is the ideal gas constant. By solving the partial differential equation (3) using a finite difference method (Corre et al., 1984), it is possible to ACOOG 2012, May 31 - June 1, 2012 Trondheim, Norway 232 estimate the evolution of the temperature of the drilling fluid as a function of depth and time (see Fig. 3). Fig. 3: Those three graphs show the evolution of the temperature of the fluid inside the drill-string and in the annulus. The calculated local temperature along the drill-string and the annulus can then be used together with the modelled local pressure to estimate the in situ density of the liquid and gaseous phases of the drilling fluid. The density of the solid particles does not change much with pressure and temperature. However the concentration of the different solid phases in the drilling fluid greatly influences the mud local density. While drilling, rock cuttings are transported along the annulus as part of the cuttings removal process. The cuttings production is simply the product of the rate of penetration (ROP) by the footprint of the bit (and the one of the under- reamers or hole-openers if any is in use). The cuttings transport (see Fig. 4) is much more complicated to estimate and depends on many parameters like the cuttings particle size distribution, the cuttings density, the fluid velocity and density, the rotational velocity of the drill-string, the inclination of the borehole (Larsen et al., 1997). Fig. 4: These three graphs show how cuttings are generated while drilling and transported along the annulus by the circulation of drilling fluid. As a result the mass fraction of cuttings varies along the annulus due to the different operations performed during the drilling process. At a given depth, the local concentration of cuttings contributes to the changes in the local mud density (see Fig. 5) which is influenced by the local temperature and pressure as previously discussed. Fig. 5: Effects of pressure, temperature and cuttings load on local mud density inside the drill-string and the annulus. Drilling fluids are thixotropic (i.e. they become more viscous when there are no fluid movements) in order to maintain the solid particles in suspension when circulation is stopped. This thixotropic suspension or gelling effect applies to both the cuttings particles and the mud weighting materials. The high specific gravity solid particles used to weight the drilling fluid have a high density (e.g., the density of barite is typically 4500kg/m3) and this means that the added barite can easily segregate from the rest of the drilling fluid if the mud does not gel: this effect is termed dynamic sagging. During dynamic sagging, when the mud flow rate is very low, no gelling takes place because the fluid is not at rest, yet the fluid velocity may not be strong enough to counteract the slip velocity of the high gravity solid particles and therefore barite may segregate from the rest of the fluid (Aas et al., 2005). This effect is also termed barite sag. In inclined (i.e. non vertical) wells, when fluid circulation is stopped, dynamic sagging may also occur simply because of natural convection flows within the well, due to variations of the mud density in a cross-sectional area, which prohibit gelling to take place (Dye et al., 2001). A radial temperature gradient caused by a large temperature difference between the interior of the drill-string and the formation may initiate convection currents that tend to accelerate the barite settling process. When the heavy particles settle on the lower side of the inclined borehole, they create a thick bed that can then slide down the well bore toward deeper depths and cause large concentrations of high gravity solids at the bottom of the hole while the density of the mud at shallower depths is reduced accordingly. ACOOG 2012, May 31 - June 1, 2012 Trondheim, Norway 233 2.3 Drilling fluid rheology The pressure loss calculations depend on the viscosity of the drilling fluid. Drilling muds are non-Newtonian fluids, which rheology is following a Herschel-Buckley type of behaviour. However a variation of the Herschel-Buckley rheology has been proposed (Robertson and Stiff, 1976) that has better properties to describe drilling hydraulic flow: ( ) , (10) where is the shear stress, is the shear rate, A, B and C are the coefficients of the model. But as with any other fluid, the rheology of drilling mud depends on temperature. In addition, the mud viscosity increases exponentially with larger pressures, this being true at any temperature (Houwe and Geehan, 1986), following an Arrhenius type of law (see Fig. 6). Fig. 6: The viscosity of drilling fluids decreases when temperature increases but increases when pressure increases. As a consequence, the rheology of the drilling fluid changes with depth and time because of the variation of temperatures and pressures along the drill-string and the annulus (see Fig. 7). Fig. 7: The local rheology of the drilling fluid in the annulus as a function of depth. 2.4 Continuous wellbore status evaluation As seen in Fig. 5 above, the cuttings concentration along the annulus depends on the performed sequence of drilling operations (e.g. drilling, circulating off bottom, etc.). For a normally long well (e.g. several kilometres in length) it may take hours to displace the cuttings up to the surface. Similarly, the temperature inside the wellbore varies as a function of the different drilling parameters being used (e.g. bit depth, drill-string rotational velocity, circulation rate, whether drilling or not). After a period of drilling, it may take many days before the temperature inside the wellbore returns to the surrounding geothermal conditions. As it has been mentioned above, during such a temperature equalisation period, barite sag can occur, therefore changing the downhole conditions even though no drilling actions are performed on the well. As a consequence, it is necessary to monitor the whole drilling process without interruptions, in order to evaluate the current downhole conditions and this from the start to the drilling operation, which is the only moment at which the initial conditions can be reasonably estimated without making reference to a temporal context. This is performed by continuously computing the evolution of the physical parameters characterizing the downhole conditions. There are three main operations involved in this process: 1. The continuous calculation of the physical quantities. 2. The real-time calibration of the thermo-hydraulic model, to account for ill-defined or unknown structural parameters. 3. The continuous estimation of down-hole conditions, to account for the evolution of unknown and non- measurable quantities. The modelling of the wellbore status can therefore provide estimates in real-time of most of the measured physical values that are not commands to the process (examples of process commands include the flow-rate, the top of string velocity, the top of string rotational speed). This estimation is associated with a tolerance (see Fig. 8) that is dependent on the current quality of the model calibration and the expected precision of the actual measurements. It is therefore possible to compare the actual measurements with their calculated counterpart to determine if there are abnormal downhole conditions. Fig. 8: The blue curves represent actual measurements. The green curves and semi-transparent green regions represent the estimated physical quantities and their associated tolerances based on calibrated physical models of the physical process. ACOOG 2012, May 31 - June 1, 2012 Trondheim, Norway 234 An additional calibration difficulty occurs when there is a long period of time without any measurements, such as when it is necessary to pull out of hole (POOH) the drill-string to perform the next drilling operation, or to replace a faulty component in the BHA. In such cases, it is still possible to perform the continuous calculation of the internal state of the wellbore, but the error or uncertainty regarding the real downhole conditions dramatically increases as it is no longer possible to calibrate the physical models due to the lack of real-time downhole measurements. Furthermore, heat transfer in both natural convection and barite sag models are far from accurate in those circumstances, thereby increasing the uncertainty on the actual downhole conditions when the drill- string is run back into the hole. 2.5 Mud pump start-up The mud pump acceleration rates are ramped or stepped up in such a manner that downhole pressures do not exceed the fracturing pressure of the open hole formations. It is important to estimate the effect of the downhole pressure variations for the entire open hole well section and not only at the casing shoe depth or at the bit depth, as is often done for the sake of simplicity. In situations with complex or narrow geo-pressure margins, the regions of maximum limitations can be situated at various places along the open hole section. The acceleration of the mud pumps must not set so as to induce a downhole pressure pulse that exceeds the maximum tolerable rock fracture limit. Such transient pressure surges would not be visible using a steady state hydraulic model and would result in allowing prohibitive mud pump accelerations that could result in fracturing the formation. Our system solves equations (1) and (2) using a finite difference method that permit the estimation of acceleration effects on downhole pressure along the open hole section of the well (see Fig. 9). Fig. 9: Effect of ramping up the mud pumps on pump and downhole pressures. Ideally, to reduce pump start-up time, the flow rate should be increased gradually and continuously to the target flow rate. In practice, several stops need to be performed while starting the mud pumps. Often, the driller desires to use several intermediate steps to check that the pump pressure is evolving normally. Each of these acceleration steps generate a pressure build-up that stabilizes when steady state conditions are reached. Therefore, independent pump accelerations must be used for each single step, depending on the current conditions and the following pump rate level. It is therefore possible to calculate the maximum pump acceleration from any given starting flow-rate to any other target flow-rate while respecting the two conditions described above: stay within the geo-pressure window and have a monotonic increase of the pump pressure (see Fig. 10). Using this 2 dimensional pump acceleration function, it is possible to optimize the pump start-up procedure for any number of stages in the ramping procedure. Fig. 10: This graph shows the maximum acceptable pump acceleration while starting from a given flow-rate to reach a target flow-rate. 2.6 Maximum pump rate Based on the maximum downhole pressure limit (for example using the fracturing pressure prognosis), it is possible to calculate an absolute maximum flow rate that guarantees that the downhole pressure will remain below the upper pressure boundary. To calculate that flow-rate limit, only steady state conditions are necessary (no need to account for mud pump accelerations) and therefore a simpler version of the hydraulic model can be used. The partial derivative on time of equation (2) can be considered to be 0 and the axial velocity of drill-string is supposed to be constant. The resulting simplified equation can easily be solved by integrating along the curvilinear abscissa for each branch of the hydraulic circuit: ( ) ( ) ( ( ) ( ) (11) where p is the pressure that should be calculated, is the measured depth at which the press