Patent Publication Number: US-11643891-B2

Title: Drilling system and method using calibrated pressure losses

Description:
BACKGROUND OF THE DISCLOSURE 
     The flow of formation fluids into a wellbore during drilling operations, when the annular pressure (AP) is below the pore pressure (PP), is called an influx or “kick.” By contrast, when the annular pressure is above the fracture pressure (FP), a fluid loss to the formation can occur. Hydrostatic pressure is the first conventional barrier for controlling the well from influxes and fluid losses. Rig blow out preventers (BOP) are a second barrier for influxes. Losses can be handled using lost circulation material (LCM) or by performing other procedures. 
     Even using available methods, both influxes and fluid losses can occur during drilling operations. Either event can have several detrimental effects. If a kick cannot be detected and controlled fast enough, it can escalate into uncontrolled flow of formation fluids to the surface, which is called a “blow-out,” resulting in operational delays (non-productive time) or even more severe consequences to the safety of personnel or loss of the well. 
     For these reasons, accurate monitoring for downhole pressure changes is critical during drilling operations to maintain proper pressure balance in the well. Warning signs that are conventionally looked for when detecting sudden downhole condition changes are not always clear (e.g., change in the rate of penetration (ROP) and standpipe pressure), or the signs may arrive late (e.g., change in cutting size, Chloride level, etc.) after the changes has started. Sometimes, the frequency at which data is collected may be too slow to detect a kick or influx early enough. Moreover, measurements of return flow (i.e., flow-out) of the well may be subject to uncertainties due to heave effects, mud transfers, and gas inside the mud. 
     So far, flow deviation detection has been achieved by continuously monitoring the return flow from the wellbore (i.e., flow-out) in a closed-loop circulation system and comparing the flow-out to the flow-in. Several controlled pressure drilling techniques have been used to drill wellbores with such closed-loop drilling systems. In general, the controlled pressure drilling techniques include managed pressure drilling (MPD), underbalanced drilling (UBD), and air drilling operations. 
     In MPD, the drilling system uses a closed and pressurize-able mud-return system, a rotating control device (RCD), and a choke manifold to control the wellbore pressure during drilling. The various MPD techniques used in the industry allow operators to drill successfully in conditions where conventional technology simply will not work by allowing operators to manage the pressure in a controlled manner during drilling. 
     As the bit drills through a formation, for example, pores become exposed and opened. As a result, formation fluids (i.e., gas) from an influx or kick zone can mix with the drilling mud. The drilling system then pumps this gas, drilling mud, and the formation cuttings back to the surface. As the gas rises in the annulus of the well, the gas may expand, and the density of the mud may decrease, meaning more gas from the formation may be able to enter the wellbore. If the pressure of the mud column is less than the formation pressure, then even more influx could enter the wellbore. 
     Conventionally, drilling operators use pressure-while-drilling (PWD) data, when available, to monitor the drilling and determine the bottom hole pressure (BHP). However, PWD data cannot be used when pump rates are low, and the PWD data has a low resolution and a slow data transfer rate. These setbacks can result in unsafe way of drilling and controlling a well. 
     Control of pressures during drilling operations may be based on a hydraulics model that calculates BHP and bottomhole temperature. Efficient control of the BHP during MPD operations requires a very precise hydraulics model, which might not always interoperate downhole condition. For example, the annular pressure profile being modeled may be different from the actual physical system. Although the hydraulic model accounts for numerous details related to the drill-pipe, drill bit and casing geometry, effect of temperature from formation, mud, effect of cuttings, it may be difficult to model the characteristics of open hole formations, fluid density, rheology, and other factors properly. 
     The subject matter of the present disclosure is directed to overcoming, or at least reducing the effects of, one or more of the problems set forth above. 
     SUMMARY OF THE DISCLOSURE 
     As disclosed herein, a method implemented by a computerized control is for a drilling system, which can have at least one pump for pumping drilling fluid at an inlet into a wellbore and can have at least one choke for choking the drilling fluid at an outlet from the wellbore. 
     The wellbore is drilled with the drilling system, and a hydraulic model is built of the drilling system drilling the wellbore. A measured value of surface backpressure SBP M  is obtained of the outlet, and a measured value of standpipe pressure SPP M  is obtained of the inlet. 
     An estimated value of standpipe pressure SPP E  is determined of the inlet based on the hydraulics model and the measured surface back pressure SBP M  value. Pressure loss in the hydraulics model is corrected based on a difference between the measured standpipe pressure SPP M  and the estimated standpipe pressure SPP E . 
     The input parameter in the drilling system is adjusted at least partially based on the hydraulics model corrected for the pressure loss calculation. 
     The inputs for the hydraulics model can include: a trajectory of the wellbore, a true vertical depth of the wellbore, an inclination of the wellbore, an azimuth of the wellbore, a geometric parameter of the drilling system, a geometry of an annulus of the wellbore, a geometry of a drillstring, a fluid property of the drilling fluid, a density of the drilling fluid, a rheology of the drilling fluid, a thermal property for the drilling fluid, a thermal property of the formation, a thermal property of the drillstring, a temperature of a formation in the wellbore, an empirical formula for local pressure loss from a component of the drilling system, operational data obtained during drilling, flow rate, rotation per minute rate (RPM), bit depth, and fluid input temperature. 
     To obtain the measured surface backpressure SBP M  value of the outlet, the value of the surface back pressure SBP can be measured with a sensor located upstream of the at least one choke. 
     The sensor can be selected from the group consisting of a pressure transducer, a pressure gauge, a diaphragm based pressure transducer, and a strain gauge based pressure transducer, an analog device, and an electronic device. 
     To obtain the measured value of the standpipe pressure SPP M  of the inlet, the value of the standpipe pressure SPP can be measured with a sensor disposed in communication with flow of the drilling fluid into the wellbore downstream of the at least one pump. As before, this sensor can be selected from the group consisting of a pressure transducer, a pressure gauge, a diaphragm based pressure transducer, and a strain gauge based pressure transducer, an analog device, and an electronic device. 
     To determine the estimated value of the standpipe pressure SPP E  of the inlet based on the hydraulics model and the measured surface backpressure SBP M  value, a pressure profile of the hydraulics model can be integrated from the measured surface backpressure SBP M  of the outlet to the inlet. 
     To integrate the pressure profile of the hydraulics model from the measured surface backpressure SBP M  of the outlet to the inlet, an estimated bottom hole pressure BHP E  can be determined by integrating the pressure profile from the measured surface backpressure SBP M  value down an annulus of the wellbore to a bottom hole assembly of a drillstring of the drilling system disposed in the wellbore. Then, the estimated standpipe pressure SPP E  value can be determined by integrating the pressure profile from the estimated bottom hole pressure BHP E  up the drillstring of the bit to the inlet from the at least one mud pump. 
     To determine the estimated value of the standpipe pressure SPP E  of the inlet, the estimated standpipe pressure SPP E  value can be calculated as a sum of the measured surface backpressure SBP M  value, a U-tube pressure loss, and a friction pressure loss. 
     The U-tube pressure loss can comprise a difference in first hydrostatic pressure in an annulus of the wellbore and second hydrostatic pressure in a drillstring of the drilling system. 
     The friction pressure loss can comprise a value of distributed friction and a value of any local pressure loss from one or more components of the drilling system. 
     To correct the pressure loss in the hydraulics model based on the difference between the measured standpipe pressure SPP M  value and the estimated standpipe SPP E  valve, a friction factor of the pressure loss in the hydraulics model can be calibrated by iteratively incrementing the friction factor at least until the estimated standpipe pressure SPP E  value matches the measured standpipe pressure SPP M  value within a threshold. 
     The method can further comprise determining a factor of the pressure loss due to rotational friction in an annulus of the wellbore by refining rheology characteristics of the drilling fluid when a drillstring is not being rotated. 
     The method can further comprise: obtaining a measured value of pressure-while-drilling indicative of bottom hole pressure at a bottom hole assembly of the drillstring; determining an estimated value of bottom hole pressure BHP E  at the bottom hole assembly based on the hydraulics model and the measured bottom hole pressure value; and correcting the pressure loss in the hydraulics model based on another difference between the measured bottom hole pressure BHP M  and the estimated bottom hole pressure BHP E . 
     To adjust the parameter in the drilling system, the at least one choke in communication with the drilling fluid from the wellbore can be adjusted. In adjusting the parameter, a flow rate or a pressure of flow of the drilling fluid out of the wellbore can be adjusted using the at least one choke. For example, the pressure can be adjusted on the surface to change downhole pressure. 
     Adjusting the parameter in the drilling system can involve adjusting at least one of: a flow rate of the drilling fluid out of the wellbore, a pressure of flow of the drilling fluid out of the wellbore using the at least one choke, a current surface backpressure SBP in the wellbore, a mass flow rate of the drilling fluid out of the wellbore, a pressure during make-up of a drillpipe connection, a pressure during a loss detected, or flow during a kick detected while drilling with the drilling system. 
     Obtaining the measured value of the parameter in the drilling system can comprise: determining outflow of the drilling fluid from the wellbore; determining inflow of the drilling fluid into the wellbore; and determining an imbalance between the outflow and the inflow as the measured parameter value. 
     To determine the outflow of the drilling fluid from the wellbore, the outflow can be measured with a flowmeter in communication with the outflow. To determine the inflow of the drilling fluid into the wellbore, the inflow can be measured with a flowmeter in communication with the inflow. 
     According to the present disclosure, a programmable storage device can have program instructions stored thereon for causing a programmable control device to perform a method of drilling a wellbore with drilling fluid using a drilling system as described above. 
     According to the present disclosure, a system is used for drilling a wellbore with drilling fluid. The system comprises at least one pump, at least on choke, storage, a first sensor, a second sensor, and a programmable control device. The at least one pump is disposed at an inlet of the system and is operable to pump the drilling fluid into the wellbore when drilling the wellbore with the drilling system. The at least one choke is disposed at an outlet of the system and is operable to adjust flow of the drilling fluid from the wellbore when drilling the wellbore with the drilling system. 
     The storage stores a hydraulic model of the drilling system drilling the wellbore. A first sensor is configured to measure a value of surface backpressure SBP upstream of the at least one choke, and a second sensor is configured to measure a value of standpipe pressure SPP downstream of the at least one pump. 
     The programmable control device is communicatively coupled to the storage, the first sensor, and the second sensor. The device is configured to perform the steps of the method described above. 
     The device is configured to obtain a measured value of surface backpressure SBP M  from the first sensor and to obtain a measured value of standpipe pressure SPP M  from the second sensor. An estimated value of standpipe pressure SPP E  of the inlet is determined based on the hydraulics model and the measured surface backpressure SBP M  value, and pressure loss is corrected in the hydraulics model based on a difference between the measured standpipe pressure SPP M  and the estimated standpipe pressure SPP E . 
     A measured value is obtained of a parameter in the drilling system. The parameter is then adjusted in the drilling system at least partially based on the hydraulics model corrected for the pressure loss. 
     The foregoing summary is not intended to summarize each potential embodiment or every aspect of the present disclosure. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG.  1    illustrates a controlled pressure drilling system having a control system according to the present disclosure. 
         FIG.  2    schematically illustrates the control system of the present disclosure. 
         FIG.  3    illustrates a flow chart of a process for correcting a pressure profile of a hydraulic model used in drilling according to the present disclosure. 
         FIG.  4    illustrates a representation of a model of the drilling system for the present disclosure. 
         FIG.  5    graphs a representation of friction pressure loss in the hydraulics model of the system. 
     
    
    
     DETAILED DESCRIPTION OF THE DISCLOSURE 
       FIG.  1    shows a closed-loop drilling system  10  according to the present disclosure for controlled pressure drilling. As shown and discussed herein, this system  10  can be a MPD system and, more particularly, a Constant Bottom-hole Pressure (CBHP) form of MPD system. Although discussed in this context, the teachings of the present disclosure can apply equally to other types of controlled pressure drilling systems, such as other MPD systems (Pressurized Mud-Cap Drilling, Returns-Flow-Control Drilling, Dual Gradient Drilling, etc.) as well as to UBD systems, as will be appreciated by one skilled in the art having the benefit of the present disclosure. 
     The drilling system  10  may be a land-based system or an offshore system. As shown here, the drilling system  10  includes a mobile offshore drilling unit  100 , such as a semi-submersible, having a drilling rig  110  and components for fluid handling. 
     The drilling rig  110  includes a derrick  112  having a traveling block supporting a top drive  116 , which couples to a flow sub  118 . A top of the drillstring  14  connects to the flow sub  118 , such as by a threaded connection, or by a gripper (not shown), such as a torque head or spear. The top drive  116  is operable to rotate the drillstring  14  extending from the derrick  112  and includes an inlet  114  coupled to a Kelly hose to provide fluid communication between the Kelly hose and the flow sub  118  and drillstring  14  extending therefrom. 
     The drillstring  14  extending from the rig  110  includes a bottomhole assembly (BHA)  16  at the end of the connected joints of drillpipe. The BHA  16  can typically include a drill bit  18 , drill collars, a drilling motor (not shown), a measurement while drilling, a logging while drilling sub, and the like for drilling a borehole  12 . 
     The drilling system  10  further includes an upper marine riser package (UMRP)  30 , a riser  22 , auxiliary lines (boost, choke, etc.)  24 , and other components. As is customary, the riser  22  extends from the rig  110  to a wellhead  20  located on the sea floor. The riser  22  typically connects to the wellhead  20  with a wellhead adapter, and the wellhead  20  typically has blow-out preventers (BOPS) and connects to the riser lines  24 , such as booster line, choke line, kill line, and the like. 
     The riser package  30  include a diverter  70 , a flex joint  72 , a telescopic joint  74 , a tensioner  76 , a tensioner ring  78 , and a rotating control device (RCD)  60 . For example, the slip joint  74  includes an outer barrel connected to an upper end of the RCD  60  and includes an inner barrel connected to the flex joint  72 . The outer barrel may also be connected to the tensioner  76  by the tensioner ring  78 . 
     The RCD  60  can include any suitable pressure containment device that keeps the wellbore  12  in a closed-loop at all times while the wellbore  12  is being drilled. (As will be appreciated, the wellbore  12  includes the borehole in the formation F and includes the riser  22  which constitutes an extension of the borehole). In this way, the RCD  60  can contain and divert annular drilling returns via a flow line  62  to complete the circulating system to create the closed-loop of incompressible drilling fluid. 
     The RCD  60  can include any typical construction. For example, the RCD  60  may include a housing, a piston, a latch, and a rider. The housing may be tubular and have one or more sections connected together, such as by flanged connections. The rider may include a bearing assembly, a housing seal assembly, one or more strippers, and a catch sleeve. The rider may be selectively longitudinally and torsionally connected to the housing by engagement of the latch with the catch sleeve. The housing may have hydraulic ports in fluid communication with the piston and an interface of the RCD  60 . The bearing assembly may support the strippers from the sleeve such that the strippers may rotate relative to the housing (and the sleeve). The bearing assembly may include one or more radial bearings, one or more thrust bearings, and a self-contained lubricant system. The bearing assembly may be disposed between the strippers and be housed in and connected to the catch sleeve, such as by a threaded connection and/or fasteners. 
     Each stripper in the RCD  60  may include a gland or retainer and a seal. Each stripper seal may be directional and oriented to seal against the drillstring  14  in response to higher pressure in the riser  22  than the UMRP  30 . Each stripper seal may have a conical shape for fluid pressure to act against a respective tapered surface thereof, thereby generating sealing pressure against the drillstring  14 . Each stripper seal may have an inner diameter slightly less than a pipe diameter of the drillstring  14  to form an interference fit therebetween. Each stripper seal may be flexible enough to accommodate and seal against threaded couplings of the drillstring  14  having a larger tool joint diameter. The drillstring  14  may be received through a bore of the rider so that the stripper seals may engage the drillstring  14 . The stripper seals may provide a desired barrier in the riser  22  either when the drillstring  14  is stationary or rotating. 
     The RCD  60  may be submerged adjacent the waterline. The RCD interface may be in fluid communication with an auxiliary hydraulic power unit (HPU) (not shown) of a control system  200  via control lines  202 . An active seal RCD may be used. Alternatively, the RCD  60  may be located above the waterline and/or along the UMRP  30  at any other location besides a lower end thereof. Alternatively, the RCD  60  may be assembled as part of the riser  22  at any location therealong. 
     The RCD  60  may be connected to other flow control devices, such as an annular seal device  50 , a flow spool  40  having controllable valves, and the like, as used in MPD. The annular seal device  50  can be used to sealingly engage (i.e., seal against) the drillstring  14  or to fully close off the riser  22  when the drillstring  14  is removed so fluid flow up through the riser  22  can be prevented. Typically, the annular seal device  50  can use a sealing element that is closed radially inward by hydraulically actuated pistons. The control lines  202  from hydraulic components on the rig  100  can be used to deliver controls to the annular seal device  50 . 
     The flow spool  40  can include a number of controllable valves (not shown) that connect to flow connections  42  to communicate the internal passage of the riser  22  with rig components on the rig  100 . Flow lines  32  from the riser package  30  may be used to communicate flow, and the control lines  202  on the riser  22  may also be used to deliver controls to open and close the controllable valves. 
     In addition to the riser package  30 , the drilling system  10  also includes a choke manifold  120 , a mud gas separator  130 , a shaker  140 , mud tanks  142 , mud pumps  150 . In addition to these, the drilling system  10  includes flow equipment  160  to deliver flow to the drillstring  14  through the Kelly hose connected to a supply line  165   a  or through a clamp  174  connected to a bypass line  165   b  and couplable to the flow sub  118 . The clamp  174  and flow sub  118  are part of a continuous flow system that allows flow to be maintained while pipe connections are being made. 
     One or more return lines  32  connects from the riser package  30  to the choke manifold  120 . A return pressure sensor  240 , return choke  122 , and return flow meter  124  communicate with the flow from the return line  32 . After the choke manifold  120 , the flow eventually communicates with the mud gas separator  130  and the shaker  140 . 
     A transfer line  144  connects an outlet of the mud tanks  142  to the mud pumps  150 . A standpipe  152  connects from the mud pumps  150  to the drilling rig  110  to conduct drilling fluid from the mud pumps  150  to the Kelly hose and other flow connections. The standpipe  152  can include a pressure sensor  250   c  near the pumps  150  or elsewhere in the flow after the pumps  150 . 
     Here, the standpipe  152  also includes flow equipment  160  connected between the mud pumps  150  and the rig  110  for directing drilling flow into the drillstring  14  via the Kelly hose or via the clamp  174 . The flow equipment  160  includes a supply line  165   a  connected from the mud pumps  150  to the top drive inlet  114 . A supply pressure sensor  250   a , a supply flow meter  166   a , and a supply shutoff valve  164   a  may be assembled as part of the supply line  165   a.    
     Additionally, the flow equipment  160  includes a bypass line  165   b  connecting the standpipe  152  from the mud pump  150  to the clamp  174 . An HPU  170  connects by hydraulic lines and manifold  172  to the clamp  174  to control its operation. For example, when the top drive  116  runs the drillstring  14  into the wellbore  12 , the clamp  174  can engage the flow sub  118 , and the pumped flow of the drilling fluid can be bypassed to the bypass line  165   b . In this way, continuous flow into the drillstring  14  can be maintained while making up new stands  13  of pipe to the drillstring  14 . A bypass pressure sensor  250   b , bypass flowmeter  166   b , and bypass shutoff valve  164   a  can be assembled as part of the bypass line  165   b.    
     Finally, the flow equipment  160  can further include a drain line  161  connecting the transfer line  144  to the supply and bypass lines  165   a - b . Drain prongs of the drain line  161  can have drain valves, pressure chokes  162   a - b , and the like connected to an outlet of the mud pump  150 . 
     The pressure sensor  240 ,  250   a - c  can use any suitable sensor for measuring pressure, such as a pressure transducer, a pressure gauge, a diaphragm based pressure transducer, a strain gauge based pressure transducer, an analog device, an electronic device, or the like. 
     Each choke  122 ,  162 , etc. may include a hydraulic actuator operated by the control system  200  via an auxiliary HPU (not shown). The return choke  122  receiving flow returns diverted from riser package  30  is operated by the control system  200  to adjust backpressure in the riser  22  and the wellbore  12  for well control. 
     The flow choke  162   a  may be operated by the control system  200  to prevent a flow rate supplied to the flow sub  118  and the clamp  174  in bypass mode from exceeding a maximum allowable flow rate of the flow sub  118  and/or clamp  174 . The pressure choke  162   b  may be operated by the control system  200  to protect against overpressure of the clamp  174  by the mud pumps  150 . Each shutoff valve  164   a - b  and others may be automated and have a hydraulic actuator (not shown) operable by the control system  200  via the auxiliary HPU. 
     The control system  200  of the drilling system  10  integrates hardware, software, and applications across the drilling system  10  and is used for monitoring, measuring, and controlling parameters in the drilling system  10 . In this contained environment of the closed-loop system  10 , for example, minute wellbore influxes or losses are detectable at the surface, and the control system  200  can further analyze pressure and flow data to detect kicks, losses, and other events. In turn, at least some operations of the drilling system  10  can be automatically handled by the control system  200 . 
     To monitor operations, the control system  200  uses data from a number of the sensors and devices in the system  10 . In particular, the control system  200  uses the one or more sensors  240  uphole of the choke manifold  120  to measure pressure in the flow returns from the riser  22  and the wellbore  12 . As the choke  122  in the manifold  120  is adjusted, the one or more sensors  240  measure the surface backpressure SBP applied to the riser  22  and the wellbore  12 . 
     In addition, the control system  200  can use the one or more sensors  250   a - c  downstream of the mud pumps  150  to measure pressure in the standpipe  152  (i.e., the standpipe pressure SPP). One or more other sensors (i.e., stroke counters) can measure the speed of the mud pumps  150  for deriving the flow rate of drilling fluid into the drillstring  14 . In this way, flow into the drillstring  14  may be determined from strokes-per-minute and/or standpipe pressure SPP. The flowmeters  166   a - b  after the pumps  150  can also be used to measure flow-in to the wellbore  12 . 
     One or more sensors (not shown) can measure the volume of fluid in the mud tanks  142  and can measure the rate of flow into and out of mud tanks  142 . In turn, because a change in mud tank level can indicate a change in drilling fluid volume, flow-out of the wellbore  12  may be determined from the volume entering the mud tanks  142 . 
     Rather than relying on conventional pit level measurements, paddle movements, and the like, the system  10  can use mud logging equipment and flowmeters to improve the accuracy of detection. For example, the system  10  preferably uses the flowmeter  124 , such as a Coriolis mass flowmeter, on the choke manifold  120  to capture fluid data—including mass and volume flow, mud weight (i.e., density), and temperature—from the returning annular fluids in real-time, at a sample rate of several times per second. Because the Coriolis flowmeter  124  gives a direct mass rate measurement, the flowmeter  124  can measure gas, liquid, or slurry. Other sensors can be used, such as ultrasonic Doppler flowmeters, SONAR flowmeters, magnetic flowmeter, rolling flowmeter, paddle meters, etc. 
     Each pressure sensor  240 ,  250   a - c  may be in data communication with the control system  200 . The return pressure sensor  240  measures surface backpressure (SBP) exerted by the returns choke  122 . The pressure sensor  250   c  and/or the supply pressure sensor  250   a  measures standpipe pressure (SPP M ) to the Kelly hose, whereas the pressure sensor  250   c  and/or the bypass pressure sensor  250   b  measures the standpipe pressure SPP to the clamp  174  during connection of a standpipe. 
     As noted above, the return flowmeter  124  may be a mass flow meter, such as a Coriolis flowmeter, and is in data communication with the control system  200 . The return flowmeter  124  connected in the return line  62  downstream of the returns choke  122  measures a flow rate of the returns. Each of the supply and bypass flowmeters  164   a - b  may be a volumetric flowmeter, such as a Venturi flowmeter. The supply flowmeter  164   a  measures a flow rate of drilling fluid supplied by the mud pump  150  to the drill string  14  via the top drive  116 . The bypass flowmeter  164   b  measures a flow rate of drilling fluid supplied by the mud pump  150  to the clamp  174 . The control system  200  can receive a density measurement of the drilling fluid from a mud blender (not shown) or other source to determine a mass flow rate of the drilling fluid. Alternatively, the bypass and supply flowmeters  164   a - b  may each be mass flowmeters. 
     Additional sensors can measure mud gas, flow line temperature, mud density, and other parameters. For example, a flow sensor can measure a change in drilling fluid volume in the well. Also, a gas trap, such as an agitation gas trap, of the mud gas separator  130  can monitor hydrocarbons in the drilling mud at surface. To determine the gas content of drilling mud, for example, the gas trap of the separator  130  mechanically agitates mud flowing in a tank. The agitation releases entrained gases from the mud, and the released gases are drawn-off for analysis. The spent mud is simply returned to the tanks  142  to be reused in the drilling system  10 . 
     A gas evaluation device can be used for evaluating fluids in the drilling mud, such as evaluating hydrocarbons (e.g., C1 to C10 or higher), non-hydrocarbon gases, carbon dioxide, nitrogen, aromatic hydrocarbons (e.g., benzene, toluene, ethyl benzene and xylene), or other gases or fluids of interest in drilling fluid. Accordingly, the device  126  can include a gas extraction device that uses a semi-permeable membrane to extract gas from the drilling mud for analysis. 
     A multi-phase flowmeter can be installed in the flow line to assist in determining the make-up of the fluid. As will be appreciated, the multi-phase flow meter can help model the flow in the drilling mud and provide quantitative results to refine the calculation of the gas concentration in the drilling mud. 
     With the overview of the drilling system  10  provided above, discussion turns to operation of the drilling system  10  in drilling a wellbore  12 . During drilling operations, the mud pumps  150  pump drilling fluid from the transfer line  144  (or fluid tank connected thereto), through the standpipe  152  and the Kelly hose to the top drive  116 . The drilling fluid may include a base liquid, such as oil, water, brine, or a water/oil emulsion. The base oil may be diesel, kerosene, naphtha, mineral oil, or synthetic oil. The drilling fluid may further include solids dissolved or suspended in the base liquid, such as organophilic clay, lignite, and/or asphalt, thereby forming a mud. 
     The drilling fluid at the inlet  114  flows into the drillstring  14  via the top drive  116  and flow sub  118 . The drilling fluid flows down through the drillstring  14  and exits the drill bit  18  of the BHA  16 , where the fluid circulates the cuttings away from the bit  18  and returns the cuttings up an annulus formed between the casing or wellbore  12  and the drillstring  14 . The returns (drilling fluid plus cuttings) flowing through the annulus to the wellhead  20  then continue into the annulus of the riser  22  up to the RCD  60 . 
     At the RCD  60 , the system  10  uses the RCD  60  to keep the well closed to atmospheric conditions. The returns are diverted into the return line  32  and continue through the returns choke  122  and the flowmeter  124 . Therefore, fluid leaving the wellbore  12  flows through the automated choke manifold  120 , which measures return flow (e.g., flow-out) and density using the flowmeter  124  installed in line with the chokes  122 . The returns then flow into the shale shaker  140 , which remove the cuttings. As the drilling fluid and returns circulate, the drillstring  14  may be rotated by the top drive  116  and lowered by the traveling block, thereby extending the wellbore  12  into the lower formation F. 
     Throughout the drilling operation, the fluid data and other measurements noted herein are transmitted to the control system  200 , which in turn operates drilling functions. In particular, the control system  200  operates the automated choke manifold  120  to manage pressure and flow during drilling. This can be achieved using an automated choke response in the closed and pressurized circulating system  10  made possible by the RCD  60 . 
     To do this, the control system  200  controls the chokes  122  with an automated response by monitoring the flow-in and the flow-out of the well, and software algorithms in the control system  200  seek to maintain a mass flow balance. If a deviation from mass flow balance is identified, the control system  200  initiates an automated choke response that changes the well&#39;s annular pressure profile and thereby changes the wellbore&#39;s equivalent mud weight. This automated capability of the control system  200  allows the system  200  to perform dynamic well control or CBHP techniques. 
     Software components of the control system  200  then compare the flow rate in and flow rate out of the wellbore  12 , the injection or standpipe pressure SPP (measured by the one or more sensors  250   a - c ), the surface backpressure SBP (measured by the one or more sensors  240  upstream from the drilling chokes  122 ), the position of the chokes  122 , and the mud density, among other possible variables. Comparing these variables, the control system  200  then identifies minute downhole influxes and losses on a real-time basis to manage the annular pressure (AP) during drilling by apply adjustments to the surface backpressure (SBP) with the choke manifold  120 . 
     By identifying the downhole influxes and losses during drilling, for example, the control system  200  monitors circulation to maintain balanced flow for CBHP under operating conditions and to detect kicks and lost circulation events that jeopardize that balance. The drilling fluid is continuously circulated through the system  10 , choke manifold  120 , and the Coriolis flowmeter  124 . As will be appreciated, the flow values may fluctuate during normal operations due to noise, sensor errors, etc. so that the system  200  can be calibrated to accommodate such fluctuations. In any event, the system  200  measures the flow-in and flow-out of the well and detects variations. In general, if the flow-out is higher than the flow-in, then fluid is being gained in the system  10 , indicating a kick. By contrast, if the flow-out is lower than the flow-in, then drilling fluid is being lost to the formation, indicating lost circulation. 
     To then control pressure, the control system  200  introduces pressure and flow changes to the incompressible circuit of fluid at the surface to change the annular pressure profile in the wellbore  12 . In particular, using the choke manifold  120  to apply surface backpressure SBP within the closed loop, the control system  200  can produce a reciprocal change in BHP. In this way, the control system  200  uses real-time flow and pressure data and manipulates the annular backpressure to manage wellbore influxes and losses. 
     To do this, the control system  200  uses internal algorithms to identify what event is occurring downhole and can react automatically. For example, the control system  200  monitors for any deviations in values during drilling operations, and alerts the operators of any problems that might be caused by a fluid influx into the wellbore  12  from the formation F or a loss of drilling mud into the formation F. In addition, the control system  200  can automatically detect, control, and circulate out such influxes and losses by operating the chokes  122  on the choke manifold  120  and performing other automated operations. 
     A change between the flow-in and the flow-out can involve various types of differences, relationships, decreases, increases, etc. between the flow-in and the flow-out. For example, flow-out may increase/decrease while flow-in is maintained; flow-in may increase/decrease while flow-out is maintained, or both flow-in and flow-out may increase/decrease. 
     In general, a possible fluid influx or “kick” can be noted when the “flow-out” value (measured from the flowmeter  124 ) deviates from the “flow-in” value (measured from the flowmeter  166   a - b  or the stroke counters of the mud pumps  150 ). As is known, a “kick” is the entry of formation fluid into the wellbore  16  during drilling operations. The kick occurs because the pressure exerted by the column of drilling fluid is not great enough to overcome the pressure exerted by the fluids in the formation being drilled. 
     On the other hand, a possible fluid loss can be noted when the “flow-in” value (measured from the stroke counters of the pumps  150  or inlet flowmeter  166   a - b ) is greater than the “flow-out” value (measured by the flowmeter  124 ). As is known, fluid loss is the loss of whole drilling fluid, slurry, or treatment fluid containing solid particles into the formation matrix. The resulting buildup of solid material or filter cake may be undesirable, as may be any penetration of filtrate through the formation, in addition to the sudden loss of hydrostatic pressure due to rapid loss of fluid. 
     Similar steps as those given above, but suited for fluid loss, can then be implemented by the control system  200  to manage the pressure and flow during drilling in this situation. In general, higher density mud loss control materials (LCM), and the like may be pumped into the wellbore  16 , and other remedial measures can be taken. For example, the operator can initiate pumping new mud with the recommended or selected kill mud weight. As the kill mud starts to go down the wellbore  12 , the chokes  122  are opened up gradually approaching a snap position as the kill mud circulates back up to the surface. Once the kill mud turns the bit  18 , the control system  200  again switches back to the standpipe pressure (SPP) control until the kill mud circulates all the way back up to the surface. 
     During drilling operations, the control system  200  operates the return choke  122  so that a target bottom hole pressure (BHP) is maintained in the annulus during the drilling operation. The target BHP may be selected within a drilling window defined as greater than or equal to a minimum threshold pressure, such as pore pressure (PP), of the lower formation F and less than or equal to a maximum threshold pressure, such as fracture pressure (FP), of the lower formation, such as an average of the pore and fracture BHPs. Alternatively, the minimum threshold may be stability pressure and/or the maximum threshold may be leakoff pressure. Alternatively, threshold pressure gradients may be used instead of pressures and the gradients may be at other depths along the lower formation F besides bottomhole, such as the depth of the maximum pore gradient and the depth of the minimum fracture gradient. Alternatively, the control system  200  may be free to vary the BHP within the window during the drilling operation. A static density of the drilling fluid (typically assumed equal to returns; effect of cuttings typically assumed to be negligible) may correspond to a threshold pressure gradient of the lower formation F, such as being greater than or equal to a pore pressure gradient. 
     During the drilling operation, the control system  200  can execute a real-time simulation of the drilling operation to predict the actual BHP from measured data, such as from the standpipe pressure SPP measured from the sensor  250   a - c , mud pump flowrate measured from the supply flowmeter  166   a , wellhead pressure from any of the sensors, and return fluid flowrate measured from the return flowmeter  124 . The control system  200  then compares the predicted BHP to the target BHP and adjust the return choke  122  accordingly. 
     During the drilling operation, the control system  200  also performs a mass balance to monitor for instability of the lower formation F, such as a kick even or lost circulation event. As the drilling fluid is being pumped into the wellbore  12  by the mud pump  150  and the returns are being received from the return line  32 , the control system  200  may compare the mass flow rates (i.e., drilling fluid flow rate minus returns flow rate) using the respective flow meters  124 ,  166   a . The control system  200  may use the mass balance to monitor for formation fluid (not shown) entering the annulus and contaminating the returns or returns entering the formation F. 
     Upon detection of instability (e.g., kick), the control system  200  takes remedial action, such as diverting the flow of returns from an outlet of the return flowmeter  124  to the mud gas separator  130 . A gas detector of the separator  130  can use a probe having a membrane for sampling gas from the returns, a gas chromatograph, and a carrier system for delivering the gas sample to the chromatograph. The control system  200  may also adjust the returns choke  122  accordingly, such as tightening the choke in response to a kick and loosening the choke in response to loss of the returns. 
     Alternatively, the control system  200  may include other factors in the mass balance, such as displacement of the drillstring and/or cuttings removal. The control system  200  may calculate a rate of penetration (ROP) of the drill bit  18  by being in communication with the drawworks and/or from a pipe tally. A mass flowmeter may be added to the cuttings chute of the shaker  140 . and the control system  200  may directly measure the cuttings mass rate. 
     Having an understanding of the drilling system  10  and the control system  200 , discussion now turns to some additional details of the components of the control system  200 .  FIG.  2    schematically illustrates some details of the control system  200  of the present disclosure. The control system  200  includes a processing unit  210 , which can be part of a computer system, a server, a programmable control device, a programmable logic controller, etc. Using input/output interfaces  230 , the processing unit  210  can communicate with choke manifold  120  and other system components to obtain and send communication, sensor, actuator, and control signals  232  for the various system components as the case may be. In terms of the current controls discussed, the signals  232  can include, but are not limited to, the choke position signals, pressure signals, flow signals, temperature signals, fluid density signals, etc. 
     In addition to the chokes  122   a - b , the flowmeter  124 , and pressure sensors  240 , the choke manifold  120  can include a local controller (not shown) to control operation of the manifold  120 , and can include a hydraulic power unit (HPU) and/or electric motor to actuate the chokes  122 . The control system  200  is communicatively coupled to the manifold  120  and has a control panel with a user interface and processing capabilities to monitor and control the manifold  120 . 
     The processing unit  210  also communicatively couples to a database or storage  220  having set points  222 , a hydraulics model  400 , and other stored information. The hydraulics model  400  characterizes the well pressure system. This information for the hydraulics model  400  can be stored in any suitable form, such as lookup tables, curves, functions, equations, data sets, etc. Additionally, multiple hydraulics models  400  or the like can be stored and can characterize the system in terms of different system arrangement, different drilling fluids, different operating conditions, and other scenarios. 
     As will be appreciated, the hydraulics model  400  of the control system  200  can be built based on the various components, elements, and the like in drilling system  10 . The hydraulics model  400  can be built with any complexity desired to model the drilling system  10 , which as noted above with reference to  FIG.  1    can have a great deal of complexity and information associated with it and which can change over time depending on drilling parameters. The processing unit  210  operates a pressure control  212  according to the present disclosure, which uses a calibration process  300  for calibrating the hydraulics model  400  (i.e., refining the pressure loss characterization in the hydraulics model  400 ). (Details of how the pressure control  212  calibrates the hydraulics model  400  with the calibration process  300  will be discussed with reference to  FIGS.  3 - 5   .) 
     Finally, the processing unit  210  uses the current pressure profile from the pressure control  212  to operate a choke control  214  according to the present disclosure for monitoring and controlling the choke(s)  122   a - b . For example, the processing unit  210  can transmits signals to one or more of the chokes  122   a - b  of the system  10  using any suitable communication. In general, the signals are indicative of a choke position or position adjustment to be applied to the chokes  122   a - b . Typically, the chokes  122   a - b  are controlled by hydraulic power so that the signals  105  transmitted by the processing unit  210  may be electronic signals that operate solenoids, valves, or the like of an HPU for operating the chokes  122   a - b.    
     As shown here in  FIG.  2   , two chokes  122   a - b  may be used. The same choke control  214  can apply adjustments to both chokes  122   a - b , or separate choke controls  214  can be used for each choke  122   a - b . In fact, the two chokes  122   a - b  may have differences that can be accounted for in the two choke controls  214  used. 
     As discussed herein, the control system  200  uses the choke control  214  tuned in real-time to manage surface backpressure SBP, and the control system  200  uses pressure measurements from sensors  240  associated with the choke(s)  122   a - b  to determine the surface backpressure SBP of the system. 
     Having an understanding of the drilling system  10  and the control system  200 , discussion now turns to a process  300  in  FIG.  3    for correcting a pressure profile of a hydraulics model  400  used in drilling according to the present disclosure. For discussion, reference is made to the drilling system  10  and control system  200  of  FIGS.  1 - 2   . 
     The process  300  begins with obtaining data for input into the hydraulics model  400  of the drilling operation at hand (Block  310 ). Using the input data, the hydraulics model  400  is built as a well pressure model from the components, arrangement, properties, and other details of the drilling system  10  used during the MPD operation (Block  320 ). 
     As some examples, the hydraulics model  400  is built using input data of the well trajectory. The input data for the well trajectory include values for measured depth (MD), inclination, and azimuth. The hydraulics model  400  is also built using geometric parameters for the drilling system  10 , including the geometry (diameter and depths) for the annulus (riser, casing, open hole) and the geometry for the drillstring segments. 
     The hydraulics model  400  is built using fluid properties of the drilling fluid used in the drilling operation. These fluid properties can include the drilling fluid&#39;s density (base type and fraction, PVT coefficients, composition fractions, salinity) and the fluid&#39;s rheology. The hydraulics model  400  is also built using thermal properties (specific heat, conductivity) for the fluid, formation, and metal elements of the system  10 , and the hydraulics model  400  is built using the formation temperature. The hydraulics model  400  is further built using empirical formulas for the local pressure losses from particular tool(s) used for the drilling operations. These particular tools are typically customized tools for the drilling operation, such as the BHA  16 , rotary steerable systems, the RCD  60 , wellhead components, etc. Finally, the hydraulics model  400  is built using at least some of the operational data  232  obtained during drilling. The operational data  232  can include: surface backpressure (SBP), flow rate, rotation rate (RPM), bit depth, fluid input temperature, standpipe pressure (SPP), and the like. 
     The complexity of the hydraulics model  400  can be defined as desired, given all of the information available. Certain assumptions can be used in the hydraulics model  400 . For example, the solution functions of the hydraulics model  400  can be assumed to depend on the measured depth (x) of the wellbore  12 . Any radial dependence of the hydraulics model  400  may be assumed to be averaged. For convenience, the drillstring segments may be assumed to have a constant diameter. These and other assumptions can be used. 
     With the hydraulics model  400  built, the MPD operation can begin by using the constructed hydraulics model  400  to manage pressure, detect flow imbalance, determine influxes and losses, adjust the surface backpressure SBP with the chokes  122   a - b , and perform other relevant operational steps as discussed previously (Block  330 ). 
     For reference,  FIG.  4    illustrates a simplified representation of the hydraulics model  400  of the drilling system  10  for the present disclosure, corresponding the pressure integration blocks  340 - 350  in  FIG.  3   . Although not represented here, the model  400  would include iterations (increments) for the fluid PVT density, as well as iterations for the fluid temperature. The mud pump  150  at the inlet of the drilling system  10  pumps drilling fluid through the standpipe  152  into the drillstring  14 , which is made up of known pipe details. The standpipe  152  includes the one or more pressure sensors  250  for measuring the standpipe pressure SPP. 
     The drilling fluid in the bore  15  of the drillstring  14  is subject to friction, hydrostatic pressures, different geometries of the drill pipes making up the drillstring  14 , the characteristics of the drilling fluid, etc., which are defined in the hydraulics model  400 . Exiting from the BHA  16 , the drilling fluid then passes up the annulus  13  of the wellbore  12 . The flow of the drilling fluid up the annulus  13  is subject to friction from the wellbore  12  and the drillstring  14 , hydrostatic pressures, the geometry of the annulus  13 , the characteristics of the drilling fluid, temperature of the formation, heat transfer variables, etc., which are defined in the hydraulics model  400 . (As will be appreciated, when a riser  22  is used, the wellbore  12  for the hydraulics model would include both the borehole in the formation and the riser  22 . Additionally, modeling of the wellhead may also be done as being part of the wellbore  12 .) 
     The drilling fluid exits the annulus  13  at the outlet of the wellbore  12  and passes to the choke manifold  120 . One or more pressure sensors  240  at the choke&#39;s inlet can measure the surface backpressure SBP. As an addition, the BHA  16  can include a pressure-while drilling (PWD) sensor  260  that can be used in determining a BHP of the drilling system  10 . Further details of this are provided later. 
     To model all of the variables, the drilling system  10  is divided into a plurality of discrete cells C1, C2, . . . C d  . . . to a cell C td  at total depth (TD) at a given point in time in the drilling operation. A cell C d  at a given depth is diagramed as a representation. The bore  15  inside the drillstring  14  can be modeled with its own cells, while the annulus  13  can be modeled with other cells. 
     The number of cells C can be suited to the given implementation, and the cells C can have similar or different intervals or increments (e.g., depths) along the wellbore  12  appropriate to the resolution of the different features of the drilling system  10 . The cells C can change as drilling progresses, the wellbore  12  reaches further depth, new formations are drilled, new pipe stands are inserted into the drillstring  14 , and new sections of the wellbore  12  are cased with liner. Modeling of the surface features, such as the standpipe  152 , flow lines  32  from the riser package  30 , etc., may also be done, although this is not shown in the representation of the drilling system  10  in  FIG.  4   . 
     Returning to  FIG.  3   , the hydraulics model  400  during the drilling operation is corrected in real-time using a calibration procedure (Blocks  340  to  382 ) in the pressure control  212  of the control system  200 . This calibration procedure (Blocks  340  to  382 ) can be repeated at any time as necessary and desired during drilling. 
     The calibration procedure begins by integrating the well pressure profile in the closed-loop drilling system (Block  340 ). The pressure integration begins with the surface backpressure SBP produced in the well pressure profile by the choke manifold  120  (Block  342 ). (As noted, one or more sensors  240  upstream of the choke manifold  120  can provide readings of the surface backpressure SBP). 
     Pressure from this starting point is then integrated in the profile&#39;s modeled cells C along the annulus  13  between the drillstring  14  and the wellbore  12  (riser, casing, open hole) to the drill bit  18  (Block  344 ). The integration of the pressure produces an estimate of a current BHP for the drilling operation (Block  346 ). (If PWD data is available from a PWD sensor  260 , the estimated bottom hole pressure BHP E  can be compared to a bottom hole pressured BHP M  determined from the PWD data, as discussed later.) 
     From the BHA  16 , the pressure is then integrated in the profile&#39;s modeled cells C up the bore  15  of the drillstring  14  to the system&#39;s inlet (e.g., standpipe  152 ), where an estimated value for the standpipe pressure SPP E  is the final calculated pressure of the integration (Block  350 ). Pressure loss at the bit  16  may also be considered. 
     Having integrated the pressure of the well pressure profile starting from the known surface backpressure SBP M  reading to an estimated standpipe pressure SPP E , the control system  200  further obtains a representative measurement of the standpipe pressure SPP M  in real-time from the inlet pressure sensors  250   a - c  and compares the measured standpipe pressure SPP M  to the estimated standpipe pressure SPP E  to determine an error or difference (Block  370 ). 
     In turn, the control system  200  uses the determined error to calibrate pressure losses in the hydraulics model  400  so that the integration of the pressure profile in the hydraulics model  400  with calibrated pressure losses can produce a more accurate estimate of the standpipe pressure SPP. Ultimately, the hydraulics model  400  and the calibrated pressure losses that the hydraulics model  400  includes would improve the model to control the MPD operation by the control system  200  as the drilling system  10  continues drilling the wellbore  12 . 
     The calibration may take several iterations of the integration in the profile&#39;s modeled cells C and may require several adjustments of the pressure loss factors, model parameters, and the like to achieve a calibration level within a defined accuracy. Overall, the entire process of the calibration may be governed by a processing interval (Block  388 ) of the control system&#39;s processing unit  210 . Preferably, the processing unit  210  includes the hydraulics model  400  in firmware to improve the processing interval. For example, the processing unit  210  may operate to provide pressure loss calibration of the hydraulics model  400  every 500-ms, 1-s, or other interval. 
     Looking at these calibration steps more closely, it is clear that the measured surface backpressure SBP M  (i.e., as measured by pressure sensors  240 ) can be known with a high degree of accuracy. Therefore, the control system  200  can assume zero error at the start of the integration process. The difference between the estimated standpipe pressure SPP E  and the reference standpipe pressure SPP M  measured by the pressure sensor  250   a - c  therefore represents how pressure losses are missing in the hydraulics model  400 . The error increases in the integration from the surface backpressure SBP E  through the annulus  13  and up drillstring bore  15  to the estimated standpipe pressure SPP E  based on how frictional pressure loss and hydraulic pressure loss are modeled in the hydraulics model  400 . 
     Once the error is determined, the control system  200  can then interpolate this error for any desired depth in the wellbore  12  and can correct the calculated pressure profile of the hydraulics model  400  based on this error. In the end, this calibration procedure provides details of the pressure losses (and more particularly the friction pressure loss in the annulus  13 ) in the drilling operation where a mud rheological reading may not be available or is not measured at the downhole condition. 
     As a brief example,  FIG.  5    graphs a representation of friction pressure loss in the hydraulics model ( 400 ) of the drilling system ( 10 ). Friction pressure loss is graphed as a function of depth in the system starting from surface, through the drillstring&#39;s bore ( 15 ) to the bit at a current total depth, and then up the annulus ( 13 ) back to surface. The total friction (and the resulting friction pressure loss it would produce) increases through the system ( 10 ) as the drilling fluid is pumped down the pipe, turns the bit, and then rises up the annulus ( 13 ) to surface. 
     In the calibration process, the measured surface backpressure SBP M  from the flow out of the annulus ( 13 ) by the pressure sensor ( 240 ) upstream of the choke manifold ( 120 ) would represent a reading with little expected error (i.e., e=0). Yet, the integration of the calibration process integrating from the measured surface backpressure SBP M , down the annulus ( 13 ), and up the drillstring&#39;s bore ( 12 ) to the standpipe ( 152 ) would produce an estimated standpipe pressure SPP E  with the greatest error because the actual frictional pressure losses may not be adequately modeled in the system ( 10 ). 
     However, the error between the estimated standpipe pressure SPP E and the measured standpipe pressure SPP M  (as measured by the standpipe sensor  250   a - c ) provides an indication of friction factors missing in the system&#39;s modeling, which would in turn lead to frictional pressure losses not accurately reflected in the hydraulics model ( 400 ). A correction of the friction pressure loss is represented in  FIG.  5   . The goal of the calibration process is therefore to determine the friction pressure losses increment, so the hydraulics model can be corrected. 
     Hydrostatic pressure estimation can be similarly characterized in the manner described above. Overall, error in the hydraulics model due to hydrostatic pressure changes may have less impact or may be corrected in a more straightforward fashion. In fact, the hydrostatic pressure from the column of mud may already be considered in the overall BHP calculation. Either way, the present section describes the techniques for calibration the friction pressure losses because they may tend to have a greater impact and may be more dynamic in nature. 
     To calibrate the friction loss, the hydraulics model  400  uses factors in the hydraulics model&#39;s pressure loss formula, which follows an American Petroleum Institute&#39;s API-13D model for “Rheology and Hydraulics of Oil-well Drilling Fluids” and is based on Herschel-Bulkley rheology. The assumed model yields the following relation for the standpipe pressure SPP and the pressure losses:
 
 SPP   E   =SBP   M   +dP   u-tube   +dP   friction  
 
     Thus, the estimated standpipe pressure SPP E  is calculated as the sum of the measured surface backpressure SBP M , the U-tube pressure difference (dP u-tube ), and the friction pressure loss (dP friction ) of the system  10 . The U-tube pressure difference dP u-tube ) is a difference in the hydrostatic pressures in the annulus (dP h,a ) and hydrostatic pressures in the drillstring (dP h,ds ) and can be characterized as:
 
 dP   u-tube   =dP   h,a   −dP   h,ds  
 
     The frictional pressure loss (dP friction ) consists of the distributed friction (P f ) and local pressure losses (dP local ), such as in the bit, tool joints and custom tools, and can be characterized as:
 
 dP   friction   =P   f   +dP   local  
 
     The distributed friction pressure loss is an integral along the flow path (in the drillstring and the annulus). It can be defined by the following known friction gradient (written in SI units as a function of the fluid density p, frictional factor f, fluid velocity V, fluid temperature T, hydraulic diameter Dh, and measured depth x): 
     
       
         
           
             
               
                 ∂ 
                 
                   P 
                   f 
                 
               
               
                 ∂ 
                 x 
               
             
             = 
             
               - 
               
                 
                   2 
                   ⁢ 
                   ρ 
                   ⁢ 
                   
                     f 
                     ⁡ 
                     
                       ( 
                       
                         ρ 
                         , 
                         V 
                         , 
                         T 
                       
                       ) 
                     
                   
                   ⁢ 
                   V 
                   ⁢ 
                   
                      
                     V 
                      
                   
                 
                 
                   D 
                   h 
                 
               
             
           
         
       
     
     As noted above, the integration of the pressure profile in the hydraulics model  400  from the measured surface backpressure SBP M  produces an estimated standpipe pressure SPP E  (Block  350 ). The calibration procedure then uses the measured standpipe pressure (SPP M ) as a reference (Block  360 ). As noted, this measured standpipe pressure SPP M  can be measured in real-time using pressure sensors  250   a - c  off the outlet of the mud pumps  150  in the drilling system  10 . 
     As already noted above, the expected error in the hydraulics model  400  due to hydrostatic pressure difference may have less impact or may be corrected in a more straightforward fashion. Accordingly, the process  300  of  FIG.  3    does not directly address the hydrostatic pressure difference, but the difference could be similarly calibrated. For this reason, the process  300  focuses on the friction pressure losses because the calculation of the estimated standpipe pressure SPP E  in the hydraulics model  400  mostly depends on the frictional pressure loss used in the hydraulics model  400 . In other words, it can be assumed that the error in the estimated standpipe pressure SPP E  is based primarily on the frictional factor (f) calculation. Therefore, the estimation of the standpipe pressure SPP may be understood to relate to the average frictional factor (f). In this way, the measured standpipe pressure SPP M  provides an indication of the frictional factors for the calibration of the hydraulics model  400 . 
     Accordingly, the process  300  of  FIG.  3    proceeds with calibrating the friction pressure loss in the hydraulics model  400  (Block  370 ). The calibration may involve several iterations (Block  380 ,  382 ) until the hydraulics model&#39;s solution with its estimated standpipe pressure SPP E  matches the measured standpipe pressure SPP M  within some threshold (Yes at Decision  380 ). The comparative match would result in a calibrated friction pressure loss in the system  10  producing an estimated standpipe SPP E  matching the measured standpipe pressure SPP M  within a needed accuracy, which can be defined by a tolerance value of ε SPP . 
     Given the calibrated factors of the friction pressure loss in the hydraulics model  400 , the calibrated pressure profile from the hydraulics model  400  is corrected ( 384 ), and the drilling system  10  continues drilling with the corrected profile of the hydraulics model  400  (Block  386 ). 
     This iterative process starts with calculating an initial friction factor f 0 (x) of the hydraulics model  400 . The initial friction factor f 0 (x) is based on input rheology data and API-13D model, as noted previously. The iterative process then repeats the following steps of pressure integration and calibration estimation for iteration index i=0, . . . I end . First, the process integrates pressures, based on the friction factor f i (x), to calculate frictional pressure loss dP f, i , and estimated standpipe pressure (SPP i ). A calibration coefficient is then estimated as: 
     
       
         
           
             
               A 
               
                 f 
                 , 
                 i 
               
             
             = 
             
               
                 d 
                 ⁢ 
                 
                   P 
                   
                     f 
                     , 
                     i 
                   
                 
               
               
                 averaged 
                 ⁡ 
                 
                   ( 
                   
                     f 
                     i 
                   
                   ) 
                 
               
             
           
         
       
     
     The calibrated frictional factor for the hydraulics model is incremented in the iterations. The calibrated frictional factor is proportional to the difference dSPP i , and is given by: 
     
       
         
           
             
               
                 
                   f 
                   
                     i 
                     + 
                     1 
                   
                 
                 ⁡ 
                 
                   ( 
                   x 
                   ) 
                 
               
               - 
               
                 
                   f 
                   i 
                 
                 ⁡ 
                 
                   ( 
                   x 
                   ) 
                 
               
             
             = 
             
               
                 d 
                 ⁢ 
                 
                   f 
                   i 
                 
               
               = 
               
                 
                   d 
                   ⁢ 
                   S 
                   ⁢ 
                   P 
                   ⁢ 
                   
                     P 
                     i 
                   
                 
                 
                   A 
                   
                     f 
                     , 
                     i 
                   
                 
               
             
           
         
       
     
     Here, the frictional factor increment may be a constant. In other implementations, the calibration can include the frictional factor increment as a function of measured depth (x). The iterations are continued until the difference between calculated SPP i  and the reference SPP M  measured by the pressure sensor  250  produces an error within a given threshold. The difference at the end of an iteration is given by:
 
 dSPP   i   =SPP   i −SPP M .
 
     If dSPP i  is within the defined threshold or margin ε SPP , further iteration steps are not needed. Otherwise, additional iterations are needed until with error is within the threshold εSPP, which may vary and can be set according to a given implementation. 
     In the end, the corrected hydraulics model  400  has the pressure profile based on the final frictional factor, which has been incremented by the iterations. The corrected model  400  is used in the pressure control  212  of the MPD operation (Block  390 ) in order to manage pressure. In the end, being able to manage pressure allows drill operations more effectively to reach target depths, stay within the drilling window, handle imbalance, and perform other operations noted herein. For example, the frictional factor can be used for an accurate estimation of the BHP in the drilling operation. The estimated BHP can be given by:
 
 BHP=SBP+dP   h,a   +dP   friction,a  
 
     In the managed pressure drilling operation (Blocks  390 ), the control system  200  measures a parameter of the drilling operation (Block  392 ), determines an adjust to the parameter ( 394 ), and performs the adjustment ( 396 ). For example, the surface backpressure SBP may need to be adjusted because there is an imbalance between the flow-in versus the flow-out indicative of a kick or influx. Therefore, a new choke position is determined to produce the needed surface backpressure SBP to control the kick, and the system  200  actuates the chokes  122   a - b  to produce the surface backpressure SBP. Comparable adjustments can be made for other well control operations with the system  200 . 
     When the calibration procedure (Blocks  340  to  382 ) is used while the drillstring  14  is not being rotated (RPM=0), then the frictional factor increment provides an improved understanding of the rheology characteristics of the fluid. Then, the measured SPP data with RPM&gt;0 can be used for a correction of rotational friction in the annulus. The frictional power loss in the annulus is assumed to be a sum of the unrotational friction and a rotational increment:
 
 P   f,a   =P   f,0   +dP   rot  
 
     As a simple model, the rotational pressure loss increment can then be assumed to proportional to the rotation rate. 
     In contrast to existing techniques, the measured SPP data is used to calibrate a calculated pressure profile of the hydraulics model  400  used during the drilling operation. Advantageously, data from the sensors ( 240 ,  250   a - c ) can be readily available in real-time at high speed. In the meantime, PWD data may not always be available and is often delayed data. For example, PWD data may only be available at flow rates above 250-gpm so there may not even be data available for calibration during drillpipe connections or during low SCR. Aside from that, the PWD data cannot be run during a cement job. For these reasons, the SPP data used in the disclosed calibration process  300  provides a useful source for knowing what is going on downhole. 
     Nevertheless, the teachings of the present disclosure can further benefit by using PWD data, as hinted to above. As noted above with respect to  FIG.  4   , a measured value of pressure-while-drilling (PWD) can be obtained with a PWD sensor  260  on the BHA  16  of the drillstring  14 . The integration of the pressure profile of the hydraulics model  400  for the system  10  can then determine two errors for calibrating the pressure losses in the hydraulics model  400 . 
     For instance, returning to  FIG.  5   , the integration starts from the surface backpressure SBP measured at the choke&#39;s sensor ( 240 ) and integrates down the annulus ( 13 ). This integration leg can be used to estimate a value of a bottom hole pressure (BHP E ). A measured value of the bottom hole pressure BHP M  as determined from PWD data measured with the PWD sensor  260  on the BHA  16  can then be compared to the estimated bottom hole pressure BHP E . This first different between estimated bottom hole pressure BHP E  and measured bottom hole pressure BHP M  can provide an intermediate error indicative of the pressure losses missing from the hydraulics model  400  in this annular leg. 
     Meanwhile, the integration from the BHA ( 16 ) up the drillstring ( 14 ) can be used to estimate a value of standpipe pressure SPP E . As before, the estimated standpipe pressure value SPP E  can be compared to the measured value of the standpipe pressure SPP M  from standpipe sensor  250   a - c  after the pumps  150 . This second difference between estimated standpipe pressure SPP E  and measured standpipe pressure SPP M  can provide another error indicative of the pressure losses missing from the hydraulics model  400  in this drillstring leg. These two differences can be used for the correction of the friction pressure loss is represented in  FIG.  5   . Accordingly, the calibration steps (Blocks  340 - 384 ) described above can be readily modified to calibrate pressure loss based on these two differences. 
     The foregoing description of preferred and other embodiments is not intended to limit or restrict the scope or applicability of the inventive concepts conceived of by the Applicants. It will be appreciated with the benefit of the present disclosure that features described above in accordance with any embodiment or aspect of the disclosed subject matter can be utilized, either alone or in combination, with any other described feature, in any other embodiment or aspect of the disclosed subject matter. 
     As will be appreciated, teachings of the present disclosure can be implemented in digital electronic circuitry, computer hardware, computer firmware, computer software, programmable logic controller, or any combination thereof. Teachings of the present disclosure can be implemented in a programmable storage device (computer program product tangibly embodied in a machine-readable storage device) for execution by a programmable control device or processor (e.g., control system  200 , processing unit  210 , etc.) so that the programmable processor executing program instructions can perform functions of the present disclosure. The teachings of the present disclosure can be implemented advantageously in one or more computer programs that are executable on a programmable system (e.g., control system  200 , processing unit  210 , etc.) including at least one programmable processor coupled to receive data and instructions from, and to transmit data and instructions to, a data storage system (e.g., database  220 ), at least one input device, and at least one output device. Storage devices suitable for tangibly embodying computer program instructions and data include all forms of non-volatile memory, including by way of example semiconductor memory devices, such as solid-state devices, EPROM, EEPROM, and flash memory devices; magnetic disks such as internal hard disks and removable disks; magneto-optical disks; and CD-ROM disks. Any of the foregoing can be supplemented by, or incorporated in, ASICs (application-specific integrated circuits). 
     The following table of abbreviations are used herein: 
     
       
         
           
               
               
               
             
               
                   
                   
               
               
                   
                 Abbreviation 
                 Definition 
               
               
                   
                   
               
             
            
               
                   
                 AP 
                 Annular Pressure 
               
               
                   
                 BHA 
                 Bottom Hole Assembly 
               
               
                   
                 BHP 
                 Bottom Hole Pressure 
               
               
                   
                 BOP 
                 Blow out preventer 
               
               
                   
                 CBHP 
                 Constant BHP 
               
               
                   
                 F 
                 Formation 
               
               
                   
                 FP 
                 Fracture Pressure 
               
               
                   
                 HPU 
                 Hydraulic Power Unit 
               
               
                   
                 LCM 
                 Lost Circulation Material 
               
               
                   
                 MPD 
                 Managed Pressure Drilling 
               
               
                   
                 PP 
                 Pore Pressure 
               
               
                   
                 PWD 
                 Pressure-while-Drilling 
               
               
                   
                 RCD 
                 Rotating Control Device 
               
               
                   
                 ROP 
                 Rate of Penetration 
               
               
                   
                 RPM 
                 Rotations per Minute 
               
               
                   
                 SBP 
                 surface back-pressure 
               
               
                   
                 SPP 
                 Stand-Pipe pressure 
               
               
                   
                 TD 
                 Total Depth 
               
               
                   
                 UBD 
                 Underbalanced Drilling 
               
               
                   
                 UMRP 
                 Upper Marine Riser Package 
               
               
                   
                   
               
            
           
         
       
     
     The following subscripts are used herein: 
     
       
         
           
               
               
               
             
               
                   
                   
               
               
                   
                 Subscript 
                 Description 
               
               
                   
                   
               
             
            
               
                   
                 E 
                 Estimated 
               
               
                   
                 f 
                 friction 
               
               
                   
                 i 
                 iteration index 
               
               
                   
                 M 
                 Measured 
               
               
                   
                   
               
            
           
         
       
     
     The following reference numerals are used for elements throughout the disclosure: 
     
       
         
           
               
               
               
             
               
                   
                   
               
               
                   
                 Numeral 
                 Element 
               
               
                   
                   
               
             
            
               
                   
                  10 
                 drilling system 
               
               
                   
                  12 
                 borehole/wellbore 
               
               
                   
                  13 
                 annulus 
               
               
                   
                  14 
                 drillstring 
               
               
                   
                  15 
                 drillstring bore 
               
               
                   
                  16 
                 bottom-hole assembly (BHA) 
               
               
                   
                  18 
                 drill bit 
               
               
                   
                  20 
                 wellhead 
               
               
                   
                  22 
                 riser 
               
               
                   
                  24 
                 auxiliary line 
               
               
                   
                  30 
                 riser package (UMRP) 
               
               
                   
                  32 
                 flow line 
               
               
                   
                  40 
                 flow spool 
               
               
                   
                  42 
                 flow connections 
               
               
                   
                  50 
                 annular seal device 
               
               
                   
                  60 
                 rotating control device (RCD) 
               
               
                   
                  70 
                 diverter 
               
               
                   
                  72 
                 flex joint 
               
               
                   
                  74 
                 slip joint 
               
               
                   
                  76 
                 tensioner 
               
               
                   
                  78 
                 tensioner ring 
               
               
                   
                 100 
                 mobile offshore drilling unit 
               
               
                   
                 110 
                 drilling rig 
               
               
                   
                 112 
                 derrick 
               
               
                   
                 114 
                 top drive inlet 
               
               
                   
                 116 
                 top drive 
               
               
                   
                 118 
                 flow sub 
               
               
                   
                 120 
                 choke manifold 
               
               
                   
                 122 
                 choke 
               
               
                   
                 124 
                 outlet flowmeter 
               
               
                   
                 126 
                 Gas evaluation device 
               
               
                   
                 128 
                 multi-phase flowmeter 
               
               
                   
                 130 
                 separator 
               
               
                   
                 140 
                 shaker 
               
               
                   
                 142 
                 mud tank 
               
               
                   
                 144 
                 transfer line 
               
               
                   
                 150 
                 mud pump 
               
               
                   
                 152 
                 standpipe 
               
               
                   
                 160 
                 flow equipment 
               
               
                   
                 162a-b 
                 pressure chokes 
               
               
                   
                 165a-b 
                 bypass line 
               
               
                   
                 166a-b 
                 inlet flowmeter 
               
               
                   
                 170 
                 hydraulic power unit (HPU) 
               
               
                   
                 172 
                 manifold 
               
               
                   
                 164a-b 
                 bypass/supply flowmeter 
               
               
                   
                 174 
                 clamp 
               
               
                   
                 200 
                 control system 
               
               
                   
                 202 
                 control lines 
               
               
                   
                 210 
                 processing unit 
               
               
                   
                 212 
                 pressure control 
               
               
                   
                 214 
                 choke control 
               
               
                   
                 220 
                 database 
               
               
                   
                 222 
                 set point 
               
               
                   
                 230 
                 input/output interface 
               
               
                   
                 232 
                 operational data 
               
               
                   
                 240 
                 outlet (choke) pressure sensor 
               
               
                   
                 250 
                 inlet (standpipe) pressure sensor 
               
               
                   
                 260 
                 PWD sensor for BHP 
               
               
                   
                 300 
                 calibration process 
               
               
                   
                 310 
                 data input for the model 
               
               
                   
                 320 
                 model build 
               
               
                   
                 330 
                 MPD start 
               
               
                   
                 340 
                 pressure integration 
               
               
                   
                 342 
                 surface backpressure (SBP) 
               
               
                   
                 344 
                 annulus pressure integration 
               
               
                   
                 346 
                 bottomhole pressure (BHP) 
               
               
                   
                 348 
                 drillpipe pressure integration 
               
               
                   
                 350 
                 standpipe pressure (SPP) estimated 
               
               
                   
                 360 
                 SPP measured 
               
               
                   
                 370 
                 frictional pressure calibrated 
               
               
                   
                 380 
                 SPP error analyzed 
               
               
                   
                 382 
                 calibration iteration 
               
               
                   
                 384 
                 calculated pressure corrected 
               
               
                   
                 386 
                 drilling continued 
               
               
                   
                 388 
                 processing interval 
               
               
                   
                 390 
                 MPD operation 
               
               
                   
                 392 
                 drilling operation parameter measured 
               
               
                   
                 394 
                 parameter adjustment 
               
               
                   
                 396 
                 system adjustment 
               
               
                   
                 400 
                 hydraulic model 
               
               
                   
                   
               
            
           
         
       
     
     In exchange for disclosing the inventive concepts contained herein, the Applicants desire all patent rights afforded by the appended claims. Therefore, it is intended that the appended claims include all modifications and alterations to the full extent that they come within the scope of the following claims or the equivalents thereof.