Method and apparatus for real-time fluid compressibility measurements

1. Apparatus for measuring the compressibility (K) of drilling mud being circulated by a positive displacement pump, the apparatus comprising:

a pressure sensing device for sensing a pressure (P) of the drilling mud confined in a fluid module of the positive displacement pump;

a position sensing device for sensing the position (X), directly or indirectly, of a fluid displacing member in the fluid module of the positive displacement pump, wherein the apparatus further comprises a control unit communicating with said pressure sensing device and said position sensing device, the control unit being adapted to: log said pressure (P) and said fluid displacing member position (X) substantially synchronously; by means of the logged position (X), calculate a volume (V) of the confined drilling mud in the fluid module of the positive displacement pump; and by means of the logged pressure (P) and the calculated volume (V), calculate the compressibility (K) of the drilling mud,

wherein the control unit is configured to utilize the calculated compressibility (K) to obtain an updated hydraulic model of a well, and utilize the updated hydraulic model of the well to perform managed pressure drilling in the well.

2. Apparatus according to claim 1 , wherein the control unit is adapted to log the pressure (P) and the position (X) at a rate of at least 100 times the maximum rotation frequency of the positive displacement pump.

3. Apparatus according to claim 1 , wherein the pressure sensing device is adapted to sample the pressure (P) of the confined drilling mud at a sampling of at least 1 kHz.

4. Apparatus according to claim 1 , wherein the control unit, when calculating the compressibility (K) of the drilling mud, further is adapted to exclude logged data when the pressure (P) of the confined drilling mud is lower than a pressure P lo .

5. Apparatus according to claim 1 , wherein the control unit, when calculating the compressibility (K) of the drilling mud, further is adapted to exclude logged data when the pressure (P) of the confined drilling mud is higher than a pressure P hi .

6. Apparatus according to claim 1 , wherein the control unit further is adapted to use regression analysis of the logged pressure (P) and logged fluid displacing member position (X) to find the drilling mud compressibility (K).

7. Apparatus according to claim 1 , wherein the control unit, when calculating a volume (V), is adapted to account for volume changes in the positive displacement pump itself.

8. Apparatus according to claim 1 , wherein the apparatus further comprises a temperature sensing device for sensing the temperature of the drilling mud.

9. Apparatus according to claim 1 further comprising a temperature sensing device for sensing the temperature of the drilling mud, and wherein the control unit, when calculating a volume (V), is adapted to account for volume changes in the positive displacement pump itself.

10. Method for measuring the compressibility (K) of drilling mud being circulated by a positive displacement pump comprising:

sensing the pressure (P) of the drilling mud confined in a fluid module of the positive displacement pump;

sensing the position (X) of a fluid displacing member in the fluid module of the positive displacement pump;

logging the sensed pressure (P) and position (X) substantially synchronously;

by means of the logged position (X) of the fluid displacing member, calculating a volume (V) of the drilling mud confined in the fluid module of the positive displacement pump;

by means of the logged pressure (P) and the calculated volume (V), calculating the compressibility (K) of the drilling mud;

utilizing the calculated compressibility (K) to obtain an updated hydraulic model of a well; and

utilizing the updated hydraulic model of the well to perform managed pressure drilling in the well.

11. Method according to claim 10 , wherein the method comprises the step of logging the sensed pressure (P) and position (X) at a rate of at least 100 times the maximum rotation frequency of the positive displacement pump.

12. Method according to claim 10 , wherein the method comprises the step of by means of the pressure sensing device sampling the pressure (P) of the confined fluid at a rate of at least 1 kHz.

13. Method according to claim 10 , wherein the method comprises the step of excluding logged data from compressibility calculations when the pressure (P) of the confined drilling mud is lower than a pressure P lo .

14. Method according to claim 10 , wherein the method comprises the step of excluding logged data from compressibility calculations when the pressure P of the drilling mud is higher than a pressure P hi .

15. Method according to claim 10 , wherein the method further comprises the step of sensing the temperature of the drilling mud.

16. Method according to claim 10 , wherein the method further comprises the step of calculating a help function defined as Y=−In ln(V) and applying regression analysis to the picked data set to find a 2 nd order polynomial fit function Y fit =ao+alP+a2p2.

17. Method according to claim 16 , wherein the method further comprises the step of finding the drilling mud compressibility (K) as the derivative of the fit function and determining the first and second order compressibility as K 1 =a 1 −a s and K 2 =a 2 /K 1 , wherein a s is a correction term accounting for pressure induced, elastic deformation of the positive displacement pump.

18. Method according to claim 17 , wherein the method further comprises:

determining that K 1 , and K 2 do not fall within a predetermined range of values; and

setting a flag to note a possible leak or malfunction of the valves or piston seals of the positive displacement pump.

19. Method according to claim 17 , wherein the method further comprises the step of accepting the compressibility measurement as valid if K 1 and K 2 fall within a predetermined range of values.

20. Method according to claim 10 , wherein the method further comprises the step of selectively picking decompression phase data satisfying a logical function (P>P lo ) & (P<P hi ) & (X>X hi ), where X hi represents maximum decompression stroke.