CN-116981828-B - Characterization of formation fractures using three-section models based on post-shut-in acoustics and pressure decay

Abstract

A method for determining a characteristic of a hydraulic fracture from a measurement of pressure in a well after stopping pumping of the fracturing fluid into the well (shut-in), comprising determining a first time after shut-in, after which a decrease in measured pressure is caused by fluid leakage in the fracture. A second time after shut-in is determined, after which the pressure drop is caused by fluid leakage, fracture growth, and fluid pressure equalization in the fracture. A third time after shut-in is determined, after which the pressure drop is caused by fluid leakage, fracture growth, fluid pressure balance in the fracture, and pressure drop in the near wellbore region. The determined values of fluid efficiency, minimum stress, and net pressure are such that the calculated pressure over time matches the pressure measurement within a predetermined threshold.

Inventors

• S. Rahimi Agdam
• I. S. Abo Said
• D Mousse
• D. Murray

Assignees

• 塞斯莫斯股份有限公司

Dates

Publication Date

20260505

Application Date

20220315

Priority Date

20210315

Claims (20)

1. 1. A method of determining hydraulic fracturing characteristics from measurements of pressure in a well after stopping pumping fracturing fluid into the well, comprising: Determining a first time after shut-in, wherein the measured pressure decrease is caused by fluid leakage in the fracture; determining a second time after shut-in, wherein the decrease in pressure is caused by fluid leakage in the fracture, fracture growth, and fluid pressure balance; Determining a third time after shut-in, wherein the decrease in pressure is caused by fluid leakage in the fracture, fracture growth, fluid pressure balance, and pressure drop in the near wellbore region, and The value of the fluid efficiency, the value of the minimum stress, and the value of the net pressure are determined such that the calculated value of the time-dependent pressure matches the pressure measurement within a predetermined threshold, wherein the time-dependent pressure is calculated based on a cause of a pressure decrease in a segment corresponding to (i) between the third time and the second time, (ii) between the second time and the first time, and (iii) after the first time.
2. 2. The method of claim 1, wherein starting the calculated pressure at the first time comprises calculating a catter leak.
3. 3. The method of claim 1, wherein calculating the pressure beginning at the second time and ending at the third time comprises calculating Where ζ f = local efficiency at shut-in or fracture growth ratio, η av = average efficiency from start of pumping fluid to shut-in, p av = average net pressure in fracture, p ∗ = fracture propagation pressure, p ̄ n = average net pressure, p n 0 = initial net pressure, t inj = injection time, t = time for pressure calculation, and Smin-minimum principal stress.
4. 4. The method of claim 1, wherein the calculated pressure from the third time to the second time comprises calculating a near wellbore pressure drop for an axisymmetric bi-wing fracture having a cylindrical cross-sectional growth according to darcy's equation flow.
5. 5. The method of claim 1, wherein the calculated pressure from the third time to the second time comprises analyzing reflection events in pressure or pressure time derivative measurements in response to acoustic pulses transmitted into the well that induce tube waves in the well to determine a near-field conductivity index, thereby constraining the calculation of near-wellbore pressure drop.
6. 6. The method of claim 1, further comprising: using the determined value of fluid efficiency, the value of minimum stress and the value of net pressure, and The length, width, height, and leakage parameters of the fracture are determined using the value of young's modulus, the value of poisson's ratio, the value of the viscosity of the fracturing fluid, the value of the pumped volume of the fracturing fluid, the value of the volumetric rate at which the fracturing fluid is pumped, the value of the number of well perforation clusters through which the fracturing fluid is pumped.
7. 7. The method of claim 6, wherein determining the length, width, and height of the fracture comprises using a Perkins-Kern-Nordgren model of fracture geometry.
8. 8. The method of claim 6, wherein the determined fracture length, fracture width, fracture height, and leak-off parameters are used to estimate fluid productivity for each fracturing treatment stage and the entire well.
9. 9. The method of claim 1, wherein the third time is determined after the water hammer caused by stopping pumping ends.
10. 10. The method of claim 1, wherein the second time is determined when the rate of change of the pressure measurement with respect to time is below a predetermined threshold.
11. 11. The method of claim 1, wherein the first time is determined when the pressure measurement is below a fracture pressure of the rock formation into which the fracturing fluid is pumped.
12. 12. The method of claim 1, further comprising estimating a fluid pressure in the formation penetrated by the fracture using the determined minimum stress.
13. 13. The method of claim 1, wherein the efficiency comprises a fraction of a fracture volume relative to a volume of fracturing fluid pumped into the fracture.
14. 14. The method of claim 1, further comprising determining fracture conductivity with respect to time after shut-in.
15. 15. The method of claim 14, further comprising determining the conductivity of the proppant pack when the fracture conductivity ceases to change over time after shut-in.
16. 16. The method of claim 1, further comprising varying at least one of a viscosity of the fracturing fluid, a pumping volume of the fracturing fluid, a volumetric rate of the pumped fracturing fluid, or a concentration of proppant in the fracturing fluid to pump the fracturing fluid into different stages in the well or different wells.
17. 17. A computer program stored in a computer readable medium, the program comprising logic operable to cause a programmable computer to perform operations based on pressure measurements in a well after stopping pumping a fracturing treatment agent into the well, the operations comprising: determining a first time after shut-in, wherein the decrease in measured pressure is caused by a fluid leak in the fracture; determining a second time after shut-in, wherein the decrease in pressure is caused by fluid leakage in the fracture, fracture growth, and fluid pressure balance; Determining a third time after shut-in, wherein the decrease in pressure is caused by fluid leakage in the fracture, fracture growth, fluid pressure balance, and pressure drop in the near wellbore region, and The value of the fluid efficiency, the value of the minimum stress, and the value of the net pressure are determined such that the calculated value of the time-dependent pressure matches the pressure measurement within a predetermined threshold, wherein the time-dependent pressure is calculated based on a cause of a pressure decrease in a segment corresponding to (i) between the third time and the second time, (ii) between the second time and the first time, and (iii) after the first time.
18. 18. The computer program of claim 17, wherein starting the calculated pressure at the first time comprises calculating a catter leak.
19. 19. The computer program of claim 17, wherein calculating the pressure beginning at the second time and ending at the third time comprises calculating Where ζ f = local efficiency at shut-in or fracture growth ratio, η av = average efficiency from start of pumping fluid to shut-in, p av = average net pressure in fracture, p ∗ = fracture propagation pressure, p ̄ n = average net pressure, p n 0 = initial net pressure, t inj = injection time, t = time for pressure calculation, and Smin-minimum principal stress.
20. 20. The computer program of claim 17, wherein the calculated pressure from the third time to the second time comprises calculating a near wellbore pressure drop for an axisymmetric double wing fracture with a cylindrical cross-sectional growth according to darcy's equation flow.

Description

Characterization of formation fractures using three-section models based on post-shut-in acoustics and pressure decay Background Pressure decay analysis is sometimes used to analyze hydraulic fracturing in subterranean formations penetrated by a well. Pressure decay analysis captures pressure data over a period of time after fluid injection into the formation. Such fluid injection may be hydraulic fracturing, in which proppants are injected to maintain fracture propagation, allowing for subsequent enhanced hydrocarbon production. There are a number of models and methods known in the art. The present invention significantly improves upon the prior art by considering the individual contributions of the near-wellbore zone to pressure decay and using direct acoustic measurements of the conductivity of the near-wellbore zone to limit the fracture and pressure decay model. This allows a more accurate determination of the fracture system and its characteristics. Disclosure of Invention According to one aspect of the present disclosure, a method for determining a characteristic of a hydraulic fracture from a measurement of pressure in a well after stopping pumping of a fracturing fluid into the well (shut-in), includes determining a first time after shut-in, after which a decrease in measured pressure is caused by fluid leakage in the fracture. A second time after shut-in is determined, after which the pressure drop is caused by fluid leakage, fracture growth, and fluid pressure equalization in the fracture. A third time after shut-in is determined, after which the pressure drop is caused by fluid leakage, fracture growth, fluid pressure balance in the fracture, and pressure drop in the near wellbore region. The determined values of fluid efficiency, minimum stress, and net pressure are such that the calculated pressure over time matches the pressure measurement within a predetermined threshold. The time dependent pressure is calculated based on the cause of the pressure decrease at a segment corresponding to (i) the third time and the second time, (ii) the second time and the first time, and (iii) after the first time. A computer program according to another aspect of the present disclosure is stored in a non-transitory computer-readable medium and includes logic operable to cause a computer to perform operations corresponding to the method of the previous aspect of the present disclosure. In some embodiments, starting the calculated pressure at the first time includes calculating a kart leak (CARTER LEAK off). In some embodiments, the calculated pressure beginning at the second time and ending at the third time comprises calculating Where ζ f = local efficiency at shut-in or fracture growth ratio, η av = average efficiency from start of pumping fluid to shut-in, p av = average net pressure in fracture, p * = fracture propagation pressure, p- n = average net pressure, p n0 = initial net pressure, t inj = injection time, t = time for pressure calculation, and Smin-minimum principal stress. In some embodiments, calculating the pressure from the third time to the second time includes calculating a darcy's equation flow (Darcy equation flow) for an axisymmetric double-wing fracture having a cylindrical cross-sectional growth. In some embodiments, calculating the pressure from the third time to the second time includes analyzing the reflection in the pressure or pressure time derivative measurements in response to the acoustic pulse transmitted into the well to calculate the near field conductivity. The acoustic pulses induce a tubular wave in the well. The near field conductivity index is used to limit the calculation of near wellbore pressure drop. Some embodiments further include determining the length, width, height, and leakage parameters of the fracture using the determined value of fluid efficiency, the value of minimum stress, and the value of net pressure, and using the value of young's modulus, the value of poisson's ratio, the value of viscosity of the fracturing fluid, the value of pumped volume of the fracturing fluid, the value of volumetric rate of pumped fracturing fluid, the value of the number of well perforation clusters through which the pumped fracturing fluid passes. In some embodiments, the determined length, width, height, and leak-off parameters are used to estimate fluid productivity in the well and throughout the fracturing treatment stage in the well. In some embodiments, determining the length, width, and height of the fracture includes using a Perkins-kernel-Nordgren model of the fracture geometry. In some embodiments, the third time occurs after the water hammer ends due to the stopped pumping. In some embodiments, the second time is determined when the rate of change of the pressure measurement with respect to time is below a predetermined threshold. In some embodiments, the first time is determined when the pressure measurement is below a fracturing pressure of the rock formation into w