Bài giảng Well drilling engineering - Chapter 6: Prediction of Fracture Gradients (Part 3) - Đỗ Quang Khánh

1 Well Drilling Engineering  Prediction of Fracture Gradients Dr. DO QUANG KHANH 2 Prediction of Fracture Gradients Well Planning Theoretical Fracture Gradient Determination Hubbert & Willis Matthews & Kelly Ben Eaton Comparison of Results Experimental Frac. Grad. Determination Leak-off Tests Lost Circulation 3 Read:  Applied Drilling Engineering, Ch. 6 HW # 4 Well Planning Safe drilling practices require that the following be considered when planning a well: Pore pressure determination Fracture gradient determination Casing setting depth selection Casing design Mud Design, H 2 S considerations Contingency planning 5 Fig. 7.21 6 7 Formation Pressure and Matrix Stress Given: Well depth is 14,000 ft. Formation pore pressure expressed in equivalent mud weight is 9.2 lb/gal. Overburden stress is 1.00 psi/ft . Calculate: 1. Pore pressure, psi/ft , at 14,000 ft 2. Pore pressure, psi, at 14,000 ft 3. Matrix stress, psi/ft 4. Matrix stress, psi 8 Formation Pressure and Matrix Stress overburden pore matrix stress = pressure + stress (psi) (psi) (psi) S = P + s 9 Fracture Gradient Determination In order to avoid lost circulation while drilling it is important to know the variation of fracture gradient with depth. Leak-off tests represent an experimental approach to fracture gradient determination. Below are listed and discussed four approaches to calculating the fracture gradient. 10 Fracture Gradient Determination 1. Hubbert & Willis: where F = fracture gradient, psi/ft = pore pressure gradient, psi/ft 11 Fracture Gradient Determination 2. Matthews & Kelly: where K i = matrix stress coefficient s = vertical matrix stress, psi 12 Fracture Gradient Determination 3. Ben Eaton: where S = overburden stress, psi g = Poisson’s ratio 13 Example A Texas Gulf Coast well has a pore pressure gradient of 0.735 psi/ft . Well depth = 11,000 ft . Calculate the fracture gradient in units of lb/gal using each of the above four methods. Summarize the results in tabular form, showing answers, in units of lb/gal and also in psi/ft . 14 2. Matthews & Kelly In this case P and D are known, may be calculated, and is determined graphically. (i) First, determine the pore pressure gradient. Example 15 Example - Matthews and Kelly (ii) Next, calculate the matrix stress. S = P + s s = S - P = 1.00 * D - 0.735 * D = 0.265 * D = 0.265 * 11,000 s = 2,915 psi 16 Example - Matthews and Kelly (iii) Now determine the depth, , where, under normally pressured conditions, the rock matrix stress, s would be 2,915 psi. S n = P n + s n n = “normal” 1.00 * D i = 0.465 * D i + 2,915 D i * (1 - 0.465) = 2,915 17 Example - Matthews and Kelly (iv) Find K i from the plot on the right, for For a south Texas Gulf Coast well, D i = 5,449 ft K i = 0.685 18 Example - Matthews and Kelly (v) Now calculate F : 19 20 Example Ben Eaton: 21 Variable Overburden Stress by Eaton At 11,000 ft S/D = 0.96 psi/ft 22 Fig. 5-5 At 11,000 ft g = 0.46 23 Summary of Results Note that all the methods take into consideration the pore pressure gradient. As the pore pressure increases, so does the fracture gradient. In the above equations, Hubbert & Willis apparently consider only the variation in pore pressure gradient. Matthews & Kelly also consider the changes in rock matrix stress coefficient, and in the matrix stress ( K i and s i ). 24 Summary of Results Ben Eaton considers variation in pore pressure gradient, overburden stress and Poisson’s ratio, and is probably the most accurate of the four methods. The last two methods are actually quite similar, and usually yield similar results. 25 Similarities Ben Eaton: Matthews and Kelly: 26 9 10 11 12 14 16 18 Pore Pressures 27 Experimental Determination of Fracture Gradient The leak-off test Run and cement casing Drill out ~ 10 ft below the casing seat Close the BOPs Pump slowly and monitor the pressure 28 29 45 80 105 120 120 120 120 120 120 40 20 30 31 32 33 Experimental Determination of Fracture Gradient Example: In a leak-off test below the casing seat at 4,000 ft, leak-off was found to occur when the standpipe pressure was 1,000 psi . MW = 9 lb/gal . What is the fracture gradient?