Fracture gradient prediction: an overview and an improved method
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Abstract
The fracture gradient is a critical parameter for drilling mud weight design in the energy industry. A new method in fracture gradient prediction is proposed based on analyzing worldwide leakoff test (LOT) data in offshore drilling. Current fracture gradient prediction methods are also reviewed and compared to the proposed method. We analyze more than 200 LOT data in several offshore petroleum basins and find that the fracture gradient depends not only on the overburden stress and pore pressure, but also on the depth. The data indicate that the effective stress coefficient is higher at a shallower depth than that at a deeper depth in the shale formations. Based on this finding, a depthdependent effective stress coefficient is proposed and applied for fracture gradient prediction. In some petroleum basins, many wells need to be drilled through long sections of salt formations to reach hydrocarbon reservoirs. The fracture gradient in salt formations is very different from that in other sedimentary rocks. Leakoff test data in the salt formations are investigated, and a fracture gradient prediction method is proposed. Case applications are examined to compare different fracture gradient methods and validate the proposed methods. The reasons why the LOT value is higher than its overburden gradient are also explained.
Keywords
Fracture gradient prediction Leakoff test Breakdown pressure Mud loss Fracture gradient in salt1 Introduction
1.1 Concept of fracture gradient
For drilling in the oil and gas industry and geothermal exploration and production, fracture pressure is the pressure required to fracture the formation and to cause mud losses from a wellbore into the induced fractures. Fracture gradient is obtained by dividing the true vertical depth into the fracture pressure. The fracture gradient is the upper bound of the mud weight; therefore, the fracture gradient is an important parameter for mud weight design in both stages of drilling planning and operations. If the downhole mud weight is higher than the formation fracture gradient, then the wellbore will have tensile failures (i.e., the formation will be fractured), causing losses of drilling mud or even lost circulation (total losses of the mud). Therefore, fracture gradient prediction is directly related to drilling safety.
If the mud weight is higher than the fracture gradient of the drilling section, it may fracture the formation, causing mud losses. To prevent mud losses caused by high mud weight, as needed where there is overpressure, a safe drilling mud weight margin is needed. Otherwise, a casing needs to be set to protect the overlying formations from being fractured, as demonstrated in Fig. 1.
Fracture gradient is defined by the Schlumberger Oilfield Glossary as the pressure gradient required to induce fractures in the rock at a given depth. Based on this definition, the fracture gradient is the maximum mud weight that a well can hold without mud losses and without uncontrolled tensile failures (fracture growth). However, there is no consensus for a method to calculate the fracture gradient in the oil and gas industry. Some pore pressure specialists use the minimum stress gradient as the fracture gradient, but others may use the maximum leakoff pressure gradient (fracture breakdown pressure gradient) or the fracture initiation pressure gradient as the fracture gradient. In this paper, the maximum leakoff pressure gradient (the peak value in the LOT test) is used as the fracture gradient. That is, the effects of the minimum stress, tensile strength, and the wellbore stress concentrations will be considered for fracture gradient prediction.
1.2 Fracture gradient from leakoff tests
Typically, a formation pressure integrity test or the formation leakoff test is performed in drilling operations to evaluate cement jobs, determine the casing setting depth, test the resistance of tensile failures of a casing shoe, and estimate formation fracture gradient (Postler 1997). Based on the injection pressure, volume, and time, pressure integrity tests can be classified into three, i.e., formation integrity test (FIT), leakoff test (LOT), and extended leakoff test (XLOT). The purpose of conducting a FIT is to test the formation fracture pressure required for kick tolerance and/or safe drilling mud weight margin. The maximum pressure in the FIT test is less than the fracture initiation and formation breakdown pressures.
For a typical LOT test, once the peak pressure, or the breakdown pressure (P _{b}), is reached, the pump is shut down to record the 10s pressure reading and then, shutin pressure is continuously recorded for more than 10 min, as shown in Fig. 2b. Fracture pressures can be measured directly from LOT, XLOT, or other similar tests, e.g., minifrac test and diagnostic fracture injection test (DFIT).
1.3 Fracture gradient and mud losses in drilling operations
Understanding the mechanism of mud losses while drilling can help to better determine the fracture gradient. The possible reasons of mud losses in drilling operations are presented in the following cases. For different cases, the methods for mud loss control and fracture gradient design are different.
Case 1 Seepage mud loss: For permeable rocks (excluding those with highly fractured preexisting fractures), once the mud pressure applied in the borehole is greater than the formation pore pressure (p _{mud} > p), the mud will invade and flow into the formation through pores due to high permeability. This is the seepage mud loss, which can easily happen in permeable sandstones and limestones, particularly for the low pore pressure or depleted reservoirs. Seepage mud loss is a slow mud volume escape or loss into the formation through porous materials or small holes. Therefore, seepage loss in most cases is minimal (normally, the loss <10 bbl/h for oilbased mud and <25 bbl/h for waterbased mud). This will have little effect on the drilling operations. Since the seepage mud loss is mainly caused by the connected pores or by formation permeability, lost circulation material (LCM) pills can be used to block the flow path.
Case 2 Small loss: If the mud pressure is greater than the fracture initiation pressure, but less than the breakdown pressure (P _{i} ≤ p _{mud} < P _{b}) in the intact shale, there will be only small volume of drilling fluid lost into the well. It can be seen from the LOT tests in Fig. 2 that it only needs 0.3 bbls of fluid pumped into the well from the initiation pressure (P _{i}) to the breakdown pressure (P _{b}). Therefore, mud loss is minor in this case.
Case 3 Partial loss: If the mud pressure is slightly greater than the fracture breakdown pressure (p _{mud} ≥ P _{b}) in the intact shale, this will be a situation when some volume of drilling fluid is lost into the formation, but some drilling mud volume still circulates back to the surface. In this case, the fluid volume not only has losses, but it may also have the ballooning issue to deal with. However, this type of fluid loss will not lead to a well control situation because the total hydrostatic pressure of the mud does not decrease.
Case 4 Partial loss and total loss in natural fractures: Once the mud pressure is greater than the minimum stress (p _{mud} > σ _{min}) in the preexisting uncemented fractures, the fractures will open and the mud will flow into the natural fractures. The degree of mud loss depends on both fracture properties (e.g., fracture aperture and spacing) and the difference of the mud pressure and the minimum stress.
Case 5 Total loss or lost circulation: It occurs either in intact rocks with p _{mud} ≫ P _{b} or in the rocks having preexisting natural fractures and faults with p _{mud} > σ _{min}. This is the worst situation because there is no mud returning to surface and the mud level will drop to any level down in the hole. Losing a lot of drilling fluids into the well will directly affect hydrostatic pressure at the bottom. If the mud cannot be kept full in the hole, it might be a time when the hydrostatic pressure of the mud is less than the reservoir pressure. Eventually, a well control situation will happen.
It should be noted that mud loss mechanisms described above are mainly for clastic formations but may not be relevant to carbonate formations. Some carbonate reservoirs contain different sizes of vugs or caves which are interconnected by natural fractures. As a result, a large amount of mud could be lost once the drilling mud weight is greater than the reservoir pressure (p _{mud} > p). Therefore, the fracture gradient in this case is not much higher than the reservoir pressure. In the following study, we will not consider this case.
Therefore, for most cases, the fracture gradient (FG) should be equal to or less than the breakdown pressure gradient (i.e., FG ≤ P _{b}) to avoid uncontrollable mud losses.
2 Some current methods for fracture gradient prediction
2.1 Hubbert and Willis' method
Later on, many empirical and theoretical equations and applications for fracture gradient prediction were presented (Haimson and Fairhurst 1967; Matthews and Kelly 1967; Eaton 1969; Anderson et al. 1973; Althaus 1997; Pilkington 1978; Daines 1982; Breckels and van Eekelen 1982; Constant and Bourgoyne 1988; Aadnoy and Larson 1989; Wojtanowicz et al. 2000; Barker and Meeks 2003; Fredrich et al. 2007; Wessling et al. 2009; Keaney et al. 2010; Zhang 2011; Oriji and Ogbonna 2012). We only review some commonly used methods in the following sections. It should be noted that the Biot coefficient is usually assumed to be 1 in fracture gradient calculation in the oil and gas industry; therefore, the Biot coefficient is not considered in the related equations. In this paper, we follow the same practice except the Biot coefficient is existed in a specific equation.
2.2 Matthews and Kelly’s method
In their paper, Matthews and Kelly (1967) obtained k _{0} from the fracture initiation pressures. Therefore, this fracture gradient is higher than the fracture extension gradient (the minimum stress gradient).
2.3 Eaton’s method
Eaton’s method enables the consideration of the effect of different rocks (e.g., shale, sandstone) on fracture gradient, because the lithology effect is considered in Poisson’s ratio calculated from Eq. (5). In fact, Eq. (4) is the equation of the minimum value of the minimum stress derived from a uniaxial strain condition (Zhang and Zhang 2017). However, in the industry applications apparent Poisson’s ratios can be used for simplification in different rocks to calculate fracture gradients, e.g., using ν = 0.43 for shales \(\left( {{\text{or}}\,\frac{\nu }{{1  \nu }} = 0.75} \right)\) and ν = 0.3 for sandstones \(\left( {{\text{or}}\, \frac{\nu }{{1  \nu }} = 0.5} \right)\). In this case, Eaton’s equation is equivalent to Matthews and Kelly’s equation if \(k_{0} = \frac{\nu }{1  \nu }\).
2.4 Daines’ method
2.5 Fracture gradient from wellbore tensile failure
For example, in a case of \(\alpha_{\text{b}} = 0.8\), \(\nu = 0.3\), and \(\eta = 0.23\), the breakdown pressure is \(P_{\text{b}} = 0.65(3\sigma_{\text{h}}  \sigma_{\text{H}}  0.46p + T_{0} )\). Compared to Eq. (8), the breakdown pressure in the permeable case is smaller than that in the impermeable case.
Equation (10) indicates that a higher mud temperature can increase the formation breakdown pressure, namely increase the fracture gradient.
2.6 Upper and lower bounds of fracture gradient
3 Improved methods for fracture gradient prediction
We start this section with the following quotation (Althaus 1997), “the purpose of this paper is to open this topic up to discussion again and to turn new studies into new directions. The old solutions have served us well in fracture gradient prediction for many years—but are they really the final answers to this problem?”.
3.1 Evaluation of Matthews and Kelly’s method
We then plot the effective stress coefficient \(k_{0} = ({\text{LOT}}  P_{\text{p}} )/({\text{OBG}}  P_{\text{p}} )\) in Fig. 4. It shows that most data points are located within k _{0} = 0.5–1. The average value of the effective stress coefficient from k _{0} = 0.5–1 is k _{0} = 0.75. Therefore, k _{0} = 0.75 can be used as the most likely value to calculate the fracture gradient by plugging k _{0} = 0.75 into Matthews and Kelly’s equation [Eq. (3)].
3.2 Improved fracture gradient prediction

For the low case of the fracture gradient: k = 0.5, a = 0.1, and b = 5100 (left line in Fig. 5);

For the high case of the fracture gradient: k = 0.9, a = 0.4, and b = 12,500 (right line in Fig. 5);

For the most likely case of the fracture gradient: k = 0.75, a = 0.15, and b = 7200 (middle line in Fig. 5).
Normally the fracture gradient in sandstones is lower than that in shales. Based on our field applications, the low case of k _{0} shown above may be used for estimating the most likely case of fracture gradient in sandstones or sandy formations.
It should be noted that k _{0} varies markedly in different basins or fields; therefore, the parameters of k, a, and b in Eq. (15) should be obtained from each field for a better application if the measured LOT data are available.

For the most likely case of the fracture gradient in shales: k = 0.75, a = 0.15, and b = 7200.
3.3 Fracture gradient in salt formations
For subsalt wells in the Gulf of Mexico and other petroleum basins, drilling needs to penetrate thick salt formations to reach the hydrocarbon reserves. Salt creep in the subsalt wells is a challenge for borehole stability (Zhang et al. 2008); therefore, a heavier mud weight (e.g., mud weight can be as high as 80%–90% of the overburden stress) needs to be used to control salt creep. This high mud weight requires a higher fracture gradient in the salt formation to avoid salt being fractured.
It should be noted that Eq. (17) is an empirical equation only for salt formations. If inclusions of rocks exist in salt formations (e.g., in salt sutures), the fracture gradient should be lower and depend on the fracture gradient in the rocks. A case study shown in Fig. 7 examines the fracture gradients in salt, presalt, and subsalt formations. The salt fracture gradient is estimated from Eq. (17) with C = 500 psi, which matches the measured FIT data in the salt. In the subsalt formations, Eaton’s method underestimates the fracture gradient based on the measured data, but the proposed fracture gradient with a depthdependent k _{0} [Eq. (16)] has a better estimate on the fracture gradient.
3.4 Reasons of LOT being greater than OBG
It is often found that some LOT values in the leakoff tests are greater than their overburden stress gradients (i.e., LOT > OBG), for example in the Green Canyon area of the Gulf of Mexico and in some subsalt formations. These may be caused by the following reasons: (a) the measured LOT value is the formation breakdown pressure and (b) the formation is in tectonic stress regimes.
3.4.1 LOT value being the formation breakdown pressure
Figure 8 plots the estimated and measured pore pressure, surface mud weight, calculated and verified overburden stress, and measured LOT values. It also plots the calculated fracture gradient bounds (high, most likely, and low cases) from the proposed method [Eq. (16)]. The figure shows that although one of the measured LOTs is greater than the overburden, all LOT data are within the calculated fracture gradient bounds.
3.4.2 In tectonic stress regimes
Figure 9 also plots the measured LOT values in the presalt and subsalt formations. There is also a measured FIT value in the salt. The highside and the most likely fracture gradients in shales calculated from the proposed method [Eq. (16)] are compared to the Matthews and Kelly’s method (with a constant k _{0} = 0.75) in Fig. 9. It should be noticed that the sandstone fracture gradient is not plotted in the figure. The most likely (C = 500 psi) and highcase (C = 1000 psi) fracture gradients in salt formation are calculated from Eq. (17) and plotted in the same figure. Figure 9 shows that the proposed methods are better for calculating the fracture gradients.
4 Conclusions
Analysis of more than 200 measured LOT data points in worldwide petroleum basins shows that the effective stress coefficient k _{0} has a higher value at the shallower depth and decreases as the depth increases. Based on this phenomenon, a new fracture gradient method using a depthdependent k _{0} is proposed. Case applications show that the proposed method can improve the fracture gradient prediction. For a better predrill prediction, the fracture gradient needs to be calibrated to the offset data, because k _{0} may behave differently for different regions.
The LOT and FIT data in salt formations in the Gulf of Mexico are also examined. The results show that the LOT and FIT pressures in most salt formations are larger than the overburden stress. The fracture gradient in salt formation is proposed based on the measured data. The reasons why LOT peak pressures are higher than their overburden stresses are also explained, particularly in the subsalt formations. Case studies are investigated to examine the proposed methods.
Notes
Acknowledgements
This work was partially supported by the Program for Innovative Research Team in the University sponsored by Ministry of Education of China (IRT17R37), National Key R&D Project (2017YFC0804108) of China during the 13th FiveYear Plan Period, and Natural Science Foundation of Hebei Province of China (D2017508099).
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