Pre-Spud Mud Loss Flow Rate in Steeply Folded Structures

Pre-Spud Mud Loss Flow Rate in Steeply Folded Structures — In this paper, a new method that predicts the pre-spud mud loss flow rate in formations with tectonic fractures of steeply folded structures is proposed. The new method is based on finite element analysis of the palaeotectonic and current tectonic stress field and fracture distribution. The steps of the method are as follows. First, palaeo-tectonic stress distribution is simulated through finite element analysis. The tectonic fracture distribution of the region is obtained by combining rock failure criteria with palaeo-tectonic stress distribution. Afterward, the tectonic fracture density, aperture, porosity and permeability are calculated by studying the rebuilding process of current stress to the fracture parameters. Finally, the mud loss flow rate is calculated according to fracture parameters and the basic data of a given well. The new method enables the prediction of the mud loss flow rate before drilling steeply folded structures. Oil & Gas Science and Technology – Rev. IFP Energies nouvelles, Vol. 69 (2014), No. 7, pp. 1269-1281 Copyright 2013, IFP Energies nouvelles DOI: 10.2516/ogst/2012105


INTRODUCTION
Steeply folded structures have complex conditions and are prone to develop cracks, thereby leading to serious circulation loss during drilling and danger during the drilling process (Xu et al., 1997;Quintana et al., 2001;Du, 2004).Thus, predicting circulation loss during the pre-spud phase is important.Currently, numerous studies on methods predicting circulation loss concentrate on rock mechanics to describe and evaluate crustal stress (Prensky, 1992;Bell and Aadnøy, 1998;Desroches and Kurkjian, 1999;Nikolaevskiy and Economides, 2000), to analyze and investigate the tectonic fracture distribution, and to obtain pressure loss (Constant David and Bourgoyne, 1988;Rocha and Bourgoyne, 1996;Sadiq and Nashawi, 2000;Rocha et al., 2004).Determining the fracture pressure gradient from well logs is another way to predict circulation loss (Anderson et al., 1973;Holbrook, 1989;Draou and Osisanya, 2000).The methods mentioned above can predict whether circulation loss occurs or not.However, these methods cannot predict the mud loss flow rate before drilling, which is more important during the actual drilling process.Therefore, we propose a new method for predicting the mud loss flow rate in tectonic fractures of steeply folded structures.This new method is based on the numerical simulation of the tectonic stress field and fracture distribution (Dai and Li, 2000;Maerten and Maerten, 2006;Deng et al., 2006) and quantitative description of tectonic fracture parameters related to the mud loss flow rate, such as density, aperture, porosity and permeability (Murray, 1968;Chen and Bai, 1998;Ji et al., 2010a).The main steps of the method are as follows.The geological structure model is established according to the local tectonic fracture distribution and main tectonic movement period.Palaeo-tectonic stress distribution is calculated through finite element analysis, and tectonic fracture distribution of the region is calculated by combining rock failure criteria and palaeo-tectonic stress distribution.Another geological structure model for current stress simulation is established according to local current stress and tectonic features.Tectonic fracture density, aperture, porosity and permeability are calculated by studying the rebuilding process of current stress to the fracture parameters.Finally, the mud loss flow rate is calculated on the basis of fracture parameters and basic data, such as pore pressure profile, mud weight and fracture pressure, among others, in a given well.Taking Block F of a gas field in Sichuan Basin, China, as an example, the tectonic stress field and fracture distribution are analyzed.The predicted value of the mud loss flow rate agrees well with the actual value in Well PG-X1, which means that the method is feasible in predicting the mud loss flow rate before drilling steeply folded structures.This method will be helpful in applying preventive measures during the actual drilling practice in steeply folded structures.

Characteristic Analysis of Geological Structure
The structure of the site, history of structural evolution, in situ basin structural characteristics, formation sequence and sediment fill were researched and analyzed by using tectonic evolution analysis to comprehend the characteristics of the geological structure (Wei Jia et al., 2008).The structural pattern, formation components, lithology and direction of the structure were determined.The depth of the layers of the structural diagram in the area was also obtained for model establishment.

Geological Model Establishment
By analyzing the geological structure characteristics, layers with similar lithology were grouped together.Geometry simplification was made by using the depth structural diagram, and the geological model of the area was established.

FINITE ELEMENT ANALOGY OF TECTONIC STRESS DISTRIBUTION
The numerical computations of stress distribution can be divided into two sections: palaeo-stress distribution and current stress distribution.As shown in Figure 1, the steps in the evaluation of palaeo-stress distribution are as follows.First, the historical period in which the fracture was formed and the shape of the geological structure pre-and after this period could be determined by using the results of the tectonic evolution analysis.A geological structure model can be established based on the shape of the geological structure before fracture formation.Afterward, the boundary conditions and loads are set by using the trial and error method, which is based on the deformation standard, until the geological structure gained by simulation agrees with the actual structure after fracture formation.Finally, palaeo-stress distribution can be determined by finite element analysis.The current stress distribution can be evaluated in the same way as the palaeo-stress distribution.However, the current geological structure, boundary conditions and loads are used during finite element analysis in the computation of current stress distribution.Current boundary loads can be determined through logging data, data of the indoor core experiment, data of hydraulic fracturing, and other kinds of well data in the area evaluated.
The constitutive law used in the simulation is a linear elastic model, which is commonly used in the fracture simulation process of pay zones (Coblentz and Sandiford, 1994;Kwon and Mitra, 2004).

Boundary Conditions and Load Parameters of Palaeo-Tectonic Stress Simulation
Accurately setting the factors influencing the control of the structural fracture is difficult because of the complexity of geological structure formation.Therefore, the boundary conditions and the load deformation of palaeo-tectonic stress simulation need repeated trial and error calculations.The deformation standard is applied in this paper.After the boundary conditions and load are loaded, the deformation of the geological body is matched with the practical characteristics.
Simulation results are checked with the real structural features, particularly the shape, length and position of the anticlines, synclines or faults.

Boundary Conditions and Load Parameters of Current Tectonic Stress Simulation
Calculating the crustal stress in a drilled well is important in determining the boundary conditions and load parameters of the geological model for current tectonic stress simulation.Currently, numerous methods are available in evaluating crustal stress.The equations below are used for the evaluation of crustal stress in this paper (Gazaniol et al., 1995;Helio Santos et al., 1999;Ge et al., 2001).In this study, the fracturing method is used to calculate horizontal principal stress: where r H and r h are the maximum and minimum horizontal principal stress, respectively (MPa); p p is the pore pressure (MPa); p s is the instant knock-off pressure (MPa); p f is fracture pressure (MPa); and S t is rock tensile strength (MPa).The flow diagram of tectonic fracture finite element analogy.
Hydraulic fracturing points are chosen as the key points of tectonic stress simulation based on the statistical hydraulic fracturing information of the wells drilled in the research area.The horizontal principal stress is obtained at the key points by using Equations ( 1), (2).Afterward, boundary conditions and load parameters are loaded using the trial and error method until the simulated tectonic stress is nearly consistent with the value calculated from the hydraulic fracturing in the key points.The differential value between simulated tectonic stress and calculated tectonic stress from hydraulic fracturing is less than 5% when few key points exist, whereas the differential value is larger than 5% when many key points exist.

Procedure of Finite Element Analogy
The procedure of finite element analogy is shown in Figure 1.

QUANTITATIVE DESCRIPTIONS FOR TECTONIC FRACTURE PARAMETERS
The parameters of tectonic fracture related to the prediction of the mud loss flow rate include fracture density, aperture, porosity and permeability.The current stress difference is low and cannot create new fractures.
Current fracture density has the same value as palaeo-fracture density.Current stress can rebuild palaeo-fractures and can cause fracture aperture, porosity and permeability to change.
3.1 Calculation Methods for Palaeo-Fracture Parameters

Fracture Density Calculation
Rock deformation can accumulate strain energy under stress.Rock failure appears when the release rate of strain energy is equal to the energy required to form the fracture per unit area (surface energy density).Part of the strain energy released is utilized to provide energy for the increasing fracture surface area, and the remaining strain energy is released in the form of an elastic wave.The energy of the elastic wave is minimal and can be neglected.The Coulomb-Mohr principle was applied in the examination of shear fracture under triaxial compression stress.The computation for fracture density under triaxial compression stress is as follows (Ji et al., 2010b): The Griffith-failure principle was applied in the examination of tension fracture under tension stress.When ðr 1 þ 3r 3 Þ > 0, then the formula for fracture density under tensile stress is as follows: Let ðr 1 þ 3r 3 Þ 0, r 3 ¼ Àr t and h ¼ 0. Thus, when h is equal to zero, the fracture plane is parallel to the direction of r 1 and perpendicular to the direction of r 3 , so the fracture linear density equals the total number of fractures in the rock volume.The formula for fracture density is as follows: where D Vf c is the fracture volume density under triaxial compression stress (m À2 ); D Vf is the fracture volume density under tensile stress (m À2 ); D lf is the fracture linear density (m À1 ); r 1 , r 2 and r 3 are the maximum principal stress, the intermediate principal stress and the minimum principal stress (Pa); E is the elastic modulus (Pa); l is the Poisson ratio; L 1 and L 3 , respectively, are the side length along the maximum principal stress direction and the minimum principal stress direction of the represent element volume (m); r d is the uniaxial compression stress when macro-fractures are going to appear, which can be confirmed by experiment (Pa); J is the surface energy density of fractures (J/m 2 ); h is the rupture angle (the angle between the maximum principal stress direction and the fracture orientation) (°); and u is the angle of internal friction (°).
The formula of fracture aperture b is as follows (Hicks et al., 1996): where e is the tension strain of the rock cell cube under current stress conditions and e 0 is the greatest tension strain of rock elastic deformation.

Fracture Porosity Calculation
Fracture porosity is the ratio of total fracture volume and total rock volume.For a single population fracture, the relationship between fracture porosity and fracture volume density and aperture is as follows (Chen and Bai, 1998): where / f is the fracture porosity (%).
For multi-bank fractures, fracture porosity is calculated as follows: where / ft is the fracture total porosity (%); m is the group number of fractures; and b i is the aperture of the ith group fracture (m).

Fracture Permeability Calculation
Fluid flow in a unitary fracture is mainly confined to a two-dimensional crack plane, and the penetration perpendicular to the crack plane can be neglected.Hence, a faceplate filtration model can be applied when calculating fracture permeability (Song et al., 1999): where K fx , K fy and K fz , respectively, are the fracture permeability along r 1 , r 2 and r 3 directions when multi-bank fractures exist (10 À3 lm 2 ), and h i is the rupture angle of the ith group fracture.

Calculation Methods for Current Fracture Parameters
Hicks et al. (1996) proposed Equation ( 14) to calculate fracture aperture in consideration of the influence of normal stress and shear stress on fracture aperture: where b m is the current fracture aperture (m); b 0 is the initial fracture aperture (m); r nref is the effective normal stress (MPa); r 0 is the effective normal stress when fracture aperture decreases 90% (MPa); b 0 is the aperture increment due to shear displacement (m); b s is the fracture aperture which is superficial under maximum normal stress (m).
Minimal shear displacement occurred in the current formation.Thus, b c usually has a low value and can be neglected; the initial fracture aperture can be considered as palaeo-fracture aperture b; r 0 is equal to the pressure difference on fractures between normal stress and formation fluid pressure.Thus, Equation ( 14) transforms into Equation ( 15): where r n is the normal stress on fractures (MPa).
The calculation methods for current fracture parameters can be obtained by replacing fracture aperture b in Equations ( 10) and ( 11) with current fracture aperture.

CALCULATION OF MUD LOSS FLOW RATE
As shown in Figure 2  The schematic diagram of mud loss in a fracture, cake and formation.

Fracture Flow
Equations ( 16), ( 17) and ( 18) can be used to describe the flow behavior of the drilling fluid loss in the fracture if the fractures are supposed to be horizontal.Lavrov and Tronvoll (2004) deduced an equation describing the flow of a power-law fluid from a borehole into a deformable fracture of finite extension: The mud loss flow rate is evaluated by the following: where b is fracture aperture (m); t is the time (s); n is the power-law exponent; K ci is the consistency index (Pa Á s n ); K n is the normal fracture stiffness (Pa/m); p is the pressure inside the fracture (Pa); r is the distance from the borehole axis in the fracture plane (m); r w is the wellbore radius (m); and u is the mud loss flow velocity (m/s).

Formation Flow
Equations (19-21) can be used to describe the flow behavior of the drilling fluid loss in formation.Equation ( 19) is the Darcy flow equation: The effective viscosity of drilling fluid changes with the rate of shearing is expressed as follows (Williams, 1990): The relationship between the flow velocity and the pressure difference can be described as Equation ( 21) in porous media (Settari, 1988).
where / is the pressure inside the formation (Pa); q is the drilling fluid density (kg/m); / d is the formation porosity (%); K d is the formation permeability (lm 2 ); C t is the formation compressibility coefficient (Pa À1 ); a u is the unit conversion coefficient; and l e is the effective viscosity of the drilling fluid.

Cake Flow
Equations (22-24) can be used to describe the flow behavior of the drilling fluid loss in the mud cake.The mud cake is considered a porous medium with the porosity / C and the permeability K C .Equation ( 22) is the flow equation in mud cake (Warpinski, 1991): The effective viscosity of drilling fluid in the mud cake is expressed as follows: The relationship between flow velocity and pressure difference can be described as Equation ( 24) in mud cake (Vitthal and McGowen, 1996).
where / c is the mud cake porosity (%); K c is the mud cake permeability (lm 2 ); C c is the mud cake compressibility coefficient (Pa À1 ); p f is the formation pressure (Pa); p w is the bottom hole flowing pressure (Pa À1 ); and L is the drilling fluid flow distance (m).Two main types of drilling fluid loss commonly exist in the fracture formation: loss due to hydraulic fracturing and loss due to pressure difference.When the annular pressure is higher than fracture pressure, the formation will form major fractures and loss due to fracturing will occur.Formation permeability is usually high in steeply folded structures.Thus, the loss due to pressure difference tends to exist when annular pressure is higher than pore pressure.The flow rate of loss due to fracturing can be calculated by using .The flow rate of loss due to over-pressure can be calculated by using .However, the mud cake is formed in the borehole wall instead of in the fracture surface.Permeability and porosity are calculated by using the quantitative description method for tectonic fracture parameters mentioned above.

CASE STUDIES ON QUANTITATIVE DESCRIPTION OF TECTONIC FRACTURE AND MUD LOSS FLOW RATE
Figure 3 is a simplified structure profile diagram of Block F of a gas field in Sichuan Basin, China.Structure formations can be divided into five groups, namely, G1, G2, G3, G4 and G5.G4 has had the highest drilling fluid loss in the drilling process; thus, G4 is taken as an example in the finite element analysis of palaeo-stress and current stress and in the quantitative description of tectonic fracture.Figure 4 shows the depth structure of G4.The parameter values of the materials used in the model are listed in Table 1.
The load value and azimuth of palaeo-stress simulation are as follows.The palaeo-maximum principal stress is considered in the EW direction, according to local fracture development.The maximum and minimum principal stress values are 296 MPa and 165 MPa, respectively.These stress values are obtained by trial and error calculation until the deformation agrees with the actual shape characteristic of the geological structure.
The load value and azimuth of current stress simulation are as follows.According to the results of the measured local stress, the current stress azimuth is between NE 76°a nd NE 88°, and the mean value is 83°.Thus, the angle between the current stress azimuth and the structure alignment direction is small.Moreover, the model profile bears extrusion force, which is mainly caused by the stress in the EW direction and gravity.According to the stress value of the key points and trial and error calculation, the maximum and minimum principal stress values are 123 MPa and 90.2 MPa, respectively.

Results of Tectonic Stress and Fracture Simulation
Tectonic fracture density distribution is calculated by using the results of the palaeo-stress simulation and by using the Coulomb-Mohr criterion and Griffithfailure criterion as criteria of shear failure and tension failure, respectively.Tectonic fracture density,     Latitudinal permeability (10 -3µm 2 ) Longitudinal permeability (10 -3µm 2 ) .0205354 .0510709 .
According to the stress distribution shown in Figure 5, the stress at the top of the anticline or fold is greater than the other areas of the anticline.A stress concentration phenomenon exists in the top area.The stress on the top region is stronger than the other areas, and the destructive effects of rock in this region are stronger than the other areas.
Figure 6 displays the tectonic fracture aperture distribution of G4 in Block F. The tectonic fracture aperture in the core of the fold or at the top of the structure is apparently greater compared with other zones.The maximum predictive value is up to 0.5 mm, and serious leakage will probably occur when drilling at this zone.The calculation of the fracture aperture not only contributes to mud loss prediction but also helps in the selection of the type and size of bridging material.
Figure 7 reveals the tectonic fracture porosity and permeability distribution of G4 in Block F. The distribution of porosity and permeability is highly inconsistent with that of the fracture aperture.The area with high porosity and permeability also has a large aperture.The porosity at the top reaches up to 0.25%, and the permeability reaches up to 50 910 À3 lm 2 .
Figure 8 shows the fracture linear density distribution.Similarly to Figure 5, the density of the tectonic fracture at the top is greater compared with the other zones in the steeply folded structure.The maximum value is up to 0.55 m À1 or even higher.
The distribution of key fracture parameters of G4 in Block F is determined by using the above analysis.The key fracture parameters at different positions of the whole structure can be obtained by utilizing the same method and finite element analysis applied in G4 in G1, G2, G3 and G5.

Results of Mud Loss Flow Rate Simulation
Predicting the mud loss flow rate at the different positions of the steeply folded structure can be carried out based on the calculation of fracture aperture, porosity, permeability and density, and by applying fluid flow mechanics.Well PG-X1 had serious mud loss, and its location is marked as "Well PG-X1" in Figure 3. Figure 9 shows the equivalent density profiles of pore pressure, fracture pressure and overburden pressure, as well as the drilling fluid density profile of Well PG-X1.Mud is a power-law fluid, with n equal to 0.75 and K ci equal to 0.03 Pa Á s 0:75 .The main part of the drill string is the 127-mm drill pipe.Table 2 illustrates the well structure of Well PG-X1.
As shown in Figure 10, the mud loss flow rate of Well PG-X1 was predicted by using the proposed method.Severe mud loss occurred when drilling at the bottom of G2 and at most parts of G4.The average mud loss flow rate reached 64 m 3 /h, and the total loss volume was approximately 560 m 3 in G4.The predictive value of the mud loss flow rate agrees well with the actual value shown in Figure 10, which verifies the feasibility of the proposed method in predicting the mud loss flow rate.
Two other wells will be drilled in the structure and are marked as "PG-X2" and "PG-X3", as shown in Figure 3.   predicting the mud loss flow rate.The density, aperture, porosity and permeability of tectonic fractures at the top of the structure are greater than those of the other zones.
The predicted value of the mud loss flow rate agrees well with the actual value in Well PG-X1, which means that the method is feasible in predicting the mud loss flow rate before drilling.The wells have more serious mud loss in the core of the structure, and the wells in the flank of the structure have less mud loss, which is in accordance with the fracture distribution of the structure.This new method makes it possible to predict the mud loss flow rate before drilling, which is helpful in applying preventive measures during the drilling practice in steeply folded structures.
Figure 1 , the flow path of mud can be divided into three parts based on the flow behavior of drilling fluid in fissured formation: flow in a fracture, flow in mud cake, and flow in formation.
Figure 2 Figure 4 G4 depth structure of Block F.

Figure 6
Figure 6Tectonic fracture aperture distribution of G4 in Block F.
Figure 5Tectonic fracture stress distribution of G4 in Block F.

Figure 7
Figure 7Tectonic fracture porosity and permeability distribution of G4 in Block F.
Figure 10 Actual value and predictive value of mud loss flow rate in Well PG-X1.

TABLE 1 Parameters
, porosity and permeability are determined by simulating the rebuilding process of current stress to the fracture parameters on the basis of the results of the palaeo-stress simulation.Figures5-8show the results of tectonic fracture density, aperture, porosity and permeability. aperture

TABLE 2
results of crustal stress and tectonic fracture distribution simulation.The bottom parts of G2 and G4 have the highest mud loss flow rate in Well PG-X2, which is