石油工程中ABAQUS数值模拟若干实践综述.pdf

1 xinpu shen xianhe du 2010 simulia china 石油工程中石油工程中abaqus数值模拟若干实践综述数值模拟若干实践综述 沈新普 哈里伯顿能源服务公司 休斯敦 77042 美国 杜显赫 沈阳工业大学 110870 沈阳 摘要 摘要 本文对作者做过的3个工程实例进行综述 展示abaqus三维数值模拟在解决石油钻井等工程方面的能 力 实例一介绍了墨西哥湾岩盐井段泥浆压力安全值的abaqus三维计算实践 实例二介绍了综合使 用abaqus三维数值模拟和一维常规石油孔隙压力分析软件 进行井壁稳定和泥浆压力计算 并应用 于苏里南某浅层疏松地层油田的例子 实例三是将abaqus三维分析技术用于英国北海ekofisk油田 计算油田生产导致的压力降引发的地层沉降和地层主应力方向改变的情况 改变后的地应力方向矢 量图可以用作增压注水井的井孔轨迹设计的参考 review of some practices of 3 dimensional numerical simulations with abaqus in petroleum engineering xinpu shen halliburton energy service houston 77042 tx usa xianhe du shenyang university of technology shenyang 110870 china abstract real cases of three dimensional numerical simulations with abaqus in petroleum engineering have been reviewed case 1 is the numerical analysis on subsalt wellbore stability in a region of gulf of mexico special concerns were given to the shear failure gradient calculation with local refined mesh at the well section of salt base case 2 is the integrated analysis made on mud weight design for deviated wells in shallow loose sand reservoirs in an oil field of suriname one dimensional analytical tool for pore pressure analysis was used together with abaqus finite element program case 3 shows numerical results of variation of stress orientation caused by pore pressure depletion in the ekofisk field north sea 1 introduction with the development of un conventional petro resources 3 dimensional numerical simulation such as abaqus has become more and more popular in petroleum engineering 1 2 3 for un conventional petro resources such as shale gas etc conventional 1 dimensional analytical tools can hardly meet the needs alone in order to simulate rather complicated mechanical behaviors of various formations particularly for those rock such salt and shale etc it is necessary to jointly use conventional 1 dimensional tool and 3 dimensional numerical tool 4 in the following three real cases of application numerical simulation in petroleum engineering are introduced the numerical analysis on subsalt wellbore stability in a region of gulf of mexico will be introduced as case 1 the integrated analysis made on mud weight design for deviated wells in shallow loose sand reservoirs in an oil field of suriname will be introduced as case 2 case 3 shows numerical results of variation of stress orientation caused by pore pressure depletion in the ekofisk field north sea 2 numerical analysis on subsalt wellbore stability in a region of the gulf of mexico the variation of water depth over a certain horizontal distance of a sub salt well in the northern region of the gulf of mexico is one reason for using a three dimensional numerical tool along with conventional one dimensional analytical tools including drillworks software 5 the first fundamental issue for a successful application of the numerical method in the analysis of sub salt wellbore stability analysis is the accurate input of the pore pressure encountered along the wellbore a second issue affecting its success is the accurate description of the three dimensional structure of the salt body and related formations which will be involved in the calculation drillworks software is a set of one dimensional 1 d tools for analysis used for pore pressure prediction and wellbore 2 xinpu shen xianhe du 2010 simulia china stability analysis it is referred to as a one dimensional tool because it analyzes wellbore stability and pore pressure based on tvd information along the well path to be more precise drillworks software is based on the linear elastic theory and the two dimensional plane strain conditions in practice drillworks software has proven to be a very powerful analytical tool in the prediction of pore pressure for many wellbores in the gulf of mexico and around the world and has laid a good foundation for a successful three dimensional numerical analysis of sub salt wellbore stability on the other hand modern seismic technology can provide accurate spatial geological and structural information for the salt dome canopy and related formations for a 2 d view consequently it is not only necessary but also practical to perform a three dimensional numerical analysis in relation to sub salt wellbore stability the first task of this study is to perform a pore pressure prediction with drillworks software a three dimensional numerical analysis with fem software will be presented for a given depth position at the salt exit of the wellbore in this way we will present a method for sub salt wellbore stability analysis which combines conventional one dimensional analytical tools such as drillworks software with a three dimensional numerical tool such as abaqus 6 2 1 pore pressure analysis with one dimensional tools fig 1 shows the results of the deriving pore pressure and local stress regime at the position investigated via analyzing wireline logs in the left first track of fig 1 is a gr curve with a shale base line shbl that was used to discrete the shale from other lithological formation the left second track shows the resistivity data the shale picks derived from the gr curve in track 1 filtered resistivity data using the selected shale points and a normal compaction trend line nctl that was used in an eaton resistivity analysis to generate a pore pressure curve green that is displayed in the right first track fig 1 pore pressure and stress analyses similarly the sonic analysis is shown in the third track with the nctl coming from the bowers method and the curves for a density analysis are in the fourth track displayed on the right track of the display in fig 1 are curves relating to the pressure analysis and the drilling of the well the casing program overburden gradient obg fracture gradient using a matthews and kelly relationship with k0 0 8 and mud weight black line three pore pressure curves are included on this track pore pressure dark green is derived from the resistivity and the lighter dark green curve is derived from the sonic data the value of pore pressure gradient at the salt exit point was calculated at 14 9 ppg because the curves derived from the various petrophysical tools and the equations that derive a pore pressure from them do not agree the resulting challenge is determining the true pore pressure at any given point in the well this interpreted curve is depicted on the plot as a light green line with square marks this curve demonstrates the best fit for all of the data considering the different properties that are measured by the various tools the calibration to the measured pressures in the sands and the well events that occurred while drilling not shown in the deep part of the well the sand pressures and rhob and dt pressures were monitored more closely in the shallow part of the well the resistivity and sonic data derived pressures were considered more valid because the dt derived pressures are above the mud weight that was used to drill the well this interpreted pore pressure was used in subsequent modeling of the wellbore stability conditions 3 xinpu shen xianhe du 2010 simulia china 2 2 the three dimensional computational model stress distribution around the salt body is directly related to both the geometry and relative position of the whole salt body to obtain accurate stress field information around the salt it is necessary to perform mechanical analysis at the field scale only then it is possible to further present correct boundary conditions for wellbore stability analysis for subsalt wells because of the large differences between field scale and wellbore scale modeling it has been difficult if not impossible to combine these models in the past in fact existing examples of numerical analysis on wellbore stability analysis were either performed at wellbore scale without direct coupling to behaviors at the field scale or performed at a much larger scale which sacrificed much needed modeling resolution abaqus submodeling techniques were used to manage the field to reservoir scale discrepancy the concept of the submodeling technique includes using a large scale global model to produce boundary conditions for a smaller scale submodel in this way the hierarchical levels of the submodel are not limited using this approach a highly inclusive field scale analysis can be linked to a very detailed casing stress analysis at a much smaller scale the benefits are bidirectional with both the larger and smaller scale simulations benefiting from the linkage this technique can be viewed as an efficient way for local refinement in the fem in this calculation a global model at field scale fig 2 has been established first to simulate structural influence of salt geometry a submodel has been built for the wellbore section where it exits the lower surface of the salt body at its center see fig 3 for the position sections in both salt and subsalt formations are included in this submodel the tvd depth i e the distance from center of the submodel to a vertical point at the sea floor of the submodel is 3 595 m 2 3 global model geometry boundary condition and loads fig 2 shows the geometric profile of the model its width and thickness are both 10 km its height on the left side is 10 km and its height on the right is 9 6 km which shows variation in water depth 10km 9 6km 10km fig 2 model geometry profile of the whole model according to information presented in the references 7 8 the geometry of the salt body was built as shown in fig 3 the outer edge of the pan cake shape salt body has the diameter of 7 01 km and the maximum thickness is 1 676 km its upper surface has a 30 angle with the horizon the depth of its top edge from the sea floor is 1 219 km the geometry and relative position of the salt body is shown in fig 3 30o location of submodel fig 3 model geometry profile of the salt body 4 xinpu shen xianhe du 2010 simulia china as shown in fig 2 the loads sustained by the model include 1 hydrostatic pressure produced by sea water at the top of the model 2 gravity load distributed within the model body and 3 pore pressure distributed in the formations because the salt body has no porosity or permeability pore pressure within salt body is assumed to be zero pore pressure existing in the subsalt reservoir formation is given as 9 950 psi about 68 6 mpa according to the predicted pore pressure value from drillworks software for a reservoir this analysis employs the modified drucker prager yielding criterion cohesive strength and frictional angle of the drucker prager model are given the following values o mpad44 56 1 which correspond to values in the mohr coulomb model as o mpac25 5 0 refer to 5 for further details between the two models the creep law given in the following equation dassault systems 2008 is adopted by m n crcr ta 1 where cr represents the equivalent creep strain rate cr represents von mises equivalent stress t is total time variable and a n and m are three model parameters which are given the following values values of material properties are listed below values of strength parameters for salt adopted here by the drucker prager model are o mpad44 4 which correspond to values in the mohr coulomb model as o mpac25 25 1 material name reservoir density in kg m3 2300 elastic modulus in pa 1e 10 0 3 drucker prager 44 1 30 drucker prager creep law time 2 5e 22 2 942 0 2 drucker prager hardening type shear in pa 1 56e 06 0 material name salt density in kg m3 2100 elastic modulus in pa 1e 10 0 3 drucker prager 44 1 30 drucker prager creep law time 2 5e 22 2 942 0 2 drucker prager hardening type shear in pa 4 e 06 0 zero displacement boundary constraints were applied in the normal direction of the four lateral surfaces as well as bottom 2 4 submodel geometry boundary condition and loads the geometry of the submodel is shown in fig 4 the upper part is salt and the lower part is reservoir formation in which a non zero pore pressure exists here the wellbore axis has an inclination angle of 30o to the vertical the submodel has been discretized with a fine mesh around the wellbore the element edge size in the radius direction is only 1 10 of the wellbore radius 12 in in diameter as shown in fig 5 loads sustained by the submodel are similar to that sustained by the global model except the hydrostatic pressure applied to the wellbore surface which is the so called mud weight pressure the numerical scheme for the calculation of a safe mud weight gradient is described in the last section and is omitted here boundary conditions of the submodel are taken from the numerical results of the global model displacement constraints are applied on all lateral surfaces because of the displacement in the radius direction around the borehole top and bottom displacement constraints were applied in the normal direction to these two surfaces the values of these displacements were also taken from the global model which is usually not zero 5 xinpu shen xianhe du 2010 simulia china 2 5 numerical results numerical results of the global model fig 6 to fig 8 show the numerical results of the global model which are used as a base for the wellbore stability analysis performed with the submodel the distribution of a vertical stress component shown in fig 6 has a reasonable accuracy with reference to the hydraulic load on the top of the model and the gravity load within the model body the initial field of geostrain is shown in fig 7 the value of geostrain is designed to be as small as possible to minimize the original strain and to focus on the strain relevant to drilling activities the distribution of deviatoric stress is shown in fig 8 this figures shows that the ratios between the three stress components are small within the salt body which has rather high creep fluidity these three figures indicate that the numerical results of the global model are reasonable and consequently can be used in the submodeling calculation fig 6 numerical results of the global model distribution of vertical stress fig 7 numerical results of global model distribution of vertical strain fig 8 numerical results of the global model distribution of deviatoric stress 2 6 scheme of calculation of safe mud weight pressure 10 m 10 m 10 m salt formation pp 50mpa fig 4 model geometry profile of the submodel fig 5 submodel geometry mesh around the borehole 6 xinpu shen xianhe du 2010 simulia china mud weight pressure will be applied to the inner surface of the borehole boundary conditions of the submodel were obtained from the numerical results of the global model in the calculation process of minimum safe mud weight pressure a reference pressure pw which is generated by static water was calculated first a loading factor 1 was then assumed here is set at 2 under action of hydraulic pressure p 2pw the wellbore is stable and no plastic deformation occurs anywhere the calculation of the minimum safe mud weight pressure is to find the minimum loading factor with which hydraulic pressure can keep the wellbore stable below this minimum value there will be plastic deformation occurring to the wellbore surface to achieve this goal a negative hydraulic pressure with loading was added incrementally to the reference pressure 2pw therefore n i i 1 2 where i was set at 5 in this calculation and n is calculated automatically by the program when plastic deformation occurs calculation stops in response to the satisfaction of a given criterion the resultant minimum mud weight pressure required for wellbore stability will be w pp 3 in this calculation the pressure gradient over the submodel section is assumed to be constant consequently the resultant mud weight gradient is a section averaged value it should be noted that the pw used in the calculation is calculated in reference to the total depth of a given section and the resultant mud weight pressure gradient is the conventional equivalent mudweight gradient the mud weight pressure value at a given point can be obtained by multiplying the depth at that point with the related pressure gradient value obtained by the calculation 2 7 numerical results of the submodel the numerical model of safe mud weight pressure obtained with the submodel is listed below mpapmw292 59 4 transferred further into gradient equivalent in ppg is ppgpmwe15 15295 1174 17794 5 the results of mwe obtained with drillworks software v12 5 are listed below table 1 shows the values of various mwe compared with the aforementioned data the numerical result obtained with abaqus is the most conservative one but it is still less than the ecd it can also be concluded from table 1 that the strength correlation model used in drillworks software from sonic data is too risky and should not be used in sub salt basins because sonic data from salt is normally not accurate and consequently should not be used directly in analysis the adjusted mwe result from drillworks software is far better than the original one with the same values of strength parameters the numerical result of mwe by abaqus software gives a better value which is closer to the ecd value than other results on the other hand with reference to numerical values listed in table 1 the mwe value of the ecd log is often too conservative and thus is not the best choice in summary for the best practice the adjusted mwe result from drillworks software is a reasonable choice if available the 3 d numerical solution for a typical sub salt wbs will be the best choice fig 9 shows the numerical stress distributions within the submodel described above table 1 comparison of values of mwe mwe by drillworks software with cs obtained by horsrud correlation model mwe by drillworks software with manually adjusted cs input mwe by abaqus 3 d numerical method mwe by ecd log 13 5ppg 14 8 ppg 15 15 ppg 16 19 ppg 7 xinpu shen xianhe du 2010 simulia china fig 9 numerical results of submodel distribution of vertical stress component left and deviatoric stress right 2 8 remarks the three dimensional numerical calculation of the lower bound of mud weight