Depletion Analysis of an Oilfield

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Damian Benson
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load: elemen functi pressu weight. materi: elasti isotro porosi soil.

1 Pore Pressure Depletion Analysis of an Oilfield analys: nonlin physic. constr: suppor. elemen: hx24l py15l solid te12l tp18l. load: elemen functi pressu weight. materi: elasti isotro porosi soil. option: iterat newton regula units. post: binary ndiana. pre: dianai. result: cauchy displa effect green pressu strain stress total.

2 Outline 1 Description 1.1 Case study 1.2 Geometry of the reservoir 1.3 Soil material properties 1.4 Modeling strategy 2 Finite Element Model 2.1 Units 2.2 Geometry definition 2.3 Properties 2.4 Boundary conditions Constraints Load Load combinations 2.5 Meshing 3 Nonlinear Analysis 3.1 Analysis commands 4 Results 4.1 Vertical stresses 4.2 Pore pressure 4.3 Vertical strains 4.4 Change in vertical stresses Depletion Analysis of an Oilfield 2/40

1 Description 1.1 Case study In this tutorial we will perform a depletion analysis of the Fulmar oilfield reservoir located in the North Sea (see [Fig. 1]) and presented in [Fig. 2].

3 1 Description 1.1 Case study In this tutorial we will perform a depletion analysis of the Fulmar oilfield reservoir located in the North Sea (see [Fig. 1]) and presented in [Fig. 2]. This is a layer-cake 3D model with the mesh being built from realistic geology data about the depth profile of the different geological formations. Here, we will use the Be zier approximation tool in for the modeling of the horizons of the geological layers. The whole soil model consists of 5 layers: Sediments (Overburden) Chalk Kimmeridge sediments Fulmar (i.e., the reservoir) Pentland chalk kimmeridge fulmar pentland Figure 1: Location of the Fulmar oilfield. Depletion Analysis of an Oilfield Figure 2: 3D view of the model. 3/40

4 1.2 Geometry of the reservoir The solid model has the dimensions of 7800 x 6800 x 8955 m [Fig. 3]. The horizon-depths of the layers separating the different geological formations will be retrieved from an excel file containing the z coordinates of each layer. These values are associated to a regular grid on the xy-plane mode of cells with dimensions of 250 x 250 m. The dimension of the grid is x m. By importing this data in, we will approximate the separation layers of the geological formations with Bézier surfaces [Fig. 4] m 7800 m 6800 m Figure 3: dimensions of the reservoir Figure 4: Bézier surface approximating the measured depths (blue symbols) of the separation layer between the chalk and kimmeridge layers Depletion Analysis of an Oilfield 4/40

5 1.3 Soil material properties For the sake of simplicity we assume that the 5 formations are linear elastic with equal mechanical properties, as listed in [Table 1]. Young s modulus (Drained) 1 GPa Poisson s ratio (Drained) 0.15 Density of dry soil 2000 kg/m 3 Porosity 0.5 Lateral pressure ratio 0.6 Table 1: Material properties of the soil 1.4 Modeling strategy The following considerations were taken into account: the geometry of the model is based on the Bézier approximation of the horizons depths. The depth values are defined according to a regular planar grid on the xy-plane with cells of size 250 x 250 m; the lateral faces of the 3D model are constrained to normal displacement; the water pressure will be assigned only to the portion of the Fulmar layer (i.e., the reservoir) at z m; the depletion stage will be defined through the gradient of pressure in the reservoir; the 3D model will be discretized with hexagonal finite elements; although the soil is linear elastic, a nonlinear structural analysis is performed to model the initial stress state of the soil. Depletion Analysis of an Oilfield 5/40

2 Finite Element Model For the modeling session we start a new project with structural analysis. The dimensions of the domain for the 3D model are set to 100 km.

6 2 Finite Element Model For the modeling session we start a new project with structural analysis. The dimensions of the domain for the 3D model are set to 100 km. Linear hexagonal finite elements will be used in the analysis. Main menu File New [Fig. 5] Figure 5: New project dialog Depletion Analysis of an Oilfield 6/40

Geometry browser Reference system Units [Fig. 6] Property Panel [Fig.

7 2.1 Units We choose meter for the unit Length, kilogram for Mass and Newton for Force (SI units). Geometry browser Reference system Units [Fig. 6] Property Panel [Fig. 7] Figure 6: Geometry browser Figure 7: Property Panel - Units Depletion Analysis of an Oilfield 7/40

8 2.2 Geometry definition We create 4 curved sheets that correspond to the top surface of the first 4 formations (starting from the bottom layer). We start with Chalk by importing the z coordinates of the corresponding layer from the excel spreadsheet shown in [Fig. 8]. Based on this data, a Bézier surface is built in using the add curved sheet command ([Fig. 9]). Excel Chalk spreadsheet select & copy the coordinates table [Fig. 8] Main menu Geometry Create Add curved sheet Paste [Fig. 9] Figure 8: Excel spreadsheet with depths values of the Chalk top surface Figure 9: Add surface - Chalk surface The tolerance value in [Fig. 9] defines the maximum admissible distance between the provided list of points and the approximating Bézier surface. If the generated surface does not satisfy such a requirement, a warning is displayed in the Messages window of. Depletion Analysis of an Oilfield 8/40

9 We fit the geometry in the workspace and hide the working plane. Main menu Viewer Fit all Main menu Viewer Show working plane <hide> [Fig. 10] Figure 10: View - Isometric view 1 Depletion Analysis of an Oilfield 9/40

10 We apply the same procedure for the curved sheet correspondent to the Kimmeridge layer. Main menu Geometry Create Add curved sheet Paste [Fig. 11] [Fig. 12] Figure 11: Add surface - Kimmeridge surface Figure 12: View - Isometric view 1 Depletion Analysis of an Oilfield 10/40

11 We apply the same procedure for the curved sheet correspondent to the Fulmar layer. Main menu Geometry Create Add curved sheet Paste [Fig. 13] [Fig. 14] Figure 13: Add surface - Fulmar surface Figure 14: View - Isometric view 1 Depletion Analysis of an Oilfield 11/40

12 And we apply the same procedure for the curved sheet correspondent to the Pentland layer. Main menu Geometry Create Add curved sheet Paste [Fig. 15] [Fig. 16] Figure 15: Add surface - Pentland surface Figure 16: View - Isometric view 1 Depletion Analysis of an Oilfield 12/40

It is also possible to import all surfaces at the

Figure 17: CVS file format Figure 19: Import CSV

13 It is also possible to import all surfaces at the same time by importing a CSV file with the format presented in [Fig. 17]. Main menu File Import CSV files [Fig. 18] [Fig. 19] [Fig. 20] Figure 18: Import CSV file - File selection Figure 17: CVS file format Figure 19: Import CSV file - Field selection Figure 20: Import CSV file - Import options Depletion Analysis of an Oilfield 13/40

14 We now create one block representing the whole model. Main menu Geometry Create Add block [Fig. 21]-[Fig. 22] t Figure 21: Add block - Block 1 Figure 22: View - Isometric view 1 Depletion Analysis of an Oilfield 14/40

We subtract all surfaces from the block to generate

25] Figure 23: Subtract shapes Figure 24: View -

15 We subtract all surfaces from the block to generate the different geological formations. Main menu Geometry Modify Subtract shapes [Fig. 23] [Fig. 24] [Fig. 25] Figure 23: Subtract shapes Figure 24: View - Isometric view 1 Figure 25: New set of shapes Depletion Analysis of an Oilfield 15/40

Model window Geometry Right click ( ) as Block 1 Rename into Sediments Model window Geometry Right click ( ) as Block 1 1 Rename into Chalk Model window Geometry Right click ( ) as

16 We rename the new shapes [Fig. 25] as their corresponding layer names [Fig. 28]. For the Pentland layer, we will need to unite 7 shapes (sse [Fig. 26]) that were formed in the previous step. Model window Geometry Right click ( ) as Block 1 Rename into Sediments Model window Geometry Right click ( ) as Block 1 1 Rename into Chalk Model window Geometry Right click ( ) as Block 1 9 Rename into Kimmeridge Model window Geometry Right click ( ) as Block 1 11 Rename into Fulmar Model window Geometry Right click ( ) as Block 1 12 Rename into Pentland Main menu Geometry Modify Unite [Fig. 26] [Fig. 27] Figure 26: Unite shapes Figure 27: Unite shapes Figure 28: Renamed shapes Depletion Analysis of an Oilfield 16/40

Model window Geometry Right click ( ) on Fulmar Show only [Fig.

17 It is possible to check the geometry of the obtained formation. For instance, we can visualize only the Fulmar shape in the model window ([Fig. 30]). Model window Geometry Right click ( ) on Fulmar Show only [Fig. 29] Figure 29: Show only Fulmar Figure 30: View - Isometric view 1 Depletion Analysis of an Oilfield 17/40

2.3 Properties We assign the properties to the soil layers.

elements, we do not have to define Geometry properties.

required. Main Menu Geometry Analysis Property assignments [Fig.

- initial stress Figure 31: Property assignments Figure 33:

18 2.3 Properties We assign the properties to the soil layers. Because we model a 3D structure using structural solid elements, we do not have to define Geometry properties. We will use the default integration scheme, thus no Data set is required. Main Menu Geometry Analysis Property assignments [Fig. 31] Property assignments Add new material [Fig. 32] [Fig. 33] [Fig. 34] [Fig. 35] Figure 32: Add new material Figure 34: Material properties - initial stress Figure 31: Property assignments Figure 33: Material properties - linear Figure 35: Material properties - capacity Depletion Analysis of an Oilfield 18/40

2.4 Boundary conditions 2.4.1 Constraints All the lateral faces of the model are supported in its normal direction.

In order to easily select these faces we choose the top view of the model and select the faces as shown in [Fig. 37].

19 2.4 Boundary conditions Constraints All the lateral faces of the model are supported in its normal direction. We start with constraining in the x-direction the side faces aligned with the y-axis. In order to easily select these faces we choose the top view of the model and select the faces as shown in [Fig. 37]. Model window Right click ( ) on Fulmar Show all Main menu Viewer Viewpoint Top view Main menu Geometry Analysis Attach support [Fig. 36] [Fig. 37] [Fig. 38] Figure 36: Attach supports Figure 37: Selection of the faces on the right side of the model (analogously, we select the faces at the opposite side of the model) Figure 38: Supports on the faces aligned with the y-axis Depletion Analysis of an Oilfield 19/40

20 Similarly, we constrain in the y-direction the faces aligned with the x-axis. Main menu Geometry Analysis Attach support [Fig. 39] [Fig. 40] Figure 39: Attach supports Figure 40: Supports on the faces aligned with the x-axis Depletion Analysis of an Oilfield 20/40

We now constrain in the z-direction the bottom face of the model.

and select the face as shown in [Fig. 42].

42] Main menu Geometry Analysis Attach support [Fig. 41] [Fig. 42] [Fig.

21 We now constrain in the z-direction the bottom face of the model. In order to easily select the bottom face we choose the front view of the model and select the face as shown in [Fig. 42]. Main menu Viewer Viewpoint Front view [Fig. 42] Main menu Geometry Analysis Attach support [Fig. 41] [Fig. 42] [Fig. 43] Figure 41: Attach supports Figure 42: Selection of the face at the bottom of the model Figure 43: Supports at the bottom face Depletion Analysis of an Oilfield 21/40

22 2.4.2 Load Dead weight We create a load case for the dead weight in order to be taken into account in the analysis. Main Menu Geometry Analysis Global load [Fig. 44] Figure 44: Global load - dead weight Depletion Analysis of an Oilfield 22/40

Pore pressure load An initial pore pressure of 8e7 N/m 2 will be applied to those parts of the reservoir (i.e., the Fulmar oilfield) higher than the gas-water contact at -4950 m depth.

23 Pore pressure load An initial pore pressure of 8e7 N/m 2 will be applied to those parts of the reservoir (i.e., the Fulmar oilfield) higher than the gas-water contact at m depth. For this we create a function dependent on the z-coordinate. Main Menu Geometry Functions Add [Fig. 45] Figure 45: Add function Depletion Analysis of an Oilfield 23/40

24 We can now set a load case for the initial pressure. Main Menu Geometry Analysis Attach load [Fig. 46] Figure 46: Attach load - Initial pressure Depletion Analysis of an Oilfield 24/40

25 For the depletion stage, we define a change of pressure of -6e7 N/m 2 to the reservoir. Main Menu Geometry Analysis Attach load [Fig. 47] Figure 47: Attach load - Pressure change Depletion Analysis of an Oilfield 25/40

26 2.4.3 Load combinations Finally, we create the load combinations. Since we will perform an incremental analysis, in the first load combination we consider the weight of the soil and the initial pressure. In the second load combination, we only consider the change of pressure. Main Menu Geometry Loads Open geometry load combination table [Fig. 48] [Fig. 49] Figure 48: Load combination table - Default settings Figure 49: Load combination table - Final settings Depletion Analysis of an Oilfield 26/40

2.5 Meshing The mesh will be defined by setting the characteristic size of the elements in Fulmar equal to 250 m, while for the other formations the element size is set equal to 500 m [Fig. 50]-[Fig.

27 2.5 Meshing The mesh will be defined by setting the characteristic size of the elements in Fulmar equal to 250 m, while for the other formations the element size is set equal to 500 m [Fig. 50]-[Fig. 51]. Main Menu Geometry Analysis Set mesh properties [Fig. 50]-[Fig. 51] Main Menu Geometry Analysis Generate mesh [Fig. 52] Figure 50: Mesh seeding for Fulmar shape Figure 51: Mesh seeding for Sediments, Chalk, Kimmeridge and Pentland shapes Figure 52: View of the mesh Depletion Analysis of an Oilfield 27/40

28 3 Nonlinear Analysis 3.1 Analysis commands We will perform a nonlinear structural analysis. Main Menu Analysis New Analysis [Fig. 53] Analysis browser Right click ( ) Analysis1 Rename Nonlin Analysis browser Right click ( ) Nonlin Add command Structural nonlinear [Fig. 54] [Fig. 55] Figure 53: Analysis window Figure 54: Add command Figure 55: Analysis tree Depletion Analysis of an Oilfield 28/40

29 We add an execute start-steps block to include the initial the stresses. In this first execution block we take into account of the weight of the soil and the initial pressure in correspondent to the Geometry load combination 1 defined in [Fig. 49]). Analysis browser Nonlin Right click ( ) Structural nonlinear Add Execute steps Start steps [Fig. 56] Analysis browser Right click ( ) new execute block 2 Rename Stress initialization Analysis browser Stress initialization Move the selected item up [Fig. 57] Analysis browser Right click ( ) new execute block Rename Depletion Figure 56: Add new execute step Figure 57: Analysis tree Depletion Analysis of an Oilfield 29/40

At the same time, we initialize a stress filed in the soil that will be in equilibrium with its self-weight and the initial pressure (Load combination 1).

30 We set up the load combination for the start step and add the physic nonlinear options for the stress initialization. Accordingly, we will suppress superpositions effects so that strains and displacements will be reset to zero at the end of the start-step. At the same time, we initialize a stress filed in the soil that will be in equilibrium with its self-weight and the initial pressure (Load combination 1). Analysis browser Nonlin Stress initialization Right click ( ) Start steps Edit properties [Fig. 58] Analysis browser Nonlin Stress initialization Right click ( ) Start steps Physic nonlinear options [Fig. 59] Figure 58: Stress initialization - Edit properties Figure 59: Stress initialization - Physic nonlinear options Depletion Analysis of an Oilfield 30/40

31 We use the Geometry load combination 2 for the Depletion analysis. We change the solver method to Iterative in order to speed-up the analysis (the other settings remain as default). Analysis browser Nonlin Solution method [Fig. 61] Figure 60: Analysis tree Figure 61: Solution method Depletion Analysis of an Oilfield 31/40

63] Main menu Nonlin Run analysis Figure 62: Results selection Global displacements Global strains Global effective stresses Global total stresses Global effective stress increments Global

32 We select the desired output results (listed in [Table 2]) and we run the analysis. Analysis browser Nonlin Structural nonlinear Right click ( ) Output Edit properties Properties - OUTPUT Modify Results Selection [Fig. 62] [Table 2] [Fig. 63] Main menu Nonlin Run analysis Figure 62: Results selection Global displacements Global strains Global effective stresses Global total stresses Global effective stress increments Global total stress increments Global total pressure DISPLA TOTAL TRANSL GLOBAL STRAIN TOTAL GREEN GLOBAL STRESS EFFECT CHAUCHY GLOBAL STRESS TOTAL CHAUCHY GLOBAL STRESS EFFECT CHAUCHY REFGLB STRESS TOTAL CHAUCHY REFGLB PRESSU TOTAL Table 2: Required output data Figure 63: Output properties Depletion Analysis of an Oilfield 32/40

before depletion. For better visualization, the limits of the contour plot are set to -1.74e+08 and -2.

Results browser Output Element results Cauchy Total Stress SZZ [Fig.

33 4 Results 4.1 Vertical stresses We make a contour plot of the vertical stresses SZZ to see the vertical pressure in the model before depletion. For better visualization, the limits of the contour plot are set to -1.74e+08 and -2.31e+06 N/m 2 (see [Fig. 65]) that are the minimum and maximum stresses on the lateral surface of the model. Results browser Output Element results Cauchy Total Stress SZZ [Fig. 64] Property panel Result view settings Contour plot settings [Fig. 65] Figure 64: Output browser Figure 65: Output settings Figure 66: Vertical stresses (SZZ) As expected, the vertical pressure SZZ increases with the depth [Fig. 66]. Depletion Analysis of an Oilfield 33/40

[Fig. 65]). Results browser Output Element results Pore pressure PR [Fig. 67] Property panel Result view settings Contour plot settings [Fig.

34 4.2 Pore pressure We check the contour plot of the pore pressure PR in the soil. The limits of the contour plot are set to 0 and 8e+07 N/m 2 that are the minimum and maximum value, respectively, that PR achieves in the reservoir (see [Fig. 65]). Results browser Output Element results Pore pressure PR [Fig. 67] Property panel Result view settings Contour plot settings [Fig. 68] Results browser Case Start-step 1, Load-factor [Fig. 69] Results browser Case Load-step 2, Load-factor [Fig. 70] Figure 67: Output browser Figure 68: Output settings Depletion Analysis of an Oilfield 34/40

35 Figure 69: Pore pressure (PR) - Start-step 1 Figure 70: Pore pressure (PR) - Load-step 2 As shown in [Fig. 65], the pore pressure in the Fulmar layer (i.e., the reservoir) is above zero only for z 4950 m. This is a consequence of the load pressure function defined in [Fig. 45]. In the depletion stage [Fig. 70], the lower pore pressure is a result of the pressure change of -6e+07 N/m 2 defined in [Fig. 47]. Depletion Analysis of an Oilfield 35/40

4.3 Vertical strains We create a clipping plane to plot the total strain in vertical direction EZZ [Fig. 73]. The plane is located at the coordinates (4340, 0, 0) m.

Results browser Output Element results Total strains EZZ [Fig. 71] Property panel Result view settings Contour plot settings [Fig.

36 4.3 Vertical strains We create a clipping plane to plot the total strain in vertical direction EZZ [Fig. 73]. The plane is located at the coordinates (4340, 0, 0) m. Moreover, for a better understanding of the deformation phenomena around the reservoir, we set the minimum and maximum limit of the contour plot to and , respectively. Results browser Output Element results Total strains EZZ [Fig. 71] Property panel Result view settings Contour plot settings [Fig. 72] Figure 71: Output browser Figure 72: Output settings Figure 73: Vertical strain (EZZ) The strain field shown in [Fig. 73] is that due to the depletion process (the strain and displacement fields were reset to zero at the end of thestart-step 1). Depletion Analysis of an Oilfield 36/40

We now plot the threshold value scale to view positive and negative strain increments. This will highlight the effects induced by the depletion stage in the model.

37 We now plot the threshold value scale to view positive and negative strain increments. This will highlight the effects induced by the depletion stage in the model. Property panel Result Contour plot settings Contour levels At specific value [Fig. 74] Property panel Result Contour plot settings Color scale type Discrete color scale [Fig. 74] Property panel Result Contour plot settings Specified values options 0.0 [Fig. 74] Contour plot settings Bounding colors Threshold value scale [Fig. 74] [Fig. 75] Figure 74: Output settings Figure 75: Vertical strain (EZZ) - Load-step 2 As illustrated in [Fig. 75], the depletion stage induces positive strain increments above and below the Fulmar region undergoing pressure change, while negative strain increments are observed at its sides. Depletion Analysis of an Oilfield 37/40

4.4 Change in vertical stresses We plot the stress changes on the clipping plane after depletion.

The change in stresses are checked both for effective and total stresses.

76] Results browser Output Element results Cauchy total stresses dszz [Fig.

38 4.4 Change in vertical stresses We plot the stress changes on the clipping plane after depletion. In this case we set the color scale limits to a minimum of -9+e07 and a maximum of -8e+07. The change in stresses are checked both for effective and total stresses. Property panel Result view settings Contour plot settings [Fig. 76] Results browser Output Element results Cauchy total stresses dszz [Fig. 77] Results browser Output Element results Cauchy effective stresses dsezz [Fig. 78] Figure 76: Output settings Figure 77: Output browser - dszz Figure 78: Output browser - dsezz Depletion Analysis of an Oilfield 38/40

39 Figure 79: Change in vertical total stress - Load-step 1 Figure 80: Change in vertical effective stress - Load-step 1 The results show that the depletion stage induces an increment of the stresses in the top part of the reservoir. 1 1 The analysis of the stress increments in a more realistic model would allow for the visualization of arching effects in the soil layers above and below the reservoir. Depletion Analysis of an Oilfield 39/40

40 DIANA FEA BV Delftechpark 19a 2628 XJ Delft The Netherlands T +31 (0) F +31 (0) DIANA FEA BV Vlamoven TN Arnhem The Netherlands T +31 (0) F +31 (0)

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