Concrete stress frame and reservoir simulation
INITIAL CONCEPT
The experiment relies on the placement of a shale sample surrounded by the flat jacks, metal plates, load cells and the power and electrical wires. The plates are to ensure that the pressure applied to each face of the shale sample is equal. The plates also house the acoustic sensors protecting them from being crushed whilst, simultaneously, allowing the detector to rest on the face of the shale to detect the emissions from the subtle pressure changes as the fracture evolves. A void had to be designed that would allow for all of the above and yet maximise the width of the concrete, which would be needed to take the immense pressures involved. This necessitated the design of a void that was based around a central cuboid shape, but which had thin arms that would protrude from each corner to house the in- flow and outflow hydraulic pipes of the flat jacks. The original design is shown below in Figure 3-4.
PRELIMINARY DESIGN
In the initial design stage a load cell of 100mm diameter was settled on to measure the loads applied to the shale. However, whilst working on the design it became obvious that space taken up by the load cell would restrict the ability to place hydraulic lines and sensors within the void. Therefore, in order to calibrate the flat jacks and ensure that they were exerting the same pressure as that shown on the pressure gauge, the flat jacks were placed in pairs and then subjected to a pressure measuring device. These results were then compared to the pressures recorded on the pressure gauge.
During the final discussion stages concern was raised that the excessive void size would create difficulties when holding the fluid at pressure within the void space. For this reason, the void size was reduced by removing the space intended for the load cells. The arms of the flat jacks were also too long so they too were reduced in order to fit within the smaller void. The updated design work is shown at full scale in drawing 12 in Appendix B and the main design evolution, as calculated with the support of the civil engineering department, is presented in Appendix C. The preliminary design is shown overleaf, in Figure 3-5.
Void Void Cut out for flat jack arms
Side view 1 Side view 2
22
Transparent view
Central void Voids for flat jack arms
Load cells
A B
Original stress calculations of the concrete and forces
applied to the metal lid and sides
The original plan was to exert a maximum pressure of 120 bar on the shale samples in the concrete void using flat jacks and to pressurise the fluid to 40 bar to represent loaded rock. The calculations to prove the concrete could withstand the pressure of the fluid that surrounds the shale sample are shown below: In order to calculate whether the rig has been designed to an adequate standard the pressures that are being exerted and applied to the surrounding concrete must also be calculated.
First the shortest distance between the concrete void and the steel face of the stress face was calculated. The longest face of the rectangular concrete void is used, as this would be the face that would have the shortest distance between the internal radius and external radius, thus would be under the greatest loading;
Internal radius of Ri=220mm
External radius (distance from the of centre of the void to the stress frame); Ro = 675mm
Maximum internal and external pressures are as follows: Internal pressure
Pi = 0.6 N mm-2 (4 bar x 1.5 factor of safety)
External pressure Po= 0 N mm-2
3.5.2.1
Lame’s Equation
Lame’s Equation can be used to measure the pressures exerted on a thick-walled cylinder, one in which the ratio diameter/thickness < 20. The thick-walled cylinder equation is used because the dissipation of stress at the inner and outer walls behaves very differently. The various components of Lame’s equation are shown in 3-1 to 3-2.
Radial Stress: 𝜎𝑟 = 𝑟𝑖2∙ 𝑝𝑖− 𝑟12∙ 𝑝𝑜 (𝑟𝑜2− 𝑟𝑖2) −(𝑝𝑖− 𝑝𝑜) ∙ 𝑟𝑖 2∙ 𝑟 𝑜2 (𝑟𝑜2− 𝑟𝑖2) ∙ 𝑟2 3-1:
Hoop stress 𝜎ℎ= [ 𝑟𝑖2∙ 𝑃𝑖− 𝑟𝑜2∙ 𝑃𝑜 (𝑟𝑜2− 𝑟𝑖2) +(𝑃𝑖− 𝑃𝑜) ∙ 𝑟𝑖 2∙ 𝑟 𝑜2 (𝑟𝑜2− 𝑟12) ∙ 𝑟2 ] 3-2: Where: Pi + inner pressure, Po is outer pressure ri is inner radius and ro is outer radius.
Simplifying the straight edges into a thick-walled cylinder means that Lame’s equation can be used. The use of Lame’s equation to work out the required thickness’s are presented in Appendix A.
3.6
Flat Jacks
The flat jacks that were used to apply a tri-axial load were supplied by Freysinet Bridge Bearings ltd. The Freysinet Sz15 flat jack (150mm) as shown in Figure 3-6 was selected. The dimensions of the jacks with their operating specifications are presented in Appendix D.
FIGURE 3-6:Flat Jack, 150mm diameter.
The flat jack is a thin circular concave cushion, which has two steel press plates in each concave position in order to press against the body being subjected to the pressure and also to protect the flat jack. Upon the injection of hydraulic fluid, the cushion expands pushing the two metal disks outwards.
Originally it was intended to have the flat jacks acting on all faces, however, it was later decided that this would potentially cut off the service holes. In order to simulate the pressures acting on all the faces the pressure would be jacked up on the ventral face and the dorsal face would sit flush against the metal
Expanding cushion Central press plate to allow equalisation of pressure Fluid-in arm Fluid-out arm
The reduction in the length of the flat jack arms (previously mentioned) will help to keep the reservoir fluid at a constant pressure and also to mitigate against potential leaks in the system.