E ff ect of pressure gradients

The pressure changes cause severe and irreversible deterioration as pointed out in Section 5.6. During the test conditions the specimens are partly filled with the gas. Furthermore, the resin is relatively soft, because it is above its glass transition temperature. When the pressure suddenly drops, the gas departs from the material. The volume of the material is suddenly decreased and the molecular chains are forced to move. When the gas has departed from the material, the glass transition temperature increases as the penetrating species no longer cause internal disorder in the molecular matrix. As the motion of the molecular chains ceases, the material turns into glass. If the molecular chains do not get reorganized before the mate-rial turns into glass, the structure will contain anomalies, which can be seen as crystallized structures in Fig. 5.56.

However, this kind of behavior can be assumed irreversible, because the materials should basically get organized again when the pressure is increased and a new amount of gas dif-fused. This means that before the depressurization runs, the materials are in equilibrium states. Certainly, such a glass transition effect is not expected to cause cracks inside the ma-terial. Therefore, another approach is needed. The materials are in equilibrium when the diffusion process has has been going on for a reasonable amount of time. At that point, the conditions can be illustrated as in Fig. 5.64. Even though it was not stated in Section 5.4, the diffusion of wellstream gas into mainwall insulation is expected to saturate completely. The depressurization is illustrated more closely in Fig. 5.65.

In equilibrium, the pressure p₁ of the gas inside the insulation is equal to the pressure p₂ of the surroundings. Accordingly, the chemical potential µ₁ inside the insulation is equal to the chemical potentialµ2of the surroundings. During the depressurization, the pressure p2and the chemical potentialµ₂of the surroundings rapidly change, but the ones inside the insulation (p1,µ₁) are not changed. Therefore, each gas particle inside the insulation are forced to flow out of the insulation. The forceFiappears towards the chemical bonds that lie in the way, as seen in Fig. 5.65a. The forceF_ithat causes a single gas particle to move can be expressed as

5.7 Aging of the insulation in the wellstream gas 179

into the polymer structure of the resin and cause permanent reduction in the glass transition temperature of the epoxy. For the difficulties in the removal of the hydrocarbons mentioned above, such an effect was not investigated in this thesis.

The insulating materials experience the diffusion not as aging or degradation, but rather as a change into a different state. The hydrocarbons penetrate into the polymer matrix and force the molecular chains to set differently. The chains are reformed into a less energy efficient form, and there are internal tensions between the chains. Therefore, the external energy needed to cut the molecular chains is lower, which is seen as a reduced mechanical strength.

If the hydrocarbons are gently removed from the polymer matrix, the chains reorganize back to their original places, and the initial properties of the material are restored. If the removal process is not gentle, the motion of hydrocarbon molecules may cut some of the polymer chains. This is illustrated in the following section.

5.7.6 E ff ect of pressure gradients

The pressure changes cause severe and irreversible deterioration as pointed out in Section 5.6. During the test conditions the specimens are partly filled with the gas. Furthermore, the resin is relatively soft, because it is above its glass transition temperature. When the pressure suddenly drops, the gas departs from the material. The volume of the material is suddenly decreased and the molecular chains are forced to move. When the gas has departed from the material, the glass transition temperature increases as the penetrating species no longer cause internal disorder in the molecular matrix. As the motion of the molecular chains ceases, the material turns into glass. If the molecular chains do not get reorganized before the mate-rial turns into glass, the structure will contain anomalies, which can be seen as crystallized structures in Fig. 5.56.

However, this kind of behavior can be assumed irreversible, because the materials should basically get organized again when the pressure is increased and a new amount of gas dif-fused. This means that before the depressurization runs, the materials are in equilibrium states. Certainly, such a glass transition effect is not expected to cause cracks inside the ma-terial. Therefore, another approach is needed. The materials are in equilibrium when the diffusion process has has been going on for a reasonable amount of time. At that point, the conditions can be illustrated as in Fig. 5.64. Even though it was not stated in Section 5.4, the diffusion of wellstream gas into mainwall insulation is expected to saturate completely. The depressurization is illustrated more closely in Fig. 5.65.

In equilibrium, the pressure p₁ of the gas inside the insulation is equal to the pressure p₂ of the surroundings. Accordingly, the chemical potential µ₁inside the insulation is equal to the chemical potentialµ2of the surroundings. During the depressurization, the pressure p2and the chemical potentialµ₂of the surroundings rapidly change, but the ones inside the insulation (p1, µ₁) are not changed. Therefore, each gas particle inside the insulation are forced to flow out of the insulation. The forceFiappears towards the chemical bonds that lie in the way, as seen in Fig. 5.65a. The forceF_ithat causes a single gas particle to move can be expressed as

Fig. 5.64. Thermodynamic conditions of the gas and insulation in equilibrium and depressurization states.

F_i=(p₂−p₁)A_i (5.9)

The gas particle may go around the adjacent chemical bond (solid green in Fig. 5.65a), which stands on its way. Alternatively, the gas particle may go through by breaking the bond.

Whichever way it proceeds, there is an area of low pressure p₃behind it (white area in Fig.

5.65b). The molecular chains A and B on both sides of the gas particle in the equilibrium state are now forced byF_{chain, A}andF_{chain, B}, respectively, to move back to their original places.

These forces create stresses to the bonds marked with yellow in Fig. 5.65b. The departure of the gas may cause either the green or yellow bonds to break. In either case, the result is a crack, which extends straight towards the surface, as seen in Fig. 5.65c and in reality in Fig.

5.60.

The enthalpy, entropy, and Gibbs free energy of the wellstream gas mixture as functions of pressure are illustrated in Fig. 5.66. Enthalpy and entropy are defined by calculations on the flash conditions of the gas mixture with PVTSim software. The Gibbs free energy is calculated according to Eq. (2.7).

Fig. 5.65. Departure of the diffused gas from the insulation as seen at the molecular level. The grey network indicates the molecular structure.

Fig. 5.64. Thermodynamic conditions of the gas and insulation in equilibrium and depressurization states.

F_i=(p₂−p₁)A_i (5.9)

The gas particle may go around the adjacent chemical bond (solid green in Fig. 5.65a), which stands on its way. Alternatively, the gas particle may go through by breaking the bond.

Whichever way it proceeds, there is an area of low pressurep₃behind it (white area in Fig.

5.65b). The molecular chains A and B on both sides of the gas particle in the equilibrium state are now forced byF_{chain, A} andF_{chain, B}, respectively, to move back to their original places.

These forces create stresses to the bonds marked with yellow in Fig. 5.65b. The departure of the gas may cause either the green or yellow bonds to break. In either case, the result is a crack, which extends straight towards the surface, as seen in Fig. 5.65c and in reality in Fig.

5.60.

The enthalpy, entropy, and Gibbs free energy of the wellstream gas mixture as functions of pressure are illustrated in Fig. 5.66. Enthalpy and entropy are defined by calculations on the flash conditions of the gas mixture with PVTSim software. The Gibbs free energy is calculated according to Eq. (2.7).

Fig. 5.65. Departure of the diffused gas from the insulation as seen at the molecular level. The grey network indicates the molecular structure.

5.7 Aging of the insulation in the wellstream gas 181

Fig. 5.66. Gibbs free energy G, enthalpy H, and entropy S as functions of pressure. The temperature is 130^◦C.

The change in the Gibbs free energy is most rapid in the pressure range close to atmospheric pressure. The Gibbs free energy is the sum of the particles in the thermodynamic system multiplied by their chemical potentials:

G=X

i

µ_iN_i (5.10)

The change in the Gibbs free energy is related to the change in chemical potentials, which in the equilibrium state are same both inside and outside of the insulation. The amount of Gibbs free energy per a single pressure step is at highest near the atmospheric pressure.

This is related to the volume of the gas. Under high pressure, the gas is compressed and its volume hardly changes as a result of small pressure gradients. Near atmospheric pressure, the gas is less compressed and allowed to expand or contract as a result of pressure gradients.

Therefore, the volume of the insulation is virtually constant during the pressure gradients at high pressure, but it changes accordingly under the pressure gradients near atmospheric pressure. The change in volume creates additional forces inside the molecular structure.

Thus, the reason for bond scission and formation of internal cracks is not only the force in Eq. (5.9), but the combination of that and other forces including the ones created by the expansions of the gas and the insulation. In other words, the case is too complicated to be approached in this way. Equation (5.9) is not valid, because it gives the highest force at high pressure. The volume change is included in the Gibbs free energy in Fig. 5.66. Therefore, the depressurization has the most severe influence near the atmospheric pressure.

5.7 Aging of the insulation in the wellstream gas 181

Fig. 5.66. Gibbs free energy G, enthalpy H, and entropy S as functions of pressure. The temperature is 130^◦C.

The change in the Gibbs free energy is most rapid in the pressure range close to atmospheric pressure. The Gibbs free energy is the sum of the particles in the thermodynamic system multiplied by their chemical potentials:

G=X

i

µ_iN_i (5.10)

The change in the Gibbs free energy is related to the change in chemical potentials, which in the equilibrium state are same both inside and outside of the insulation. The amount of Gibbs free energy per a single pressure step is at highest near the atmospheric pressure.

This is related to the volume of the gas. Under high pressure, the gas is compressed and its volume hardly changes as a result of small pressure gradients. Near atmospheric pressure, the gas is less compressed and allowed to expand or contract as a result of pressure gradients.

Therefore, the volume of the insulation is virtually constant during the pressure gradients at high pressure, but it changes accordingly under the pressure gradients near atmospheric pressure. The change in volume creates additional forces inside the molecular structure.

Thus, the reason for bond scission and formation of internal cracks is not only the force in Eq. (5.9), but the combination of that and other forces including the ones created by the expansions of the gas and the insulation. In other words, the case is too complicated to be approached in this way. Equation (5.9) is not valid, because it gives the highest force at high pressure. The volume change is included in the Gibbs free energy in Fig. 5.66. Therefore, the depressurization has the most severe influence near the atmospheric pressure.