# An Innovative System of Deep In Situ Environment Reconstruction and Core Transfer
## 4 Temperature and Pressure Decoupling Control Based on the Iso-Density Curves of Water
### Initial Environment Reconstruction  
As shown in Figure 4, let the initial state of a reconstruction process be A(\(\rho_{a}\), \(P_{a}\), \(T_{a}\)), and the reconstruction goal be F(\(\rho_{f}\), \(P_{f}\), \(T_{f}\)). The straight line \(\overline{\text{AF}}\) is the ideal P-T control curve which is a P-T coupling control.  
The proposed decoupling control method decouples \(\overline{\text{AF}}\) by interpolation. First, heat the water from A to B along the iso-density curve \(Curve_{a}\) where point A is located; then, conduct iso-thermal pressure relief from B to D. \(\overline{\text{BD}}\) is a vertical line. \(\bar{\text{AB}}\) and \(\overline{\text{BD}}\) are decoupled independent temperature and pressure controls, respectively. They constitute an interpolation step. Repeat the interpolation step until point F is reached.  
However, a real heating process does not run along an iso-density curve because, with the increase of temperature, the internal volume of the working chamber becomes larger, resulting in the reduction of the density of water. Therefore, the real heating process is a process of migration between iso-density curves. For example, in Figure 4, to reach point C, the real process is not to heat from A to B along the iso-density curve \(Curve_{a}\) first and then iso-thermal depressurize to C, but to heat directly from A to C along the dotted curve between them, which is called an iso-mass heating process. Under the condition that the  
Figure 4: The iso–density P-T curve cluster of water and the interpolation control paths.  
temperature difference between A and C is determined, the density difference between them can also be specified.  
Suppose that the temperature difference between A and C is: \(\Delta T_{ac}=T_{c}-T_{a}\), the change of the inner diameter of the chamber is \(\Delta d=d\cdot\alpha_{c}\cdot\Delta T_{ac}\), and the change of the length of the chamber is \(\Delta L=L\cdot\alpha_{c}\cdot\Delta T_{ac}\), where \(\alpha_{c}\) is the coefficient of linear expansion of the chamber at the temperature of \(T_{c}\); \(d\) and \(L\) are the inner diameter and the length of the chamber, respectively, at the temperature of \(T_{a}\).  
The water density difference between A and C is:  
\[\Delta\rho_{ac}=\rho_{c}-\rho_{a}=\rho_{c}[1-(d+\Delta d)^{2}(L+\Delta L)/(d^{ 2}L)] \tag{6}\]  
Ignore the high order small terms; then:  
\[\Delta\rho_{ac}=-3\rho_{a}a_{c}\Delta T_{ac} \tag{7}\]  
So, after decoupling, the reconstruction process from point A to point E is: iso-mass heating from A to C, then iso-thermal depressurization from C to D, and then iso-mass heating from D to E.  
The specified temperature and density differences between the start and the end points of each iso-mass heating process can be used to plan the start point by the end point. The temperature and pressure of the end point as the control targets are known, and its density can be obtained by finding the iso-density curve according to Equation (5). Then, the temperature, pressure and density of the start point can be determined by Equation (7) according the differences of temperature and density.