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Orr, F. M. - Theory of Gas Injection Processes Episode 7

Tham khảo tài liệu 'orr, f. m. - theory of gas injection processes episode 7', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 5.5. STRUCTURE OF TERNARY GAS OIL DISPLACEMENTS 111 7. Construct a rarefaction along the shortest tie line that connects the equal-eigenvalue point or the intermediate shock point to the tangent shock point for the single-phase composition oil or gas associated with the shortest tie line. 8. Determine whether a tie-line rarefaction can occur on the longest tie line. A rarefaction can occur if variation along the tie line from the landing point of the intermediate shock or the intersection of the nontie-line path with the tie line to the tangent shock point satisfies the velocity rule. If so the shock from the single-phase composition to the longest tie line is a semishock. If not a genuine shock is constructed from the landing or intersection point to the single-phase composition. The fact that solution construction must begin on the shortest tie line arises from two observations about the geometry of composition paths and shocks. The first observation applies to displacements in which a rarefaction connects the two key tie lines. In that case there are two points at which the appropriate nontie-line path intersects the two key tie lines . Both points must be switch points at which the velocity rule is satisfied. The argument given in Section 5.3 indicates that one of the two points must be the equal-eigenvalue point. The geometry of nontieline paths see Fig. 5.9 indicates that the point of tangency of the nontie-line path to a tie line which is the point at which eigenvalues are equal occurs on the shorter of the two tie lines. If the equal-eigenvalue point on the longer tie line were selected instead the paths traced would not reach the shorter tie line. Solution construction can proceed by the steps outlined above once the equal-eigenvalue point is found on the shorter of the two key tie lines. The second observation applies to displacements in which the two key tie lines are connected by a shock. In that case the nontie-line rarefaction is replaced by a .