computed around the rectangle and all nodes outside the buffer are
excluded. For example, by subsetting this way, the time to calculate
a 50-mi tieback drops by a factor of 100.
Within the subset-network, starting at the origin node, an algorithm
developed by Dijkstra (1959) is applied. This evaluates the eight edges
surrounding a node, picking the lowest-weight edge and making the
node connected to it the next evaluation point. That simple rule is
then applied at the second node to find a third. At the third node, the
algorithm then looks back and examines if there were any lower-cost paths to get from the first to third nodes (i.e., other than via the
second). If not, the initial route from the first to the third is retained;
if a cheaper (i.e., lower-weight) path exists, it is substituted. Given
the least-cost way to get from the first node to the third, the process
is then repeated until the optimal path from origin to destination is
found. This method was implemented in Python.
As edge length and slope and the presence and areas of obstacles
are all considered, the final path is optimal subject to these variables.
Smoothing the route
Given the grid arrangement of network nodes, the final path, even
though mathematically optimal, is almost always very “jagged,”
composed of short, straight segments. To create a more practical
path, the optimal path from the process above is subject to a centered
five-point moving average:
Each xi,ȳi pair are projected coordinates of nodes along the smoothed
path and N is the total number of nodes along the original pipeline
path, composed of points xi and yi. This results in a smoothed path
version of the optimal line between the origin and destination.
Once the inputs are submitted, the algorithm generally takes several
minutes to compute the solution and prepare a zip file emailed to the
user. The file includes a report showing inputs, a map and the characteristics (e.g., length, average and maximum slope) of the optimal path.
A .csv file is included with the path coordinates, which can be imported
into Excel, CAD or other packages. So is a shapefile representing the
optimal path; it can be added for further analysis with the other data
and tools it contains or loaded into other packages that read shapefiles.
In the example above examining tieback routes from AC079 to the
Hoover, Nansen and Gunnison spars, four cases were tested. Three
used the default slope importance factor and were set to avoid seafloor
anomalies. The fourth test was a second route to Nansen in which no
provision was made for avoiding seafloor anomalies.
The alternative test of a no-obstacle-avoidance path to Nansen
produced an apparently paradoxical result:
the route avoiding obstacles is shorter than
the one that does not. The reason is that the
route avoiding obstacles was forced to take a
higher-maximum slope route, 12.5%, to mini-
mize length; the unconstrained route is longer
but encounters a maximum slope of 10.7%. This
type of influence in the trade-offs between slope,
obstacle-avoidance and length can be explored
further by changing the value of the slope
importance factor and rerunning the analysis.
Going for ward, we anticipate further develop-
ment of the tie-back tool to include the following
types of improvements, described below:
Cost. A rough cost could be estimated, either
using available public data or user inputs. Costs could be refined by
disaggregating seafloor obstacles and grading them from strict no-go
zones to zones that can be transited but at a higher cost. Additionally,
whereas only the absolute value of slope is currently used, positive and
negative slopes could be weighted separately.
Excess capacity. The estimates of each platform’s current excess
capacity could be expanded to include decline curve-based forecasts
of future production from existing wells and thereby estimate future
Slope importance. Empirical estimates of the slope importance factor,
statistically inferred from the paths of existing pipes, could be offered
to the user as guidance.
Computation speed. To increase model speed, we are exploring further
optimization of our network analysis algorithms and use of special-
purpose hardware for the matrix manipulation the approach requires.
A web-based tool for reconnaissance evaluation of tie-back options
from a prospect or discovery provides a first careful look at transportation options for new oil and gas volumes. Estimated excess capacity of
proximate platforms not only filters unrealistic destinations but sets a
foundation for expected tarif fs from different platform operators. Likewise,
the sensitivity of routing to seafloor characteristics, like slope and the
presence of obstacles, affords quick evaluation of engineering options.
Running the tool over the web brings it in line with the accelerating
move to light, mobile software applications that used anywhere and can
be easily updated. •
Dijkstra, E. W., 1959, A Note on Two Problems in Connexion with Graphs, Nu-merische Mathematik, vol. 1, no. 1, pp. 269-271.
The authors wish to thank the other members of the project team at Earth Science
Associates: Tony Dupont, Scott Morris and Deepal Saraf; and acknowledge the helpful discussions with Walter Stromquist.
Elka Lacno received her bachelor of science in mathematics and masters of science
in applied statistics from California State University Long Beach. She joined Earth
Science Associates as a Data Scientist specializing in network analysis, bidding
theory and modeling auctions.
John D. Grace received his Ph.D. in economics for Louisiana State University and
taught geology and mathematics at LSU, University of Southern California and California State University Fullerton. He began his career as a mathematical geologist
at ARCO’s research lab then went to their corporate planning group. He has been
president of Earth Science Associates since 1991 and is a member of the Society of
Petroleum Engineers and Society of Exploration Geophysicists.
Ten nearest platforms within 75 mi of Alaminos Canyon.
Block Structure Operator
Est.’d Excess Capacity Currently
(ft) Oil (bopd) Gas (Mcfpd)
AC025 HooverSpar ExxonMobil 72,190 292,346 Yes 4,825
EB602 NansenSpar Anadarko 32,900 202,673 Yes 3,650
EB643 Boomvang Spar Anadarko 32,215 176,805 Yes 3,650
GB668 Gunnison Spar Anadarko 17,779 134,061 Yes 3,150
Lengths and slopes for tieback options.
Block Structure Avoid Subsea Obstacles Distance (mi) Average/Max Slope (%)
AC025 HooverSpar Yes 48 0.15/5
EB602 NansenSpar Yes 49 0.3/12.5
EB602 Nansen Spar No 52 0.28/10.7
GB668 GunnisonSpar Yes 63 0.42/5.4