Assisted History Matching by Using Recursive Least Square and Discrete Cosine Transform

History matching is the act of adjusting a model of a reservoir until it closely reproduces
the past behavior of a reservoir. Before the computer was invented, history matching is
done manually by trial and error method and personal judgment which only can be done
by experienced engineer. Because of these factors, manual history matching technique
consume a lot of time. Thus, this project is carried to do assisted history matching and to
determine whether Recursive least square as optimization method and Discrete cosine
transform as parameter reduction method can be combined or not.
In order to achieve the objective, a number of steps have been done. First, a synthetic
model has been built by modifying ODEH data. Two sets of permeability value have
been selected to get two data which are historical and simulated data from the model.
Then, the fluid flow equation is derived to get the forward model. Forward model is then
used to design the objective function. After objective function has been designed, DCT
is applied to the reservoir data in order to minimize the number of parameters. Next,
RLS is applied to the parameter which has been reduced to optimize the data. These
steps are repeated until the threshold value is lower than the set threshold. For this
project, RLS and DCT methods are compared with the literature review to know the
successfulness of this combination.
For the first part of final year project, the derivation of forward model has been done.
For the second part of final year project, a synthetic model has been built and objective
function has been design from the forward model. Before applying the RLS and DCT,
the illustrations of these methods need to be done to see how it work and then RLS and
DCT were applied to the reservoir data.
The outcomes at the end of this project are first two set of data is obtain from the
synthetic model which are historical and simulated data. Then algorithms for DCT and
v
RLS are proposed which can be applied to the history matching problem. From the
result, the combination of RLS and DCT are successful and can be used for history
matching purpose.