Exhibit 10.4


                                September 8, 2004


Blue Dolphin Exploration Company
801 Travis Street, Suite 2100
Houston, Texas 77002


Gentlemen:

         This letter sets forth the terms pursuant to which Ivar Siem and
certain other persons will acquire all of the issued and outstanding stock of
American Resources Offshore, Inc. ("ARO") from Blue Dolphin Exploration Company
("Blue Dolphin").

         1. The Purchase. It is my understanding that we have agreed that for
and in consideration of the payment at the Closing of $1,000 cash, the
assumption of the transaction costs, including incremental costs associated with
the reporting and disclosure of the transaction incurred by Blue Dolphin Energy
Company in its filings with the Securities and Exchange Commission and any other
required filings or announcements, and the assumption of any and all liabilities
of ARO (the "Purchase Price") Blue Dolphin will sell, transfer, assign and
convey to the Acquirors (as hereinafter defined) 100 shares of the common stock
of ARO, $0.01 par value per share (the "ARO Shares").

         2. Other Consideration. Blue Dolphin shall be reimbursed from the
proceeds, if any, received from Southern Gas Holdings, LLC pursuant to their
indemnification of ARO for the Wright Enterprises lawsuit for all costs it paid
associated with the defense and settlement of the lawsuit after ARO shall have
first recovered any and all costs it may pay in connection with said lawsuit
from this date forward.

         3. The Closing. The closing of the purchase of the ARO Shares (the
"Closing") will occur on the same day as this letter agreement.

         4. The Acquirors. The "Acquirors" will be Ivar Siem, Harris A. Kaffie
and Colombus Petroleum Limited, Inc. and those shareholders of Blue Dolphin
Energy Company who hold a number of shares of Blue Dolphin Energy Company common
stock above a threshold to be determined by Ivar Siem, provided, however, that
such threshold shall be set at a level, which will include at a minimum the 30
largest shareholders on a proportionate basis. Only Ivar Siem and ARO will be
responsible for the payment of the Purchase Price.

         5. Representations. Blue Dolphin hereby represents and warrants that as
of the date hereof and as of the Closing: (i) it owns the ARO Shares free and
clear of any liens or


Blue Dolphin Exploration Company


encumbrances, (ii) the ARO Shares represent all of the issued and outstanding
stock of ARO, and (iii) no party holds any right to acquire any shares of the
stock of ARO.

         6. Other. Upon execution of this agreement, all notes, advances and any
other intercompany balances between Blue Dolphin and ARO are hereby terminated
and eliminated. TO THE FULLEST EXTENT PERMITTED BY APPLICABLE LAW, IVAR SIEM AND
THE ACQUIRERS HEREBY AGREE TO DEFEND, INDEMNIFY AND HOLD HARMLESS BLUE DOLPHIN,
BLUE DOLPHIN ENERGY COMPANY, THEIR RESPECTIVE SUBSIDIARIES, SHAREHOLDERS AND
AFFILIATES, AND ALL DIRECTORS, OFFICERS, MANAGERS, MEMBERS, EMPLOYEES, ATTORNEYS
AND AGENTS OF ANY OF THE FOREGOING ("INDEMNIFIED PARTIES") FROM AND AGAINST ANY
AND ALL LOSS, COST, EXPENSE OR LIABILITY (INCLUDING ATTORNEYS' FEES AND COURT
COSTS) INCURRED BY ANY INDEMNIFIED PARTY IN CONNECTION WITH OR OTHERWISE ARISING
OUT OF ANY AND ALL CLAIMS OR PROCEEDINGS FROM PAST, PRESENT OR FUTURE BUSINESS
OF ARO.

         If the foregoing sets forth the terms of our agreement, please execute
this letter where indicated below.


                                                              Sincerely,

                                                                /s/ Ivar Siem
                                                              ------------------
                                                              Ivar Siem

ACCEPTED AND AGREED TO:

BLUE DOLPHIN EXPLORATION COMPANY


By:   /s/ Michael J. Jacobson
   -----------------------------------
Name:    Michael J. Jacobson
Title:   President

AMERICAN RESOURCES OFFSHORE, INC.

By:   /s/ Ivar Siem
   -----------------------------------
Name:    Ivar Siem
Title:   President