<PAGE>

NEITHER THIS WARRANT NOR THE SECURITIES ISSUABLE UPON EXERCISE HEREOF HAVE 
BEEN REGISTERED UNDER THE SECURITIES ACT OF 1933, AS AMENDED (THE "SECURITIES 
ACT"), OR  THE SECURITIES LAWS OF ANY STATE.  SUCH SECURITIES MAY NOT BE SOLD 
OR OTHERWISE DISPOSED OF UNLESS PURSUANT TO A REGISTERED OFFERING OR BY 
TRANSFER EXEMPT FROM REGISTRATION UNDER THE SECURITIES ACT AND APPLICABLE 
STATE SECURITIES LAWS. 
                                       
                         ENERGY BIOSYSTEMS CORPORATION       

                         COMMON STOCK PURCHASE WARRANT

No. W-1

     This certifies that, for value received, PetroStar Inc. or registered 
assigns (the "holder"), upon due exercise of this Warrant, is entitled to 
purchase from Energy BioSystems Corporation, a Delaware corporation (the 
"Company"), at any time on or after September 6, 1999 (the "Initial Exercise 
Date"), and before the close of business on March 6, 2002, or if not a 
trading date on the New York Stock Exchange, the next following trading date 
(the "Expiration Date"), all or any part of 200,000 fully paid and 
nonassessable Shares (the "Warrant Shares") of the Common Stock, par value 
$0.01 per share, of the Company ("Common Stock"), at a purchase price of 
$3.11 per share (the "Purchase Price"), both the Purchase Price and the 
number of Warrant Shares issuable upon exercise of this Warrant being subject 
to possible adjustment as provided below.

     This Warrant is hereinafter called the "Warrant." The holder hereof and 
all subsequent holders of this Warrant shall be entitled to all rights and 
benefits provided to the holder or holders hereof pursuant to the terms of 
this Warrant.

     SECTION 1.  EXERCISE OF WARRANT.  The holder of this Warrant may, at any 
time on or after the Initial Exercise Date and on or before the Expiration 
Date, exercise this Warrant in whole at any time or in part from time to time 
for the purchase of the Warrant Shares or other securities which such holder 
is then entitled to purchase hereunder ("Warrant Securities") at the Purchase 
Price (as hereinafter defined).  In order to exercise this Warrant in whole 
or in part, the holder hereof shall deliver to the Company (i) a written 
notice of such holder's election to exercise this Warrant, which notice shall 
specify the number of Warrant Shares to be purchased, (ii) payment of the 
aggregate purchase price of the Warrant Shares being purchased by certified 
or bank cashier's check, and (iii) this Warrant, provided that, if such 
Warrant Shares or other Warrant Securities have not then been registered 
under the Securities Act or applicable state securities laws, the Company may 
require that such holder furnish to the Company a written statement that such 
holder is purchasing such Warrant Shares or other Warrant Securities for such 
holder's own account for investment and not with a view to the distribution 
thereof, that none of such shares will be offered or sold in violation of the 
provisions of the Securities Act and applicable state securities laws and as 
to such other matters relating to the holder as the Company may reasonably 
request to permit the issuance of such Warrant Shares or other Warrant 
Securities without registration under the Securities Act and applicable state 
securities laws.  Upon receipt thereof, the Company shall, as promptly as 
practicable, execute or cause to be executed and deliver to such holder a 
certificate or certificates representing the aggregate number of Warrant 
Shares (or if applicable, other Warrant Securities) specified in said notice. 
The stock certificate or certificates so delivered shall be in the 
denomination of 100 shares each or such 

<PAGE>

other denominations as may be specified in said notice and shall be 
registered in the name of such holder or such other name as shall be 
designated in said notice.

     No fractional Warrant Shares are to be issued upon the exercise of this 
Warrant, but the Company shall pay a cash adjustment in respect of any 
fraction of a share which would otherwise be issuable in an amount equal to 
the same fraction of the fair market value per share of the Warrant Shares on 
the day of exercise, as reasonably determined by the Company.  If this 
Warrant shall have been exercised only in part, the Company shall, at the 
time of delivery of said certificate or certificates, deliver to such holder 
a new Warrant evidencing the rights of such holder to purchase the remaining 
Warrant Shares called for by this Warrant, which new Warrant shall in all 
other respects be identical with this Warrant, or, at the request of such 
holder, appropriate notation may be made on this Warrant and same returned to 
such holder.  The Company shall pay all expenses, taxes and other charges 
payable in connection with the preparation, execution and delivery of share 
certificates under this Section, except that, if such share certificates are 
requested to be registered in a name or names other than the name of the 
holder of this Warrant, funds sufficient to pay all stock transfer taxes 
which shall be payable upon the execution and delivery of such share 
certificates shall be paid by the holder hereof at the time of delivering the 
notice of exercise mentioned above.

     The Company represents, warrants and agrees that all Warrant Shares 
issuable upon any exercise of this Warrant in accordance herewith shall be 
validly authorized and issued, fully paid and nonassessable.

     This Warrant shall not entitle the holder hereof to any of the rights of 
a stockholder of the Company prior to exercise in the manner herein provided.

     SECTION 2.  TRANSFER, DIVISION AND COMBINATION.  The Company shall keep 
at its principal executive office a register for the registration and 
registration of transfers of Warrants.  The name and address of each holder 
of one or more Warrants, each transfer thereof and the name and address of 
each transferee of one or more Warrants shall be registered in such register. 
Prior to due presentment for registration of transfer, the person in whose 
name any Warrants shall be registered shall be deemed and treated as the 
owner and holder thereof for all purposes hereof, and the Company shall not 
be affected by any notice or knowledge to the contrary.  The Company shall 
give to any holder of a Warrant promptly upon request therefor, a complete 
and correct copy of the names and addresses of all registered holders of 
Warrants.

     Subject to the provisions of Section 3, upon surrender of any Warrant at 
the principal executive office of the Company for registration of transfer or 
exchange (and in the case of a surrender for registration of transfer, duly 
endorsed or accompanied by a written instrument of transfer duly executed by 
the registered holder of such Warrant or his attorney duly authorized in 
writing and accompanied by the address for notices of each transferee of such 
Warrant or part thereof), the Company shall execute and deliver, at the 
Company's expense, one or more new Warrants (as requested by the holder 
thereof) in exchange therefor, exercisable for an aggregate number of Warrant 
Shares equal to the number of shares for which the surrendered Warrant is 

                                      -2-
<PAGE>

exercisable and issued to such person or persons as such holder may request, 
which Warrant or Warrants shall in all other respects be identical with this 
Warrant.  

     Upon receipt by the Company of evidence reasonably satisfactory to it of 
the ownership of and the loss, theft, destruction or mutilation of any 
Warrant, and (a) in the case of loss, theft or destruction, of indemnity 
reasonably satisfactory to it (provided that if the holder of such Warrant 
is, or is a nominee for, an original holder, such person's own unsecured 
agreement of indemnity shall be deemed to be satisfactory), or (b) in the 
case of mutilation, upon surrender and cancellation thereof, the Company at 
its own expense shall execute and deliver, in lieu thereof, a new Warrant 
identical in all respects to such lost, stolen, destroyed or mutilated 
Warrant.

     SECTION 3.  COMPLIANCE WITH SECURITIES ACT; RESTRICTIONS ON TRANSFER.  
(a)  Each certificate for Warrant Shares (or other Warrant Securities) 
initially issued upon the exercise of this Warrant and each certificate for 
Warrant Shares (or other Warrant Securities) issued to subsequent transferees 
of any such certificate shall (unless otherwise permitted by this Section 3) 
be stamped or otherwise imprinted with legend in substantially the following 
form:

     "THE SECURITIES REPRESENTED BY THIS CERTIFICATE HAVE NOT BEEN
     REGISTERED UNDER THE SECURITIES ACT OF 1933, AS AMENDED (THE
     "SECURITIES ACT") OR THE SECURITIES LAWS OF ANY STATE.  SUCH
     SECURITIES MAY NOT BE SOLD OR OTHERWISE DISPOSED OF UNLESS PURSUANT TO
     A REGISTERED OFFERING OR BY TRANSFER EXEMPT FROM REGISTRATION UNDER
     THE SECURITIES ACT AND APPLICABLE STATE SECURITIES LAWS."
     
     (b)  The holder understands that it may be entitled to certain 
registration rights pursuant to the Registration Rights Agreement dated as of 
March 6, 1998 which are applicable to its Warrant Shares (and, if applicable, 
other Warrant Securities).

     SECTION 4. ADJUSTMENT OF PURCHASE PRICE.  

     (a)  The Purchase Price and the number of Warrant Shares and the number 
or amount of any other securities and property as hereinafter provided for 
which this Warrant may be exercisable shall be subject to adjustment from 
time to time effective upon each occurrence of any of the following events.

     (b)  If the Company shall declare or pay any dividend with respect to 
its Common Stock payable in shares of Common Stock, subdivide the outstanding 
Common Stock into a greater number of shares of Common Stock, or reduce the 
number of shares of Common Stock outstanding (by stock split, reverse stock 
split, reclassification or otherwise than by repurchase of its Common Stock) 
(any of such events being hereinafter called a "Stock Split"), the Purchase 
Price and number of Warrant Shares issuable upon exercise of this Warrant 
shall be appropriately adjusted so as to entitle the holder hereof to receive 
upon exercise of this Warrant, for the same aggregate consideration provided 
herein, the same number of shares of Common Stock (plus cash in lieu of 

                                      -3-
<PAGE>

fractional shares) as the holder would have received as a result of such 
Stock Split had such holder exercised this Warrant in full immediately prior 
to such Stock Split.

     (c)  If the Company shall merge or consolidate with or into one or more 
corporations or partnerships and the Company is the sole surviving 
corporation, or the Company shall adopt a plan of recapitalization or 
reorganization in which the Common Stock is exchanged for or changed into 
another class of stock or other security or property of the Company, the 
holder of this Warrant shall, for the same aggregate consideration provided 
herein, be entitled upon exercise of this Warrant to receive in lieu of the 
number of shares of Common Stock as to which this Warrant would otherwise be 
exercisable, the number of shares of Common Stock or other securities (plus 
cash in lieu of fractional shares) or property to which such holder would 
have been entitled pursuant to the terms of the agreement or plan of merger, 
consolidation, recapitalization or reorganization had such holder exercised 
this Warrant in full immediately prior to such merger, consolidation, 
recapitalization or reorganization.

     (d)  If the Company is merged or consolidated with or into one or more 
corporations or partnerships under circumstances in which the Company is not 
the sole surviving corporation, or if the Company sells or otherwise disposes 
of substantially all its assets, and in connection with any such merger, 
consolidation or sale the holders of Common Stock receive stock or other 
securities convertible into equity of the surviving or acquiring corporations 
or entities, or other securities or property after the effective date of such 
merger, consolidation or sale, as the case may be, the holder of this Warrant 
shall, for the same aggregate consideration provided herein, be entitled upon 
exercise of this Warrant to receive, in lieu of the shares of Common Stock as 
to which this Warrant would otherwise be exercisable, shares of such stock or 
other securities (plus cash in lieu of fractional shares) or property as the 
holder of this Warrant would have received pursuant to the terms of the 
merger, consolidation or sale had such holder exercised this Warrant in full 
immediately prior to such merger, consolidation or sale.  In the event of any 
consolidation, merger or sale as described in this Section 4(d), provision 
shall be made in connection therewith for the surviving or acquiring 
corporations or partnerships to assume all obligations and duties of the 
Company hereunder or to issue substitute warrants in lieu of this Warrant 
with all such changes and adjustments in the number or kind of shares of 
stock or securities or property thereafter subject to this Warrant or in the 
Purchase Price as shall be required in connection with this Section 4(d).

     (e)  If the Company (other than in connection with a sale described in 
Section 4(d)) proposes to liquidate and dissolve, the Company shall give 
notice thereof as provided in Section 5(b) hereof and shall permit the holder 
of this Warrant to exercise any unexercised portion hereof at any time within 
the 10 day period following delivery of such notice, if such holder should 
elect to do so, and participate as a stockholder of the Company in connection 
with such dissolution.

     (f)  Whenever any adjustment is made as provided in any provision of 
this Section 4:

               (i)  the Company shall compute the adjustments in accordance with
          this Section 4 and shall prepare a certificate signed by an officer of
          the Company setting forth the adjusted number of shares or other
          securities or property and Purchase 

                                      -4-
<PAGE>

          Price, as applicable, and showing in reasonable detail the facts upon 
          which such adjustment is based, and such certificate shall forthwith 
          be filed with the Company or its designee; and

               (ii) a notice setting forth the adjusted number of shares or
          other securities or property and the Purchase Price, as applicable,
          shall forthwith be required, and as soon as practicable after it is
          prepared, such notice shall be delivered by the Company to the holder
          of record of each Warrant.

     (g)  If at any time, as a result of any adjustment made pursuant to this 
Section 4, the holder of this Warrant shall become entitled, upon exercise 
hereof, to receive any shares other than shares of Common Stock or to receive 
any other securities, the number of such other shares or securities so 
receivable upon exercise of this Warrant shall be subject to adjustment from 
time to time in a manner and on terms as nearly equivalent as practicable to 
the provisions contained in this Section 4 with respect to the Common Stock.

     SECTION 5.  SPECIAL AGREEMENTS OF THE COMPANY.

     (a)  The Company covenants and agrees that it will reserve and set apart 
and have at all times a number of shares of authorized but unissued Common 
Stock (and, if applicable, other Warrant Securities) then deliverable upon 
the exercise of the Warrants or any other rights or privileges provided for 
therein sufficient to enable it at any time to fulfill all its obligations 
thereunder; and if at any time the number of authorized but unissued shares 
of Common Stock shall not be sufficient to effect the exercise of this 
Warrant at the Purchase Price then in effect, the Company will take such 
corporate action as may, in the reasonable opinion of its counsel, be 
necessary to increase its authorized shares but unissued shares of Common 
Stock (and, if applicable, other Warrant Securities) to such number of shares 
as shall be sufficient for such purposes.

     (b)  In case the Company proposes

               (i)   to pay any dividend upon the Common Stock or make any
          distribution or offer any subscription or other rights to the holders
          of Common Stock, or

               (ii)  to effect any capital reorganization or reclassification
          of capital stock of the Company, or

               (iii) to effect the consolidation, merger, sale of all or
          substantially all of the assets, liquidation, dissolution or winding
          up of the Company,

then the Company shall cause notice of any such intended action to be given 
to each holder of the Warrants not less than 15 nor more than 60 days prior 
to the date on which the transfer books of the Company shall close or a 
record be taken for such dividend or distribution, or the date when such 
capital reorganization, reclassification, consolidation, merger, sale, 
liquidation, dissolution or winding up shall be effected, or the date of such 
other event, as the case may be.

                                      -5-
<PAGE>

     SECTION 6.  NOTICES.  Any notice or other document required or permitted 
to be given or delivered to holders of Warrants and holders of Common Stock 
(or other Warrant Securities) shall be in writing and sent (a) by telecopy if 
the sender on the same day sends a confirming copy of such notice by a 
recognized overnight delivery service (charges prepaid), or (b) by registered 
or certified mail with return receipt requested (postage prepaid) or (c) by a 
recognized overnight delivery service (with charges prepaid).

          (i)  if to the Company, at Energy BioSystems Corporation, 4200
     Research Forest Drive, The Woodlands, Texas 77381, Telecopy No.: 
     (281) 364-6110, or such other address as it shall have specified to the 
     holders of Warrants in writing; or

          (ii) if to a holder, at its address set forth below, or such other
     address as it shall have specified to the Company in writing.

Notices given under this Section 6 shall be deemed given only when actually 
received.

     SECTION 7.  AMENDMENT.  This Warrant may not be amended, modified or 
otherwise altered in any respect except by the written consent of the 
registered holder of this Warrant and the Company.

     SECTION 8.  SUCCESSORS AND ASSIGNS.  This Warrant shall be binding upon 
and inure to the benefit of the Company and the holder of this Warrant and 
their respective successors and permitted assigns.

     SECTION 9.  GOVERNING LAW.  This Warrant shall be governed by and 
construed in accordance with the laws of the State of Delaware, without 
reference to the conflicts of law principles thereof.






                                      -6-
<PAGE>

          IN WITNESS WHEREOF, the Company has caused this Warrant to be 
signed in its name by its duly authorized officers and accepted by the holder 
of this Warrant this 6th day of March, 1998.

ATTEST:                                    ENERGY BIOSYSTEMS CORPORATION

By:                                        By:                                
   -----------------------------              --------------------------------
Name:  Paul G. Brown, III                  Name:                         
Title: Secretary                                ------------------------------
                                           Title:                        
                                                 -----------------------------

HOLDER:

--------------------------------

Address for Notices:

James F. Boltz
Petro Star Inc. 
201 Arctic Slope Avenue #200
Anchorage, Alaska   99518







                                      -7-
<PAGE>

                                   ASSIGNMENT

                   TO BE EXECUTED BY THE REGISTERED HOLDER IF IT
                          DESIRES TO TRANSFER THE WARRANT

          FOR VALUE RECEIVED, ___________ hereby sells, assigns and transfers 
unto _____________________________ the right to purchase ________________ 
shares of ___________________ stock, evidenced by the within Warrant, and 
does hereby irrevocably constitute and appoint ____________________________ 
Attorney to transfer the said Warrant on the books of the Company, with full 
power and substitution.



                                             ----------------------------------
                                             Signature



                                             ----------------------------------

                                             ----------------------------------
                                             Address


Dated: _________________, 19____.

In the presence of:

---------------------------------

                                       
                                    NOTICE

          The signature of the foregoing Assignment must correspond to the 
name as written upon the face of the within Warrant in every particular, 
without alteration or enlargement or any change whatsoever.

                                      -8-
<PAGE>

                               SUBSCRIPTION FORM

                 TO BE EXECUTED BY THE REGISTERED HOLDER IF IT
                        DESIRES TO EXERCISE THE WARRANT

          The undersigned hereby exercises the right to purchase ____________ 
shares of stock covered by this Warrant according to the conditions thereof 
and herewith makes payment of the Purchase Price of such shares in full.



                                             ----------------------------------
                                             Signature



                                             ----------------------------------
                                             Name


                                             ----------------------------------

                                             ----------------------------------
                                             Address


Dated: _________________, 19____.




                                      -9-