<PAGE>
                                                                   EXHIBIT 10.4


                                  July 30, 2002



Mr. John Sfondrini
Essex Royalty Joint Venture
Essex Royalty Limited Partnership
36 Catoonah St., Unit 16
Ridgefield, CT    06877



Dear John,

         Pursuant to our recent discussions, this will confirm the verbal
settlement agreement reached in June 2002 concerning Essex Royalty Joint Venture
(Essex I). This letter will further modify the Amendment to Joint Venture
Agreement for Essex I between Edge Petroleum Corporation (Edge) and Essex
Royalty Limited Partnership dated effective January 1, 2001, reference to which
is hereby made. It is agreed that "Sharing Ratio Shift" on account of Essex 1
has occurred, and Essex I will begin paying Edge 40% on account of the
after-payout interest of the net royalty distributions from Essex I, effective
with the April 2002 cash distribution and monthly thereafter. Essex I will be
entitled to deduct from Edge's 40% share of the distributions, 40 % of the
following amounts: an accounting fee of $1,000 per month (currently being paid
to Richard Dale) subject to increase to cover actual increases in the fee paid
to Mr. Dale or another person, actual fees for preparation of Essex I's tax
return, and a management fee payable to the Managing Venturer of 3% per month of
the gross distribution from Essex I. (It is understood that this shall not
derogate from the right of the Managing Venturer to retain other persons for the
Joint Venture.) Edge has agreed to waive and release all claims to the arrearage
amount owed to it as of March 31, 2002 on account of its 40% after-payout
interest, which arrearage amount as of March 31, 2002 Edge has calculated to be
$111,480, in return for a general release of all claims Essex I and Essex
Royalty Limited Partnership may claim to exist against Edge in its capacity as
managing venturer of Essex I. In consideration of this waiver and release, Essex
I and Essex Royalty Limited Partnership release Edge, in its capacity as
managing venturer of Essex I, from all claims of alleged mismanagement, breach
of fiduciary duty, breach of contract, negligence or other claims or
controversies, whether similar or dissimilar, relating to or arising out of
Edge's acts or omissions while serving as the managing venturer of Essex I,
including specifically, but without limitation, claims relating to the East Lake
Boudreaux royalty interests. In connection with this release, Edge does not
admit that any such claims or liability exists, all liability being denied; this
settlement agreement being solely an attempt to avoid protracted litigation,
settle disputed and contested issues and buy peace. Edge likewise releases Essex
I, the Managing Venturer and Essex Royalty Limited Partnership of any and all
claims except to the extent arising under this agreement with respect to the 40%
after payout interest. Edge is holding $5,259.11 in royalties due Essex I. The
parties agree that Essex I may take a one-time offset of this amount from the
amount due Edge on account of its after-payout interest in the distributions,
and Edge shall be entitled to keep the $5,259.11.

<PAGE>

         The parties agree that the Edge Group Partnership is entitled to a
share of Edge's after payout interest in distributions. As a result, Edge Group
Partnership shall be entitled to a portion of the distributions as follows:
..377135% of all distributions shall be payable to Edge Group Partnership, and
39.622865% of all distributions shall be payable Edge. The balance is paid to
Essex Royalty Limited Partnership.


                                   Sincerely,

                                   Edge Petroleum Corporation


                                   By:  /s/ John W. Elias
                                       -------------------------------------
                                       John W. Elias


Agreed to this 9th day of September, 2002

Essex Royalty Joint Venture
Essex Royalty Limited Partnership

By  /s/ John Sfondrini
   -------------------------------
   John Sfondrini, Managing Partner/
   General Partner