UNITED STATES
                 SECURITIES AND EXCHANGE COMMISSION
                        Washington, DC 20549

                            SCHEDULE 13G
            Under the Securities and Exchange Act of 1934
                         (Amendment No.)

                      Epsilon Energy Ltd.
------------------------------------------------------------------
                         (Name of Issuer)

                           Common Stock
------------------------------------------------------------------
                  (Title of Class of Securities)

                             294375209
------------------------------------------------------------------
                          (CUSIP Number)

                         December 31, 2019
------------------------------------------------------------------
    (Date of Event Which Requires Filing of this Statement)

Check the appropriate box to designate the rule pursuant to
which this Schedule is filed:

          [ ]     Rule 13d-1 (b)
          [X]     Rule 13d-1 (c)
          [ ]     Rule 13d-1 (d)

* The remainder of this cover page shall be filled out for a
reporting person's initial filing on this form with respect to
the subject class of securities, and for any subsequent amendment
containing information which would alter the disclosures provided
in a prior cover page.

The information required in the remainder of this cover page
shall not be deemed to be "filed" for the purpose of Section 18
of the Securities Exchange Act of 1934 ("Act") or otherwise
subject to the liabilities of that section of the Act, but shall
be subject to all other provisions of the Act (however, see
the Notes.)


CUSIP NO. 294375209   13G


1     Name of Reporting Person
      Advisory Research Energy Fund, L.P.

------------------------------------------------------------------
2     Check the Appropriate Box if a Member of a Group    (a)  [ ]
      			                                  (b)  [ ]

------------------------------------------------------------------
3     SEC Use Only

------------------------------------------------------------------
4     Citizenship or Place of Organization
      Illinois

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



   Number of
                   5     Sole Voting Power
    Shares               2,716,809 Shares
                   -----------------------------------------------
 Beneficially
                   6     Shared Voting Power
   Owned By              0 Shares
                   -----------------------------------------------
     Each
                   7     Sole Dispositive Power
   Reporting             2,716,809 Shares
                   -----------------------------------------------
    Person
                   8     Shared Dispositive Power
     With                0 Shares
------------------------------------------------------------------
9     Aggregate Amount Beneficially Owned by Each Reporting Person
      2,716,809 Shares

------------------------------------------------------------------
10    Check if the Aggregate Amount in Row (9) Excludes Certain
      Shares  [ ]

------------------------------------------------------------------
11    Percent of Class Represented by Amount in Row (9)
      9.9%

------------------------------------------------------------------
12    Type of Reporting Person
      PN

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



Item 1     (a)  Name of Issuer:
		Epsilon Energy Ltd.

           (b)  Name of Issuer's Principal Executive Offices:
                16701 Greenspoint Park Drive, Suite 195
                Houston, TX  77060


Item 2     (a)  Person Filing:
		Advisory Research Energy Fund, L.P.

	   (b)  Address:
		180 N. Stetson Ave., Suite 5500
                Chicago, IL 60601

           (c)  Citizenship:
		Advisory Research Energy Fund, L.P. is a Limited Partnership

           (d)  Title of Class of Securities:
		Common Stock

           (e)  CUSIP Number:
		294375209

Item 3     If this statement is filed pursuant to sections
           240.13d-1(b) or 240.13d-2(b) or (c), check whether the
           person filing is a:

           (a) [ ]  Broker or Dealer registered under Section
                         15 of the Act

                (b) [ ]  Bank as defined in Section 3(a)(6) of the
                         Act

                (c) [ ]  Insurance Company as defined in Section
                         3(a)(19) of the Act

                (d) [ ]  Investment Company registered under
                         Section 8 of the Investment Company Act

                (e) [ ]  Investment Advisor in accordance with
                         section 240.13d-1(b)(1)(ii)(E)

                (f) [ ]  Employee Benefit Plan or Endowment Fund
                         in accordance with section 240.13d-1(b)
                         (1)(ii)(F)

                (g) [ ]  Parent Holding Company or Control Person
                         in accordance with section 13d-1(b)
                         (1)(ii)(G)

                (h) [ ]  A savings association as defined in
                         section 3(b) of the Federal Deposit
                         Insurance Act

                (i) [ ]  A church plan that is excluded from
                         the definition of an investment company
                         under section 3(c)(14) of the Investment
                         Company Act of 1940

Item 4     Ownership

           (a)  Amount Beneficially Owned:
                Advisory Research, Inc.     2,716,809 Shares

           (b)  Percent of Class            9.9%

           (c)  Number of shares as to which reporting person has:
                (i)    Sole Voting Power            2,716,809 Shares
                (ii)   Shared Voting Power          0 Shares
                (iii)  Sole Dispositive Power       2,716,809 Shares
                (iv)   Shared Dispositive Power     0 Shares

Item 5     Ownership of Five Percent or Less of a Class:
           If this statement is being filed to report the fact
           that as of the date hereof the reporting person has
           ceased to be the beneficial owner of more than five
           percent of the class of securities, check the
           following [ ]

Item 6     Ownership of More than Five Percent on Behalf of Another
	   Person:

	   Not Applicable

Item 7     Identification and Classification of the Subsidiary
           Which Acquired the Security being Reported on by the
           Parent Holding Company:

           Not Applicable

Item 8     Identification and Classification if Members of
           the Group:

	   Not Applicable

Item 9     Notice of Dissolution of Group:

	   Not Applicable

Item 10    Certification

   	   By signing below I certify that, to the best of my
           knowledge and belief, the securities referred to
           above were acquired and are held in the ordinary
           course of business and were not acquired and are
           not held for the purpose of or with the effect of
           changing or influencing the control of the issuer
           of such securities and were not acquired and are
           not held in connection with or as a participant
           in any transaction having such purposes or effect.

           In accordance with Rule 13d-4 of the Securities Exchange
	   Act of 1934, each of the persons filing this statement
	   expressly disclaim the beneficial ownership of the securities
	   covered by this statement and the filing of this report
	   shall not be construed as an admission by such persons that
	   they are the beneficial owners of such securities.


			SIGNATURE

	   The undersigned certify, after reasonable inquiry
	   and to the best knowledge and belief of the undersigned,
	   that the information set forth in this Statement is true,
	   complete and correct.  The undersigned agree to the
	   filing of this single Statement on Schedule 13G.


		           Advisory Research, Inc.

Date:  February 13, 2020   By:  /s/ Matthew K. Swaim
                           Name: Matthew K. Swaim
                           Title: Chief Executive Officer