Exhibit 4

DESCRIPTION OF THE REGISTRANT’S SHARES OF LLC MEMBERSHIP INTEREST

REGISTERED PURSUANT TO SECTION 12 OF THE

SECURITIES EXCHANGE ACT OF 1934

The following summary of Ridgewood Energy S Fund, LLC’s shares of LLC membership interests is based on and qualified by the Fund’s Limited Liability Company Agreement (the “LLC Agreement”). For a complete description of the terms and provisions of the Fund’s shares refer to the LLC Agreement, which is filed as an exhibit to this Annual Report on Form 10-K.

The shares are membership interest in the Fund, which is a limited liability company (“Shares”). The following is a summary of certain provisions of the Fund’s LLC Agreement.

Control of LLC Operations

The powers vested in the Ridgewood Energy Corporation (the “Manager”), as manager of the Fund, under the LLC Agreement are broad. The Manager has full, exclusive and complete discretion in the management and control of the affairs of the Fund and shareholders have no power to take part in the management of, or to bind, the Fund.

The Fund’s officers are appointed by the Manager and may be removed by it at any time. Additionally, the Manager may authorize any sale, lease, pledge or other transfer of substantially all of a Fund’s assets without a vote of the shareholders.

Amendments and Voting Rights

The Manager may amend the LLC Agreement without notice to or approval of the holders of Shares for the following purposes:

Other amendments to the LLC Agreement may be proposed either by the Manager or by Fund shareholders. A vote on the proposal may be made by either by calling a meeting of the shareholders or by soliciting written consents. Proposed amendments require the approval of shareholders who hold of record at least a majority of the total Shares on the record date for the action, given at a meeting of shareholders or by written consents. Any amendment requiring shareholder action (other than an amendment to allow the Fund to be taxed other than as a partnership) may not increase any shareholder’s liability, change the capital contributions required of him or her or his or her rights in interest in the Fund’s profits, losses, deductions, credits, revenues or distributions in more than a de minimis matter, or change his or her rights on dissolution or any voting rights without the shareholder’s consent. Any amendment that changes the Manager’s management rights requires its consent. Generally, shareholders have no right to vote on matters not involving an amendment to the LLC Agreement or the removal of the Manager. However, if any other matter does require a vote of shareholders, it must be approved by shareholders who own of record at least a majority of the total Shares, or if a different vote is required by law, each shareholder will have voting rights equal to his or her total Shares for purposes of determining the number of votes cast or not cast.

For all purposes, a majority of the Shares is a majority of the issued and outstanding Shares, including those owned, if any, by the Manager or its affiliates. A majority of the Shares voted is insufficient if it is less than a majority of the outstanding Shares.

The consent of all holders of Shares is required for dissolving or terminating the Fund, other than as provided by the LLC Agreement; or adding a new Manager except as described below.

Participation in Costs and Revenues

Available cash determines what amounts in cash the Fund will be able to distribute in cash to shareholders. There are two types of available cash:

Available Cash from Dispositions and Available Cash from Operations are defined in the LLC Agreement and are not defined by and are not the same as similar concepts under generally accepted accounting principles.

There is no fixed requirement to distribute available cash. Instead, available cash will be distributed to shareholders to the extent, and at such times, as the Fund believes is advisable. Once the amount and timing of a distribution is determined, it shall be made to shareholders as described below.

Distributions from Operations

At various times during a calendar year, the Fund will determine whether there is enough available cash from operations for a distribution to shareholders. The amount of available cash from operations determined to be available, if any, will be distributed to the shareholders. At all times, the Manager will be entitled to 15% and shareholders will be entitled to 85% of the available cash from operations distributed.

Distributions of Available Cash from Dispositions

Available cash from dispositions that the Fund decides to distribute will be paid as follows:

General Distribution Provisions

Distributions to shareholders under the foregoing provisions will be apportioned among them in proportion to their ownership of shareholder Shares. The Manager has the sole discretion to determine the amount and frequency of any distributions. However, distributions may not be made selectively to one shareholder or group of shareholders, but must be made ratably to all shareholders entitled to that type of distribution at that time. The Manager in its discretion nevertheless may credit select persons with a portion of its compensation from the Fund or distributions otherwise payable to the Manager.

Return of Capital Contributions

If the Fund for any reason at any time does not find it necessary or appropriate to retain or expend all capital contributions, it may, in its sole discretion, return any or all of such excess capital contributions ratably to shareholders. A return of capital contributions is not treated as a distribution. The Fund and the Manager will not be required to return any fees deducted from the original capital contribution or any costs and expenses incurred and paid by the Fund. The shareholders will be notified of the source of the payment. Any such return of capital will decrease the shareholders’ capital contributions.

Voluntary Additional Capital Contributions and Supplemental Offering of Shares

The LLC Agreement does not provide for any mandatory assessments of capital from shareholders. This means that the Fund cannot require any shareholder to contribute more money after such shareholder completes his subscription and pays his initial capital contributions.

If voluntary additional capital contributions are requested by the Fund to fund additional project activities, the Manager will do so through a supplemental offering of shares in the Fund. The LLC Agreement provides the Manager with discretion in determining the nature, scope, amount and terms of such supplemental offering.

A shareholder who elects to not participate in any supplemental offering of shares and does not provide additional capital contributions for such additional project activities will have no interest in such additional project activities, but will retain his interest in the projects in which the Fund has already invested. The failure of a shareholder to participate in a supplemental offering may have a dilutive effect on such shareholder’s investment.

Removal of Manager

Shareholders may propose the removal of the Manager, either by calling a meeting or soliciting consents in accordance with the terms of the LLC Agreement. Removal of the Manager requires the affirmative vote of shareholders who are holders of record of at least a majority of the total shareholder Shares. Removal of a Manager causes the Fund to terminate the Fund’s operations and dissolve the Fund unless a majority of the shareholder Shares elects to continue operations. The shareholders may replace the removed Manager or fill a vacancy by vote of shareholders who hold of record a majority of the total shareholder Shares.

If the Manager is removed, resigns (other than voluntarily without cause) or is unable to serve, it may elect to exchange its management rights and rights to distributions, if any, for a series of cash payments from the Fund in amounts equal to the amounts of distributions to which the Manager would otherwise have been entitled under the LLC Agreement in respect of investments made by the Fund prior to the date of any such removal, resignation or other incapacity. The removed Manager would continue to receive its pro rata share of all allocations to shareholders as provided in the LLC Agreement which are attributable to any shareholder Shares owned by it.

Alternatively, the removed Manager may elect to engage a qualified independent appraiser and cause the Fund to engage another qualified independent appraiser (at the Fund’s expense in each case) to value the Fund property as of the date of such removal, resignation or other incapacity as if the property had been sold at its fair market value so as to include all unrealized gains and losses. If the two appraisers cannot agree on a value, they would appoint a third independent appraiser (whose cost would be borne by the Fund) whose determination, made on the same basis, would be final and binding.

Based on the appraisal, the Fund would make allocations to the removed Manager’s capital account of profits, losses and other items resulting from the appraisal as of the date of such removal, resignation or other incapacity as if the Fund’s fiscal year had ended, solely for the purpose of determining the Manager’s capital account. If the removed Manager has a positive capital account after such allocation, the Fund would deliver a promissory note of the Fund to the Manager, the principal amount of which would be equal to the Manager’s capital account and which would bear interest at a rate per annum equal to the prime rate in effect at Chase Bank USA, N.A. on the date of removal, resignation or other incapacity, with interest payable annually and unpaid principal payable only from 25% of any available cash before any distributions thereof are made to the shareholders under the LLC Agreement.

If the capital account of the removed Manager has a negative balance after such allocation, it would be obligated to contribute to the capital of the Fund in its sole discretion either cash in an amount equal to the negative balance in its capital account or a promissory note to the Fund in such principal amount maturing five years after the date of such removal, resignation or other incapacity, bearing interest at the rate specified above. If the removed Manager chose to elect the appraisal alternative, its entire interest in the Fund would be terminated other than the right to receive the promissory note and payments thereunder as provided above.

Dissolution of Fund

The Fund will dissolve and terminate its operations on the earliest to occur of (a) December 31, 2045, (b) the sale of substantially all of the Fund’s Property, (c) the removal, dissolution, resignation, insolvency, bankruptcy, death or other legal incapacity or disqualification of the Manager, (d) the vote of either all shareholders or of the Manager and shareholders who own at least a majority of the shareholder Shares of record or (e) any other event requiring dissolution by law. The Fund will wind up its business after dissolution unless (i) the Manager and shareholders who own at least a majority of the shareholder Shares of record or (ii) if there is no Manager, shareholders who own at least a majority of the shareholder Shares of record, elect to continue the Fund. The Manager (or in the absence thereof, a liquidating trustee chosen by the shareholders) will liquidate the Fund’s assets if it is not continued.

Transferability of Interests

No shareholder may assign or transfer all or any part of his or her interest in the Fund and no transferee will be deemed a substituted shareholder or be entitled to exercise or receive any of the rights, powers or benefits of a shareholder other than the right to receive distributions attributable to the transferred interest unless (i) such transferee has been approved and accepted by the Fund, in its sole and absolute discretion, as a substituted shareholder, and (ii) certain other requirements set forth in the Fund’s LLC Agreement (including receipt of an opinion of counsel that the transfer does not have adverse effects under the securities laws and the Investment Company Act of 1940) have been satisfied.

The Manager may not resign except for cause (which cause does not include the fact or determination that continued service would be unprofitable to it) and may not transfer its interest in the Fund except to pledge it as security for a loan to the Manager if the pledge does not reduce cash flow distributable to other shareholders.

Liability

Assuming compliance with the LLC Agreement and applicable formative and qualifying requirements in Delaware and any other jurisdiction in which the Fund conducts its business, a shareholder will not be personally liable under Delaware law for any obligations of the Fund, except to the extent of any unpaid capital contributions, except for the amount of any wrongful distributions that render the Fund insolvent and except for indemnification liabilities arising from any misrepresentation made by him or her to the Fund when purchasing Shares.