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Unitization: A Mathematical Formula To Calculate Redeterminations

Unitization equity redeterminations cause nightmares for those working in the upstream sector. The concept is not the problem; the process is. The typical equity redetermination process is ambiguous and contentious, often resulting in arbitration and/or litigation.

We are beginning to witness a marked increase in the number of unitizations, and the upstream sector is struggling with how best to handle equity redeterminations. This trend will continue as the oil and gas industry matures. The United States was the first to develop unitization or pooling rules, followed by the United Kingdom, other North Sea regimes and, more recently, Indonesia and other mature producing areas. As other oil and gas areas mature and exploration blocks become smaller, the likelihood of reservoirs crossing boundary lines becomes increasingly more common. Moreover, today's sophisticated geophysics is allowing the industry to better understand the subsurface and to detect reservoir interrelationships. Finally, host governments are now assuming a more pro-active role in managing their oil and gas resources and are encouraging or forcing companies to unitize oil and gas fields.[1]

Unitization is a contractual or legal consolidation of multiple areas or blocks to permit the field or a pool to be efficiently developed. Historically, this has meant that unitized areas have been created to allow the reservoir to be efficiently developed. Conceptually, multiple reservoirs could be developed similarly in a unit, as opposed to using a cost sharing agreement to share the cost of certain production facilities.[2]

In many units, notably units created outside the United States, a mechanism exists to allow the parties to readjust their individual economic returns to the extent that it is later substantiated that their individual equity interest or ownership of the reservoir, on a percentage basis, increases or decreases. This mechanism to readjust the individual equity interests is called redetermination.

The parties initially agree on individual track participations; that is, the ownership or percentage interest in each area, lease or block in the unit. In the United States, there is often no mechanism to redetermine the equity interest. The parties negotiate a single determined equity and take the risk that future development will substantiate that their area, lease or block holds more producible reserves than is originally thought. Perhaps, this concept developed in the United States because most of the more recent unitizations involve smaller discoveries that do not justify involved redetermination processes. Secondary or tertiary unitizations are common in the United States, but in such situations there is a comprehensive and generally accurate subsurface understanding and redeterminations are not necessary.

Equity redetermination, also known as Participating Interest[3] redeterminations, serve a valid and legitimate purpose. They allow the parties owning interests in multiple areas to efficiently develop areas or blocks prior to fully understanding the subsurface and the quality and quantity of oil and gas reserves on separate areas or blocks, As information is acquired and the subsurface is better understood, the equities or Participating Interests of the parties can be adjusted.

Two problems have developed in effectuating the operation of redetermination provisions and, as the issues in redeterminations tend to involve significant value, these problems have precipitated costly arbitration and litigation. First, the parties have argued over the technical interpretation of the subsurface. To control the number of redetermination requests, unitization agreements often now contain provisions that: (1) limit the number of redeterminations, (2) require a specified vote to initiate a redetermination, (3) mandate that equity or Participating Interest cannot be adjusted unless a specified change has been found and (4) impose costs upon parties initiating redeterminations when certain specified equity interest changes have not been agreed to or determined by the dispute resolution procedure (arbitration or litigation).

The second problem involves how to adjust the equities or Particpating Interests after it has been technically proven that the original determination was incorrect. Most unitization agreements do not contain a redetermination mathematical formula to allow the parties to simply transfer value from those who overpaid to those who underpaid. This failing has caused controversy and has further cast a pall over the concept of redetermination. The process of adjusting or redeterminating equity or Participating Interests has precipitated an adverse reaction among many in the oil and gas industry, spawning burdensome and expensive arbitrations and lawsuits. Our contention is that the concept of redetermination is sound but that the contractual redetermination processes incorporated in most unitization agreements are primitive and ambiguous.

We set out to develop a mathematical formula that could be incorporated into unitization agreements that would easily allow the parties to adjust value to address redetermined equities or Participating Interests. Such a formula must consider all economic and fiscal aspects to return the parties to the economic position they would have been in had redetermined equities or Participating Interests existed originally.

The mathematical formula described in this article is based on the Nigerian offshore model. In the narrative accompanying it, we note how the formula could be adjusted to account for differences in economic and fiscal regimes. Our formula can be used to calculate value transfer from those who were over-allocated barrels to those who were under-allocated. The concepts involved in this calculation can be used to transcend the peculiarities of the Nigerian system. An analysis of the following formula will allow the reader to better appreciate the significance of this development. The concepts underpinning this formula can be applied elsewhere to address other economic and fiscal regimes.

Our formula is divided into several sections; the results of each contribute to the final value to be paid. Like a jigsaw puzzle, the formula dissects a fiscal regime and allows the party to recreate the picture of what should have been had the proper amount of oil been allocated to each of the parties. Note that the formula contains "if" statements that allow it to be applied in flexible fashion to a plethora of economic and fiscal regimes.

Redetermination Formula

A=Group A: Group with decreasing Tract Participation
B=Group B: Group with increasing Tract Participation
Y=number of barrels in given year excluding production outside of the Unit Area
X1=A's Tract Participation Determination (decimal)
X2=A's Tract Participation Redetermination (decimal)
D=difference between A's Tract Participation Determination and A's Tract Participation Redetermination: D = X1 - X2
O=Over-allocated barrels: O = (D * Y)
R(x)=Royalty on x
Rp=Realizable Price
P1=Profit Oil actually allocated to Group A
P2=Profit Oil that would have been allocated to Group A had the Redetermined Tract Participation for Group A been in effect
T1=Petroleum Profit Tax (PPT) paid by Group A
T2=Petroleum Profit Tax (PPT) that would have been allocated to Group A had the Redetermined Tract Participation for Group A been in effect
I=Total Approved Investments ($)
M=top threshold for first level (initial) Profit Split tranche
C=percentage allocated to Concessionaire at the first level (initial) Profit Split tranche (decimal)
L=percentage allocated to Concessionaire at the maximum/cumulative Profit Split tranche (decimal)
Co=Cost Oil
Pnnpc1=Over-Allocated Profit Split allocated to Concessionaire
Pnnpc2=Redetermined Profit Split that would have been allocated to Group A had the Redetermined Tract Participation for Group A been in effect

Section 1: Redetermination Formula

Part 1:

If the quantum of Available Cost Oil is greater than or equal to Crude Oil minus Royalties (all calculations are to be made on an annualized basis):

[ O - [R(Y * X1) - R(Y * X2) ] ] * Rp = $ A pays B

Part 2:

If the quantum of Available Cost Oil is less than Crude Oil minus Royalties:

[ [ (P1 - T1) - (Pnnpc1 *) ] - [ (P2 - T2) - (Pnnpc2 *) ] ] + [ Co - [ R(Y * X1) - R(Y * X2) ] ] * Rp = $ A Pays B

* Profit Split Formula

Part 3:

If the over-allocated barrels (O) fall exclusively within one production tranche, then:

Pnnpc1 = (P1 - T1) * L

Pnnpc2 = (P2 - T2) * L

Part 4:

If the over-allocated barrels (O) fall within the first two production tranche, then:

Pnnpc1= [ (Y - M) * L ] + [ C * (P1 - T1) - (Y - M) ] ]

Pnnpc2= [ (Y - M) * L ] + [ C * [ (P2 - T2) - (Y – M) ] ]

(Should over-allocated barrels (O) fall within more than two production tranches, then the above shall be adjusted to include all production tranches and the concomitant percentage differences.)

Section 2: Approved Recoverable Investment Reimbursement

Group B pays Group A: D * I

Section 3: Production Bonus
If Group A paid a Production Bonus as a result of O, then:

Group B owes Group A interest annually on the Production Bonus (at LIBOR + _ [ ] percent) until Group A's Post-Redetermined production reaches the level which would have triggered payment of the Production Bonus.

Upon termination of the Contract, if the Post-Redetermination cumulative production does not trigger the Production Bonus payment, then:

Group B also pays to Group A the Production Bonus paid by Group A.

Total Formula

Group A pays Group B the summation of the result of Section 1 calculated annually minus the value in Section 2, adjusted by the results of Section 3, if applicable. (Should the summation of Section 1 calculated annually be less than the value of Section 2, then Group B shall pay Group A such amount, adjusted by the results of Section 3, if applicable.)

In the first "if" statement of Section 1 of the formula, we calculated the monetary payment Group A must make to Group B if there is no profit oil by first determining the number of barrels that were over-allocated. To do this, the difference between Group A's Participation Determination and Group A's Participation Redetermination was multiplied by the total number of barrels produced in the given year. Group A should therefore pay Group B for the monetary benefit of these barrels minus the additional royalties that Group A was required to pay on Group B's oil. This value can be found by subtracting the redetermined royalties on all barrels produced in that year from the royalties on the determined number of barrels. When this value is in turn deducted from the total nuinber of over‑allocated barrels and multiplied by the realizable price, the monetary value that Group A pays Group B results.

The second "if" statement of Section 1 deals with the possibility that the cost recovery limits have been reached due to sufficient production and the excess production is allocated based on the profit oil split. The cost oil and profit oil are split and calculations are performed separately before being added together to determine what Group A owes to Group B. To calculate the discrepancy in the profit oil, the Petroleum Profit Tax is subtracted from the number of barrels of profit oil initially allocated to Group A. Then the portion allocated to the Concessionaire (calculated in a later part of the formula) is subtracted because Group A should not be held responsible for repaying the PPT and the money paid to the Concessionaire on the barrels in question because Group B would have paid this value had they been allocated these barrels initially. The same calculation is then performed with values from the redetermination to ascertain how barrels should have been allocated. Subtracting these values, the determination from the redetermination, reveals the amount that Group A owes Group B in profit oil. This is added to the amount Group A owes in cost oil, which is calculated by deducting royalties from the amount of cost oil. The subtracted royalties are calculated on all of the over-allocated barrels because Group A had to pay royalties on all of them regardless of whether they qualified for profit oil. Adding the profit oil calculation and the cost oil and royalties and multiplying by the realizable price results in the monetary sum that Group A owes to Group B.

The value allocated to the Concessionaire is calculated for both the determined and redetermined Tract Participation. By subtracting the Petroleum Profit Tax paid on the initial amount of profit oil from the determined amount of profit barrels and then multiplying by the percentage allocated to the Concessionaire at the maximum/cumulative Profit Split tranche, the amount paid to the Concessionaire is determined. This value is subtracted from the profit oil owed from Group A to Group B in the previous paragraph. The same calculation is performed with the redetermined values to find the redetermined amount paid to the Concessionaire.

If the over-allocated barrels fall within two production tranches, the formula is slightly more complex because, as a result of the sliding scale, the Concessionaire receives a larger percent of the second portion of the barrels. Our formula assumes that a final redetermination will occur within the first two production tranches but should be modified if a final redetermination occurs after this point. This part of the formula basically determines the number of barrels in each tranche, then calculates the amount allocated to the Concessionaire for each tranche before adding them together to get a total amount. The top threshold for the first (initial) Profit split tranche is subtracted from the total number of barrels produced in the Unit Area to determine the number of barrels of profit oil in the second tranche. This value is then multiplied by the percent allocated to the Concessionaire to determine the number of barrels the Concessionaire received from profit oil in the second tranche. To determine the number received in the first production tranche, Petroleum Profit Tax is deducted from the amount of profit oil, giving the total amount of profit oil dealt with in the Profit Split formula. The total number of barrels produced in the Unit Area minus the top threshold for the first (initial) Profit split tranche (which amounts to the nurnber of profit barrels in the second tranche) is subtracted from the profit oil with PPT deducted to determine the total number of profit barrels in the first (initial) tranche. Finally, this number of barrels is multiplied by the percent allocated to the Concessionaire in the first (initial) tranche and added to the amount previously determined for the second tranche to calculate the amountof profit oil allocated to the Concessionaire for use in Part 2 of Section 1 of the formula. The initial value and a redetermined value are calculated in this manner; the only difference in the calculation is the use of original or redetermined values for amount of profit oil and PPT.

Section 2 of the formula deals with reimbursement of approved investments. The Unit Participants will in the course of exploration and development make certain investments, which for purposes of cost recovery will be sanctioned and approved by the host government. This portion of the formula addresses a cash payment from Group A (the party that overpaid) to Group B (the party that underpaid). This monetary sum is calculated by subtracting A's Tract Participation Redetermination (in decimal form) from A's Tract Participation Determination (in decimal form) to find the discrepancy in the allocation and then multiplying this value by the Total Approved Investments. In other words, the percent that Group A overpaid is multiplied by the investments, and Group A is reimbursed for this value. Note that we have intentionally not subjected the Approved Recoverable Investment Reimbursement to interest. In doing so, financial incentives exist for the parties to agree on realistic determined equity interests. A party who insists on a determined equity interest that is unrealistically high runs a real risk that it will shoulder a disproportionately high percentage of development costs and not receive interest on the amounts that it carried. The formula can easily be redrafted to include an interest component to keep Group A (the party that overpaid) financially whole.

Section 3 addresses production bonuses that may exist in certain host government contracts. This portion of the formula provides a mechanism for cash payment from Group B (the party with increasing Tract Participation) to Group A (the party with decreasing Tract Participation). In the event that Group A's over-allocated barrels cause premature payment of a production bonus, Group B is required to pay interest on this production bonus until such time as Group A reaches the level at which it would have paid the bonus. This is because Group A would have had the benefit of this money longer had it not been for the extra barrels and should therefore gain interest on this money. If Group A never reaches the level of paying the production bonus (for example, if the reservoir depletes prior to a production bonus being due), Group B must compensate Group A for the production bonus Group A should not have paid. Once again, this provides financial incentives for the parties to agree on realistic determined equity interests (and negotiated redetermined equities where the unitization agreement provides for multiple redeterminations). The formula addresses a single production bonus or multiple production bonuses and allows the drafting parties to establish a contractual interest rate.

Section 4 provides the mechanisms to balance payments between the Parties. After Sections 1, 2 and 3 have been completed, Group A owes Group B the results of Section 1 minus those of Section 2 and Section 3, if applicable. Section 1 is a cash payment from the party of decreasing Tract Participation to that of increasing Tract Participation, which is intended to equalize the value that each party should have received. Sections 2 (Approved Recoverable Investment Reimbursement) and 3 (Production Bonus) are possible values that Group B owes Group A and are therefore deducted from the results of Section 1. It is possible, if the redetermination occurs early after first oil and significant investments have been made, that the result of Section 2 would be greater than that of Section 1 - in which case a payment would be made in the opposite direction.


With the maturing of the oil and gas industry, unitizations will become increasingly more prevalent. By allowing for redeterminations, the parties can more comfortably agree upon specified equities or Participating Interests to allow for expeditious and efficient development of oil and gas fields while preserving their right to seek adjustment if it can be demonstrated that the track equities or Participating Interests should be revised. The formula presented allows for a relatively easy transfer of value to restore the parties to the positions they would have held had the equities or Participating Interests originally been more accurately established. As the upstream industry adopts formulas like this, development projects will move forward more quickly and efficiently and the process of redetermining equities or Participating Interests will be accomplished with decreasing debate, delays and arbitration/litigation costs.


[1] A hotly contested debate has now ensued between some host governments and oil and gas companies over the definition of a "field" or a "pool." Although beyond the scope of this article, this billion dollar debate determines the area "earned" as a consequence of exploration success and the application of sliding scale royalties and production splits.

[2] For a more detailed discussion of unitization, see, "Unitization," AIPN Advisor, No. 215, January, 2002 (Co‑authored with Kyle Vollus).

[3] Participating Interest is the equity ownership interest held pursuant to the host government contract with such interest governed in accordance with the terms of the Operating Agreement.

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