
    DELTIC TIMBER CORPORATION, et. al., Plaintiff, v. GREAT LAKES CHEMICAL CORPORATION, Defendant.
    Civil No. 95-1090.
    United States District Court, W.D. Arkansas, El Dorado Division.
    April 3, 1998.
    
      William Prewett, Robert Compton, Floyd Thomas, El Dorado, AR, Richard Donovan; Little Rock, AR, for Plaintiff.
    Dennis Shackleford, El Dorado, AR, Thomas Daily, Fort Smith, AR, Theresa Wineland, El Dorado, AR, for Defendant.
   MEMORANDUM OPINION

BARNES, District Judge.

This lawsuit was filed by Deltic Timber Corporation (Deltic) on November 3, 1995. In essence, the complaint alleges unlawful taking and displacement by Great Lakes Chemical Corporation (Great Lakes) of bromine-rich brine from Deltic properties, and compensation is sought on grounds of trespass, conversion, and unjust enrichment (quasi-contract) and restitution. Following the commencement of this action, portions of the brine rights claimed by Deltic were purchased by its former parent company, Murphy Oil Co., Inc., as well as Murphy Exploration & Production, (hereinafter, jointly referred to as Murphy). Murphy was therefore added as a plaintiff to this case by the second amended complaint.

A trial of this matter was held on December 3-10, 1997, and at the conclusion of testimony the Court took the case under advisement. Post-trial briefs were submitted by both sides. This Court has carefully considered the testimony and exhibits introduced at trial, and the following constitutes the Court’s findings of fact and conclusions of law.

I. BACKGROUND

Great Lakes is a diversified specialty chemicals company which manufactures various chemicals and products utilizing bromine. The Smackover Lime Formation, found in Union and Columbia Counties in South Arkansas, contains substantial reserves of valuable bromine-rich brine. This brine is commonly extracted through a method using two (2) types of wells. Production wells remove the bromine-rich brine from the Smackover Formation, and “disposal” or “injection” wells return the brine back into the formation after the bromine has been extracted.

Both parties acknowledged that injection wells are used not only as a means of disposing of that brine which has been processed of its bromine (“spent brine”), but also as a means of enhancing recovery of the bromine-rich brine underground (“virgin brine”). Through the strategic placement of injection wells, virgin brine is pushed ahead by injected, spent brine towards production wells. This process, known as “secondary recovery” or “waterflooding,” results in the production of more virgin brine than would be realized through production wells alone (“production by depletion”). The operation continues until the spent brine reaches production wells, thereby diluting the virgin brine to such an extent that production is no longer economically feasible.

In this instance, Great Lakes placed its wells in a “modified line drive.” Injection wells were placed in an imperfect horizontal line in order to. displace virgin brine towards a roughly parallel line of producing wells to the north. However, as noted by the testimony of Dr. William Cobb and other reservoir engineers, injection wells inject brine in all directions. Thus, when Great Lakes expanded its area of operations by adding production wells to the south of its injection wells in 1994 and 1995, brine was displaced towards producing wells both to the north and south of Great Lakes’s line of injection wells. This southward expansion brought Plaintiffs lands into the area between Great Lakes’s injection and production wells (the “recycling area”). Plaintiffs seek recovery for any virgin brine taken from these lands, as well as for brine taken from lands lying outside of, but adjacent to, the recycling area.

II. DISCUSSION

This case marks the fourth time in which suit has been brought by a plaintiff alleging that the bromine-rich brine underneath its lands have been affected by the recovery operations of a brine producer. The resulting case law in this area has been dynamic.

In Budd v. Ethyl Corp., 251 Ark. 639, 474 S.W.2d 411 (1971), the Arkansas Supreme Court was faced with a plaintiff alleging damages to two separate tracts of land. As to virgin brine allegedly drained from lands lying outside of, but adjacent to, an area bounded by injection wells, the Court held that the law of capture denied recovery. Budd at 412 (citing Osborn v. Ark Territorial Oil & Gas Co., 103 Ark. 175, 146 S.W. 122 (1912)). In doing so, the Court noted that the law of capture had not been “comnullified by the statute which permits the Oil and Gas Commission to bring about compulsory unitization in oil and gas fields.” Budd, 474 S.W.2d at 413. The Court applied a different analysis to lands lying within the recycling area, however, and denied recovery on the basis of an inadequate interest in the brine allegedly drained. Id. at 412-413 (noting the ownership of merely a leasehold interest).

In Young v. Ethyl Corp. 521 F.2d 771 (8th Cir.1975) (hereinafter Young I), the Eighth Circuit applied Arkansas law to allow recovery for brine displaced from a tract of land located within a brine producer’s recycling area. The Court noted the separate analysis afforded such lands in Budd, supra, and held that the law of capture was inapplicable because: (1) the plaintiffs virgin brine would not have been displaced but for the increase in pressure supplied by the producer’s injection wells; and (2) using a waterflood process to force minerals under one’s neighbor’s lands to migrate to production wells when they would not have otherwise done so amounts to an abuse of correlative rights. Young I at 774.

This holding was later adopted by the Arkansas Supreme Court in Jameson v. Ethyl Corp., 271 Ark. 621, 609 S.W.2d 346 (1980). In refusing to extend the law of capture to brine displaced through secondary recovery processes, the Jameson court noted that such processes were “obviously necessary” for the efficient, maximum recovery of bromine-rich brine. Jameson, 609 S.W.2d at 349. However, the Court pointed out that some balance was needed between the continued production of a valuable natural resource and the effect of waterflooding upon the brine rights of neighboring landowners. Seizing upon the rationale of Young I, supra, as well as recently enacted Arkansas legislation providing for the unitization of brine fields, the Court allowed damages for brine which would not have been displaced but for the producer’s injection wells. Id. at 351. Damages were not afforded for brine which would have been merely drained by the use of supply wells alone (“depletion”), rather than as a result of removal which “had occurred due to the added differential pressures.” Id. at 349.

The ease at hand is the first to include allegations that a Plaintiffs brine rights were affected subsequent to the enactment of Act 937 of 1979. Ark.Code Ann. § 15-76-301 et seq. The Act, which establishes unitization procedures for brine production in an attempt to balance the interests of landowners and brine producers, was essential to the rule of law espoused in Jameson, supra. In resolving this matter, the Court has considered this legislation in addition to the aforementioned case law.

A. Brine Extracted From Lands Outside the Recycling Area

While admitting that liability may be proven for brine extracted from lands within a recycling area, Great Lakes relies upon Budd, supra, to argue that the law of capture is applicable to the brine outside that area. This Court does not agree.

Where jurisdiction is founded upon diversity of citizenship, it is the duty of the federal courts to apply the law of the forum state in which it sits. Guillard v. Niagara Machine & Tool Works, 488 F.2d 20, 24 (8th Cir.1973). The responsibility of the federal courts is not to formulate the legal mind of the state but only to ascertain and apply it. Smithey v. St. Louis Southwestern Ry. Co., 237 F.2d 637 (8th Cir.1956). Where state law is uncertain, a federal court must do its best to determine what state law is under state decisions. Heeney v. Miner, 421 F.2d 434 (8th Cir.1970); Young I, 521 F.2d at 773, n. 4.

“The underlying reason for adoption of the rule of capture by Arkansas and other states was the acknowledged impracticality of tracing ownership of a transient substance which migrated from lands of one owner to lands of someone else.” Jameson, 609 S.W.2d at 350. The rule has long been criticized as the result of new developments in geology and an increased ability to measure amounts drained by a producer. Young I, 521 F.2d at 774; (citing Summers, The Law of Oil and Gas § 63 (1956)). The rule as applied in Budd has been neither distinguished nor overruled. Obviously, the Arkansas Supreme Court would not have treated the tracts in that case differently from one another if it “had reached the decision in the Budd case that it was immaterial whether the lands were inside or outside of [a brine producer’s] peripheral area of input wells.” Jameson, 609 S.W.2d at 346.

Yet, this rule of law appears grounded on the fact that brine between the injection and supply wells will necessarily be produced, as that brine is displaced towards an injection well. Indeed, Kenneth Karmell, a chemical engineer and former vice president of Great Lakes, noted that the company’s reaction to the Young I decision was to lease all the property between the supply and disposal wells, since Great Lakes knew all along that brine from this area would be produced. As such, the determinative issue with regard to the rule of capture in.the case of a waterflood operation seems not to be based upon whether lands are within a “recycling area”, as defined by a straight line from one outer well to another. Rather, the issue is whether displaced brine is being forced into the production wells' of a producer when it would not have otherwise moved.

An owner’s "just and equitable share of brine” in a developed unit is that part of the actual production of brine from the unit which is in the same proportion to the total production of brine from the unit as the interest of the owner in the brine of the unit expressed in surface acres is to the total surface acreage of the unit.

In refusing to extend the law of capture to brine drained from lands within a recycling area, the Jameson Court noted:

Inherent in [Arkansas’s unitization laws] is the realization that transient minerals such as oil, gas, and brine will be wasted if a single landowner is able to thwart secondary recovery processes, while conversely acknowledging a need to protect each landowner’s rights to some equitable portion of pools of such minerals. A determination that a trespass or nuisance occurs through secondary recovery processes within a recovery area would tend to promote waste of such natural resources and extend unwarranted bargaining power to minority landowners. On the other hand, a determination that the rule of capture should be expanded to cover the present situation could unnecessarily extend the license of mineral extraction companies to appropriate minerals which might be induced to be moved from other properties through such processes and, in any event, further extend the bargaining power of such entities to reduce royalty payments to landowners who are financially unable to ‘go and do likewise’ as suggested by [the bromine producer].

Where the rule of capture is applied to brine which has been displaced but not recovered, no license to appropriate minerals is extended. Moreover, Arkansas’s brine unitization law, upon which the Jameson court strongly relied, defines a landowners “fair and equitable share of brine” in terms of the amount of brine which is actually produced. By refusing to extend the rule of capture to brine which is recovered through secondary recovery processes, the Arkansas Supreme Court has prevented mineral extraction companies from utilizing such processes in order to recover and profit from another’s brine without providing compensation. In light, of the fact that waterflooding is indeed “obviously necessary”, Jameson at 349, a requirement that producers pay for brine from which they have received no benefit would be inconsistent with established Arkansas policy encouraging recovery of that natural resource. See Ark.Code Ann. 15-76-301. Accordingly, the Plaintiffs’ claim of trespass should be dismissed.

The facts of this ease, however, show that waterflooding resulted in additional recovery from areas outside the mathematical boundaries of Great Lakes’s production wells. Unlike the well pattern present in Budd, the facts of this case involve roughly parallel lines of injection and production wells, followed by a pattern which is precisely opposite to a “circle of input wells,” Budd, 474 S.W.2d at 413. Indeed, by adding production wells to the South, Great Lakes surrounded its line of injection wells with production wells. Dr. William Cobb, a reservoir engineer offering expert testimony for the plaintiffs, stated that, because fluids move from areas of higher pressure to lower pressure, all the brine displaced by injection wells would arrive at the low pressure areas generated by these production wells. As such, even brine displaced from outside Great Lakes’s expanded recycling area was, and will be, recovered.

As noted in Jameson, the law of capture does not envision the use of injection wells as employed through secondary recovery processes. Jameson, 609 S.W.2d at 350. Rather, the rule is applied to brine which is merely drained through “natural depletion.” Id. 609 S.W.2d at 351. Compensation may be had, however, where additional brine is extracted as a result of the producer’s secondary recovery methods. Compare Young I, supra, and Jameson, supra, with R.R. Com’n of Texas v. Manziel, 361 S.W.2d 560, 568 (1962) (applying the “negative law of capture”).

B. Quantity of Brine Extracted Through Waterflooding

Much of the factual dispute at trial centered around the amount of bromine-rich brine displaced from the plaintiffs’ properties. In presenting evidence on this issue, engineering experts for both the Plaintiffs and Defendant employed computer technology to simulate the effects of Great Lakes operations upon surrounding lands. Although data produced from Great Lakes’s well logs, core samples, and other sources were used in the calculations of both parties, the results produced by the competing simulations differed greatly. The Plaintiffs’ simulation showed that a total of 5,770,000 pounds of bromine were displaced from underneath 3,511.80 net brine acres of Deltic and Murphy properties, while the Defendant’s simulator showed a displacement of only 3,263,948.17 pounds (1,786,515.93 barrels of brine).

It is the opinion of this Court that the results produced by the Plaintiffs’ simulator are the more accurate. The Plaintiffs’ model divided the subterranean layer from which brine is produced (the “net pay zone”) into separate intervals to account for variations in porosity and permeability from the top of the net pay zone to the bottom. On the other hand, the Defendant’s model was only capable of performing calculations with regard to the zone as a whole. Thus, while the Plaintiffs’ model reflects specific variations through the zone, the Defendant’s model relies upon a mere average of those variations. Because water travels more quickly through zones of higher permeability and porosity, variations in the zone more accurately reflect the movement of brine through the reservoir.

In addition, the Plaintiffs’ model was designed to simulate a waterflood recovery process in which water pushes water, while the Defendant’s model was designed to simulate a process in which water pushes oil. As such, the Defendant’s expert reservoir engineer, Henry Coutret, was forced to account for the difference in displacement ratios. No such adjustment was necessary for the Plaintiffs’ model.

Finally, the Plaintiffs’ simulator did not account for displacement from zones with less than ten percent porosity, while the Defendant’s model used a porosity cutoff of five percent. Dr. William Cobb, a reservoir engineer consulted by the Plaintiffs, noted that such a determination is based on analysis of the Smackover formation core, and explained that a ten percent cutoff is more appropriate. Cobb noted that the ten percent cutoff produced excellent history matches when compared with actual data from the prior performance of Great Lakes’s wells, and that a lower cutoff results in a smaller area of recovery. Although Great Lakes’s experts professed the higher cutoff to be inaccurate, it is clear that they had relied upon a ten percent cutoff to at least some degree in the past. McKay Moore, a petroleum geologist with many years of experience in the Smack-over formation, testified that he originally relied upon a ten percent cutoff in performing his consultation, but that the cutoff was later altered to five percent upon orders by Great Lakes. Similarly, Henry Coutret, a petroleum engineer consulted by Great Lakes, acknowledged on cross examination that he had previously relied upon a ten percent porosity cutoff used by another geologist in the South unit of the Smackover formation.

Accordingly, after a thorough consideration of the evidence and expert opinions in this ease, the Court finds , that the results produced by the Plaintiffs’ simulator are accurate, and that brine was extracted from a total of 8511.80 net brine acres of Plaintiffs’ unleased properties. It is important to note, however, that unlike the computations submitted by the Defendant, the Plaintiffs’ figures do not distinguish the amount of brine extracted from lands within the recycling area as it was expanded. As noted below, such a determination is necessary to distinguish good faith extraction from bad in this case. Therefore, the Court has relied upon the figures provided by the Defendant in determining amounts extracted from lands within the recycling area as it was expanded in 1994 and 1995.

C. Good Faith

Although Great Lakes’s operations resulted in the extraction of bromine-rich brine from vast amounts of Plaintiffs’ lands outside the expanded recycling areas, the Court cannot say that such operations were performed in bad faith. The burden of proof lies with .the Defendant to show that its conversion of minerals was in good faith. Young v. Ethyl Corp., 444 F.Supp. at 209-10 (hereinafter Young II) (citing Ward v. Spadra Coal Co., 168 Ark. 853, 272 S.W. 353 (1925)). A conversion is held to be in good faith where it is due to inadvertence or honest mistake, rather than a callous disregard of the rights of others. Ward v. Spadra Co., supra; National Lead Co. v. Magnet Cove Barium Corp. 231 F.Supp. 208, 220 (W.D.Ark.1964).

As discussed above and noted during trial by numerous witnesses, Great Lakes operated under the belief that it was accountable only for those lands within the recycling area. Mikie Hazelwood, manager of Great Lakes’s land department, stated that Great Lakes officials relied on the opinion of counsel in doing so. Compare Young II, 444 F.Supp. at 210-11. Although no written legal memoranda were introduced by Great Lakes at trial, its belief in this regard is corroborated by the massive leasing program begun in 1977 following the Young I decision. Kenneth Williams, a long-time chemist for Great Lakes’s only U.S. competitor, Albemarle, noted that Albemarle likewise followed a policy of leasing all lands situated between its production and supply wells. Teresa Swint, records administrator for Great Lakes, stated that as a result of this leasing program, Great Lakes acquired the brine rights to approximately ninety-five percent (95%) of those lands which were within the recycling area prior to its expansion. The remaining lands were overlooked because they were only partially within the recycling area and subject to fragmented ownership interests. Thus, operations resulting in extraction from all lands except those in the expanded recycling area were performed in good faith.

However, an altogether different matter is presented by the extraction of brine from those lands which were included within the recycling area by Great Lakes’s southward expansion. Great Lakes had an existing recovery operation from a pool underneath lands to which it owned brine rights. The impact upon the brine rights of Plaintiffs was not the result of a good faith effort “to maximize recovery from a common pool.” Jameson, 609 S.W.2d at 351. Rather, it was the result of a deliberate expansion of operations so as to specifically include the lands of plaintiffs and others. Great Lakes’s belief that it was accountable only for unleased lands within the recycling area does not explain why such an expansion was made before the brine rights to plaintiffs’ lands were acquired.

Tom Mathis, a chemical engineer and manager of Great Lakes’s natural resources department, testified that unsuccessful efforts were made to lease Plaintiffs’ lands on terms similar to those agreed to by the parties in the past. Upon failing to acquire brine rights through such negotiations, however, Great Lakes did not pursue the alternative provided to it by the Arkansas legislature via permissive unitization. Mikie Hazelwood noted that Great Lakes had long been reluctant to unitize the area for fear of detriment to its local good will. Thus, Great Lakes proceeded with its planned expansion to the south without accomplishing either means of obtaining the brine rights to plaintiffs lands. Indeed, Great Lakes’s new production wells were in operation before the proceedings for unitizing the West Unit were even begun, much less accomplished. As noted, Great Lakes’s expansions were made with full knowledge of the accountability due the owners of these newly encompassed lands, and without obtaining the brine rights or compensating the plaintiffs “at the time of taking.” Jameson, supra, at 351. Great Lakes made no mistake in this regard. Accordingly, it is the opinion of this Court that Great Lakes failed in its burden of proving good faith with regard to those lands which were included within the recycling area as the result of its southward expansions in 1994 and 1995.

D. Damages

Under Arkansas law, the measure of damages awarded for good faith conversion of minerals differs according to that which . would make the plaintiff whole. Where it is determined that the plaintiff would have mined the mineral himself, he is awarded the value of the mineral at the surface, less the cost of its retrieval. Killam v. Texas Oil & Gas Corp., 303 Ark. 547, 798 S.W.2d 419, 423-24 (1990) (citing National Lead Co. v. Magnet Cove Barium Corp., 231 F.Supp. 208, 218 (W.D.Ark.1964)); see also Young I, 581 F.2d at 718. As to a landowner who has not the opportunity nor the equipment to develop minerals, the value for which he can lease them, or royalty value, is the accepted measure of damages. Id.

It is clear that plaintiffs would not have produced the brine themselves. Plaintiff Murphy is engaged in the business of oil production and exploration. However, Steve Cosse, vice president of Murphy, testified that Murphy had neither the facilities nor the expertise to produce brine. Thus, with regard to unitization, Cosse noted that Murphy was not interested in the statutory option of taking produced brine in kind. Indeed, the plaintiffs have a history of leasing out their brine rights to Great Lakes, and have leased substantial brine acreage to Great Lakes’s primary competitor as well. As such, it is the opinion of this Court that the plaintiffs would not have actually mined the brine extracted by Great Lakes, but would have leased out the right to do so in exchange for royalty payments.

In this instance, the values of brine royalties during years 1992 through 1995 were the same as the statutory mínimums required upon unitization. Mikie Hazelwood and others testified that royalty values corresponded with the minimum amounts required under unitization because landowners would otherwise refuse to lease — preferring to wait for the higher value guaranteed to them once a brine owner was forced to unitize. As such, both testimony and the brine leases in evidence demonstrate a royalty value of twenty-five dollars ($25) per acre per year until April of 1995. After that time, royalties were increased to thirty two dollars ($32) per acre per year.

Compensation for the total brine acreage damaged outside the recycling area during the recovery period is calculated as follows:

3511.80 total damaged brine acreage, as shown by plaintiffs’ calculation
damaged brine acreage with-in last expanded recycling area, as shown by defendant’s - 678.58 calculations
2833.22 total damaged brine acreage outside Great Lakes’s first expanded recycling area.
X $25.00 (2 years) royalty value (11/5/92-11/5/94)
$141,661.00 compensation for brine acreage outside final expanded recycling area. (11/5/92 — 11/5/94)
[2833.22 acres outside last recycling area
X $32.00 (1.24 years)] royalty value (11/5/94-2/1/96)
$254,083.16 total compensation for brine displaced from lands outside Great Lakes’s final expanded recycling area. (11/5/92-2/1/96)
[350.26 brine acreage inside first expanded recycling area
x $25.00 (2.08 years)] royalty value during period before first recycling area expansion (11/92-12/94)
[346.12 brine acreage inside second expanded recycling area
average royalty value during period before second recycling X $25.47 (2.92 years)] area expansion (11/92 — 10/95)
$298,038.46 total compensation for brine displaced from lands damaged while situated outside any recycling area.

Where a conversion is performed wilfully or in bad faith, the “enhanced value” or “harsh” measure of damages is applied, and the plaintiff is awarded the value of the mineral at the surface without deducting the costs of production. National Lead Co. v. Magnet Cove Barium Corp., 231 F.Supp. 208, 218 (W.D.Ark.1964); Young I, 581 F.2d at 718. This measure “is punitive because of intentional conduct or willfulness or bad faith in addition to depriving the wrongdoer of any profits.” National Lead, 231 F.Supp. at 218; see also Wronski v. Sun Oil Co., 89 Mich. App. 11, 279 N.W.2d 564 (1979); Lightner Mining Co. v. Lane, 161 Cal. 689, 120 P. 771, 777-78 (1911) (noting the punitive nature of the “harsh measure”).

Because of the absence of any viable market for the sale of virgin brine, experts from both parties agreed that its wellhead value should be found through “net back” methodology, in which the cost of processing the bromine from brine is subtracted from the value of bulk bromine. However, both the value of bromine and the cost of processing it from brine were disputed by the parties.

For proof of the value of bromine, the plaintiffs relied primarily upon the figures used in depletion allowances taken by Great Lakes in its 1992-94 tax returns. This value was 56 cents per barrel (Pl.’s Ex. 6), and was obtained by Great Lakes from the Chemical Marketing Reporter, a trade publication which estimates the market values of various minerals and chemicals. However, Peter Harben, an expert on the values published by such chemical journals, acknowledged on cross examination that figures found in publications such as the Chemical Marketing Reporter are necessarily limited as estimates. Harben explained that publishers do not have access to the sale prices actually agreed upon by purchasers and sellers. Thus, these publications often rely upon a company’s list price. Dr. Chip • Bamberger, an economist hired by the Defendant to offer expert testimony on the value of brine, noted that there is usually a substantial difference between a producer’s list price and its negotiated sale price. Indeed, Ken Williams, a chemist and long-time employee of Great Lakes’s only competitor in the bromine industry, Albe-marle, noted that the figures reported in the Chemical Marketing Reporter were higher than those normally received for bulk bromine by that company. Likewise, Steve Bruhn, a tax accountant employed by Great Lakes, noted that, although the published values were once consistent with Great Lakes’s actual delivered sales price, such values were found to be inaccurate in 1995, and a much smaller figure has been used in calculating Great Lakes’s depletion allowance since that year.

Accordingly, the better value for bromine is found in the actual, negotiated sale price used by Great Lakes from 1992 to 1995, the period of liability in this case. Dr. Bamberger testified that Great Lakes’s average sale price for bulk bromine during this time was 36.0 cents per pound (see Def.’s Ex. 25). This figure was derived from Dr. Bamberger’s examination of Great Lakes’s financial records, and appears accurate when checked against other evidence of bromine market value.

When the costs of processing bromine from brine is subtracted from the market value of bromine, the value of brine at the wellhead is determined. Dr. Bamberger stated that the processing costs amounted to 46.95 cents per barrel of virgin brine, while Jay Marsh, an economist who testified on behalf of the plaintiffs, calculated the relevant costs to be much less. This discrepancy was due primarily to a difference of opinion with regard to whether processing costs should encompass all operation and capital costs or be limited to incremental costs only. Both Marsh and Bamberger agreed that the additional production of even a small amount of brine results in a number of processing costs which increase in proportion with the additional production (such as raw materials, utility, and boiler costs). Marsh expressed the view that the remaining costs should only be deducted from the price of bromine on an incremental basis, as a small increase in production does not necessitate a proportionate increase in all processing costs (such as labor and plant facility costs). However, this Court disagrees. Dr. Bamberger explained that the market value of an item must be sufficient to cover all of a producer’s capital costs over the long term, and an increase in market value therefore necessarily accompanies any cost increase in proportion to the total cost. Because market value serves as the numerator for the net back process at hand, total cost should not be limited to the incremental cost of processing a specific portion of all the brine produced by Great Lakes. Indeed, such methodology would serve simply to increase the processing cost attributed to the remaining produced brine. As such, the value of brine at the wellhead is more appropriately determined by deducting total processing costs from the market value of bromine. Dr. Bamberger calculated this figure to be $.1719 per barrel, which appears accurate to this Court.

As previously noted, the figures produced by the plaintiffs simulation do not distinguish the brine displaced from lands within the recycling area as it was expanded. Therefore, the Court has relied upon the figures provided by the Defendant in determining amounts displaced from lands within the recycling area subsequent to its expansion in 1994 and 1995. These figures show damages in the amount of $117,602.45 (See Def.’s Ex. 85C).

Accordingly, damages in this case total $415,640.91, exclusive of interest and costs. Plaintiffs argue that pre-judgment interest should be added to this amount. However, prejudgment interest is not recoverable on claims that are neither liquidated as a dollar sum nor ascertainable by fixed standards. Woodline Motor Freight, Inc. v. Troutman Oil Co., Inc., 327 Ark. 448, 938 S.W.2d 565 (1997) (citing Lovell v. Marianna Federal Savings and Loan Ass’n., 267 Ark. 164, 589 S.W.2d 577 (1979); City of Fayetteville v. Stanberry, 305 Ark. 210, 807 S.W.2d 26 (1991)); Stein v. Lukas, 308 Ark. 74, 823 S.W.2d 832 (1992) (“requiring damage to be capable of exact determination both in time and amount”). Rather, prejudgment interest is allowable only where the amount of damages is definitely ascertainable by mathematical computation, or if the evidence furnishes data that make it possible to compute the amount without reliance on opinion or discretion. Id. In this case, the damages sustained by the Plaintiffs occurred gradually over a period of three years. The opinions of expert witnesses differed substantially, and were essential to the determination of: 1) the extent of lands from which bromine was extracted as the result of Great Lakes’s secondary recovery operations; 2) the amount of virgin brine extracted from within the expanded recycling areas through those operations; and even 3) the value of that brine. Thus, it was impossible to compute the amount of Plaintiffs’ damages without reliance on opinion or discretion, and an award of pre-judgment interest would be improper.

III. CONCLUSION

The Court finds that, as a result of Defendant’s secondary recovery operations, Great Lakes extracted virgin brine from 3511.80 net brine acres of Plaintiffs’ lands. Great Lakes expanded its operations so as to include Plaintiff’s lands within an area which Great Lakes knew itself to be accountable for, and did so without leasing brine rights, unitizing the lands, or otherwise providing the Plaintiffs with any of the economic reward bestowed upon Great Lakes as a result of its expanded operations. To that extent only, this Court is persuaded by the measure of damages utilized by Arkansas courts in the instance of bad faith conversion. In short, the defendants profited at the expense of the plaintiffs, and did so deliberately with regard to those lands within its expanded recycling area.

Defendant’s Exhibit 85C 
      
      . For reasons disclosed upon the record-in open court, the Plaintiffs’ claims of drainage, breach of contract, and nuisance were dismissed upon motion for directed verdict by the Defendant.
     
      
      . Likewise, production wells produce brine not only from the direction of the injection wells, but from all directions.
     
      
      . Paul Ramsey, a long-time reservoir engineer for Murphy, noted that production by depletion (or “primary recovery methods”) alone would result in substantially higher, production costs for Great Lakes.
     
      
      . Ark.Code.Ann. § 15-76-302(12) states:
     
      
      . Ark.Code Ann. § 15-76-301 states in part:
      It is declared to be in the public interest to:
      (1) Foster, encourage,' and promote the development and production in the state of the natural resource of brine;
      (2) Authorize and provide for the operation and development of brine properties in such a manner that the greatest ultimate recovery of brine, and the chemical substances con-tamed therein, is had and that the correlative rights of all owners are fully protected
     
      
      . Dr. William Cobb, a reservoir engineer, defined porosity as a measure of that portion of rock which can be filled with water. Permeability was defined by Dr. Cobb as a measure of the ability of a rock to allow water to move through it.
     
      
      . All of the lands which form the basis for suit were unitized as part of Great Lakes’s "West Unit.” Great Lakes argues the defense of unclean hands should apply due to plaintiffs’ attempts at defeating and opposing unitization. Yet, testimony showed that prior to its expanded operations, Great Lakes possessed the amount of lands necessary to apply for unitization. Moreover, expanded operations were begun in December of 1994 and October of 1995, while the unitization application and proceedings were not begun until November of 1995. Thus, Great Lakes’s argument holds little weight. Indeed, Plaintiffs' opposition and appeals should have been anticipated in light of the prior unsuccessful negotiations between these parties.
     
      
      . Although one-time "bonus payments” were often included in addition to royalties, Mikie Ha-zelwood testified that such bonus payments were not in consideration of brine to be taken in the future. Rather, the bonuses were paid in consideration of any brine which had already been taken from the landowner during the applicable limitations period. As such, the one-time bonuses were akin to payments to forego claims, and do not bear upon the value to be attributed to long term brine royalties for the future. In any event, neither the number of bonuses paid nor their precise amounts were submitted as evidence of the value of brine royalties in this case.
     
      
      . This figure does not include the brine acreage of tracts marked by the parties to this action as numbers 2, 3, 38, 56, 107, and 114, as no damage was shown to have occurred to these tracts during the limitations period. (See Pl.'s Ex. 4). Likewise, tract 108 is not included within this figure, since the brine rights to that tract was leased to Great Lakes.
     
      
      . This figure does not include damages to brine acreage for tracts labeled by the defendants as numbers 73, 74, and 84A. These tracts, although partially within the recycling area, were not damaged as the result of Great Lakes’s expansion or bad faith. Thus, they are included in the calculation of royalty payments owed.
     
      
      . This Court denied the defendant's motion for partial summary judgment that, regardless of whether a good or bad faith trespass is proven, the damages in this case should be based upon the value of brine rather than its end products, such as bromine. In doing so, the Court noted:
      Thus, [for bad faith trespass or conversion], the damages would be expressed as the value of the brine at the wellhead. See, e.g. Young I at 718. Yet, viewing the facts in a light most favorable to the Plaintiffs, such a measure would not even guarantee the preclusion of profit, much less that a defendant would be punished sufficiently to deter repetition of the alleged conduct. As noted in Dow Chemical Co. v. Commissioner of Internal Revenue, 433 F.2d 283 (6th Cir.1970), there is a great difference in the value and commercial marketability of brine and bromine. Thus, if the profits realized from the production of bromine exceed the award of damages to be paid out by Great Lakes under the harsh rule (when such rule is based on brine), a profit is still realized, and no deterrent is afforded. Rather, Great Lakes would enjoy a private right of eminent domain to force a sale of brine from lands which it has not leased.
      At trial, however, the Defendant's valued brine by subtracting only the costs of converting brine from the market price of bromine. Thus, all profit realized by Great Lakes was encompassed in the remainder, which Great Lakes submitted as the value of brine. In particular, this Court is hesitant to include a fifteen percent (15%) return on capital investment (in the form of shareholder distribution) with “costs.” However, Dr. Bam-berger opined that, like interest, such a return is essential to the generation of shareholder investment, and the plaintiffs expert made no argument to the contrary.
      While an award of damages based on brine rather than bromine serves to reduce the amount of production costs which must be paid by Great Lakes to the plaintiffs, it is clear that the purpose for awarding the “enhanced value” of a mineral is to guarantee that a trespasser makes no profit from his wrongdoing. Killam, 798 S.W.2d at 423 (citing National Lead, supra). When brine is valued in the manner submitted by the defendants, the Court can no longer be concerned that a profit might be realized from bromine sufficient to swallow even the “harsh” measure of brine damages. Therefore, the enhanced value of brine should not be the value of bromine, but the value of brine after being extracted from the earth.
     
      
      . In 1995, the delivered sales price for bromine used by Great Lakes in computing its depletion allowance was 40.5 cents.
     
      
      . Evidence was offered that the sale of bulk bromine represents only twenty-five percent (25%) of Great Lakes’s outside sales of bromine. As noted by economist Chip Bamberger, however, this percentage contemplates more than sufficient sales to establish a representative market price.
     
      
      . For instance, Great Lakes submitted evidence that Albemarle, the only other major producer of bromine in the U.S., had an average bulk sale price of 36.1 cents per pound in 1995.
     
      
      . Marsh defined incremental costs as the additional cost of production for each and every additional pound of bromine produced by Great Lakes from plaintiffs’s properties.
     
      
      . Ken Williams, a chemist and longtime employee of Albemarle, noted that, pursuant to a value determined by the Arkansas Oil and Gas Commission, Albemarle sells brine to Great Lakes at 18.25 cents per barrel.
     
      
      . This amount does not include damages of $17,062.31 to tracts labeled by the Defendant as numbers 73, 74, and 84A in its Exhibit 85C. See footnote 10.
     